api.research-repository.uwa.edu.au · ii Abstract Multiphase flow metering provides vital flow...

Development of an Earth’s Field Nuclear

Magnetic Resonance Multiphase Flow Meter

Keelan Thomas O’Neill, B. Eng. (Hons)

This thesis is presented for the degree of Doctor of Philosophy of

The University of Western Australia

School of Mechanical and Chemical Engineering

Fluid Science and Resources Division

2019

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Thesis Declaration

I, Keelan Thomas O’Neill, certify that:

This thesis has been substantially accomplished during enrolment in the degree.

This thesis does not contain material which has been submitted for the award of any other

degree or diploma in my name, in any university or other tertiary institution.

No part of this work will, in the future, be used in a submission in my name, for any other

degree or diploma in any university or other tertiary institution without the prior approval

of The University of Western Australia and where applicable, any partner institution

responsible for the joint-award of this degree.

This thesis does not contain any material previously published or written by another

person, except where due reference has been made in the text and, where relevant, in the

declaration that follows.

The work(s) are not in any way a violation or infringement of any copyright, trademark,

patent, or other rights whatsoever of any person.

This thesis contains published work and/or work prepared for publication, some of which

has been co-authored.

Signature:

Date: 21st April 2019

ii

Abstract

Multiphase flow metering provides vital flow information essential for the

development and operation of oil and gas fields. Current multiphase flow meters

(MPFMs) often do not achieve the desired measurement performance in order to provide

reliable information for reservoir management, production monitoring and flow assurance

purposes. Therefore a market exists to produce a reliable, accurate and robust MPFM.

Nuclear magnetic resonance (NMR) offers attractive technology for multiphase flow

metering. NMR is a non-invasive measurement technique which can provide quantitative

characterisation of fluid behaviour.

This thesis presents the development of the apparatus and measurement

techniques relevant to an Earth’s field nuclear magnetic resonance (EFNMR) MPFM.

The flow meter consists a mobile pre-polarising permanent magnet positioned upstream

of an EFNMR radio frequency coil. The system excites a 1H NMR signal (at a Larmor

frequency of 2.29 kHz) from fluid moving through the flow meter. The free induction

decay (FID) signal is then acquired and appropriate signal interpretation techniques allow

determination of the composition and flowrate of the measured fluid stream.

The initial flow meter development focusses on establishing an appropriate

velocity measurement technique. The FID acquisition time is identified as a suitable

experimental parameter to ensure velocity measurement sensitivity and accuracy.

Velocity probability distributions are determined by fitting the measured FID signal of a

flowing water stream with a NMR fluid model using Tikhonov regularisation. The

accuracy of the measured velocity distributions are validated against in-line rotameter

measurements of water flowrate. The measured velocity distributions have a comparable

shape to theoretical turbulent distributions. The measurement technique demonstrates

robust behaviour with the ability to accurately capture artificially constructed multi-

modal (two-pipe) velocity distributions.

The next stage of system development involved measuring flow information in

two-phase gas/liquid flows. The flow meter is used to accurately measure the liquid

velocity distribution in air/water flows in the stratified and slug flow regimes. The signal

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interpretation technique is then applied in a ‘single-shot’ analysis to provide real-time

tracking of the liquid holdup and velocity (at 0.55 – 1.25 Hz). The NMR estimate of

liquid holdup is shown to be comparable against a simultaneous video track of holdup.

Temporal variation in the liquid flowrate can be used as a metric to distinguish stratified

and slug flow.

The final stage of flow meter development involves applying the flow meter to

measure two-phase canola oil/water flows. The metering methodology is extended via

the use of a dual polarisation scheme which utilises the in-built electromagnetic pre-

polarising coil as well as the mobile permanent magnet. The combined polarisation

technique provides sensitivity to a range (50 ms – 3 s) of fluid spin-lattice relaxation times

(T1). The fluid relaxation behaviour is used as a distinguishing mechanism to quantify

the fractions of canola oil and water in two-phase flow. A multi-FID sequence (with

variable polarisation conditions) is developed to provide simultaneous measurement of

fluid velocity and spin-lattice relaxation behaviour. Measured multi-FID signals are fit

with a joint 2D velocity-T1 distribution using the developed NMR flow model via a 2D

Tikhonov regularisation algorithm. Analysis of the measured 2D distributions enables

measurement phase fractions and flowrate. Measurements are performed on two-phase

canola oil/water flows across a range of flow regimes. Flowrate measurements in the

stratified flow with mixing, dispersion of oil-in-water and water, and oil-in-water

emulsion flow regimes demonstrate excellent accuracy relative to independent

measurements of individual oil and water phase flowrates. Furthermore; the measured

2D velocity-T1 distributions captured multiphase flow characteristics such as velocity

slip. However the developed metering system could not be accurately validated for flow

regimes where water-in-oil emulsions are present. Such emulsions cannot be sufficiently

separated during the total measurement time which results in flowrate quantification

errors.

The EFNMR MPFM demonstrates very good flow measurement performance for

single-phase flows, two-phase gas/liquid flows and two-phase oil/water flows. The work

presented in this thesis provides an excellent foundation for further developing the

measurement system towards a fully capable NMR MPFM.

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Contents

Thesis Declaration ............................................................................................................ i

Abstract ............................................................................................................................ ii

Contents .......................................................................................................................... iv

List of Figures ................................................................................................................ vii

List of Tables .................................................................................................................. ix

Abbreviations .................................................................................................................. x

Nomenclature ................................................................................................................. xi

Acknowledgements........................................................................................................ xv

Authorship Declaration for Co-authored Publications ........................................... xvii

Chapter 1. Introduction and motivation .................................................................... 1

Chapter 2. Nuclear magnetic resonance .................................................................... 6

2.1 Fundamentals of NMR ....................................................................................... 6 2.1.1. Introduction to NMR ................................................................................... 6

2.1.2. Fundamental NMR Theory ......................................................................... 6 2.1.3. The vector model ........................................................................................ 9 2.1.4. Measuring the free induction decay .......................................................... 10

2.1.5. Spin-lattice relaxation ............................................................................... 12 2.1.6. Spin-spin relaxation .................................................................................. 14

2.2 Application of low-field NMR ......................................................................... 17 2.2.1. Low-field NMR......................................................................................... 17

2.2.2. Earth’s Field NMR .................................................................................... 18

2.3 Inversion techniques in NMR........................................................................... 22

2.3.1. 1D Tikhonov regularisation ...................................................................... 22 2.3.2. 2D Tikhonov regularisation ...................................................................... 24

Chapter 3. Multiphase flow ....................................................................................... 26

3.1 Multiphase Flow Concepts ............................................................................... 26 3.1.1. Multiphase flow information .................................................................... 27 3.1.2. Gas-liquid flows ........................................................................................ 28 3.1.3. Liquid-liquid flows ................................................................................... 31

3.2 Multiphase Flow Metering ............................................................................... 35 3.2.1. Introduction to multiphase flow metering ................................................. 35 3.2.2. Classification of multiphase flow meters .................................................. 36

3.2.3. Velocity measurement principles .............................................................. 37 3.2.4. Phase fraction measurement technologies ................................................ 38 3.2.5. NMR in flow measurement ....................................................................... 43 3.2.6. Validation of flow measurement accuracy ................................................ 46

Chapter 4. Quantitative velocity measurements of single-phase flows ................. 47

4.1 Introduction ...................................................................................................... 47

4.2 Equipment and methodology............................................................................ 47

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4.2.1. Experimental apparatus ............................................................................. 47 4.2.2. NMR signal model .................................................................................... 51

4.2.3. Velocity probability distributions via regularisation................................. 53 4.2.4. Theoretical turbulent velocity distributions .............................................. 54

4.3 Results and discussion ...................................................................................... 55

4.3.1. Optimum Velocity Determination Methodology ...................................... 55 4.3.2. Single Pipe Experiments ........................................................................... 57 4.3.3. Two pipe experiments ............................................................................... 61

4.4 Conclusions ...................................................................................................... 64

Chapter 5. Characterising two-phase gas/liquid flows ........................................... 65

5.1 Introduction ...................................................................................................... 65

5.2 Equipment and methodology ............................................................................ 66 5.2.1. Equipment for gas/liquid flows ................................................................. 66

5.2.2. Gas/liquid NMR signal interpretation ....................................................... 67

5.3 Results and discussion ...................................................................................... 68 5.3.1. Calibrating the Reference Signal Magnitude ............................................ 68 5.3.2. Gas/liquid time-averaged results ............................................................... 69 5.3.3. Gas/liquid single-scan measurements ....................................................... 72

5.3.4. Statistical analysis of single-scan results .................................................. 79

5.4 Conclusions ...................................................................................................... 81

Chapter 6. Developing a technique for simultaneous oil and water flowrate

measurement .................................................................................................................. 82

6.1 Introduction ...................................................................................................... 82

6.2 Equipment and methodology ............................................................................ 82

6.2.1. NMR fluid quantification of oil/water systems ......................................... 82

6.2.2. Equipment for oil/water measurements .................................................... 83

6.2.3. T1 measurements of stationary fluids ........................................................ 87 6.2.4. Measuring T1 of flowing fluids ................................................................. 91

6.2.5. NMR flow model development for signal polarisation ............................ 95 6.2.6. Velocity–T1 distribution determination via 2D inversion ......................... 97 6.2.7. Component flowrate calculations .............................................................. 99

6.3 Experimental procedure ................................................................................. 100

6.3.1. Choice of experimental parameters ......................................................... 100 6.3.2. Experimental measurement workflow .................................................... 101

6.4 Results and discussion .................................................................................... 104 6.4.1. Single-phase measurements – Water ...................................................... 104 6.4.2. Single-phase measurements – Oil ........................................................... 110

6.5 Conclusions .................................................................................................... 117

Chapter 7. Quantitative characterisation of two-phase oil/water flows .............. 119

7.1 Introduction .................................................................................................... 119

7.2 Experimental methodology ............................................................................ 119 7.2.1. Flow regimes ........................................................................................... 119

7.2.2. Fluid separation ....................................................................................... 122

7.3 Results and discussion .................................................................................... 124 7.3.1. Stratified flow with mixing ..................................................................... 124 7.3.2. Dispersion of oil-in-water & free water layer ......................................... 126 7.3.3. Oil-in-water emulsion ............................................................................. 127

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7.3.4. Dispersion of oil-in-water & Dispersion of water-in-oil ........................ 128 7.3.5. Water-in-oil emulsion ............................................................................. 131

7.3.6. Summary and discussion of results ......................................................... 132

7.4 Conclusions .................................................................................................... 136

Chapter 8. Conclusions and future work ............................................................... 137

8.1 Conclusions .................................................................................................... 137

8.2 Future work .................................................................................................... 138 8.2.1. Improving the flow loop equipment ........................................................ 139 8.2.2. NMR magnetic hardware improvements ................................................ 139 8.2.3. Advancing NMR flow measurement techniques .................................... 141

References .................................................................................................................... 143

Appendices ................................................................................................................... 167

Appendix A. Calibrations for NMR flow measurements ..................................... 167

A.1 Magnetic field inhomogeneity........................................................................ 167

A.2 Relaxation in variable magnetic field strengths ............................................. 170

A.3 Signal diminishment during repolarisation .................................................... 173

Appendix B. Fluid relaxometry .............................................................................. 184

B.1 T2 measurements of canola oil and water ....................................................... 184

B.2 Comparative relaxometry measurements ....................................................... 186

Appendix C. Flow system design considerations .................................................. 188

C.1 Separation of oil and water emulsions ........................................................... 188

C.2 Influence of the Halbach array stray field ...................................................... 190

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List of Figures

Figure 1.1 Schematic of a typical offshore production scenario. ................................................ 2 Figure 1.2 The Schlumberger Vx multiphase flowmeter. ........................................................... 4 Figure 2.1 Zeeman diagram illustrating the energy states for a 1H atom with the energy

difference between the states indicated. .................................................................... 8 Figure 2.2 Illustration of Larmor precession. ........................................................................... 10 Figure 2.3 Illustration of a pulse and collect sequence used to measure a free induction decay.

................................................................................................................................. 11 Figure 2.4 Classical mechanics representation of the stages of a pulse and collect experiment.

................................................................................................................................. 12 Figure 2.5 Inversion recovery method. ..................................................................................... 14 Figure 2.6 Demonstration of the CPMG experiment. ............................................................... 17 Figure 2.7 Two alternative solutions for pre-polarisation......................................................... 21 Figure 3.1 Example flow regime map for air-water flow in a horizontal pipe. ........................ 30 Figure 3.2 Flow regime map for oil-water flow in a horizontal pipe. ....................................... 34 Figure 3.3 Illustration of the cross-correlation principle. ......................................................... 38 Figure 3.4 Schematic of the gamma-ray attenuation measurement principle. .......................... 39 Figure 3.5 Strip-type electrode configuration for impedance measurements of multiphase flows.

................................................................................................................................. 41 Figure 3.6 A cut-open schematic of the M-Phase 5000 magnetic resonance multiphase flow

meter. ....................................................................................................................... 45 Figure 4.1 Illustrations of the single-phase experimental flow loop apparatus. ....................... 49 Figure 4.2 Illustration of the two-pipe experimental flow loop. ............................................... 50 Figure 4.3 Velocity distribution measurements obtained using separation distance as the

independent variable. ............................................................................................... 56 Figure 4.4 Velocity distribution measurements obtained using FID acquisition time as the

independent variable. ............................................................................................... 58 Figure 4.5 Comparison of the mean velocity predicted using regularisation of NMR data to the

measured mean velocity from in-line rotameter data. ............................................. 59 Figure 4.6 Comparison of velocity probability distribution standard deviations. ..................... 60 Figure 4.7 Velocity measurements for the two-pipe flow system. ........................................... 62 Figure 4.8 Comparison of the predicted mean velocity in pipes A and B to the measured

superficial velocity from the corresponding rotameter. ........................................... 63 Figure 5.1 Reference overall signal magnitude (S0,ref) relative to the measured velocity (single-

phase flows). ............................................................................................................ 69 Figure 5.2 Flow regime map (from Taitel and Dukler (1976)) indicating the relevant flow

regime position of each experimental trial. ............................................................. 70 Figure 5.3 Velocity measurements of air-water flows. ............................................................. 71 Figure 5.4 Comparison of the NMR measurement of time-averaged liquid volumetric flowrate

(ql) to the in-line rotameter measurement of volumetric flowrate. .......................... 72 Figure 5.5 Single-scan velocity measurement of air-water flow. ............................................. 73 Figure 5.6 Tracking the liquid velocity over time for two-phase air/water flows. ................... 75 Figure 5.7 Tracking the liquid holdup over time for two-phase air/water flows. ..................... 76 Figure 5.8 Normalised cross-correlation (rNV) at time lag (τL) between NMR holdup and video

holdup for experimental trials. ................................................................................ 77 Figure 5.9 Liquid flowrate standard deviation for the stratified and slug flow experiments. ... 79 Figure 5.10 Comparison of the NMR predicted average liquid flowrate to the independent

rotameter measurement of liquid flowrate. ............................................................. 80 Figure 6.1 Illustration of the experimental oil/water flow loop system. ................................... 86 Figure 6.2 T1 measurements of oil/water mixtures. .................................................................. 88 Figure 6.3 Phase fraction comparison for oil and water. .......................................................... 91 Figure 6.4 SNR for FID measurements of canola oil flowing through the NMR flow meter with

signal pre-polarisation achieved using the Halbach array. ...................................... 92 Figure 6.5 SNR for FID measurements of canola oil flowing through the NMR flow meter with

signal pre-polarisation achieved using the EPPC. ................................................... 93

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Figure 6.6 Model SNR of fluid phases in velocity-T1 space with application of two separate

polarising techniques in the EFNMR flow metering system. ................................. 94 Figure 6.7 Summarisation of the polarising conditions for the 40 FID measurements. ......... 101 Figure 6.8 Flow chart outlining the NMR flow measurement procedure............................... 103 Figure 6.9 An example 2D velocity-T1 measurement for single-phase water. ....................... 106 Figure 6.10 Measured signal data and corresponding velocity and T1 distributions for single-

phase water measurements. ................................................................................... 108 Figure 6.11 Comparison of the NMR and rotameter measurements of water flowrate. .......... 110 Figure 6.12 An example 2D velocity-T1 measurement for single-phase canola oil. ................ 112 Figure 6.13 Measured signal data and corresponding velocity and T1 distributions for single-

phase oil measurement. ......................................................................................... 115 Figure 6.14 Comparison of the NMR and rotameter measurements of oil flowrate. ............... 117 Figure 7.1 The experimental matrix of oil and water superficial velocities for two-phase flowing

measurements conducted in this work. ................................................................. 121 Figure 7.2 An example 2D velocity-T1 distribution for a stratified with mixing flow regime.

.............................................................................................................................. 125 Figure 7.3 An example 2D velocity-T1 distribution for the dispersion of oil-in-water and water

flow regime. .......................................................................................................... 126 Figure 7.4 An example 2D velocity-T1 distribution for the oil-in-water flow regime. ........... 128 Figure 7.5 An example 2D velocity-T1 distribution for the dispersion of water-in-oil and

dispersion of oil-in-water flow regime. ................................................................. 129 Figure 7.6 An example 2D velocity-T1 distribution for the emulsion of water-in-oil flow regime.

.............................................................................................................................. 131 Figure 7.7 Direct comparison of the NMR measured flowrates and rotameter measured

flowrates (for both oil and water) for two-phase oil/water flow measurements. .. 133 Figure 7.8 Statistical summary of NMR flow measurement performance in the five different

flow regimes. ......................................................................................................... 134 Figure 8.1 Model SNR of fluid components in velocity-T1 space using the Halbach array alone

at a separation distance of 5 cm. ........................................................................... 140

Figure A.1 NMR water measurements used for field inhomogeneity function determination.

.............................................................................................................................. 169 Figure A.2 Experimentally acquired FID signals at varying separation distances of 45 – 150 cm.

.............................................................................................................................. 170 Figure A.3 Illustration of the three separate magnetic field strengths present in the flow metering

system. .................................................................................................................. 171 Figure A.4 Measuring T1 in the EPPC polarising field. .......................................................... 172 Figure A.5 Demonstration of the signal diminishment with introduction of the EPPC. ......... 174 Figure A.6 Experimental measurement of the signal diminishment as a function of velocity and

the polarisation-excitation delay (tPE). .................................................................. 175 Figure A.7 Illustration of effective signal development during variable polarisation scenarios

using a pulse and collect experiment. ................................................................... 177 Figure A.8 Illustration of the impact of the non-adiabatic transition on different regions of fluid

within the pipeline. ................................................................................................ 179 Figure A.9 Model fit of equation A.8 to experimentally measured signal diminishment ratios

(SRatio) as a function of fluid velocity and time since excitation pulse (tPE). ......... 183 Figure B.1 Measuring T2 of oil and water in the EFNMR system. ......................................... 185 Figure B.2 Measuring canola oil T1 in the Magritek 2 MHz Rock Core Analyser. ................ 186 Figure B.3 Measuring canola oil T1 in the Magritek 2 MHz Rock Core Analyser. ................ 187 Figure C.1 Photographs of emulsion stability bottle tests for a 50% canola oil/ 50% water

mixture. ................................................................................................................. 189 Figure C.2 Change in the local magnetic field strength as a function of the separation distance

between the polarisation and detection coil. ......................................................... 191

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List of Tables

Table 3.1 Summary of gas-liquid flow regimes ...................................................................... 29 Table 3.2 Summary of oil-water flow regimes adapted from Trallero et al. (1997). .............. 33 Table 3.3 Comparison of key flowmeter specifications for the Krohne M-Phase 5000 and the

EFNMR flow meter. ................................................................................................ 46 Table 7.1 Summary of the five relevant oil-water flow regimes. .......................................... 120

Table A.1 Movement of the separate signal variation regions at different times since the

polarisation switch on. ........................................................................................... 181 Table C.1 Summary of emulsion stability bottle test results. ................................................. 190

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Abbreviations

CPMG – Carr-Purcell-Meiboom-Gill

Do/w & w – dispersion of oil in water and water flow regime

Dw/o & Do/w – dispersion of water in oil and dispersion of oil in water flow regime

DNP – dynamic nuclear polarization

EMFM – electromagnetic flow meter

EFNMR – Earth’s field nuclear magnetic resonance

Eo/w – emulsion of oil in water

EPPC – electromagnetic pre-polarising coil

Ew/o – emulsion of water in oil

FID – free induction decay

GCV – generalized cross validation

GRA – gamma ray attenuation

IR – infrared

ME – mean error

MPFM – multiphase flow meter

MRI – magnetic resonance imaging

NMR – nuclear magnetic resonance

RCA – rock core analyser

r.f. – radio frequency

RMSE – root mean square error

SNR – signal to noise ratio

St – stratified flow regime

St w/ mix – stratified with mixing flow regime

1D – one dimensional

2D – two dimensional

3D – three dimensional

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Nomenclature

English alphabet

A – pipe cross-sectional area

B0 – static magnetic field scalar

B0 – static magnetic field vector

B1 – oscillating magnetic field vector

cNV – cross-covariance of two variables

D – pipe diameter

E – spin energy state

fs – slugging frequency

h – Planck’s constant

HIoil – hydrogen index of oil phase

hl – liquid holdup

hl,I – liquid holdup for scan i

hN – liquid holdup from NMR measurement

hV – liquid holdup from video measurment

I – spin quantum number

I(t) – inhomogeneity as a function of time

Im(e) – measured gamma ray intensity at energy level e

Iv(e) – gamma ray intensity for empty pipe at energy level e

ji – volumetric flux of phase i

k – Boltzmann’s constant

K – model kernel matrix

K – Model kernel function

kP – fraction of polarised fluid experiencing non-adiabatic signal decay

kI – fraction of intermediate fluid experiencing non-adiabatic signal decay

L – length

LD – detector length

LI – intermediate length between polarisation zone and detection zone

LP – length of polarisation zone

LPC – polarisation length of pre-polarising coil

LPD – polarisation-detection separation distance

LPH – polarisation length of Halbach array

Ls – sensor separation length

m – nuclear spin state

mi – mass flowrate of phase i

mT1 – number of steps in T1 distribution

mv – number of steps in velocity distribution

M – total mass flowrate

M – net magnetisation vector

MXY – transverse component of magnetisation vector

MZ – longitudinal component of magnetisation vector

M0 – equilibrium magnetisation

N – number of data points

nF – number of points recorded in FID

nL – number of separation distances

np – power law exponent

npp – number of pre-polarising conditions

nT – number of pre-polarising times

xii

Nscans – number of scans or averages applied in an NMR experiment

nw – number of windows in compressed FID

N1/2 – number of spins in spin up state

N-1/2 – number of spins in spin down state

P(x) – probability distribution of a variable x

P(T1) – T1 probability distribution

P(v) – velocity probability distribution

P(vo) – velocity probability distribution of the oil phase

P(vw) – velocity probability distribution of the water phase

P(v,T1) – 2D joint velocity-T1 probability distribution

p – probability distribution vector

qi – volumetric flowrate of phase i

qg – volumetric flowrate of gas phase

ql – volumetric flowrate of liquid phase

ql,I – volumetric flowrate of liquid for scan i

qo – volumetric flowrate of oil

qo,nmr – rotameter measured volumetric flowrate of oil

qw,rot – NMR measured volumetric flowrate of oil

qw – volumetric flowrate of water

qw,nmr – rotameter measured volumetric flowrate of water

qw,rot – NMR measured volumetric flowrate of water

Q – second derivative smoothing parameter matrix

Q – total volumetric flowrate

Qprobe – NMR probe quality factor

r – radial position within pipe cross-section

Re – pipe flow Reynolds number

RI – Gaussian relaxation constant

RT – T1/T2 ratio

RF – ratio of T1 in the polarising field to T1 in the Earth’s field

s – measured signal vector

S – measured NMR signal

SD – NMR signal attenuation during detection

Sdim – Signal diminishment ratio due to non-adiabatic attenuation

SE – NMR signal prior to excitation

Sfit – model signal fit

SI,EPPC – initial signal of FID decay with pre-polarising coil

SI,Hal – initial signal of FID decay with Halbach array

Sloss – initial signal loss between excitation and acquisition

Smodel – overall NMR signal model

SNA – signal variation due to non-adiabatic decay

So – NMR signal of oil phase

SP – polarised NMR signal

SPH – effective signal polarisation due to pre-polarising coil

SPD – NMR signal attenuation between polarisation and detection

SPH – effective signal polarisation due to Halbach just prior to excitation

Sw – NMR signal of water phase

S0 – NMR signal after an infinite magnetisation time

S0C – NMR signal after an infinite magnetisation time in the pre-polarising

coil

S0H – NMR signal after an infinite magnetisation time in the Halbach field

S0,TP – overall signal magnetisation for a two-phase measurement

xiii

S0,ref – reference value for the overall signal magnetisation for single-phase

flow

t – time

T – Temperature

ta – acquisition time

tdelay – excitation to acquisition delay time

te – time since excitation pulse

TE – inter-echo spacing for CPMG experiment

tI – delay time between inversion and excitation pulses

tPE – polarisation to excitation delay time

tPS – time since polarisation switch on

tpolz – time of polarisation pulse

T1 – spin-lattice relaxation constant

T1,C – spin-lattice constant cut-off for oil and water phases

T1,EF – spin-lattice relaxation constant in the Earth’s magnetic field

T1,LM – log-mean spin-lattice relaxation constant

T1,min – minimum spin-lattice relaxation value for distribution

T1,max – maximum spin-lattice relaxation value for distribution

T1,PF – spin-lattice relaxation constant in the polarising magnetic field

T2 – spin-spin relaxation constant

T2* – effective spin-spin relaxation constant

T2,I – spin-spin relaxation from field inhomogeneity

v – velocity

vi – linear velocity of phase i

vl – liquid linear velocity

vM – mean velocity

vmax – maximum velocity bound in velocity distribution

vM,o – mean oil velocity

vM,w – mean water velocity

vsg – superficial gas velocity

vsi – superficial velocity of phase i

vsl – superficial liquid velocity

vsi – superficial velocity of phase i

vso – superficial oil velocity

vsw – superficial water velocity

xD – volumetric fraction in detection zone

xi – volumetric fraction of phase i

xI – volumetric fraction in intermediate zone

xo – volumetric fraction of oil phase

xP – volumetric fraction in polarisation zone

xw – volumetric fraction of water phase

zi,obs – observed measurement of the variable of interest for sample i

zi,ref – reference measurement of the property of interest for sample i

xiv

Greek alphabet

α – regularisation smoothing parameter

γ – Gyromagnetic ratio

ΔB0 – Inhomogeneity of the static field

ΔE – spin energy difference

μ – fluid viscosity

μemulsion – emulsion viscosity

μi – viscosity of phase i

μi(e) – gamma ray attenuation coefficient at energy level e

μo – oil viscosity

μw – water viscosity

ρ – fluid density

ρi – density of phase i

ρo – oil density

ρw – water density

𝜎ℎ𝑁 – standard deviation of the NMR predicted liquid holdup track

𝜎ℎ𝑉 – standard deviation of the video estimated liquid holdup track

𝜎𝑞𝑙 – standard deviation of the video estimated liquid flowrate track

σv – standard deviation of a velocity distribution

τ – time between 90o and 180o pulse in a spin-echo experiment

τC – cross correlation traversal time

τL – cross-correlation time lag

τPC – fluid residence time in polarisation coil

τs – slug flow time period

τPD – residence time between polarisation and detection

ΦGCV – GCV score

ω – frequency

ω0 – Larmor frequency

xv

Acknowledgements

First and foremost, I would like to sincerely thank my primary supervisor

Professor Michael Johns for the tremendous support throughout my time as a PhD

student. You have given me wonderful opportunities, provided fantastic guidance and

helped me develop a great range of skills for the future. I greatly appreciate all of the

time and effort you have put towards myself and my project.

A big thankyou to my co-supervisor, Dr Einar Fridjonsson. Your stimulating

discussions and valuable insights have greatly helped me to understand the complex

science of nuclear magnetic resonance. Many thanks for your excellent guidance and

support throughout the course of my PhD.

I would like to thank the staff in the Fluid Science and Resources Division who

have assisted me along my journey. Thanks to John Zhen for his collaborative work with

the Q-switch as well as providing much needed assistance in magnetic resonance

electronics for the flow loop. Thanks to Dr Paul Stanwix for providing valuable

assistance in building the apparatus and the initial stages of flow metering system

development. Thanks to Professor Eric May and Dr Brendan Graham for providing

feedback and guidance throughout my research as well as assistance across a variety of

tasks.

Also thanks to my student peers in the Fluid Science and Resources Division.

Particular thanks to Nick Bristow; your technical support in the lab as well as your

engineering knowledge has been extremely helpful throughout my project. Furthermore,

you have been a wonderful friend and provided a listening ear to discuss problems as well

as the development of new ideas throughout my PhD.

Thanks to Andy Sederman and the group at the Magnetic Resonance Research

Centre in Cambridge for providing me with a wonderful opportunity and further

developing my research skills.

Thanks to all the housemates and Louise your support and putting up with me

when I came home from tough days at uni.

Finally, a huge thanks to my parents. Your continual encouragement as well as

immeasurable love and support through my entire education has made it possible for me

to be where I am today.

xvi

This research is supported by an Australian Government Research Training Program

Scholarship.

xvii

Authorship Declaration for Co-authored Publications

This thesis contains published work and work prepared for publication, some of

which has been co-authored. The bibliographical details of this work and where it appears

in the thesis are outlined below.

1. Keelan T. O’Neill, Einar O. Fridjonsson, Paul L. Stanwix, Michael L. Johns,

“Quantitative velocity distributions via nuclear magnetic resonance flow

metering”. Journal of Magnetic Resonance 2016, vol. 269, p. 179-185.

I was responsible for conducting experiments, associated data analysis, and

manuscript writing. Einar O. Fridjonsson and Paul L. Stanwix were responsible for the

construction of the experimental apparatus. Einar O. Fridjonsson and Michael L. Johns

provided project guidance and review of the final manuscript prior to submission. This

paper forms the basis of Chapter 4.

2. Keelan T. O’Neill, Adeline Klotz, Paul L. Stanwix, Einar O. Fridjonsson,

Michael L. Johns, “Quantitative multiphase flow characterisation using an Earth’s

Field NMR flow meter”. Flow measurement and Instrumentation 2017, vol. 58,

p. 104-111.

I was responsible for conducting the primary experiments used for publication,

associated data analysis, and manuscript writing. Adeline Klotz was involved with

conducting initial experiments and development of the experimental apparatus. Einar O.

Fridjonsson and Paul L. Stanwix were responsible for the construction of the

experimental apparatus. Einar O. Fridjonsson and Michael L. Johns provided project

guidance and review of the final manuscript prior to submission. This paper forms the

basis for Chapter 5.

3. John Z. Zhen, Keelan T. O’Neill, Einar O. Fridjonsson, Paul L. Stanwix, Michael

L. Johns, “A Resistive Q-switch for low-field NMR systems”. Journal of

Magnetic Resonance 2018, vol. 287, p. 33-40.

This paper involved joint first authorship between John Zhen and I. John Zhen

was responsible for the design and development of the resistive Q-Switch equipment

whilst I was responsible for demonstrating the application of the equipment by conducting

relevant experiments and data analysis. John Zhen and I had equal contribution in

xviii

drafting the manuscript. Einar O. Fridjonsson and Michael L. Johns provided project

guidance and review of the final manuscript prior to submission. This paper is not

incorporated in any single chapter, however the material assists in experimental signal

measurements throughout the thesis.

4. Keelan T. O’Neill, Lorenzo Brancato, Einar O. Fridjonsson, Paul L. Stanwix,

Michael L. Johns, “Two-phase oil/water flow measurement using an Earth’s field

nuclear nuclear magnetic resonance flow meter”. Chemical Engineering Science

2019, vol. 202, p. 222-237.

I was responsible for conducting experiments, associated data analysis, and

manuscript writing. Lorenzo Brancato assisted with conducting experiments as well as

associated data analysis. Einar O. Fridjonsson and Paul L. Stanwix were responsible for

assisting me with construction of the experimental apparatus. Einar O. Fridjonsson and

Michael L. Johns provided project guidance and review of the final manuscript prior to

submission. This paper forms the basis of Chapters 6 and 7.

1

Chapter 1. Introduction and motivation

The global energy demand continues to increase due to world population growth,

economic development and technological advances in society (British Petroleum, 2017,

Holditch and Chianelli, 2008). Oil and gas are predicted to continue to be key sources of

primary energy for the foreseeable future (British Petroleum, 2018, International Energy

Agency, 2017b, US Energy Information Administration, 2017). The world’s conventional

oil and gas reserves are being depleted and therefore petroleum companies are seeking

alternative production techniques to develop hydrocarbons (IBM Institute for Business

Value, 2010, International Energy Agency, 2017a). Stimulation techniques such as enhanced

oil recovery or gas lift are used to improve output from current fields (Alvarado and

Manrique, 2010, Sheng, 2010). Reservoir lifetimes are being extended which is increasing

the quantity of water produced from oil and gas fields (Igunnu and Chen, 2014).

Furthermore; petroleum companies are now developing fields of increasing technical

difficulty, such as marginally economical fields with tighter profit margins or deeper offshore

fields (Millheim, 2008, Speight, 2011). Such difficulties in modern oil and gas production

require improved monitoring of field production and therefore are driving demand for

improving flow metering technology (Fee and O'Dea, 2014).

The measurement of multiphase fluid flowrates and compositions in industrial

pipelines provides vital information for production monitoring, optimisation and flow

assurance purposes (Falcimaigne and Decarre, 2008, Falcone et al., 2009). Metering of

component flowrates from produced multiphase fluid streams has historically been achieved

using conventional test separators (McAleese, 2000). These vessels separate the multiphase

fluid phases (typically oil, gas and water) into individual phase streams using gravimetric

separation. The flowrate of individual phases is then measured by single-phase flow meters

(e.g. orifice-plate meters or Coriolis meters) (Crawford, 1981, Jahn, 1998).

2

Recent advances in flow metering technology have allowed commercial multiphase

flow meters (MPFMs) to provide a competitive alternative to conventional test separators

(Mehdizadeh, 2001, Pinguet et al., 2010, Ross and Stobie, 2010). MPFMs are instruments

which simultaneously measure the individual component flowrates in a multiphase fluid

stream without the need for phase separation (Falcimaigne and Decarre, 2008, Pinguet,

2010). MPFMs were initially developed to meet several challenges in North Sea oil fields

(Falcone et al., 2009); the discovery and development of satellite marginal fields which were

to be connected to existing infrastructure required an alternative cost-effective flow metering

technology where the cost of an additional test separator could not be justified (Falcone et

al., 2002, Miller, 2008, Syre et al., 2013). Furthermore, continual production from maturing

fields has led to changing process conditions (e.g. increasing water and gas fractions) which

require a robust and flexible flow measurement technology (Appel et al., 2011, Bruvik and

Hjertaker, 2016, Pinguet et al., 2006). Today it is widely recognised that MPFMs provide a

considerable range of benefits relative to test separators in terms of well-testing, reservoir

management, production allocation and flow assurance (Pinguet, 2010, Thorn et al., 2013).

The metering positions of MPFMs and test separators are schematically demonstrated in

Figure 1.1 for a typical offshore production scenario.

Figure 1.1 Schematic of a typical offshore production scenario. Oil, water and natural gas produced

from an underground reservoir is transported through a subsea pipeline and riser to an offshore

production platform. The oil, gas and water flowrates of the multiphase stream can be measured; (i)

using a test separator (at the offshore platform) where the fluid streams are separated into individual

components and then metered using single-phase flow meters, and/or (ii) direct in-line measurement

at the manifold using a multiphase flow meter.

The test separator provides multiphase flow measurement at the offshore production

platform whilst the MPFM may be installed in the subsea architecture near or at the

3

production manifold. The MPFM provides a direct in-line measurement of the multiphase

fluid stream close to the wellbore. Conventional test separators have a considerable time

delay between fluids leaving the wellhead and flow measurement occurring on the production

platform (Berge, 2011, Rajan et al., 1993). Furthermore, the equipment can require several

hours to achieve stable separation (Atkinson et al., 2004). In comparison, MPFMs installed

to monitor pipelines at subsea production manifolds can provide a continuous near real-time

measurement of fluid composition and flowrate (Falcone et al., 2001). This can provide

critical information for well-testing, production monitoring and optimisation (Corneliussen

et al., 2005). The correct implementation of MPFMs can result in improved reservoir

management with a 6-9% gain in the value of oil produced (Douglas-Westwood Limited,

2004). MPFMs are considerably cheaper relative to test separators; MPFMs cost

US$100,000 – 500,000 compared to US$1 – 5 million for a conventional test separator layout

(the cost of both instruments can vary with installation location (i.e. onshore, offshore or

subsea) and the size of the apparatus) (Falcone et al., 2009). Several authors have indicated

that the ability to incorporate non-invasive process tomography within a MPFM would be of

considerable benefit in terms of understanding the multiphase flow behaviour for flow

assurance purposes (Chaouki et al., 1997, Thorn et al., 1999).

The multitude of advantages provided by MPFMs has resulted in increasing demand

for these instruments, with the MPFM market anticipated to grow at an annual rate greater

than 5.4 % until 2022 (Research and Markets, 2016, Yoder et al., 2016). Multiple multiphase

flow metering technologies exist which provide unique solutions for measuring the relevant

component phase flowrates. MPFMs typically measure phase flowrates through separate

measurements of the total flowrate (e.g. using Venturi meters) and phase fractions. Gamma-

ray attenuation and electrical impedance are the two most widely used multiphase flow

metering techniques for phase fraction determination and have achieved reasonable

commercial success (Falcone et al., 2009). For example, the Vx multiphase flowmeter

produced by Schlumberger (shown in Figure 1.2) uses a Venturi meter to provide the total

flowrate of the multiphase stream whilst a gamma ray attenuation meter provides phase

fraction measurement (Atkinson et al., 2004).

4

Figure 1.2 The Schlumberger Vx multiphase flowmeter. The meter consists of a venturi meter

with absolute and differential pressure sensors for overall flowrate measurement. A dual energy

gamma-ray detector and source are used to simultaneously measure the phase fractions of oil, gas and

water of the multiphase flow stream (Atkinson et al., 2004).

Current MPFMs often do not meet the desired accuracy required for successful

implementation and thus there is a market for developing a reliable, accurate and robust

MPFM (Thorn et al., 2013). Nuclear magnetic resonance (NMR) is a technology which has

previously been recognised to form the basis for a universal MPFM (Ong et al., 2004). Of

interest are the recent developments in Earth’s field nuclear magnetic resonance (EFNMR)

which offers cost-effective and robust solutions for industrial process control (Mitchell et al.,

2014).

This study outlines the development of the apparatus and associated measurement

techniques required for an Earth’s field nuclear magnetic resonance multiphase flow meter.

Chapter 2 outlines the fundamentals of NMR which are relevant to this thesis. Chapter 3

explores key concepts in multiphase flow and multiphase flow metering.

Chapter 4 describes the development of the EFNMR flow metering system towards

measuring fluid velocity. Quantitative velocity distribution measurements of single-phase

flows are determined using appropriate signal analysis techniques. The accuracy and

robustness of the measurement technique is assessed for flows through a standard single-pipe

as well as a more complex two-pipe system.

5

Chapter 5 details the advancement of the MPFM system towards measuring

velocities and phase fractions in two-phase gas/liquid flows. The measurement technique

demonstrated in chapter 4 is extended in order to quantitatively characterise air-water flows

in both stratified and slug flow regimes; including tracking the liquid velocity and holdup

with time.

Chapter 6 discusses the development of both the flow metering system and signal

interpretation techniques towards measuring two-phase liquid/liquid (oil/water) flows. This

involves incorporating a dual polarisation mechanism for the system to allow the 1H NMR

signal to be measured across a range of fluid relaxation times. The proposed method for

measuring fluid phase fractions is demonstrated for stationary fluids in preparation for two-

phase flowing measurements.

Chapter 7 demonstrates the application of a new signal interpretation methodology

towards the quantitative measurement of two-phase oil/water flows. This involves

simultaneously distinguishing the fluid signal contributions (to quantify phase fractions) and

providing the relevant fluid velocity distributions. The accuracy of the technique in terms of

measuring individual fluid volumetric flowrates is verified.

Chapter 8 summarises the key contributions of this thesis and provides

recommendations for future work.

6

Chapter 2. Nuclear magnetic resonance

2.1 Fundamentals of NMR

2.1.1. Introduction to NMR

The measurement of nuclear magnetic resonance (NMR) within molecular beams was

first reported by Rabi et al. (1938). This was followed by separate demonstrations of NMR

in bulk materials; both in liquid water (Bloch, 1946) as well as in paraffin wax (Purcell et al.,

1946). Since its discovery NMR has developed into a well-established scientific technique

used for a range of academic and industrial purposes. NMR is renowned for its

implementation in the medical industry in the form of magnetic resonance imaging (MRI)

where it can provide in-situ examination of anatomies for clinical diagnosis (Brown et al.,

2014, Luiten et al., 2013, Westbrook and Talbot, 2018). NMR spectroscopy is applied in

chemistry to study the local chemical environment of atomic nuclei; providing structural

information about complex molecules such as proteins (Bovey et al., 1988, Levitt, 2013,

Szilágyi, 1995). The application of NMR to engineering and industrial processes has only

been realised more recently (Gladden and Alexander, 1996, Gladden and Sederman, 2013).

The use of low-field NMR (<1 T) in industrial applications has received considerable

attention, particularly due to recent developments of relevant NMR hardware (Blümich et

al., 2009a, Mitchell et al., 2014). The following sections provide information on NMR

theory relevant to this thesis.

2.1.2. Fundamental NMR Theory

NMR involves the interaction of sub-atomic particles with an external magnetic field.

Nucleons (neutrons and protons) possess a fundamental quantum property known as nuclear

spin which is an intrinsic angular momentum (Callaghan, 1991, Farrar, 1989, Levitt, 2013).

The angular momentum is described by the spin quantum number (I) which is quantised into

increments of ½. Nuclei are able to take one of 2I+1 possible energy states (m) between -I

7

and +I. The spin quantum number relates to the structure of atomic nuclei; nuclei which

contain an even number of both neutrons and protons have zero spin, nuclei which contain

an odd number of both neutrons and protons possess integer spin, whilst nuclei with an odd

number of nucleons (combined total of neutrons and protons) have half-integer spin. In this

work, all measurements performed involve the NMR of hydrogen atoms (1H) which have a

spin quantum number I = ½. Thus a hydrogen atom is able to exist in one of two possible

energy states; m = ½ (spin-up state) or m = -½ (spin-down state).

In the presence of no external magnetic field, the two energy states will possess equal

energy and therefore equal likelihood of a nucleus being in each level. The presence of an

external magnetic field (B0) will orientate the such that they are either generally aligned or

opposed to the external field. This results in each spin energy state having different energy

levels. The interaction between the quantised spin angular momentum and the external

magnetic field is known as the Zeeman interaction (Hore, 2015). The spin states have an

energy (E) which quantifies the Zeeman interaction;

𝐸 = −𝑚ℎ𝛾𝐵0 (2.1)

where γ is the gyromagnetic ratio of the nuclei (for 1H γ is 4.258 × 107 Hz/T), h is Planck’s

constant (6.63 × 10-34 J/s) and B0 is the strength of the external static magnetic field (in T).

Nuclei move between energy states in discrete transitions which can be induced by

electromagnetic radiation of the appropriate energy. For a 1H nuclei with m = ±½; the

transition between energy levels (ΔE) is quantified by (Slichter, 1996);

𝛥𝐸 = ℎ𝑣 = ℎ𝛾𝐵0 (2.2)

where v is the frequency of electromagnetic radiation inducing the energy level transition.

Figure 2.1 provides an illustration of the Zeeman interaction including the relative energy of

the spin-up (m = ½) and spin-down states (m = -½) as well as the energy level difference

(ΔE).

8

Figure 2.1 Zeeman diagram illustrating the energy states for a 1H atom with the energy difference

between the states indicated.

In order to observe magnetic resonant absorption from the nuclear spins, the sample

must be supplied with electromagnetic radiation (typically with a pulse of radio frequency

(r.f.) radiation) exactly matching the energy difference between the spin states. The exact

frequency required is called the Larmor frequency (ω0, in rad/s) and is proportional to the

external static magnetic field (Callaghan, 1991);

𝜔0 = 2𝜋𝛾𝐵0 (2.3)

For example, to detect 1H NMR (γ of 4.258 × 107 Hz/T) in the local Earth’s magnetic

field (~54 µT in Perth, Western Australia), an excitation pulse of ~2.29 kHz is required. The

excitation pertubes the nuclei from their initial equilibrium energy state and causes the

individual nuclear precessions to synchronise to a net coherent precession at the Larmor

frequency. The precession of nuclear moments is known as the free induction decay (FID)

and can be observed using an NMR detection coil.

The relative population of spins in each energy state is described by the Boltzmann

distribution. For 1H with I = ½; the ratio of the number of spins in the spin-down state (N-

1/2) to the number of spins in the spin-up state (N1/2) is given by (Abragam, 1961);

𝑁−1/2

𝑁1/2 = exp (−

𝛥𝐸

𝑘𝑇) (2.4)

Inte

raction

en

erg

y (

E)

Magnetic field strength (B0)

m = -½

m = ½

ΔE = hγB0

9

where ΔE is the energy level transition, k is the Boltzmann’s constant (1.38 × 10-23 J/K) and

T is the absolute temperature. For 1H nuclei in the local Earth’s magnetic field at room

temperature (20 °C); this ratio is extremely small (3.8 × 10-10). The Boltzmann distribution

of spins results in a very slight excess (1 1H proton in every 2.7 × 109) of nuclei in the lower

energy (spin-up) state. These spins contribute towards the net magnetic moment which is

observable during NMR. The very small disproportion of spins between the two energy

states results in a small net magnetic moment and constrains the sensitivity of NMR

experiments. This is the reason why NMR is generally considered as a comparatively low

signal-to-noise-ratio (SNR) technique. However the large number of nuclei available (100

mL of water contains ~6.7 × 1024 1H atoms) results in a net magnetic moment. For Earth’s

field NMR, pre-polarisation of the sample (at a higher magnetic field) is usually required to

achieve a detectable signal; this is discussed in section 2.2.2.

2.1.3. The vector model

A classical mechanics approach is utilised to describe the remainder of the NMR

theory. The net magnetic moment generated by a sample in an external magnetic field can

be considered as a net magnetisation vector (M). The precession of the net magnetisation

vector around the external magnetic field vector (B0) is described using a classical angular

momentum analogy (Bloch, 1946);

𝑑𝐌

𝑑𝑡= 𝐌 × 𝛾𝐁𝟎 (2.5)

where t is time. This description of nuclei spin precession is known as the Bloch vector

model. The net magnetisation vector will align with the direction of the applied static

magnetic field (B0). However if the vector is disturbed from thermal equilibrium (i.e.

perturbed from away the z-axis); the vector is observed to precess about the z-axis at the

Larmor frequency (Keeler, 2005). This behaviour is called the Larmor precession and is

illustrated in Figure 2.2.

10

Figure 2.2 Illustration of Larmor precession. (a) A net magnetisation vector (M) is generated in the

direction of the external static magnetic field (B0), and (b) tilting M away from the direction of B0

(i.e. the z-axis) causes the precession of M about the z-axis at the Larmor frequency (ω0).

The perturbation of the net magnetisation vector into the transverse (X-Y) plane is

necessary in order to detect a signal in a receiver coil and is induced by the application of a

secondary oscillating magnetic field (B1). This is the excitation pulse (of r.f. radiation) which

is applied perpendicular to the direction of B0. The excitation pulse must be applied in

resonance with the spins oscillating about B0 in order to cause M to precess simultaneously

about B0 and B1. The length and amplitude of B1 pulses is used to control the effective

position of M relative to B0. The two commonly applied pulses are; (i) the 90° pulse which

is used to rotate M by 90° into the transverse plane, and (ii) the 180° pulse which inverts M

180°.

2.1.4. Measuring the free induction decay

The detection of the Larmor precession is the observed signal during standard pulse

NMR experiments. The signal is detected by aligning a receiver coil (r.f. coil) near the

sample. The coil must be placed in the transverse plane relative to the static magnetic field;

often a small coil of wire is mounted around the sample perpendicular to the direction of the

static field (Fukushima and Roeder, 1993). The same r.f. coil is often used for excitation and

detection; the coil is switched between transmit and receive during the NMR pulse sequence.

The rotation of the component of M through the transverse plane induces an electromotive

force in the receiver coil; the detected signal is the free induction decay (FID) (Levitt, 2013).

The application of a simple “pulse and collect” experiment, as executed when detecting at

the earth’s magnetic field in practice, is now discussed.

B0

X

Z

Y

(a)

Direction of M B

0

X

Z

Y

ω0

(b)

11

The key components of the pulse and collect experiment are illustrated by the pulse

sequence diagram in Figure 2.3.

Figure 2.3 Illustration of a pulse and collect sequence used to measure a free induction decay. Key

timing parameters are indicated.

The definitions of timing parameters are presented in the pulse sequence, including;

the length of the polarisation pulse (tpolz), the delay between polarisation and excitation (tPE),

the acquisition delay (tdelay) and the time of acquisition (ta). The time since excitation (te) is

the combination of the acquisition delay and acquisition time (i.e. te = tdelay + ta).

The sequence consists of three key stages; polarisation, excitation and detection. A

net magnetisation vector is developed in the sample of interest by imposing a static magnetic

field for a time tpolz. Note that polarisation is not usually applied as a pulse but rather a

permanent static magnetic field; however the Earth’s field nuclear magnetic resonance

(EFNMR) Terranova system (Magritek, New Zealand) utilises an electromagnetic pre-

polarising coil to provide magnetisation (this is discussed in section 2.2.2). Once sufficient

polarisation has been achieved; the B1 excitation pulse at the Larmor frequency is transmitted

using the r.f. coil to rotate M by 90° into the transverse plane. A short acquisition delay is

then required in order to allow ring-down time for the r.f. probe to dissipate unwanted voltage

oscillation due to residual stored energy from the excitation pulse (Zhen et al., 2018). The

r.f. coil is switched to receive and the FID of the excited sample induces an electromotive

force in the coil which is amplified and recorded. Finally the FID will return to thermal

equilibrium according to magnetic relaxation processes (which are discussed in sections 2.1.5

and 2.1.6). The magnetic processes involved in a pulse and collect experiment are captured

using the classical mechanics vector model in Figure 2.4.

te

Polarisation pulse

tpolz

tPE

tdelay

ta

90° excitation pulse Free induction

decay

12

Figure 2.4 Classical mechanics representation of the stages of a pulse and collect experiment. (a)

Polarisation of the sample induces a net magnetisation vector (M) in the direction of the external

magnetic field (B0), (b) M is excited using a 90° r.f. pulse, (c) excitation causes the magnetisation

vector to rotate into the transverse plane which allows observation of the Larmor precession (at a

frequency ω0), (d) The longitudinal component (z) of M relaxes to thermal equilibrium according to

the spin-lattice relaxation time T1, (e) T2* relaxation causes dephasing of M, (f) Net effect of relaxation

processes on M.

The shape of the measured FID signal is characterised by relaxation processes (T1, T2

and T2* relaxation) which will be discussed in the following sections.

2.1.5. Spin-lattice relaxation

Nuclear spins interact with the surrounding environment (“lattice”) resulting in a

process known as spin-lattice relaxation. This process involves energy transfer from the

excited spins to the lattice as a result of molecular motion of spins rotating at the Larmor

frequency. Spin-lattice relaxation is also referred to as longitudinal relaxation and describes

the return to thermal equilibrium for the longitudinal component of the net magnetisation

vector (Mz) with respect to time (t) according to;

𝑑𝑀𝑍

𝑑𝑡=

−(𝑀𝑍−𝑀0)

𝑇1 (2.6)

B0

X

Z

Y

(a)

M r.f. pulse

X

Z

Y

(b)

M

X

Z

Y

(d)

M X

Z

Y

(e)

M X

Z

Y

(f)

M

13

where M0 is the equilibrium magnetisation and T1 is the spin-lattice relaxation constant. The

value of T1 is dependent on the matter of investigation; for example the T1 of water (at 25°C

and at ω0 > 50 kHz) is ~ 2.9 s (Graf et al., 1980). The spin-lattice relaxation behaviour is

dependent on the applied magnetic field as well as the temperature (Korb and Bryant, 2002,

Krynicki, 1966). Integrating equation 2.6 demonstrates that T1 effectively describes the

exponential growth of the longitudinal magnetisation;

𝑀𝑍(𝑡) = 𝑀𝑧(0) exp (−𝑡

𝑇1) + 𝑀0 (1 − exp (−

𝑡

𝑇1)) (2.7)

where Mz(0) is the initial longitudinal magnetisation. Directly after a 90° pulse, Mz(0) = 0

such that the return of Mz to equilibrium is described by;

𝑀𝑍(𝑡) = 𝑀0 (1 − exp (−𝑡

𝑇1)) (2.8)

The T1 relaxation rate can be measured using a range of experimental methods (Fukushima

and Roeder, 1993). One of the most common approaches to measure T1 is the inversion-

recovery method which utilises an initial 180° pulse to invert the magnetization vector M

from the +Z axis into the –Z axis (Vold et al., 1968). This is followed by a pulse and collect

experiment with a 90° pulse used to excite the magnetization into the transverse plane where

finally the FID signal is acquired. The sequence is repeated multiple times with the inversion

delay time (tI; time between the 180° and the 90° excitation pulse) varied in order to capture

signal contrast according to T1. For the inversion recovery pulse sequence; the initial

longitudinal magnetization Mz(0) = -M0 after the application of the inversion pulse, thus the

FID signal amplitude at varying inversion delay times (M(tI)) is described by;

𝑀(𝑡𝐼) = 𝑀0 (1 − 2 exp (−𝑡𝐼

𝑇1)) (2.9)

The measured FID signal amplitudes can be fit using equation 2.9 in order to determine the

T1 in the system of interest.

The inversion recovery method is illustrated in Figure 2.5; with (a) showing the

inversion recovery pulse sequence and (b) the longitudinal magnetisation development for

water (T1 of 2.9 s).

14

Figure 2.5 Inversion recovery method. (a) the inversion recovery pulse sequence, and (b) the

longitudinal magnetisation development during an inversion recovery measurement of a water sample

(T1 ~ 2.9 s).

2.1.6. Spin-spin relaxation

The second relaxation mechanism in NMR is spin-spin relaxation. Each spin in a

Larmor precession interacts with the local magnetic fields of neighbouring spins causing

dephasing of the transverse component of the magnetisation vector (MXY). The decay of MXY

with respect to time is described by (Bloch, 1946);

𝑑𝑀𝑋𝑌

𝑑𝑡=

−𝑀𝑋𝑌

𝑇2 (2.10)

where T2 is the spin-spin relaxation constant. The integral of equation 2.10 demonstrates that

T2 describes the exponential rate of decay for magnetisation in the transverse plane;

𝑀𝑋𝑌(𝑡) = 𝑀𝑋𝑌(0) exp (−𝑡

𝑇2) (2.11)

where MXY(0) is the initial magnetisation in the transverse plane.

In practice two factors influence the decay of MXY; the first being the spin-spin

decoherence according to T2 as described above, whilst the secondary decay mechanism

results from magnetic field inhomogeneity. It is very difficult to produce homogenous

magnetic fields; thus inhomogeneity in the magnetic field results in spins experiencing

different Larmor frequencies in different positions. The distribution of Larmor frequencies

results in a net dispersion of phase in the spin ensemble. The overall or effective spin-spin

relaxation rate (T2*) observed during a FID measurement is described by;

-1

0

1

0.01 0.1 1 10 100

MZ

tI [s]

(b)

te

180° inversion

pulse

tI t

delay t

a

90° excitation

pulse

Free induction decay

(a)

15

1

𝑇2∗ =

1

𝑇2+ 𝛾Δ𝐵0 (2.12)

where ΔB0 quantifies the inhomogeneity of the static field. Dephasing as a result of natural

atomic interactions between neighbouring spins is known as spin-spin relaxation (i.e. T2) and

is an irreversible energy transfer whilst dephasing due to magnetic field inhomogeneity is

reversible.

The magnetic field inhomogeneity is often described using T2,i which quantifies the

exponential relaxation rate caused by field inhomogeneity. However this assumes that the

magnetic field inhomogeneity induces an exponential signal decay which is not always valid;

therefore assuming an exponential decay can result in significant error during signal analysis

(Grombacher et al., 2013, Grunewald and Knight, 2012). Experimental FID measurements

using the EFNMR system have been observed to produce a half-Gaussian line shape (Zhen

et al., 2018). The field inhomogeneity signal decay (I(t)) can be described by the following

half-Gaussian model (Sukstanskii and Yablonskiy, 2001)

𝐼(𝑡) = exp(−(𝑅𝐼𝑡)2) (2.13)

where RI is a Gaussian relaxation rate constant (in s-1) accounting for the rate of signal decay

introduced by magnetic field inhomogeneity. Therefore a FID signal (S(t)) measured in the

Earth’s magnetic field can effectively be described by;

𝑆𝐹𝐼𝐷(𝑡) = exp (− (𝑡

𝑇2+ (𝑅𝐼𝑡)2)) (2.14)

Most magnetic resonance apparatus are designed to reduce the magnetic field inhomogeneity

using shim systems. The Earth’s magnetic field is homogenous; however it is also very weak

such that nearby ferrous or magnetic materials are able to disrupt the local magnetic field.

The Terranova EFNMR system (Magritek, New Zealand), which is applied in this thesis,

utilises shim coils which introduce small magnetic field gradients in order to negate the

impact of inhomogeneity in the local Earth’s magnetic field. The shim coils are applied in

three orthogonal directions (X, Y and Z) which thus correspond to first-order shims. The

current through each coil controls the shim field strength and is manipulated in order to

optimise the impact of each coil relative to the field inhomogeneity. In more complex NMR

16

systems, higher order shims are utilised to create more complex shim fields allowing for

improved correction of the static magnetic field.

The spin-spin relaxation rate (T2) can be directly measured using a Carr-Purcell-

Meiboom-Gill (CPMG) pulse sequence (Carr and Purcell, 1954, Meiboom and Gill, 1958).

This sequence utilises Spin or Hahn echoes which are produced with the application of a

180° r.f. pulse a time τ after the initial 90° excitation pulse. The 180° pulse inverts the phase

accumulated as a result of the Larmor precession. Spin dephasing which has occurred as a

result of magnetic field inhomogeneity is “flipped” and begins to refocus. At a time 2τ after

the initial pulse, phase dispersion will have been reversed (i.e. field inhomogeneity dephasing

has been fully reversed) resulting in a signal maximum which is the spin echo (Hahn, 1950).

The irreversible dephasing caused by spin-spin relaxation is not reversed and thus spin echoes

are able to remove the effect of field inhomogeneity decay and capture T2 decay in isolation.

The CPMG sequence utilises a train of 180° pulses in order to produce multiple spin echoes

which decay according to equation 2.11. The 180° pulses occur every 2τ implying the time

between the measured echoes or the echo spacing is TE = 2τ. The measurement of T2 using

a CPMG experiment is demonstrated in Figure 2.6; with (a) showing the CPMG pulse

sequence including the 90° excitation and 180° refocussing r.f. pulses, whilst (b) shows the

measured spin echoes and resultant echo amplitude envelope which are fit with equation 2.11

in order to determine the T2 for the sample of interest.

17

Figure 2.6 Demonstration of the CPMG experiment. (a) the CPMG pulse sequence with the 90°

excitation pulse followed by a train of 180° pulses at a spacing of 2τ. (b) The measured signal forms

spin echoes at a spacing of TE = 2τ. The echoes refocus and dephase according to T2* whilst the echo

amplitudes decay according to T2. The echo peak amplitudes can be fit with equation 2.11 in order

to obtain a T2 measurement.

2.2 Application of low-field NMR

2.2.1. Low-field NMR

The science of NMR has been utilised across a vast range of practical applications.

Many implementations of NMR (such as MRI for medical diagnosis or spectroscopy for

chemical analysis) involve the use of high magnetic fields (B0 > 3 T (Mitchell et al., 2014))

to provide sufficient sensitivity and/or resolution. However high-field NMR equipment is

impractical for implementation in industrial and process engineering environments due to the

considerable cost of such systems, lack of portability and safety hazards associated with high

magnetic fields (Blümich et al., 2009a). Low-field NMR (B0 < 1 T (Mitchell et al., 2014))

has recently seen a range of technological developments, including; the design and

construction of magnetic hardware (e.g. Blümich et al., 2009b, Danieli et al., 2010,

McDowell and Fukushima, 2008, Raich and Blümler, 2004), advances in spectrometer

electronics (e.g. Kentgens et al., 2008, Lee et al., 2008, Olson et al., 1995) and improvements

Pulse sequence

Signal

T2 T

2*

90° excitation pulse

180° pulse train

𝑴𝑿𝒀(𝒕) = 𝑴𝒙𝒚(𝟎)𝒆𝒙𝒑 ൬−𝒕

𝑻𝟐൰

(a)

(b)

τ 2τ 2τ 2τ 2τ 2τ 2τ 2τ

TE TE T

E T

E T

E T

E T

E

18

in the signal processing and data interpretation of low-field data (e.g. Holland and Gladden,

2015, Keeler, 2005, Mitchell et al., 2012, Mitchell et al., 2014).

The technological advancement of low-field NMR has led to the utilisation of such

systems across a range of process and industrial engineering applications (Mitchell et al.,

2014). One of the most significant applications of low-field NMR is well logging in the oil

and gas industry which is used to provide petrophysical assessment of reservoir formations

(e.g. Freedman and Heaton, 2004, Hürlimann and Heaton, 2015, Kleinberg, 2001a, Kleinberg

and Jackson, 2001). Low-field NMR laboratory studies of rock cores are also used to provide

insights and guidance for interpretation of well logs (e.g. Borgia et al., 1996, Song, 2010).

NMR has seen uptake in process and quality control in the food industry (Constantinesco et

al., 1997). NMR can provide robust and reliable characterisation of relevant food properties

such as composition or droplet size and has been applied to a variety of products such as;

bread (e.g. Lucas et al., 2005, Lucas et al., 2012), potatoes (e.g. Mortensen et al., 2005,

Thybo et al., 2003) and cheese (e.g. Andersen et al., 2010, Hurlimann et al., 2006).

Quantitative measurements using low-field NMR spectroscopy can be used in process

control and reaction monitoring in industrial processes (e.g. Dalitz et al., 2012, Danieli et al.,

2014, Silva Elipe and Milburn, 2016). Finally low-field NMR has been successfully applied

to characterise oilfield chemistry with droplet sizing in emulsions (e.g. Fridjonsson et al.,

2014a, Ling et al., 2016, Ling et al., 2014, Ling et al., 2017) and quantitative analysis of oil

contamination in produced water (e.g. Wagner et al., 2018, Wagner et al., 2016). These

applications demonstrate the commercial capability of low-field NMR in industrial

environments. The application of NMR towards flow measurement is discussed in section

3.2.5.

2.2.2. Earth’s Field NMR

Earth’s Field NMR (EFNMR) involves the application of NMR experiments where

the nuclear spins are excited and detected in the Earth’s magnetic field (Béné, 1980).

EFNMR is considered a special case of ultra-low-field NMR (B0 < 1 mT (Mitchell et al.,

2014). In this thesis, experiments are conducted in Perth, Western Australia, where the local

Earth’s magnetic field in the laboratory is measured as 54 µT (corresponding to a Larmor

19

frequency of 2.29 kHz). Packard and Varian (1954) first observed free nuclear induction in

the Earth’s magnetic field. Nuclear precession in the Earth’s magnetic field was measured

using a robust and portable experimental apparatus (Waters, 1955). The low cost and

transportable nature has not only contributed towards EFNMR becoming an excellent tool

for teaching the principles of NMR (Callaghan and Le Gros, 1982, Callaghan et al., 2007)

but has also provided an opportunity for developing systems for quantitative analysis (Halse

et al., 2008).

EFNMR has been utilised for a variety of interesting applications and developments

in recent history. The initial nuclear magnetism logging tools operated using the Earth’s

magnetic field during petrophysical reservoir characterisation prior to the development of

logging tools at higher magnetic fields (Dunn et al., 2002). Modern application of EFNMR

in the georesources sector uses a surface NMR technique to conduct hydrogeological surveys

for monitoring and characterising groundwater aquifers (e.g. Grunewald and Knight, 2011,

Knight et al., 2012, Shushakov, 1996). An interesting application of EFNMR utilised an

Earth’s field detection coil to measure the diffusivity of brine in Antarctic sea ice (e.g.

Callaghan et al., 1998, Callaghan et al., 1997).

More recent developments have seen EFNMR provide spectroscopic and imaging

measurements. Earth’s field spectroscopy measurements have been performed which reveal

behavioural information of nuclear spins in 129Xe gas (Appelt et al., 2005, Appelt et al.,

2006). Further development of spectroscopic techniques allowed 2D correlation

spectroscopy measurements to be performed in the Earth’s magnetic field (Robinson et al.,

2006). Hardware developments in pre-polarisation coils, imaging gradients and shim

gradients enabled imaging in an EFNMR system; including self-diffusion imaging, velocity

imaging and slice selection (Mohoric et al., 1999, Planinsic et al., 1994, Stepišnik et al.,

1990). The Magritek EFNMR Terranova system has even been developed to be able to

perform 3D MRI (Halse et al., 2006).

The discussed developments and applications certainly illustrate the potential of

EFNMR. However the application of EFNMR towards quantitative measurement systems is

20

limited due to the inherent lack of measurement sensitivity. The poor signal strength

associated with EFNMR is due to the ultra-low magnetic field strength (SNR α B01.75

(Fukushima and Roeder, 1993)). A number of strategies have been developed in order to

overcome the poor sensitivity and provide signal enhancement (Blümich et al., 2009a). The

first strategy applies dynamic nuclear polarisation (DNP) in the form of the Overhauser effect

(Abragam, 1955, Kernevez and Glenat, 1991). A target nuclear spin (e.g. 1H) receives a net

polarisation transfer from an excited unpaired electron causing considerable polarisation

enhancement (Halse and Callaghan, 2008). The technique requires free electrons to be

introduced using free radicals (e.g. nitroxide radicals) (Armstrong et al., 2009). Whilst this

technique provides excellent signal strength (enhancement factor ~ 3000) it is not feasible to

implement in a subsea multiphase pipeline due to the free radical requirement.

A more practical approach (relative to DNP) for signal enhancement is to use a pre-

polarising magnetic field. There are two approaches for generating a pre-polarising magnet

field; using an electromagnet or a permanent magnet array. The Magritek EFNMR

Terranova system incorporates an in-built electromagnet pre-polarising coil (EPPC) in the

form of a coaxial solenoid. This coil is created from multiple copper windings surrounding

the r.f. detection coil. The EPPC provides a maximum pre-polarising field of 18.7 mT (using

a current of 6 A). This is a relatively easy and cost-effective approach for producing a pre-

polarising field; with the advantage of being able to quickly switch the coil on and off. This

allows a fast transition (delay time is 60 ms) from the relatively inhomogeneous polarising

field to the highly homogenous Earth’s field (used for excitation and detection). The primary

disadvantage of the EPPC is the limit on magnetic field strength. The significant current

required to achieve the pre-polarising field causes resistive heating in the coil; this restricts

the maximum current (and hence the maximum field to 18.7 mT) and the time which the pre-

polarising field is applied (tpolz); which is problematic for long T1 samples.

The alternative option to generate a pre-polarising magnetic field is the use of a

permanent magnet. This has been demonstrated with the use of a Halbach array to

hyperpolarise fluids for ultrahigh resolution NMR spectroscopy in the Earth’s magnetic field

(Appelt et al., 2005, Appelt et al., 2006, Armstrong et al., 2008, Moulé et al., 2003). The

21

cylindrical Halbach array can be designed to generate a strong uniform magnetic field within

the inside of the cylinder whilst a very small stray field is generated externally from the

cylinder (Halbach, 1980). The Halbach array magnetic field geometry is advantageous for

many practical applications (Zhu and Howe, 2001) including mobile low-field NMR (Raich

and Blümler, 2004). Cylindrical Halbach arrays can be produced with an effective magnetic

field strength of up to 3-4 T (Leupold et al., 1993); allowing very considerable pre-

polarisation for EFNMR measurements. The permanent magnet array has a limited stray

field, thus can typically be located within 1 – 1.5 m of the detection coil (Halse and Callaghan,

2008). The primary issue regarding the use of Halbach arrays for EFNMR is the sample

transfer from the permanent Halbach magnet to the EFNMR detection probe. The transfer

must be repeatable with unchanging parameters (e.g. polarisation time and transfer time) in

order to ensure consistent results. Flowing systems (e.g. multiphase pipeline flows) lend

themselves towards such a transfer process; thus the Halbach array is ideally suited for an

EFNMR flow meter. The two pre-polarisation systems are shown in Figure 2.7 with (a)

illustrating the EFNMR system which includes an electromagnetic pre-polarising coil and

(b) showing a cylindrical Halbach array.

Figure 2.7 Two alternative solutions for pre-polarisation. (a) the EFNMR system which includes

an electromagnetic co-axial solenoid (can be seen as copper windings) which provides a magnetic

field of 18.7 mT (with a 6 A current), and (b) a cylindrical Halbach array which provides a permanent

magnetic field of 300 mT.

NMR remote detection systems have been designed to capture information (such as

velocity or composition) from a flowing medium (Granwehr et al., 2005, Harel et al., 2006).

These systems apply a time-of-flight measurement where the fluid of interest is tagged in

order to encode magnetisation information. The fluid then travels to a separate detection coil

in order to recover the appropriate information. The excitation tagging may be optimised in

(a) (b)

22

terms of sequence design (manipulating r.f. pulses and gradients) in order to encode the

relevant information of interest (e.g. spatial encoding for MRI recovering fluid geometry).

2.3 Inversion techniques in NMR

NMR is used to characterise a wide range of substances; providing macroscopic and

microscopic property information. This is particularly useful in chemical engineering, where

NMR can be used to non-invasively probe systems to monitor properties such as diffusion,

velocity and chemical exchange during transport processes (Gladden, 1994, Gladden and

Alexander, 1996, Gladden and Sederman, 2013, Stapf and Han, 2006). However, such

processes can be highly complex; involving distributions of the value of material properties

rather than a single component value. For example; during the petrophysical analysis of

reservoir formations (either from well logging or laboratory based measurements) T2

relaxation distributions are obtained which are reflective of the complex pore geometry

within geological formations (Freedman and Heaton, 2004). In this work, Tikhonov

regularisation is the inversion technique used to capture distributions for relevant parameters

of interest. The following sections (2.3.1 and 2.3.2) will discuss 1D and 2D Tikhonov

regularisation.

2.3.1. 1D Tikhonov regularisation

Tikhonov regularisation is a robust mathematical inversion technique useful in

extracting relevant distributions of parameters. Regularisation is effective at handling noisy

signal data (Mitchell et al., 2014) and does not require any assumptions regarding the shape

of the resultant probability distribution (Hollingsworth and Johns, 2003). The applicability

of regularisation to analysing NMR signal data has previously been demonstrated for

complex systems, primarily in evaluating porous geology in well logging (Coates et al., 1999,

Dunn et al., 2002) and laboratory core analysis (Grunewald and Knight, 2009, Morriss et al.,

1997). Inversion techniques have enabled determination of fluid relaxation distributions, as

well as multi-dimensional relaxation and diffusion distributions within porous media

(Hürlimann et al., 2003, Hürlimann and Venkataramanan, 2002, Mitchell et al., 2012). Such

distributions provide petrophysical characterisation of porous geology such as measurement

of porosity, pore size distribution as well as fluid typing and quantification (Hürlimann et al.,

23

2002, Munn and Smith, 1987). Further applications of Tikhonov regularisation towards

complex systems include droplet sizing of emulsions (e.g. Fridjonsson et al., 2012,

Hollingsworth and Johns, 2003, Hollingsworth et al., 2004, Ling et al., 2014, Ling et al.,

2017) as well the distribution and mobility of water within meat (e.g. (Pearce et al., 2011)).

A probability distribution of a variable x (i.e. P(x)) may be expressed as a function of

an experimentally acquired NMR signal (S(t)) using a first-order Fredholm integral equation

(Delves and Walsh, 1974);

𝑆(𝑡) = ∫ 𝐾(𝑡, 𝑥)∞

0𝑃(𝑥) 𝑑𝑥 (2.15)

where the NMR signal is (S) is a function of an experimental parameter (t) and K(t,x) is a

model kernel function describing the mathematical relationship between the acquired NMR

signal and the relevant probability distribution. Equation 2.15 is discretised and rewritten in

matrix algebra;

s = Kp (2.16)

where s is the measured signal vector, K is the model kernel matrix and p is the discretised

probability distribution vector. Equation 2.16 requires inversion to determine p, however

direct inversion is not possible as the transfer matrix (K) is typically rank deficient (i.e. the

matrix rows are linearly dependent). Equation 2.16 can be solved by minimising the sum of

squared residuals (i.e. least squares fit):

min{‖𝐊𝐩 − 𝐬‖2} (2.17)

however experimental noise in the signal vector produces an unrealistic probability

distribution with large oscillations. Regularisation provides a stable inversion method which

determines a realistic probability distribution in the presence of experimental noise by

applying a penalty function. In Tikhonov regularisation, the following expression is

minimised in order to acquire p (Tikhonov et al., 1995);

min{‖𝐊𝐩 − 𝐬‖2 + 𝛼‖𝐐𝐩‖2} (2.18)

where α is the smoothing parameter and Q is a smoothing operation matrix. In this work, the

Q is designed to calculate the finite second derivative of the resultant probability distribution

to ensure smoothness (Mitchell et al., 2014). The first term in equation 2.18 (‖𝐊𝐩 − 𝐬‖2) is

24

the residual norm whilst the second term (‖𝐐𝐩‖2) is the penalty function. The smoothing

parameter is used to optimise the compromise between finding the true solution (minimising

the residual norm) and limiting the impact of noise on the solution (minimising the penalty

function).

The value of α is selected using the generalised cross-validation (GCV) method

(Golub et al., 1979, Wahba, 1977, Wahba, 1982). This method sequentially removes a data

point in the solution (s) and determines the value of the smoothing parameter which predicts

the removed point with the best accuracy (Hollingsworth and Johns, 2003). This is repeated

for each data point in s, and a GCV score is determined as a function of α. The GCV score

(ΦGCV) may be calculated using;

𝛷𝐺𝐶𝑉 =1

𝑁‖𝐊𝐩−𝐬‖2

൬1−1

𝑁𝑡𝑟(𝐊(𝐊𝑇𝐊 + 𝛼𝐐)−𝟏𝐊𝑻)൰

2 (2.19)

where N is the total number of data measurement points in s, tr(..) denotes the trace of a

matrix and T denotes the matrix transpose. The value of α which minimises this GCV score

is the optimal smoothing parameter; this is a methodology that has been widely validated for

NMR data interpretation (e.g. Hollingsworth and Johns, 2003, Hollingsworth et al., 2004).

2.3.2. 2D Tikhonov regularisation

The extension of NMR measurements into two dimensions requires careful

consideration of appropriate inversion techniques (Mitchell et al., 2012). Two-dimensional

(2D) NMR measurements are useful in probing local surroundings as well as providing

chemical information for complex systems. 2D NMR provides simultaneous measurement

of two parameters of interest (e.g. T1, T2 or self-diffusion coefficients (D)). Such

measurements have been previously been applied to study systems such as; reservoir

structures (e.g Hürlimann et al., 2003, Hürlimann and Venkataramanan, 2002, Mitchell et

al., 2010b, Song et al., 2002), food products (e.g. Godefroy et al., 2003, Hills et al., 2004,

Song, 2009) and biological systems (e.g. Hornemann et al., 2009, Vogt et al., 2013). The

type of 2D measurements commonly applied include; T1-T2 distributions (e.g. Hills et al.,

2004, Song et al., 2002, Vashaee et al., 2018), D-T2 distributions (e.g. Callaghan et al., 2003,

Godefroy and Callaghan, 2003, Hürlimann et al., 2003, Hürlimann and Venkataramanan,

25

2002) and T2-T2 distributions (e.g. Hornemann et al., 2009, Mitchell et al., 2007, Washburn

and Callaghan, 2006).

The measurement of 2D NMR data usually requires two separate independent

variables or experimental parameters; which can be considered as the “direct” and “indirect”

measurements (Mitchell et al., 2012). For example; in the measurement of a T1-T2

distribution, the direct measurement is the single-shot acquisition of the CPMG echo train to

measure T2 whilst the indirect measurement is the determined over multiple experiments with

the variation of pre-polarising conditions (e.g. inversion recovery experiment) to measure T1.

2D NMR signal measurements may be described by extending the first-order Fredholm

integral equation (i.e. equation 2.15) into two dimensions (Van Landeghem et al., 2010);

𝑆(𝑡1, 𝑡2) = ∫ ∫ 𝐾(𝑡1, 𝑡2, 𝑥1, 𝑥2)∞

0𝑃(𝑥1, 𝑥2)

∞

0 𝑑𝑥1𝑑𝑥2 (2.20)

where t1 and t2 are experimental parameters varied in order to see signal contrast in the

measured parameters x1 and x2, with subscripts 1 and 2 denoting the first (direct) and second

(indirect) dimensions respectively. K(t1, t2, x1, x2) is the model kernel function describing the

mathematical relationship between the acquired 2D NMR signal (S(t1,t2)) and the relevant

2D relaxation distribution P(x1,x2). For most 2D NMR measurements, the kernel function is

separated into two components (direct and indirect dimensions) and a singular value

decomposition of each kernel is performed during data processing in order to improve the

computational efficiency of implementing a 2D inversion (Venkataramanan et al., 2002).

However this requires the two data dimensions to be independent and separable (i.e. the

dimensions do not share a common variable) (Mitchell and Fordham, 2011). For 2D

measurements where the dimensions are non-separable, it is often preferable to construct a

full kernel (i.e. non-separable matrix) to avoid undesirable consequences during data analysis

(Mitchell et al., 2010a, Mitchell and Fordham, 2011).

26

Chapter 3. Multiphase flow

3.1 Multiphase Flow Concepts

Multiphase flow is considered the simultaneous flow of two or more phases (or

constituent components of the mixture) within a closed conduit (Corneliussen et al., 2005).

Modern society contains a vast array of multiphase flow systems in both natural and

industrial environments (Kolev, 2011). Multiphase flows are encountered within many

industrial processes, including; oil and gas flows in petroleum production, granular flows in

agricultural processing, ore flows in mineral processing and process flows in chemical plants

(Yadigaroglu and Hewitt, 2017). These processes are described by fundamental physical

principles such as; fluid mechanics, mass transfer, chemical reactions and particle mechanics

(Prud’homme, 2010). The considerable complexity of multiphase flows has caused difficulty

in both characterising and measuring them (Gidaspow, 1994). This has contributed towards

significant research interest in furthering the current understanding of multiphase flow as

well as developing multiphase flow metering technologies.

Within the oil and gas industry, multiphase flow is encountered throughout

production and processing systems (Falcimaigne and Decarre, 2008). Multiphase flow

information of the production stream is crucial for flow assurance, reservoir management,

production allocation and monitoring purposes (Economides et al., 1994, Falcone et al.,

2009). This fluid stream typically consists of oil and natural gas but can also contain water,

condensate (hydrocarbon components which have condensed from the natural gas phase) and

a range of solid phases (e.g. sand, hydrates, waxes and asphaltenes). Most multiphase flow

metering systems focus on measuring the three key phases, being oil, gas and water (Thorn

et al., 2013). Multiphase flows can exist in a variety of flow regimes which describe the

geometric arrangement of the phases within the pipeline. For example gas-liquid flows (e.g.

natural gas and oil) can exist as slug flow or bubble flow, whilst liquid-liquid flows (e.g. oil

27

and water) can exist as stratified liquid layers or emulsified mixtures. The qualitative visual

description of three-phase flow patterns becomes even more complex. The classification of

flow regimes is discussed with reference to gas-liquid flow in section 3.1.2 and liquid-liquid

flow in section 3.1.3.

3.1.1. Multiphase flow information

Multiphase flow is traditionally quantified via the mass or volumetric flow rate of the

individual phases (Thorn et al., 2013). The total volumetric flowrate (Q) of a multiphase

stream is given by (Kolev, 2011);

𝑄 = ∑ 𝑞𝑖𝑁𝑖 = 𝐴 ∑ 𝑥𝑖𝑣𝑖

𝑁𝑖 (3.1)

where i indicates the phase (e.g. oil, water, gas), N is the number of phases present, qi is the

volumetric flowrate of phase i, A is the cross-sectional area of the pipeline, xi is the volumetric

fraction of phase i and vi is the instantaneous velocity of phase i. The total mass flowrate (M)

incorporates the phase densities (ρi) and can be determined by (Brennen, 2005);

𝑀 = ∑ 𝑚𝑖𝑁𝑖 = ∑ 𝑞𝑖𝜌𝑖

𝑁𝑖 = 𝐴 ∑ 𝑥𝑖𝑣𝑖𝜌𝑖

𝑁𝑖 (3.2)

where mi is the mass flowrate of phase i. It is useful to consider the component volumetric

flowrates in terms of cross-sectional averaged volumetric fluxes (ji) which are equivalent to

the superficial phase velocities (vsi) and can be considered as the velocity of the phase if that

was the only phase occupying the pipe cross-section. The superficial velocity for phase i is

given by (Michaelides et al., 2016);

𝑗𝑖 = 𝑣𝑆𝑖 =𝑞𝑖

𝐴= 𝑥𝑖𝑣𝑖 (3.3)

The relative velocity between two phases within a multiphase fluid stream is quantified using

a velocity slip term. The velocity slip ratio (Sab) of phase a relative to phase b is defined as;

𝑆𝑎𝑏 =𝑣𝑎

𝑣𝑏 (3.4)

where va is the velocity of phase a and vb is the velocity of phase b. These multiphase flow

properties provide quantitative information for characterising multiphase flow streams.

28

3.1.2. Gas-liquid flows

Two-phase gas-liquid flows (e.g. natural gas and oil) exhibit interesting

hydrodynamic flow characteristics due to the compressible nature of the gas phase and

naturally occurring fluid turbulence (Yadigaroglu and Hewitt, 2017). The behaviour and

shape of the gas-liquid interface is governed by competing interfacial forces and mechanisms

(Hanratty, 2013). Significant research has previously been undertaken to improve the

understanding of gas-liquid flow regimes (e.g. Al‐Sheikh et al., 1970, Michaelides et al.,

2016, Taitel et al., 1980). There are a range of factors which influence the flow patterns

observed in gas-liquid flow, such as; the phase fractions, velocities, fluid properties (e.g.

densities and viscosities), surface tension, pressure, temperature and flow dynamics (e.g.

steady-state or transient) (Hanratty, 2013, Hetsroni, 1982, Hewitt et al., 2013). The flow

regime is also impacted by the pipe inclination which controls the influence of gravitational

forces on pipe flow (Mukherjee and Brill, 1985a, Mukherjee and Brill, 1985b). In this thesis,

the focus is on horizontal pipe flow due to the orientation of the flow metering apparatus;

therefore only gas-liquid flow regimes for a horizontal pipe are considered.

Flow regimes are typically classified using a flow regime map (Baker, 1953,

Mandhane et al., 1974, Taitel and Dukler, 1976). The qualitative description of each flow

regime is based on visual investigation of the flow patterns and is therefore subject to

interpretation. In this work, the gas-liquid flow regimes are compared to the well-known

flow regime map and classifications presented by Taitel and Dukler (1976). The observed

flow patterns are classified into five separate flow regimes; stratified smooth, stratified wavy,

intermittent (slug and plug), annular and dispersed flows. Table 3.1 provides a summary of

each gas-liquid flow regime in terms of a brief description and visual illustration.

29

Table 3.1 Summary of gas-liquid flow regimes

Name Description Illustration

Stratified

smooth

flow

The gas and liquid exist as segregated phases

with gas flowing above the bottom layer of

liquid.

Stratified

wavy flow

The two phases are separated into two layers

however increased gas velocity introduces

small waves at the interface.

Intermittent

flow

The gas phase exists as long bubbles separated

by liquid “slugs” with small gas bubbles

entrained in the liquid. Intermittent flow can

be separated into “slug flow” and “plug flow”

depending on the size of the gas bubbles and

liquid slugs.

Annular

flow

The liquid flows as an annular film along the

pipe walls whilst the gas flows as a central

core. Liquid droplets are entrained in the gas

phase.

Dispersed

flow

Gas bubbles are dispersed throughout the

continuous liquid phase. Also known as

bubble flow.

Gas-liquid flow regime maps are presented as a function of the superficial liquid

velocity (vsl) and superficial gas velocity (vsg). Figure 3.1 shows the flow regime map for

air-water flow in a horizontal pipe (25 mm in diameter) at 25°C as presented by Taitel and

Dukler (1976).

30

Figure 3.1 Example flow regime map for air-water flow in a horizontal pipe. The pipe has a 25 mm

internal diameter and the fluid temperature is 25°C (Taitel and Dukler, 1976).

A brief description of the physical mechanisms which cause flow regime transitions

will now be discussed starting with the base case of stratified smooth flow at very low liquid

and gas velocities. In stratified smooth flow, the low fluid velocities result in a stable

equilibrium between the two phases which remain as separate layers. If either the liquid or

gas velocity is increased beyond velocity thresholds, then instability is introduced at the gas-

liquid interface. The instability initiates wave propagation resulting in capillary waves at the

interface (i.e. stratified wavy flow). When the liquid velocity is substantially increased the

liquid level rapidly rises forming a liquid bridge and a blockage. The blockage results in

pressure oscillations in the gas phase and subsequently intermittent slug or plug flow will be

observed. At very high liquid flowrates and low gas flowrates, the turbulent mixing forces

between the gas and liquid layer overcome the buoyancy forces of the gas resulting in

dispersion of the gas phase as small bubbles within a continuous liquid layer.

Increasing the gas velocity from the stratified smooth flow regime also introduces

instability at the gas-liquid interface which initiates wave propagation resulting in a transition

to the stratified-wavy flow regime. At very high gas velocities, there is insufficient liquid to

maintain a liquid bridge; thus the liquid in the waves is swept up and around the pipe to form

an annular film along the pipe walls resulting in the annular flow regime. Some of the liquid

is entrained as droplets within the central core gas phase.

0.01

0.1

1

10

0.1 1 10 100

Su

pe

rifi

cia

l li

qu

id

velo

cit

y,

vs

l[m

/s]

Superficial gas velocity, vsg [m/s]

Dispersed flow

Intermittent flow Annular flow

Stratified wavy flow

Stratified smooth flow

31

3.1.3. Liquid-liquid flows

Liquid-liquid flow exhibits different hydrodynamic characteristics relative to gas-

liquid flow as the two phases are generally incompressible. One of the most common forms

of liquid-liquid flow is oil-water flow. The oil and water typically have similar densities

relative to the large density difference present in gas-liquid flow. The turbulent mixing forces

which control the dispersion between oil and water is more influential in determining the

flow characteristics in liquid-liquid flow compared to buoyancy forces. This results in a

variety of flow regimes involving oil/water emulsions.

During crude oil production, water is coproduced with oil from the reservoir

formation (Fink, 2016). Emulsions are encountered through oil production and processing

including in the reservoir, pipelines and equipment (e.g. at wellhead choke points) (Kokal,

2005). These locations are subject to high shear conditions providing sufficient turbulent

force for the formation of stable oilfield emulsions. Water-in-oil emulsions typically form

(depending on the liquid water-cut) with a rigid interfacial film surrounding water droplets

preventing coalescence (Tadros, 2013). Emulsion stability is dependent on a range of process

conditions, such as; crude oil composition, temperature, presence of solids (e.g. asphaltenes,

resins and waxes), pH, salinity and droplet size (Becher, 1996).

Understanding emulsion formation as well as developing strategies for breaking

emulsions is an area of considerable research interest. A variety of demulsification

techniques can be applied to destabilise oilfield emulsions for oil and water phase separation.

These techniques include; chemical demulsifiers, thermal treatment, electro-coalescence,

biological treatment or membrane separation (Sjoblom, 2001, Zolfaghari et al., 2016).

Treating oilfield emulsions requires large processing equipment resulting in significant

capital and operational expenditure (Stewart and Arnold, 2008). The successful operation of

such equipment requires knowledge of the emulsion characteristics, such as the emulsion

droplet size distribution (Johns, 2009, Schramm, 2006). The hydrodynamics of emulsions

can also influence the degree of pipeline corrosion during crude oil transportation (Becerra

et al., 2000).

32

In the context of MPFM development, the presence of emulsions is important for the

design and operation of flow measurement techniques. For example; electrical impedance

flow measurements utilise either electrical resistance or capacitance measurements

depending on whether the flow is water or oil continuous (Dykesteen et al., 1985). Emulsion

formation influences the distribution of phases within the pipeline and therefore the operation

of electrical impedance MPFMs. A robust MPFM should be independent of the oil/water

flow regime and provide accurate measurement across a wide range of oil and water flowrates

(Thorn et al., 2013). Furthermore; newer MPFM technologies are developing measurement

techniques for identifying flow regimes (Salgado et al., 2010, Tjugum et al., 2002, Wu et al.,

2001). Therefore it is necessary to understand the formation and flow characteristics of the

various oil/water flow regimes (including emulsions) in order to develop a robust MPFM.

Two-phase oil/water flows regimes have been extensively studied due to their

prevalence in the petroleum industry. However there is difficulty in comparing experimental

results due to the complex nature of such flows and variety of possible measurement

conditions (Xu, 2007). Similar to the gas/liquid flow regimes, the description and

classification of oil/water flow regimes is based on visual description and therefore subject

to interpretation. Flow regimes in two-phase oil/water pipe flows are influenced not only by

the velocities of oil and water but a range of flow conditions including; the density difference

between the two phases, the fluid viscosities and wetting properties of the wall (Angeli and

Hewitt, 2000, Charles et al., 1961, Lovick and Angeli, 2004).

The oil/water flow regime map proposed by Trallero et al. (1997) is presented as an

example of liquid-liquid flow regime classification. Trallero et al. (1997) used a mineral oil

and water flow system with a 50.13 mm (internal diameter) pipeline. The two-phase oil and

water fluid properties (measured at 25.6 °C) include; a viscosity ratio (μo/μw) of 29.6, a

density ratio (ρo/ρw) of 0.85 and an interfacial surface tension (γo/w) of 36 mN/m. Six flow

regimes were identified; stratified flow (St), stratified flow with mixing at the interface (St

w/ mix), a dispersion of oil-in-water over a free water layer (Do/w & w), a dual dispersion

of water droplets in oil over oil droplets in water (Dw/o & Do/w), a full oil-in-water emulsion

33

(Eo/w) and a full water-in-oil emulsion (Ew/o). A variety of other oil/water flow regimes

are also possible (e.g. annular flow); however different flow conditions (e.g. a much higher

viscosity ratio) are required in order to achieve such flow regimes (Charles and Lilleleht,

1966, Oliemans et al., 1987, Yao et al., 2009). Table 3.2 provides a summary in terms of a

brief description and visual illustration of each oil-water flow regime.

Table 3.2 Summary of oil-water flow regimes adapted from Trallero et al. (1997).

Name Description Illustration

Stratified flow Two separate fluid phases with oil at the

top of the pipe cross-section above water.

The oil-water interface is smooth.

Stratified flow

with mixing

Fluids exist as segregated layers with the

presence of small capillary waves at the

interface. Small quantities of droplets of

each fluid are dispersed into the alternate

phase.

Dispersion of

oil-in-water and

water

A dispersion layer exists at the top of the

pipe with oil droplets entrained within a

continuous water phase. The bottom layer

consists of free water alone.

Dispersion of

water-in-oil and

dispersion of

oil-in-water

A dual dispersion with; water droplets

dispersed into a continuous oil layer (top)

above oil droplets dispersed into a

continuous water layer (bottom).

Oil-in-water

emulsion

A full emulsion of oil droplets dispersed

in a continuous water layer.

Water-in-oil

emulsion

A full emulsion of water droplets

dispersed in a continuous oil layer.

Oil-water flow regime maps are presented as a function of the superficial oil and

water velocities (vso & vsw respectively). Figure 3.2 shows the flow regime map for oil-water

flow in a horizontal pipe (50.13 mm internal diameter) at 25.6°C presented by Trallero et al.

(1997).

34

Figure 3.2 Flow regime map for oil-water flow in a horizontal pipe. The pipe is 50.13 mm inside

diameter and the fluid temperature is 25.6 °C presented by Trallero et al. (1997).

A brief description of the physical mechanisms relating to the flow regime transitions

will now be discussed beginning with the base case of stratified flow at very low oil and

water velocities. A small increase in either the oil or water velocity leads to stratified flow

with mixing at the interface; the increase in flow rate introduces shear at the interface

inducing instability in the form of small capillary waves. Small quantities of droplets begin

to disperse between the phases at the interface.

A further increase in superficial oil or water velocities pushes the system into the

semi-dispersed flow regimes. For an increase in water flowrate – the system transitions from

the stratified with mixing flow regime to the dispersion of oil-in-water and water flow regime.

The increase in shear provided by the water phase forces the small quantity of oil to discretise

into small droplets and disperse within the water phase. For large superficial water velocities

(vsw>1.5 m/s) and low oil fraction the mixture becomes a full emulsion with oil dispersed into

the water phase. For mixtures which are just within the oil-in-water emulsion flow regime;

the oil droplets will have a size distribution which is dependent on radial position and height;

with larger oil droplets observed towards the top of the pipe due to buoyancy forces as well

as towards the pipe wall due to frictional forces. At very high superficial water velocities the

droplet distribution is more homogenous throughout the pipeline as the turbulent shear forces

dominate.

0.01

0.1

1

0.01 0.1 1

Su

pe

rfic

ial w

ate

r ve

loc

ity,

vs

w

[m/s

]

Superficial oil velocity, vso [m/s]

Stratified

Stratified with mixing

Oil-in-water emulsion

Disp. o/w & w

Water-in-oil emulsion

Disp. w/o & Disp. o/w

35

An increase in superficial oil velocity from the stratified with mixing flow regime

will cause the mixture to transition into the dual dispersion of water-in-oil and oil-in-water

flow regime. The turbulent shear forces in both layers are sufficient to overcome buoyancy

forces and induce dispersion of droplets of each component within the alternate phase. For

large superficial oil velocities, the turbulent mixing is sufficiently high such that a full water-

in-oil dispersion exists with water droplets suspended in the continuous oil phase. The

droplet size distribution gradients which are observed in oil-in-water emulsions are similarly

observed for the water-in-oil emulsions; with larger water droplets sinking to the bottom of

the pipe due to gravitational forces. At very high superficial oil velocities for a water-in-oil

emulsion, the water droplets will be dispersed homogenously across the pipe cross-section.

3.2 Multiphase Flow Metering

3.2.1. Introduction to multiphase flow metering

The purpose of a flow meter is to measure the flowrate of a fluid stream of interest

(Baker, 2016). MPFMs measure the flowrate for each individual constituent phase within a

multiphase fluid stream; providing information on the velocity, fraction and flowrate for each

phase (Corneliussen et al., 2005, Falcone et al., 2009). This information has historically been

provided by test separators on production platforms; where the multiphase stream is

separated into individual components and the component flowrates are determined by single-

phase flowmeters after separation. Whilst test separators provide accurate flowrate

information, they are expensive and measurements are time-consuming (Thorn et al., 1999).

A typical test separator is often designed to be larger than initially required in order to

accommodate for changes in flow conditions, using valuable space on offshore production

platforms (Atkinson et al., 2004). The range of flow regimes and multiphase conditions often

cause problems for test separators. For example, slug flow, tight emulsions (emulsions with

small, closely distributed droplets which are difficult to separate), foams and viscous oils all

create difficulty in obtaining reasonable separation therefore can often result in inaccurate

flowrate measurements (Falcimaigne and Decarre, 2008, Pinguet, 2010, Rajan et al., 1993).

Finally, the oil and gas industry are seeing increased subsea completions with multiphase

pipelines developed over long distances. Such installations require monitoring of multiphase

flowrates subsea for flow assurance and production monitoring (Falcone et al., 2001, Lunde

36

and Hoseth, 1994). Installation of conventional test separators subsea is too costly and more

compact measurement technology is required for subsea multiphase flow metering.

3.2.2. Classification of multiphase flow meters

MPFMs can be classified into several categories; in-line flow meters, separation type

meters and wet gas flow meters (Corneliussen et al., 2005). In-line flow meters provide a

direct measurement of the multiphase flow stream without phase separation; these are the

MPFMs of interest in this work. Separation type meters involve the full or partial separation

of components into individual phases prior to obtaining flow measurements (Falcone et al.,

2009, Thorn et al., 1997). Separating the components is expensive and pushes the cost of

separation type meters towards that of test separators. In this work a separation type meter

is not considered a true MPFM as it does not directly measure the multiphase fluid stream

(Falcone et al., 2009). Wet gas meters are MPFMs with the measurement technology

specifically targeted towards accurately metering multiphase fluid streams with high gas

content (Mehdizadeh et al., 2002). Wet gas meters can be either in-line type or separation

type MPFMs (Corneliussen et al., 2005).

A secondary classification for in-line type MPFMs considers the intrusive nature of

flow metering technologies. There is difficulty for MPFMs to accurately meter flow under

some of the complex flow regimes (Rajan et al., 1993). Therefore many MPFMs homogenise

the multiphase stream of interest such that accurate volumetric flow measurements may be

performed on a well-mixed stream (Falcone et al., 2002). MPFMs utilising homogenisation

or disrupting the natural pipeline flow (e.g. Venturi or orifice style flow meters) are

considered invasive flow meters. There is motivation to move towards non-invasive flow

meters which provide a true and direct measurement of the multiphase fluid stream (Thorn

et al., 2013). A non-invasive MPFM could provide information of multiphase flow

behaviour such as flow regime identification or velocity slip characteristics which is useful

for flow assurance diagnostics as well as production optimisation (Falcone et al., 2009).

Many MPFMs utilise a combination of velocity measurement and phase fraction

measurement techniques in order to determine the phase volumetric flowrates. The velocity

37

and phase fraction measurement principles for in-line type MPFMs will now be discussed

separately in sections 3.2.3 and 3.2.4.

3.2.3. Velocity measurement principles

Velocity measurement in MPFMs is categorised into two classes; differential pressure

measurement and the cross-correlation method.

Differential pressure measurement

Many MPFMs measure differential pressure across pipeline constrictions to

determine fluid velocity. The most common differential pressure meter for multiphase flow

is the Venturi flow meter (Falcone et al., 2002), although alternative flow constrictions such

as orifice plates are also used (Lin, 1982, Murdock, 1962). Venturi flow meters apply the

Venturi effect in a pipeline choke; fluid will accelerate at a constriction whilst its dynamic

pressure will decrease according to Bernoulli’s principle (Baker, 2016). The application of

differential pressure measurements towards multiphase flows requires appropriate

correlations to account for the fluid properties of each phase (Steven, 2002). Such

correlations are often proprietary information, although some well-used correlations have

been published publicly (De Leeuw, 1997). Multiphase Venturi correlations are often

designed and calibrated towards specific flow conditions such as wet gas applications with

low liquid content (Xu et al., 2011). Therefore there is difficulty applying these correlations

across a range of multiphase flow conditions resulting in a lack of robustness in Venturi

MPFMs (Steven, 2008).

The cross-correlation method

The fluid stream velocity can be determined using a signal processing technique

known as the cross-correlation method (Beck and Pląskowski, 1987). This technique

measures a fluid property of a dispersed phase (which depends on the sensor type; e.g.

acoustic signal measured in an ultrasonic flowmeter) at two different locations (Lysak et al.,

2008). The cross-correlation method determines the time taken (τC) to traverse the known

sensor separation length (Ls) from the signal evolution between the sensors. The fluid

velocity may then be determined from the traversal time. The principle of the cross-

correlation technique is illustrated in Figure 3.3.

38

Figure 3.3 Illustration of the cross-correlation principle. The signals captured via separate upstream

and downstream sensors are input into a cross-correlation function to determine the traversal time and

subsequently fluid velocity.

The measurement of the carrier phase velocity requires a tracer for detection or an

empirical model for the slip between the carrier and dispersed phases (Rodriguez et al.,

2011). An empirical model will describe the turbulent velocity profile of the system in order

to relate the linear velocity of the dispersed phase to the overall average phase velocity (Lysak

et al., 2008, Sanderson and Yeung, 2002). The use of a tracer can be problematic for subsea

flow metering; particularly when the carrier phase requires a unique tracer (Thorn et al.,

2013). There can be considerable difficulty in applying the cross-correlation method to

measure velocity under slug flow (Falcone et al., 2002). When the cross-correlation method

is used with gamma or capacitance meters, a distinct flow feature such as a liquid slug is

required. The relationship between slug velocity and the average fluid velocity is highly

complex (Nydal et al., 1992) and thus in this case robust measurements based on slug flow

velocity are difficult to implement.

3.2.4. Phase fraction measurement technologies

A variety of measurement principles have been applied to non-invasively measure

phase fractions (composition). A discussion is provided for three commercially established

measurement techniques; gamma-ray attenuation, electrical impedance and microwave

attenuation meters. This is followed by a brief description of some of the less prominent

multiphase volumetric fraction measurement techniques.

Ls

Flow

Upstream sensor

Downstream sensor

Receivers

Transmitters

Cross-correlation τC v = Ls/τc

39

Gamma-ray attenuation meters

Gamma-ray attenuation (GRA) or densitometry is one of the most common phase

fraction measurement technique in multiphase flow metering (Falcimaigne and Decarre,

2008). Numerous examples demonstrate the multiphase flow measurement capability of

GRA in both laboratory (Blaney and Yeung, 2008, Tjugum et al., 2002) and field conditions

(Pinguet et al., 2010, Pinguet et al., 2006). The attenuation of gamma-rays is dependent on

the density of the medium of propagation (Pedrotti et al., 2017). GRA multiphase flow

systems consist of an ionising radiation source (e.g. 137Cs) and collimator which transmit

gamma-rays across the pipe cross section (Åbro and Johansen, 1999). The transmitted beams

are attenuated by the multiphase fluid stream within the pipeline according to the

photoelectric effect, positron-electron pair production and the Compton effect (Falcone et

al., 2009). The attenuated signal is measured at a detector diametrically opposite the

radiation source (Scheers and Noordhuis, 1999). The GRA measurement principle for

multiphase flow measurement in a pipe is illustrated in Figure 3.4.

Figure 3.4 Schematic of the gamma-ray attenuation measurement principle.

The signal decay is quantified by the Beer-Lambert law for the attenuation of

radiation through a material (Ingle and Crouch, 1988). For gamma radiation transmitted from

a source of energy e through a pipe of diameter D containing a multiphase fluid, the radiation

decay is described by (Abouelwafa and Kendall, 1980);

𝐼𝑚(𝑒) = 𝐼𝑣(𝑒) exp(− ∑ 𝑥𝑖𝜇𝑖(𝑒)𝑁𝑖 𝐷) (3.5)

where Im(e) is the transmitted intensity measured at the detector, Iv(e) is the calibrated

intensity for an empty pipe, N is the number of components in the multiphase stream, xi is

the volumetric fraction of phase i and μi(e) is the linear attenuation coefficient for phase i for

the given source radiation energy. A single radiation source is used to solve the phase

fractions in two-phase flow. For more complex multiphase flows; two or more radiation

Multiphase flow

Gamma-ray source

Detector

Collimator

Pipe wall

40

sources are used at different energy levels (e.g. 137Cs at 662 keV and 170Tm at 84 keV)

(Pinguet et al., 2006, Scheers and Slijkerman, 1996). The detection of two or more

attenuation measurements can thus be used to determine volumetric fractions for three or

more phases (Frøystein et al., 2005). Developments towards multi-beam and fan collimators

have also extended the range of flow regimes over which GRA meters can operate (Åbro and

Johansen, 1999, Arvoh et al., 2012, Sætre et al., 2010, Tjugum et al., 2002), nonetheless

there is still evidence of a lack of versatility of gamma ray meters under varying flow

conditions (Corneliussen et al., 2005, Folgerø et al., 2013). There is also motivation to move

away from ionising radiation sources (Thorn et al., 2013). For example; uncertainty in the

actual values of gamma ray attenuation coefficients will lead to systematic errors in measured

fractions and flowrates (Bruvik and Hjertaker, 2016).

Electrical impedance meters

Electrical impedance flow meters have also achieved reasonable commercial success

in the MPFM industry (Thorn et al., 1997, Thorn et al., 1999). Such meters operate on the

principle that the measured impedance is dependent on the fluid dielectric properties (i.e.

conductivity and permittivity) (Ceccio and George, 1996). The measured electrical

impedance across a pipe containing a multiphase flow stream is therefore dependent on the

conductivity and permittivity of the individual components and their respective volumetric

fractions (Chun and Sung, 1986). Impedance is a function of conductance and capacitance;

however most systems operate such that only one electrical property dominates the

measurement (e.g. operating at high frequency such that capacitance dominates) (Falcone et

al., 2009). The functional relationship between the measured impedance and the multiphase

component fractions is dependent on the electrical sensor configuration (Dykesteen et al.,

1985) thus considerable work has focussed on optimising impedance sensor design (e.g.

García-Golding et al., 1995, Jin et al., 2008, Klug and Mayinger, 1994). Several authors

have indicated the potential for electrical based meters to provide tomographic images of

multiphase pipe flows through the use of electrical capacitance tomography and/or electrical

resistance tomography (e.g. Da Silva, 2008, Huang et al., 2003, Ismail et al., 2005).

41

The simplest sensor design consists of two strip-type electrodes mounted on the pipe

diametrically opposite each other (Green and Cunliffe, 1983). The electrical impedance of

the multiphase mixture is measured across the two electrodes. Figure 3.5 presents a

schematic of the strip-type electrode configuration for impedance measurements in

multiphase flow metering.

Figure 3.5 Strip-type electrode configuration for impedance measurements of multiphase flows.

The most significant problem for impedance type multiphase flow meters is the flow

regime dependence. In gas/liquid flows the impedance measurements are observed to vary

considerably as a function of the geometry of the fluid within the pipeline (e.g. between

stratified and annular flow) (Chun and Sung, 1986). Specific sensors have been designed to

reduce the parameter sensitivity to the flow regime (Merilo, 1977). In oil/water mixtures the

impedance sensors are often designed to switch between capacitance measurement for oil-

continuous mixtures and conductivity measurements for water-continuous mixtures

(Dykesteen et al., 1985). However such systems require correct identification of the phase

inversion point in oil/water emulsions; which is a complex process (Piela et al., 2008) and

therefore the incorrect meter response can result in considerable measurement errors (May et

al., 2008). Electrical impedance MPFMs are also susceptible to systematic errors due to

uncertainty in the values of electric permittivity (Bruvik and Hjertaker, 2016).

Microwave attenuation meters

Microwave attenuation meters are similar to electrical impedance meters in terms of

measuring dielectric fluid properties. The attenuation of microwave radiation through a

multiphase fluid is dependent on permittivity and phase fraction of each multiphase

component (Wu et al., 2009). There are two types of microwave sensors used for MPFMs;

transmission and resonator sensors (Nyfors and Vainikainen, 1989). Transmission sensors

Multiphase mixture

Z

Electrode

Pipe wall

42

use two antennas to transmit and receive microwaves through a medium (Corneliussen et al.,

2005). The transmitted waves may be at a single or variable frequency. Resonator sensors

measure the resonant frequency of microwaves through a medium. Microwave resonance is

a function of fluid permittivity thus the measured resonant frequency can be related to the

multiphase fluid (Khan, 2014).

The commercial application of microwave attenuation MPFMs is much more limited

compared to gamma-ray attenuation or electrical impedance. Several examples illustrate

successful application of microwave-based MPFM technology in laboratory and field trials

in combination with other technologies (Ashton et al., 1994, Mehdizadeh et al., 2009, Xie,

2007). Microwave attenuation meters need careful calibration and are suggested to be

problematic in the presence of gas (Falcone et al., 2009). Consequently, microwave

attenuation meters lack the robustness required for accurate flowrate measurement across

variable multiphase flow conditions in the modern oil and gas industry.

Alternative multiphase flow metering technologies

A variety of alternate technologies have been applied to analyse multiphase flows,

often providing solutions to unique multiphase flow metering problems. The use of acoustic

emission in the form of ultrasonic waves has been used to measure two-phase gas/liquid

flows (Al-Lababidi et al., 2012). Acoustic emission is particularly useful in bubble flow

where the attenuation of ultrasonic waves is influenced by the gas void fraction and the size

of bubbles (Bensler et al., 1987, Jones et al., 1986). However application to three-phase flow

measurement is complicated by the array of propagation mechanisms for sound waves (e.g.

diffraction or reflection) through complex media (Hoyle, 1996) such that ultrasonic MPFMs

are only sensitive to flows with small phase fractions (Goncalves et al., 2011).

Electromagnetic flow meters (EMFM) have had success as single-phase flow meters

(Baker, 2016). EMFM operate on the principle that an electrically conductive fluid passing

through a magnetic field induces an electrical potential perpendicular to the magnetic field

and velocity (Shercliff, 1962). The measurement principle has been extended to analyse

gas/liquid flows (Bernier and Brennen, 1983) and to determine fluid velocity profiles

43

(Leeungculsatien and Lucas, 2013, Wang et al., 2007). However there is difficulty in

measuring non-conductive fluids such as hydrocarbons and therefore further research is

required in order to develop the measurement principle towards full multiphase flow

metering (Falcone et al., 2009).

Infrared (IR) spectroscopy has received some attention in terms of monitoring

multiphase flows; particularly as a water-cut meter. The adsorption of IR radiation by a

material is dependent on the wavelength of the emitted light; thus infrared adsorption

spectroscopy (across a range of IR wavelengths) can be used to distinguish oil and water

(Sarkodie et al., 2018). Analysis of IR spectra has been shown to give accurate phase fraction

measurements for flows with high water content (>85 %) (Falcone et al., 2009). A MPFM

which incorporated infrared technology showed positive results for water-cut measurement

during field trials (Nassereddin et al., 2010). However IR MPFMs require further research

in order to measure flow at lower water content, analyse gas/liquid flows (Sarkodie et al.,

2018) and to quantify the influence of emulsified droplets (Borges et al., 2015).

3.2.5. NMR in flow measurement

NMR has seen extensive application as a tool for examining flow characteristics

(Fukushima, 1999). The ability to provide non-invasive interrogation of complex flow

behaviour is particularly advantageous (Caprihan and Fukushima, 1990). This is evident in

the application of high-field MRI to provide tomographic characterisation of process flows.

For example, MRI has been used to provide quantitative hydrodynamic characterisation of

gas-liquid bubbly flow (Holland et al., 2011, Leblond et al., 1998, Tayler et al., 2012), oil-

water homogenisation (Lakshmanan et al., 2016) and gas-solid flow in packed beds (Müller

et al., 2006, Muller et al., 2007). This is very useful in improving our understanding of such

complex flows and for validation of computational fluid dynamic simulations (Lemonnier,

2010). NMR has also been used to examine hydrodynamic and diffusive flow behaviour in

porous media (Seymour and Callaghan, 1997, Song, 2013) as well as examining the fluid

dynamics and rheology of complex fluids (Callaghan, 2006, Callaghan, 1999).

44

The use of NMR as an industrially capable flow meter is much more limited relative

to its application to studying flow behaviour. This can be attributed to the high cost and low

portability of high-field NMR equipment (Danieli et al., 2010) which makes it impractical as

a measurement technology for industrial multiphase flow metering. The first NMR flow

meter was used to measure the flowrate of blood (Battocletti et al., 1981, Singer, 1959). The

initial NMR flow meter designed towards industrial applications was developed by Vander

et al. (1968) for laminar flow whilst the first NMR flow meter for multiphase flow probed

the water velocity and fraction in two-phase nitrogen-water flows (Krüger et al., 1996,

Krüger et al., 1984). Recent developments in low-field NMR (Blümich et al., 2009a,

Mitchell et al., 2014) provides attractive technology for developing a low cost and

transportable instrument for industrial multiphase flow measurement.

The most prominent low-field NMR MPFM is the commercially available M-Phase

5000 developed from a collaboration between Shell, Krohne and Spinlock. The system

operates at a 1H resonance of 8 MHz and utilises a remote detection system with separate

regions for polarisation and detection (Hogendoorn et al., 2015). The polarising field is

produced by a series of Halbach magnets which can be rotated to modify the strength and

orientation of the magnetic field (Appel et al., 2011). The detection field is generated by

another series of Halbach magnets which are fixed. The system utilises a CPMG

measurement of an “effective signal decay” which incorporates a linear flush-out effect (Ong

et al., 2004). The velocity is then measured from the effective rate of signal decay of the

measured CPMG (Osán et al., 2011). Gradient coils are also incorporated into the detection

region in order to produce 1D MRI measurements to capture flow profiles (Hogendoorn et

al., 2015). The flow meter uses differences in fluid pre-polarisation (according to fluid T1)

to quantify phase fractions (Hogendoorn et al., 2013). The system has undergone prototype

testing in commercial multiphase flow loops as well as a field trial (Hogendoorn et al., 2016,

Hogendoorn et al., 2014).

45

Figure 3.6 A cut-open schematic of the M-Phase 5000 magnetic resonance multiphase flow meter.

The key components of the magnetic resonance measurement section are highlighted (Hogendoorn

et al., 2013).

Despite generally positive results for the M-Phase 5000 there are still several

drawbacks. The key problems which are limiting commercial application include; the size

(3.5 m long, 1150 kg), power consumption (180 W) and cost of the system (Krohne, 2017).

There is difficulty capturing accurate flow information under dynamic flow regimes; for

example in the presence of slug flow the system requires considerable signal averaging to

obtain time-averaged fluid properties and has difficulty in measuring the instantaneous flow

features (Hogendoorn et al., 2015). The system requires a-priori knowledge of the magnetic

relaxation properties (e.g. T1, T2) which are sensitive to process conditions such as pressure,

temperature and oil compositions. This can lead to flow measurement errors when the

calibrated properties are incorrect (relative to the real properties), however measurement of

the changing relaxation parameters has been demonstrated to be useful for process

diagnostics (Hogendoorn et al., 2017).

An alternative NMR flow meter in development utilises the Earth’s magnetic field

(Fridjonsson et al., 2014b). This system utilises a remote detection system with a mobile

pre-polarising Halbach array upstream of an Earth’s field radio frequency detection coil. A

parameter-free model is presented which is shown to accurately describe the NMR signal of

a fluid flowing through the system at velocities from 0 – 1.0 m/s. The Earth’s field NMR

flow meter is the basis of the work presented in this thesis.

46

Table 3.3 compares some of the key flow meter specifications for the commercially

available Krohne M-Phase 5000 and the alternative EFNMR flow meter.

Table 3.3 Comparison of key flowmeter specifications for the Krohne M-Phase 5000 and the

EFNMR flow meter.

Flowmeter Dimensions

(L x W x H, in m)

Larmor Frequency

(kHz)

Velocity range

(m/s)

Krohne M-Phase

5000 3.5 x 0.8 x 0.9 m 8000 0.1 - 6

EFNMR flow

meter 2.0 x 0.4 x 0.4 m 2.29 0.1 - 3

3.2.6. Validation of flow measurement accuracy

In this work, NMR flow measurement techniques are developed across a range of

flowing conditions and are validated against reference flow measurements to quantify

accuracy. Two sample statistics are used in order to compare the NMR measurements

relative to reference measurements. The mean error (ME) is a sample statistic which

quantifies measurement accuracy in terms of how well an observed measurement (e.g. NMR

measurement of water flowrate) matches a reference measurement (e.g. rotameter

measurement of water flowrate). The mean error for a sample (of size N) is defined as;

𝑀𝐸 = ∑ 𝑧𝑖,𝑜𝑏𝑠− 𝑧𝑖,𝑟𝑒𝑓

𝑁𝑛=1

𝑁 (3.6)

where zi,obs is the observed measurement of the variable of interest for sample i and zi,ref is the

reference measurement of the property of interest for sample i.

The root-mean-square error (RMSE) is a sample statistic which quantifies accuracy

in terms of the quadratic mean of the residual errors of observed measurements relative to a

reference measurement. The RMSE for a set of flow measurements (of sample size N) is

calculated using;

𝑅𝑀𝑆𝐸 = √∑ (𝑧𝑖,𝑜𝑏𝑠− 𝑧𝑖,𝑟𝑒𝑓)2𝑁

𝑛=1

𝑁 (3.7)

where zi,obs and zi,ref have the same meanings as in equation 3.6.

47

Chapter 4. Quantitative velocity measurements of single-

phase flows

4.1 Introduction

The first stage of developing the Earth’s field nuclear magnetic resonance (EFNMR)

multiphase flow metering system will focus on establishing a velocity measurement

technique. This chapter demonstrates the capability of the EFNMR system in terms of

measuring velocity probability distributions of single-phase fluid flows. The EFNMR flow

metering system is detailed in terms of the apparatus and associated NMR signal model. The

optimal method of velocity encoding is examined with respect to appropriate experimental

parameters. The velocity measurement methodology is then demonstrated; with the

instrument being applied to determine the velocity probability distribution of a flowing

stream. Determination of the velocity distribution is a necessary precursor to application of

the instrument to multi-phase flow; it is required to distinguish flow regime (e.g. stratified

flow or slug flow) and to determine the velocities of multiple phases within the measured

flowing stream.

4.2 Equipment and methodology

4.2.1. Experimental apparatus

Figure 4.1(a) shows a photo of the flow metering measurement section including the

pre-polarising magnet and detection coil whilst Figure 4.1(b) shows a schematic of the NMR

flow meter and the associated flow loop for experimental validation. The pre-polarisation

magnet (0.3 T Halbach array provided by Magritek, New Zealand) of length LPH is located a

variable distance, LPD, upstream of the EFNMR radio frequency (r.f.) detection coil (of length

LD). The pre-polarisation magnet is required to boost the NMR signal in the r.f. coil to

detectable levels (Appelt et al., 2006, Halse and Callaghan, 2008). The Halbach array is

contained within a mu-metal enclosure (Magnetic Shield Corp., USA) in order to minimise

48

stray magnetic field interference at the detection coil. The r.f. detection coil (Magritek, New

Zealand) is used to excite and detect the NMR signal at a frequency of ~2.29 kHz (the 1H

NMR Larmor frequency associated with the local Earth’s magnetic field of ~54 µT). The

detection coil is orientated with its axis perpendicular to the Earth’s magnetic field and is

shielded from external electrical fields by a Faraday cage. A photo of this flow metering

instrument (magnet and coil) is shown in Figure 4.1(a), in which the Faraday cage, pre-

polarisation magnet, detection coil and mu-metal shielding are indicated. The flow loop

includes a 44 mm internal diameter acrylic pipe in the measurement section (E-Plas,

Australia) and a centrifugal pump (CHI4-40, Grundfos, Australia). A 4 to 60 L/min glass

rotameter (Cole Parmer, Australia) is used to independently measure the volumetric flow

rate.

49

Figure 4.1 Illustrations of the single-phase experimental flow loop apparatus. (a) Photo of the

measurement section of the flow loop with flow direction indicated. The detection coil is protected

by a simple Faraday cage. (b) Schematic of experimental flow loop, which includes a mobile pre-

polarisation magnet (Halbach array) and an EFNMR excitation and detection coil. The distances

relevant to the model, i.e.; polarisation coil length (LPH), distance between polarisation and detection

(LPD) and the detection coil length (LD) are indicated.

In Figure 4.1(b), the video analysis region just prior to the EFNMR detection coil and

the air inlet line are relevant for gas/liquid flow experiments are discussed in section 5.2.1.

In order to access multi-modal velocity distributions, the flow loop was also modified to

accommodate two separate pipes (29 mm internal diameter, both with independent flow

control and rotameter velocity measurement) through the NMR flow meter. A photo of this

two-pipe system is shown in Figure 4.2(a) with a schematic of the instrument configuration

shown in Figure 4.2(b).

(a)

Pre-polarising Halbach array

EFNMR detection coil

Flow direction

Mu-metal shielding

Faraday cage

(b) LPD LPH LD

50

Figure 4.2 Illustration of the two-pipe experimental flow loop. (a) Photo of the two-pipe system

with flow direction indicated. (b) Schematic of two-pipe flow loop. Ball valves are located after the

pipe split in order to control the flowrate in each pipe.

The NMR pulse sequence used was a basic ‘pulse and collect’, as shown in Figure

2.3. Note that no pre-polarisation pulse is applied; polarisation is provided by the upstream

Halbach array alone. The EFNMR r.f. detection coil was shimmed prior to running a

sequence of experiments (at a given separation distance, LPD) in order to optimise the signal

obtained relative to the surrounding magnetic environment. The following key sequence

parameters were used for the ‘pulse and collect’ experiments: an acquisition delay between

excitation and detection (tdelay) of 25 ms (see further discussion regarding Q-switch below);

a total acquisition time per scan (tacq) of 0.5 s, a repetition time of 0.8 s and 64 scans (Nscans)

per experiment.

Pre-polarising Halbach array

EFNMR detection

coil

Liquid rotameters

Flow direction

(a)

(b)

51

Nuclear magnetic resonance systems observe unwanted voltage oscillation (referred

to as ringdown) within the r.f. probe. Ringdown is a consequence of residual stored energy

following the 90o r.f. pulse (Hoult, 1984). The effective efficiency of NMR probes is

quantified by the probe quality factor (Qprobe) which is generally designed to be high in order

to improve the SNR (SNR √𝑄𝑝𝑟𝑜𝑏𝑒) (Andrew and Jurga, 1987). A consequence of using

a high Qprobe is increased ringdown time (the ringdown time constant τ Qprobe). This

problem can be overcome by the use of a Q-switch damping circuit which switches on a

resistive load immediately after the r.f. excitation pulse to accelerate energy dissipation

during ringdown (Hopper et al., 2011, Peshkovsky et al., 2005). A Q-switch circuit was been

incorporated in the EFNMR system used for the MPFM developed within this thesis which

allows the excitation-acquisition time delay (tdelay) to be reduced from 25 ms to 9 ms (Zhen

et al., 2018). The Q-switch was primarily implemented to allow earlier FID acquisition for

the measurements with oil and was completed prior to the work presented in Chapters 6 and

7 (results presented in Chapters 4 and 5 do not incorporate a Q-switch; except for the single-

pipe results in section 4.3.2).

4.2.2. NMR signal model

In the following section, a model of the NMR signal detected with the apparatus

shown in Figures 4.1 and 4.2 is detailed. This expands from the initial model development

and validation presented by Fridjonsson et al. (2014b). The measured NMR signal is a

composite of three contributions: signal accumulation due to polarisation (SP), signal

attenuation from intermediate decay between the polarisation magnet and the EFNMR

detector (SPD), and signal attenuation during detection (SD). Each of these components are

dependent on the residence time in the relevant section of the system and are detailed below.

When a fluid containing NMR active nuclei (nuclei with a net magnetic moment (i.e.

spin quantum number I ≠ 0)) is placed in a static magnetic field, the detectable NMR signal

(S) develops according to (Krüger et al., 1996, Pendlebury et al., 1979):

𝑆 = 𝑆0 (1 − exp (−𝑡

𝑇1)), (4.1)

52

where S0 is the NMR signal after an infinite time in the magnetic field (which is related to

the static magnetic field strength (B0), usually by S0 B01.75 (Fukushima, 1999)), t is the time

spent in the magnetic field and T1 is the fluid spin-lattice relaxation time. Consider a fluid

element travelling through the flow meter with a velocity v. The development of the potential

signal due to polarisation (SP) may be determined by applying;

𝑆𝑃 = 𝑆0 (1 − exp (−𝐿𝑃𝐻

𝑣𝑇1)), (4.2)

where LPH is the length of the pre-polarising Halbach array and S0 is the potential NMR signal

after an infinite residence time in the polarisation field. Following polarisation, the signal

attenuation between polarisation and detection (SPD) due to spin-lattice relaxation is modelled

by;

𝑆𝑃𝐷 = 𝑆𝑃 exp (−𝐿𝑃𝐷

𝑣𝑇1), (4.3)

where LPD is the separation distance between the polarisation magnet and detection coil.

Once the fluid element reaches the detection coil, its NMR signal is excited by

applying a r.f. pulse via the EFNMR coil at the relevant Larmor frequency. The free

induction decay (FID) signal is detected in the EFNMR coil, however an acquisition delay

time (tdelay) is required between excitation and detection to allow transient currents to

dissipate during coil ring-down. The resultant FID signal measured under flow is affected

by; (i) stationary FID behaviour, and (ii) a ‘flush-out’ effect as excited fluid leaves the

detection volume. The FID behaviour for stationary fluid involves spin-spin relaxation (T2)

as well as relaxation due to magnetic field inhomogeneity and is given by equation 2.14. The

consequential signal behaviour during detection (SD) is modelled as:

𝑆𝐷(𝑡𝑒) = (1 −𝑡𝑒𝑣

𝐿𝐷) exp (− (

𝑡𝑒

𝑇2+ (𝑅𝐼𝑡𝑒)2)), for 𝑡𝑒 ≤

𝐿𝐷

𝑣, (4.4)

where te is the time since excitation, LD is the length of the detection coil and RI is the

Gaussian relaxation rate constant accounting field inhomogeneity signal decay (and is a

function of polarisation-detection separation distance).

53

By combining equations, 4.2, 4.3 and 4.4, the overall model signal (Smodel) at the

detection coil is obtained:

𝑆𝑚𝑜𝑑𝑒𝑙(𝐿𝑃𝐷 , 𝑣, 𝑡𝑒) = 𝑆𝑜 (1 − exp (−𝐿𝑃𝐻

𝑣𝑇1)) exp (−

𝐿𝑃𝐷

𝑣𝑇1) (1 −

𝑡𝑒𝑣


𝑡𝑒

𝑇2+ (𝑅𝐼𝑡𝑒)2))

for 𝑡𝑒 ≤ 𝐿𝐷

𝑣, (4.5)

thus by measuring S as a function of either LPD or te, the velocity (v) may be determined. The

following section considers how to determine the probability distribution of v for a flowing

sample, P(v).

4.2.3. Velocity probability distributions via regularisation

One-dimensional Tikhonov regularisation will be applied in order to extract velocity

probability distributions (P(v)) from the measured FID signals. Further details regarding 1D

Tikhonov regularisation are discussed in section 2.3.1. In order to measure a probability

distribution using Tikhonov regularisation, an experimental parameter must be varied in

order to observe signal contrast with respect to the parameter of interest (i.e. velocity for the

flow meter). For the EFNMR flow metering system outlined in section 4.2.1 either the

polarisation-detection separation distance (LPD) or the time since excitation (te) may be varied

in order to observe signal contrast with respect to velocity. If the separation distance is used

as the independent variable, then the appropriate first-order Fredholm equation is given by;

𝑆(𝐿𝑃𝐷) = ∫ 𝐾(𝐿𝑃𝐷 , 𝑣)∞

0𝑃(𝑣) 𝑑𝑣 (4.6)

where S(LPD) is the NMR signal measured as a function of separation distance and K(LPD,v)

is the kernel transfer function which describes the NMR signal attenuation as a function of

separation distance and velocity. However if the velocity is measured with respect to the

time since excitation (i.e. a FID measurement), then the appropriate first order Fredholm

equation is;

𝑆(𝑡𝑒) = ∫ 𝐾(𝑡𝑒 , 𝑣)∞

0𝑃(𝑣) 𝑑𝑣 (4.7)

where S(te) is the NMR signal measured as a function of time since excitation and K(te,v) is

the kernel transfer function which describes the NMR signal attenuation as a function of time

since excitation and velocity.

54

For both scenarios; the velocity probability distribution is determined using the

Tikhonov regularisation optimisation expression given in equation 2.18. The appropriate

model kernel matrix must be used according to the relevant independent parameter. The

smoothing parameter (α) is selected using the generalised cross-validation method (as

detailed in section 2.3.1).

The following parameters (in Equation 4.5) are experimentally measured prior to

flowing measurements and are fixed for when performing regularisation on signals measured

in flowing experiments; LPH, LD, T1, T2 and RI. Measurement of relaxation constants for

water (T1 and T2) are discussed in section 6.2.3 as well as Appendix A.2 whilst measurement

of the Gaussian relaxation rate constant (RI) is discussed in Appendix A.1. The physically

measured length of the Halbach array (20 cm) is used as the length of the Halbach (LPH). A

hall effect sensor was used to measure the strength of the Halbach magnetic field just outside

the Halbach cylinder and has been used to verify that the Halbach magnetic field length

approximately corresponds to the physical length of the Halbach. A 1D MRI (with the pipe

full of stationary water) along the longitudinal axis of the detector coil in order to capture a

weighted profile of the detector length (LD). The final variable in Equation 4.5 is S0; the

NMR signal after an infinite time in the Halbach magnetic field. S0 can effectively be

considered a free, dependent variable in regularisation analysis and can be determined via

appropriate interpretation of the model fit (see section 5.2.2). It is possible to fix and

constrain S0 prior to inversion, however this was found to introduce artefacts into the

probability distribution. Furthermore, allowing S0 to be a dependent variable was determined

to be useful in two-phase gas/liquid measurements (discussed in Chapter 5).

4.2.4. Theoretical turbulent velocity distributions

Theoretical turbulent velocity distributions are determined for comparative purposes.

Turbulent velocity flows are often approximated by a power law velocity profile, where the

velocity (v) at a radial position (r) in a pipe of diameter D is given by (Iguchi and Ilegbusi,

2013);

𝑣(𝑟) = 𝑣𝑀𝑛𝑝+1

𝑛𝑝(1 −

2𝑟

𝐷)

1

𝑛𝑝 (4.8)

55

for a mean velocity vM and a power law exponent np. An np value of seven is often used for

fully developed turbulent flow, leading to the well-known 1/7th power law distribution

(Iguchi and Ilegbusi, 2013). In this work, the theoretical turbulent velocity distributions are

determined using the correlation for the power law exponent (np) presented in Zagarola et al.

(1997);

1

𝑛𝑝=

1.085

ln (𝑅𝑒)+

6.535

(ln(𝑅𝑒))2 (4.9)

where Re is the pipe flow Reynolds number of the fluid.

4.3 Results and discussion

4.3.1. Optimum Velocity Determination Methodology

Fridjonsson et al. (2014b) demonstrated that equation 4.5 (with te = tdelay and

assuming exponential decay behaviour for T2*) could reliably describe acquired NMR signals

as a function of mean velocity (vM) and separation distance (LPD). Initial experiments

progress from these results, with NMR data acquired over a range of mean velocities (0.11

to 0.55 m/s) and separation distances (68 to 128 cm). A minimum separation distance of 62

cm between the pre-polarising magnet and detection coil was required to ensure that

distortion of the Earth’s magnetic field in the detection region was sufficiently low as to allow

consistent NMR signal acquisition. Figure 4.3(a) shows the resultant data, along with the fit

of equation 4.6 – agreement is excellent. The resultant distributions of P(v), as produced

using regularisation, are shown in Figure 4.3(b).

56

Figure 4.3 Velocity distribution measurements obtained using separation distance as the

independent variable. (a) Experimental data and the model fit (determined using equation 4.6) for

varying NMR signal as a function of separation distance. The measured superficial velocities range

from 0.11 to 0.55 m/s. (b) Resultant velocity probability distributions (P(v)) with clear regularisation

artefacts at larger velocities (~2.5 m/s).

The distributions in Figure 4.3(b) clearly contain erroneous artefacts, evident in the

appearance of peaks at unfeasibly large velocities (~2.5 m/s). These artefacts occur due to

the inability of the methodology to access NMR data at low values of LPD, for reasons detailed

above, and to a much lesser extent large values of LPD, due to physical constraints on

instrument size. Such limitations are a lot less stringent when acquiring the NMR signal (as

per equation 4.7) as a function of te (i.e. the FID); this was shown to be the case in the data

that follows and thus is exclusively used henceforth.

0

2

4

6

8

10

12

0.6 0.8 1 1.2 1.4

NM

R s

ign

al [µ

V]

Separation distance [m]

Expt. data

Model fit

vM

[m/s]0.110.220.330.440.55

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

P(v

)

Velocity [m/s]

0.11m/s

0.22m/s

0.33m/s

0.44m/s

0.55m/s

(b)vM

57

4.3.2. Single Pipe Experiments

For the single pipe system, five separation distances (LPD) from 62 to 132 cm and

velocities (vM) of 0.18 m/s to 1.83 m/s were explored (corresponding to pipe flow Reynolds

numbers (Re = ρvMD/μ, for density ρ, mean velocity vM, pipe diameter D and dynamic

viscosity μ) of 9030 – 90300; indicating turbulent flow for all velocities). Figure 4.4(a) shows

sample NMR signal data as a function of te (i.e. the FID) for a separation distance of 62 cm

and mean velocities ranging from 0.37 to 1.83 m/s. The regularised fit of equation 4.7 for

each mean velocity is also shown. Figure 4.4(b) shows a comparison of velocity probability

distributions, P(v); with measured distributions determined via regularisation of the FID

signals, whilst theoretical distributions are determined using from the power law velocity

profile (equation 4.8) with the power law exponent determined from the Reynold’s number

correlation (Zagarola et al., 1997).

58

Figure 4.4 Velocity distribution measurements obtained using FID acquisition time as the

independent variable. (a) Equation 4.7 fit to FID experimental data at a separation distance of 62 cm

and mean velocities ranging from 0.37 to 1.83 m/s. (b) Velocity probability distributions (P(v))

returned by this regularisation analysis, as well as comparative theoretical velocity distributions.

The model fit to the experimental FID signals is excellent for all measurements in

Figure 4.4(a). Furthermore; the fit is determined across the majority of the signal decay (tdelay

= 9 ms); which allows a velocity probability distribution to be determined without the

presence of erroneous signal artefacts. The measured distributions in Figure 4.4(b) compare

favourably to the theoretical distributions in terms of the mean value and width of the

distributions. Perfect agreement is not expected as the theoretical distributions correspond

to instantaneous velocity whereas the NMR experimental velocity distributions are a

complex average over the polarisation and acquisition time-frame. In addition, the second

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5

NM

R S

ign

al [µ

V]

Time since excitation pulse [s]

Expt. data

Model fit

(a)

vM

[m/s]0.370.731.101.461.83

0

2

4

6

8

0 0.5 1 1.5 2 2.5 3

P(v

)

Velocity [m/s]

vM

[m/s]0.370.731.101.461.83

(b)Measureddistribution

Theoretical distribution

59

derivative penalty function imposed during regularisation will smooth out the sharp

interfaces evident in the theoretical probability distributions.

The accuracy of the NMR velocity measurement technique is now considered with

respect to the measured mean velocity. Figure 4.5 compares the mean velocity determined

as the expected value of each experimental probability distributions shown in Figure 4.4(b)

with the mean velocity measured from the in-line rotameter. There are five sets of data

corresponding to the five sets of experiments run at different separation distances (ranging

from 62 to 132 cm).

Figure 4.5 Comparison of the mean velocity predicted using regularisation of NMR data to the

measured mean velocity from in-line rotameter data. Five sets of data were obtained at separation

distances of 62 to 132 cm.

In Figure 4.5, the NMR predicted mean velocity compares reasonably well to the

superficial velocity measured using the in-line rotameter. There is no obvious systematic

deviation with separation distance in the accuracy of the mean velocity predicted by the NMR

measurement. For all fifty velocity measurements (across five separation distances and ten

velocities); the mean error (calculated according to equation 3.6) is 0.006 m/s and the root

mean square error (RMSE, calculated according to equation 3.7) is 0.089 m/s indicating good

agreement between the NMR and rotameter measurements. A small error is observed at the

highest velocity (1.83 m/s); the impact of signal loss during the initial acquisition delay (tdelay

= 9 ms) is prevalent. For lower velocities the signal loss during the acquisition delay is

0

0.5

1

1.5

2

0 0.5 1 1.5 2

NM

R m

ea

su

red

ve

loc

ity [

m/s

]

Rotameter measured velocity [m/s]

627893109132

LPD [cm]

60

minimal (e.g. 3.1 % signal loss for 0.37 m/s) however at higher velocities the signal loss from

fluid flush-out during the acquisition delay is much more significant (e.g. 15.3 % at 1.83

m/s). This leads to error in fitting the appropriate velocity distribution to the measured signal

data such that there is discrepancy between the NMR and rotameter velocity measurements

(at higher velocities).

The accuracy of the NMR velocity measurement methodology with respect to

capturing the width of the velocity distribution is now considered. The standard deviation of

each velocity probability distribution is calculated for the velocity measurements at a

separation distance of 62 cm. Figure 4.6 compares the NMR measured velocity distributions

to the theoretical prediction for turbulent velocity distributions in terms of their standard

deviations’ (σv).

Figure 4.6 Comparison of velocity probability distribution standard deviations. Experimentally

determined standard deviations (σv) for the NMR measured velocity distributions (at LPD = 62 cm)

and the corresponding standard deviations of theoretical turbulent velocity distributions.

Figure 4.6 demonstrates that the measured distribution width is underpredicted

relative to the theoretical distribution width (in terms of standard deviation). However the

measured distributions are still competent in capturing the appropriate trend and relative

magnitude of the velocity distribution standard deviation. As highlighted previously (with

respect to Figure 4.4(b)), perfect agreement between the measured and theoretical

distributions is not anticipated. The measured distributions capture a complex time-average

of the flow profile and the smoothing imposed by the regularisation penalty function in the

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2

σv

[m/s

]

Rotameter measured velocity [m/s]

Measured distribution

Theoretical distribution

61

measured distributions will restrict the ability to capture sharp interfaces observed for the

theoretical distributions.

4.3.3. Two pipe experiments

The second set of experiments conducted involved the two-pipe flow loop shown in

Figure 4.2, in order to test the velocity measurement methodology with an artificially created

bimodal velocity distribution. The ball valves used to control the flow in each pipe were

adjusted such that the velocity in pipe A was 33% of the velocity in pipe B. For the two-pipe

experiments; separation distances of 68, 78, 88 and 98 cm were used and the total water

flowrate through the system varied from 0.9 to 3.0 m3/h (in 0.3 m3/h intervals). Figure 4.7(a)

shows an example of the model fit (obtained through regularisation using equation 4.7) to

the experimental FID data for a separation distance of 68 cm and overall flowrates of 1.8, 2.4

and 3.0 m3/h respectively. Figure 4.7(b) shows the resultant velocity probability distributions

returned by the regularisation analysis. Note that the FID measurements captured in the two-

pipe experiments do not use a Q-switch; thus the initial acquisition delay is 25 ms.

62

Figure 4.7 Velocity measurements for the two-pipe flow system. (a) The model fit (equation 4.7)

to FID experimental data for the two-pipe experiments. The polarisation-detection coil separation

distance is 68 cm and overall flowrates are 1.8 m3/h (with measured velocities of 0.18 and 0.56 m/s

in pipes A and B respectively), 2.4 m3/h (with measured velocities of 0.24 and 0.75 m/s) and 3.0 m3/h

(with measured velocities of 0.32 and 0.96 m/s). (b) The resultant velocity probability distributions

returned by regularisation analysis of the two-pipe NMR data shown in (a).

Figure 4.7(a) demonstrates very good agreement between the experimentally

measured FID signals and the regularised model fit; as would be expected. The two-pipe

velocity distributions in Figure 4.7(b) show two distinct peaks; clearly the methodology is

able to deal with a multi-modal velocity distribution. Each peak is representative of the

contribution from the respective pipe (i.e. the lower velocity peak is from pipe A and the

higher velocity peak is from pipe B). The overall probability distributions were split into the

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5

NM

R s

ign

al [µ

V]

te [s]

Model fit

1.8 m3/h

2.4 m3/h

3.0 m3/h

Expt. data

(a)Overall flowrate

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

P(v

)

Velocity [m/s]

30 l/min

40 l/min

50 l/min

1.8 m3/h

2.4 m3/h

3.0 m3/h

(b)

63

two peaks (using the minima between them) and the mean velocity calculated for each peak.

These mean velocity data are shown in Figure 4.8 plotted against the superficial velocity as

measured using the respective rotameter on each pipe.

Figure 4.8 Comparison of the predicted mean velocity in pipes A and B to the measured superficial

velocity from the corresponding rotameter. Predicted mean velocities are obtained using

regularisation of acquired NMR data, followed by velocity peak splitting. Four sets of data are

obtained at separation distances of 68, 78, 88 and 98 cm with the overall flowrate being varied from

1.8 to 3.0 m3/h .

The mean velocity determined using NMR regularisation agrees reasonably well with

the rotameter velocity measurements for both pipes respectively. For the two pipe

measurements; the RMSE (calculated according to equation 3.7) for pipe A is 0.055 m/s (or

a relative RMSE of 23.9 %) whilst the RMSE for pipe B is 0.062 m/s (or a relative RMSE of

11.1 %). The larger relative error with respect to pipe A is due to the poorer signal-to-noise

ratio (SNR) values at such low velocities. For example, for the 1.2 m3/h two pipe experiment

(with rotameter measured velocities of 0.12 and 0.38 m/s in pipes A and B respectively) at a

separation distance of 68 cm the effective SNR is 16.3 for pipe A and 40.1 for pipe B. This

is as the residence time (and therefore signal decay) between polarisation and detection

becomes significant at lower velocities (v < 0.2 m/s), such that the signal measured at the

detector will have a considerably poorer SNR compared to the SNR at higher velocities. For

each bi-modal velocity probability distribution in Figure 4.7(b), the two peaks are not equal

in magnitude, even though the pipes are of equivalent diameter. The relative magnitude of

the velocity peak attributed to pipe B diminishes in intensity as flowrate increases. This is

partially a consequence of the inability to acquire data for te < tdelay, the initial 25 ms following

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

NM

R p

red

icte

d m

ea

n v

elo

cit

y

[m/s

]

Measured velocity [m/s]

Pipe A Pipe B

0.68 m

0.78 m

0.88 m

0.98 m

64

signal excitation. As flowrate increases this region of the FID (te < 25 ms) becomes more

influential in determining the relative contribution of pipe B (the larger velocity) to the

overall velocity distribution.

4.4 Conclusions

In this chapter, the EFNMR flow meter demonstrated the ability to accurately

quantify velocity distributions in single-phase pipe flows. Details of the flow metering

equipment is outlined featuring detection using an EFNMR r.f. coil positioned downstream

of a mobile pre-polarisation magnet. In principle, velocity distributions could be determined

by varying this separation distance, however this was shown to be impractical primarily due

to restraints on the minimum distance between the pre-polarisation magnet and the detection

coil. Analysis of the acquired FID signal, however, proved to be much more successful, with

measured velocity distributions demonstrated to be consistent with theory and whose mean

is consistent with independent rotameter measurements for flow through a single pipe.

Furthermore, this approach was successfully demonstrated for artificially constructed multi-

modal (two-pipe) velocity distributions, a key step towards realising MPFMs capable of

measuring the velocity distribution of multi-phase flow.

65

Chapter 5. Characterising two-phase gas/liquid flows

5.1 Introduction

The ability to identify and quantify different gas/liquid flow regimes (e.g. slug flow)

is a considerable challenge in MPFM development (Falcone et al., 2009, Falcone et al., 2002,

Thorn et al., 2013). Fluids transported in subsea pipelines during oil and gas production

exhibit a range of multiphase flow regimes. The most problematic flow regime is slug flow,

which is characterised by the intermittent flow of liquid slugs separated by large gas bubbles.

Slug flow has been shown to reduce the integrity of pipelines and equipment through

increased corrosion (Hill et al., 1996, Jepson et al., 1996, Sun and Jepson, 1992, Villarreal

et al., 2006) and pipe vibration (Zhong et al., 2007). Additionally, slug flow can cause

significant pressure oscillations, with severe pressure fluctuations potentially leading to

safety trips and platform shutdown, increasing operational and capital expenditure as

processing equipment (e.g. separators and compressors) require larger operating margins

(Havre et al., 2000).

Significant research has previously been undertaken to improve the knowledge base

of slug flow through experimental measurement and modelling of multiphase flow

characteristics. The measurement of key slug flow characteristics (e.g. liquid holdup and

slug frequency) has traditionally been achieved by the use of conductance and impedance

probes (Andreussi et al., 1988, Costigan and Whalley, 1997, Nydal et al., 1992) or pressure

transducers (Lin and Hanratty, 1987, Matsui, 1984). Such measurements have been used to

develop a number of widely used slug flow correlations (Andreussi et al., 1993, Barnea et

al., 1980, Dukler and Hubbard, 1975, Issa and Kempf, 2003). However the considerable

range of parameters that influence the complex nature of slug flow has often resulted in

difficulty applying such correlations, particularly in industrial pipelines (Al-Safran, 2009,

66

Zabaras, 2000). Furthermore, these measurement techniques are intrusive, which is an

undesirable characteristic for a true non-invasive MPFM (Falcone et al., 2009).

In this chapter, the EFNMR measurement system is extended to analyse two-phase

air-water flows with the ability to identify and measure flow characteristics in gas/liquid

flows (stratified and slug flow). Continuous monitoring of multiphase flow (particularly slug

flow) is inherently more difficult due to the complex time-varying flow behaviour. NMR

signal interpretation (via Tikhonov regularisation) has been applied to monitor the liquid

holdup and velocity with time. The liquid holdup measurement is compared to a video

analysis of the liquid height of the flowing stream at a transparent pipe section. Finally, the

accuracy of the full NMR measurement procedure applied to two-phase flow is verified by

comparing the average liquid volumetric flowrate (determined by combining the liquid

velocity and holdup tracking) to an in-line rotameter measurement of the liquid volumetric

flowrate in the flow loop water feed.


5.2.1. Equipment for gas/liquid flows

The EFNMR flow metering apparatus was previously outlined in section 4.2.1

(including a photo and schematic in Figure 4.1). In this section, details relevant to the

introduction of a gas stream to the flow loop apparatus are discussed. Compressed air (20

psi) is injected at a controlled flowrate prior to the pre-polarisation magnet and a 10 – 100

L/min rotameter (Cole Parmer, Australia) is used to measure the gas flowrate prior to mixing.

The compressed air is injected into the flowing water stream and the gas/liquid fluid stream

flows through a transparent acrylic pipe (31 mm internal diameter) in the NMR measurement

section. The upstream Halbach array is maintained at a separation distance of 62 cm relative

to the EFNMR detection coil for the results presented in this chapter. NMR measurements

of the gas/liquid stream acquire free induction decay (FID) signals using the ‘pulse and

collect’ sequence (illustrated in Figure 2.3). The following key parameter ranges were used

for the ‘pulse and collect’ experiments; an acquisition delay between excitation and detection

(tdelay) of 25 ms; a total acquisition time per scan (ta) of 0.5 – 1.0 s and a repetition time of

0.80 – 1.80 s (corresponding to a scan frequency of 0.55 – 1.25 Hz).

67

Video analysis is used to obtain an independent measurement of the liquid holdup. A

video (at 30 frames per second) of the flowing stream is captured during the same

experimental time as the NMR measurements. The video captures a 10 cm transparent

section of the pipe just prior to the detection coil (indicated in Figure 4.1(b)). The flowing

water stream is dyed red when required (using food colouring) to assist video interpretation.

The video is processed using an analysis code developed in Matlab R2017b. The analysis

identifies the colour of the pixels in order to determine the liquid height in the region. The

known cross-sectional area of the pipe is used to adjust the measured liquid height to an

estimate of the liquid holdup.

5.2.2. Gas/liquid NMR signal interpretation

In this chapter, FID measurements are obtained of two-phase air/water flows. During

measurements of air/water flows, only the liquid is contributing to the measurable NMR

signal. This has two important implications; firstly the velocity probability distribution

determined from the FID signals are representative of the liquid velocity distribution alone.

This observation means that the FID signals acquired from two-phase gas/liquid flows may

be described by the model for the NMR signal detected using the flow meter (equation 4.5)

which was developed in Chapter 4. The velocity probability distribution of the liquid phase

within the air/water flows may be measured using the Tikhonov regularisation procedure

described in section 4.2.3; with distributions determined by fitting to the FID signal (i.e.

signal as a function of te)

The second implication of only the liquid phase contributing to the NMR signal is

that the overall level of signal magnetisation (S0) is in principle directly proportional to the

liquid holdup in the detector. This observation can be used to estimate the liquid holdup (hl)

during two-phase flow via the following equation (Krüger et al., 1996);

ℎ𝑙 =𝑆0,𝑇𝑃

𝑆0,𝑟𝑒𝑓 (5.1)

where S0,TP is the overall signal magnetisation for a two-phase measurement, and S0,ref is a

reference value for the overall signal magnetisation determined from single-phase

68

experiments with the pipe full of equivalent liquid. S0 can be obtained from the model signal

fit following regularisation analysis. The model signal fit (Sfit) is determined by combining

the contribution of all velocities to the measured signal via the velocity probability

distribution vector, P(v).

𝑆𝑓𝑖𝑡(𝑡𝑒) = 𝑆0[𝐾(𝑣, 𝑡𝑒)]P(𝑣) (5.2)

where K(v,te) is the model kernel matrix as a function of velocity and time since excitation

described by equation 4.5. S0 can be determined by back-extrapolation from the first point

of acquisition (i.e. at time te = tdelay):

𝑆0 =𝑆𝐹𝑖𝑡(𝑡𝑑𝑒𝑙𝑎𝑦)

[𝐾(𝑣,𝑡𝑒)]𝑃(𝑣) (5.3)

Following calculation of the liquid holdup, the liquid flowrate may be determined. The mean

linear liquid velocity (vl) is determined as the expected value of the liquid velocity probability

distribution (as was done in 0). Then the time-averaged liquid volumetric flowrate ql is;

𝑞𝑙 = 𝑣𝑙ℎ𝑙𝐴 = 𝑣𝑙𝑆0,T𝑃

𝑆0,𝑟𝑒𝑓𝐴 (5.4)

where A is the pipe cross-sectional area.


5.3.1. Calibrating the Reference Signal Magnitude

The reference signal magnitude (or full liquid overall signal magnitude, S0,ref) is

determined at a range of velocities (0.09 to 1.14 m/s corresponding to water flowrates of 0.24

to 3.12 m3/h respectively, as measured using the in-line liquid rotameter) for single-phase

water flows. The value should be independent of the fluid velocity as the velocity-related

contributions have been removed from the measured signal. Figure 5.1 displays the measured

S0 values as a function of velocity.

69

Figure 5.1 Reference overall signal magnitude (S0,ref) relative to the measured velocity (single-

phase flows).

The results shown in Figure 5.1 confirm that the S0 is independent of velocity over an

intermediate mean liquid velocity range. The mean value of 352 µV is used as the reference

S0 value for two-phase analysis. The measured reference signal magnetisation at low mean

liquid velocities (v<0.24 m/s) shows some variation. The FID signals acquired at these low

velocities have significantly poorer signal-to-noise (SNR) ratio compared to the SNR of FID

signals at higher velocities (as discussed in section 4.3.3). This is a consequence of the

significant polarisation to detection residence time (τPD = LPD/v) at low velocities. The

reference signal magnitude is also observed to reduce at higher mean liquid velocities (v >

1.00 m/s). The signal loss during the initial acquisition delay (t < tdelay) becomes increasingly

significant at higher velocities as the ‘flush-out’ effect (i.e. excited fluid leaving the detection

region) is more substantial. This signal loss results in an artificial reduction of the predicted

reference signal magnitude for such higher velocities.

5.3.2. Gas/liquid time-averaged results

Two-phase air-water trials were conducted at liquid superficial velocities (vsl) of 0.09

– 0.26 m/s (corresponding to liquid flowrates of 0.24 – 0.72 m3/h) and gas superficial

velocities (vsg) of 0.22, 0.44 and 0.88 m/s (corresponding to gas flowrates of 0.6, 1.2 and 2.4

m3/h). Figure 5.2 shows the position of the fifteen experimental trials on a flow regime map.

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2

Re

fere

nc

e o

ve

rall

sig

nal

ma

gn

eti

sati

on

[µ

V]

Measured mean liquid velocity [m/s]

+ 5%

- 5%

Mean value

70

The visually confirmed flow regimes (i.e. stratified smooth or slug flow) correspond to the

predicted flow regimes from Taitel and Dukler (1976) for all experimental trials.

Figure 5.2 Flow regime map (from Taitel and Dukler (1976)) indicating the relevant flow regime

position of each experimental trial. The trials visually observed to be stratified smooth flow are

indicated by blue circles whilst the trials visually observed to be slug flow are indicated by red crosses.

The experimentally acquired FID signals from each of the fifteen trials were initially

time-averaged (across Nscans = 128) and subsequently analysed using the NMR signal

interpretation procedure discussed in section 5.2.2. Figure 5.3 displays sample time-

averaged analysis for superficial liquid velocities of 0.09 – 0.26 m/s and a superficial gas

velocity of 0.44 m/s. Figure 5.3(a) shows time-averaged NMR signal data as a function of te

(the FID signal) as well as the model fit according to equation 4.5. Figure 5.3(b) shows the

corresponding liquid velocity probability distributions, P(v).

0.01

0.1

1

0.1 1 10

vs

l[m

/s]

vsg [m/s]

Dispersed flow

Intermittent flow

Annular flow

Stratified wavy flow

× – Slug flow

(from visual observation)

– Stratified

smooth flow (from visual observation)

Stratified smooth flow

71

Figure 5.3 Velocity measurements of air-water flows. (a) Equation 4.5 fit to FID experimental data

for two-phase air/ water flows with vsl = 0.09 – 0.26 m/s and vsg = 0.44 m/s. (b) Resultant liquid

velocity probability distributions (P(v)) returned by regularisation analysis of the FID signals.

The stratified flow experiments (vsl = 0.09 and 0.13 m/s) show a single peak

corresponding to the continuous liquid linear velocity distribution anticipated for time-

invariant flow. The slug flow experiments (vsl = 0.18, 0.22 and 0.26 m/s) clearly exhibit a

bimodal velocity distribution, with the larger lower velocity peak corresponding to the

background stratified liquid layer whilst the smaller higher velocity peak corresponds to the

faster moving slugs.

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

NM

R s

ign

al [µ

V]


(a)Expt.data

Model fit

vSL

[m/s]

0.090.130.180.220.26

0

4

8

12

16

20

0 0.2 0.4 0.6 0.8 1

P(v

)

Liquid velocity [m/s]

vSL [m/s] Flow regime

0.09 stratified flow


0.18 slug flow

0.22 slug flow

0.26 slug flow

Contribution of slug component

(b)

72

For each of the fifteen experimental trials shown in Figure 5.2, the time-

averaged liquid volumetric flowrate is calculated using equation 5.4. Figure 5.4

compares the NMR measured liquid volumetric flowrates to the in-line water

rotameter measurements of volumetric flowrate. Excellent agreement is observed

between the two flowrate measurements with a mean error (calculated using equation

3.6) of -0.004 m3/h and a root mean square error (calculated using equation 3.7) of

0.029 m3/h.

Figure 5.4 Comparison of the NMR measurement of time-averaged liquid volumetric flowrate (ql)

to the in-line rotameter measurement of volumetric flowrate.

5.3.3. Gas/liquid single-scan measurements

The results presented in section 5.3.2 demonstrate that the NMR signal interpretation

procedure is accurate and can resolve the presence of slugs from the measured FID signal

(via the liquid velocity probability distribution). However this procedure does not provide

time resolved information of flow characteristics (e.g. liquid velocity and liquid holdup). In

order to provide such time-variant information, the individual FID scans must be interpreted

in a ‘single-shot’ analysis (i.e. each single FID signal acquired is analysed individually as

opposed to analysing the overall time-averaged FID signal as done in section 5.3.2).

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8

NM

R m

ea

su

red

ql[m

3/h

]

Rotameter measured ql [m3/h]

Strat.flow

Slug flow

qg

[m3/h]

0.6

1.2

2.4

73

Figure 5.5(a) shows an example of two 'single-shot’ NMR signal measurements as a

function of te obtained during two-phase flow with vsl = 0.18 m/s, vsg = 0.44 m/s. The first

scan (blue crosses) is obtained when a stratified water layer (flowing underneath an elongated

gas bubble) is detected whilst the second scan (red circles) is obtained when a liquid slug is

flowing through the detection region. The regularised model fit of equation 4.5 to each scan

is also shown. Figure 5.5(b) shows the corresponding liquid velocity probability

distributions, P(v).

Figure 5.5 Single-scan velocity measurement of air-water flow. (a) Equation 4.5 fit to non-time-

averaged experimental signal scans for two-phase air/water flows with vsl = 0.18 m/s, vsg = 0.44 m/s.

The first signal is acquired when the background stratified liquid layer is visually observed to be in

the detection region, whilst the second signal is obtained when a slug is visually observed to be in the

0

2

4

6

8

10

12

14

16

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

NM

R s

ign

al [µ

V]


Model fit

Expt. data

Stratified layer

Liquidslug

(a)

Photo

0

1

2

3

4

0 0.5 1 1.5 2

P(v

)

Liquid velocity [m/s]

Stratified layer

Liquid slug

(b)

74

detection region. Photos (obtained from the video analysis of two-phase flow) are also shown to

indicate the relevant flow regimes. (b) The corresponding liquid velocity probability distributions

(P(v)) returned by regularisation analysis.

Two key differences can be observed by comparing the detectable signals from the

stratified layer and a liquid slug in Figure 5.5. Firstly, the overall signal magnitude is

considerably higher for the liquid slug signal relative to the stratified layer signal. This is

anticipated due to the higher liquid holdup, which corresponds to an increase in the number

of observable nuclear spins in the detection region. The second difference is that the

observable signal decays faster when detecting a liquid slug due to the increased ‘flush-out’

effect at higher velocity. This is captured in the regularised liquid velocity distribution that

shows the liquid slug is travelling at a higher velocity relative to the stratified liquid layer.

The NMR signal interpretation procedure for two-phase flows discussed in section

5.2.2 and demonstrated in section 5.3.2 for the time-averaged NMR signal data is now

applied to all ‘real-time’ NMR signal scans (i.e. for each scan in Nscans (= 128)) for each of

the fifteen experimental trials. Regularisation is used to fit equation 4.5 to each individual

non-time-averaged FID signal acquired. The corresponding velocity distributions are

returned via the regularisation analysis. The mean of each velocity probability distribution

is used as a measure of the liquid velocity with time. Figure 5.6 shows this liquid velocity

tracked over 60 s at superficial liquid velocities of 0.09, 0.18 and 0.26 m/s and at a gas

superficial velocity of 0.44 m/s (as measured using the in-line rotameters).

75

Figure 5.6 Tracking the liquid velocity over time for two-phase air/water flows. The superficial

liquid velocities are 0.09, 0.18 and 0.26 m/s, whilst the superficial gas superficial velocity is 0.44 m/s

for all three trials. The visually observed flow regime is indicated for each superficial liquid velocity.

The liquid velocity tracking can be observed to be relatively constant (a standard

deviation of 0.018 m/s for 128 scans) during the stratified flow experiment (vsl = 0.09 m/s).

The slug flow experiments show greater fluctuations in the velocity tracking due to the

periodic presence of fast-moving slugs (relative to the slower background stratified liquid

layer). In the first slug flow experiment (vsl = 0.18 m/s) the periodic fluctuations in liquid

velocity are less frequent compared to the second slugging experiment (vsl = 0.26 m/s). This

observation corresponds to longer but less frequent (0.07 Hz) liquid slugs occurring at lower

velocities and shorter but more frequent (0.16 Hz) slugs occurring at higher velocities (the

method for estimating the slug frequency from the liquid holdup is discussed below with

respect to Figure 5.8).

The overall signal magnetisation values (S0,TP) are extracted from the resultant fit of

each individual scan (via equation 5.3) and used to estimate the liquid holdup (using equation

5.1). Figure 5.7 shows the liquid holdup being tracked over 60 s for superficial liquid

velocities of: (a) 0.09, (b) 0.18 and (c) 0.26 m/s. The superficial gas velocity is 0.44 m/s for

all three trials. The NMR measurement of liquid holdup is compared to the simultaneous

video analysis of liquid holdup (described in section 5.2.1).

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60

Liq

uid

ve

loc

ity [

m/s

]

Experimental Time [s]

vsl [m/s] Flow regime


0.18 slug flow

0.26 slug flow

76

Figure 5.7 Tracking the liquid holdup over time for two-phase air/water flows. The superficial

liquid velocities are; (a) 0.09 m/s (stratified flow), (b) 0.18 m/s (slug flow) and (c) 0.26 m/s (slug

flow), whilst the superficial gas velocity is 0.44 m/s for all trials. The liquid holdup determined from

NMR analysis is compared to the liquid holdup determined from video analysis.

A time series cross-correlation between the NMR holdup (hN) and video holdup (hV)

has been applied in order to verify the periodic correlation in the slugging data. The cross-

covariance (cNV) of the NMR holdup (hN) and video holdup (hV) for a time lag of τL is given

by (Chatfield, 2016);

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p


NMR holdup

Video holdup

(a)

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p


NMR holdup

Video holdup

(b)

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p


NMR holdup

Video holdup

(c)

77

𝑐𝑁𝑉(𝜏𝐿) = {

∑(ℎ𝑁,𝑡−ℎ𝑁 )(ℎ𝑉,𝑡+𝜏−ℎ𝑉 )

𝑁

𝑁𝑡=1

𝑓𝑜𝑟 𝜏𝐿 = 0, 1, … , 𝑁 − 1

∑(ℎ𝑁,𝑡−ℎ𝑁

)(ℎ𝑉,𝑡+𝜏−ℎ𝑉 )

𝑁

𝑁𝑡=1−𝜏𝐿

𝑓𝑜𝑟 𝜏𝐿 = −1, −2, … , −(𝑁 − 1)

(5.5)

where t is the video frame number, N is the total number of video frames analysed, ℎ𝑁 is the

mean NMR liquid holdup and ℎ𝑉 is the mean video liquid holdup. The normalised cross-

correlation (rNV) is given by (Chatfield, 2016);

𝑟𝑁𝑉(𝜏) = 𝑐𝑁𝑉(𝜏)

𝜎ℎ𝑁𝜎ℎ𝑉

(5.6)

where 𝜎ℎ𝑁 is the standard deviation of the NMR predicted liquid holdup track and 𝜎ℎ𝑉

is the

standard deviation of the video estimated liquid holdup track. Figure 5.8 shows example

normalised cross correlation relationships for the following experimental trials; (a) vsl = 0.18

m/s, vsg = 0.44 m/s and (b) vsl = 0.26 m/s, vsg = 0.44 m/s.

Figure 5.8 Normalised cross-correlation (rNV) at time lag (τL) between NMR holdup and video

holdup for experimental trials. Measurements are conducted at (a) vsl = 0.18 m/s, vsg = 0.44 m/s and

(b) vsl = 0.26 m/s, vsg = 0.44 m/s.

The maximum peak (at zero time lag) in Figure 5.8 is representative of the similarity

between the two signals (with a value of 1 representing an exact match). The time lag

difference between the peaks in the cross-correlation plot is indicative of the average time

period of the slug units (τs) and can be used to estimate the slugging frequency (fs) for a given

experimental trial (e.g. for trial (a) τs = 15.5 s and fs = 0.07 Hz, whilst for trial (b) τs = 6.1 s

and fs = 0.16 Hz).

-1

-0.5

0

0.5

1

-20 -10 0 10 20

No

rmali

sed

cro

ss-c

orr

ela

tio

n

Time lag [s]

0.18 m/s

0.26 m/s

vsl

(a) (b)

78

From Figures 5.7 and 5.8 it can be observed that the NMR holdup estimate correlates

relatively well to the video holdup. The NMR measurement procedure is successfully able

to identify the presence of slug flow (relative to stratified flow) and give a reasonable estimate

of the liquid holdup. The NMR measurements underestimate the liquid holdup relative to

the video holdup; minor deviations are expected in the video holdup estimate as the analysis

does not account for gas bubbles entrained in the liquid phase and measures the upper edge

of a concave meniscus for the liquid height. Both of these physical reasons cause a slight

over-estimation of the liquid holdup in the video analysis. Furthermore, the presence of gas

bubbles can increase the observable rate of signal decay (as the effective NMR spin-spin

relaxation is faster) in gas-liquid flow, leading to an overestimation of liquid velocity and an

underestimation of liquid holdup using the NMR signal interpretation procedure.

The difference between the holdup estimates is particularly significant immediately

following the measurement of a slug in the system (e.g. at 6 s in Figure 5.7(b)). This

difference can be attributed to the model assumption that the linear velocity of fluid elements

is constant whilst they travel through the flow metering system. This is obviously not true

for time-variant slug flow. The fluid detected immediately following the slug (the

‘subsequent fluid’) will have been subject to shear drag forces by the slug layer. The

subsequent fluid is predominantly composed of fluid shed from the back of the slug layer and

has therefore undergone a complex change in velocity whilst it travels through the flow

metering apparatus. The regularisation procedure will fit the fluid velocity distribution that

was observed at the detection coil. However this ‘subsequent fluid’ will have been travelling

at a significantly higher velocity through the polarisation magnet when subjected to the shear

drag of the slug. The assumed degree of signal polarisation (SP) will therefore be

considerably over-estimated, leading to a significant under-estimation of the liquid holdup

using the back-extrapolation estimation method (equations 5.1 and 5.3).

The NMR holdup measurement procedure is currently unable to detect all slugs at

higher velocities. The current NMR repetition time (0.8 s) limits the measurable velocity

range of the system. As the superficial liquid and gas velocities increase, the residence time

79

of the slug in the EFNMR detection region is reduced. For example, for the experiment trial

shown in Figure 5.7(c) where vsl = 0.26 m/s and vsg = 0.44 m/s, the slug residence time in the

detection coil ranges from 0.2 – 0.4 s (determined from video analysis) meaning such slugs

may be missed or only partially excited (e.g. at 18 s in Figure 5.7(c)).

5.3.4. Statistical analysis of single-scan results

Important flow characteristics can be determined from the analysis of the liquid

volumetric flowrate track. For an individual FID signal scan i, the liquid volumetric flowrate

(ql,i) can be calculated from the liquid holdup for scan i (hl,i) and the liquid velocity for scan

i (vL,i) using equation 5.4.

The gas/liquid flow regimes can be distinguished by analysing the variation (i.e.

standard deviation) in the liquid flowrate track for a given experiment across all scans. Figure

5.9 plots the standard deviation of liquid flowrate (𝜎𝑞𝑙) across each experiment (Nscans = 128)

for all fifteen trials.

Figure 5.9 Liquid flowrate standard deviation for the stratified and slug flow experiments.

Experimental trials in the stratified flow regime are observed to have very little

variation in the liquid flowrate (𝜎𝑞𝑙<0.06 m3/h) as anticipated for time-invariant flow,

whereas trials in the slug flow regime have more significant spread in the liquid flowrate

0.01

0.1

1

10

0 0.2 0.4 0.6 0.8

NM

R m

ea

su

red

qls

tan

da

rd

devia

tio

n [

m3/h

]


Stratified flow

Slug flow

qg [m

3/h]

0.6 1.2

2.4

80

(𝜎𝑞𝑙>0.27 m3/h). The significant difference in the spread of flowrates that is highlighted here

may be used as a practical measurement technique to differentiate stratified and slug flow.

The accuracy of the NMR velocity measurement procedure applied to individual

acquisitions can be verified using the liquid flowrate measurement. The average liquid

volumetric flowrate (ql) for an entire NMR experiment (i.e. for Nscans = 128 scans) is

determined by:

𝑞𝑙 = ∑ 𝑞𝑙,𝑖

𝑁𝑠𝑐𝑎𝑛𝑠𝑖=1

𝑁𝑠𝑐𝑎𝑛𝑠 (5.7)

where ql,i is the NMR predicted liquid volumetric flowrate for scan i. Figure 5.10 compares

the NMR predicted average liquid flowrate (determined from analysis of individual scans) to

the measured liquid flowrate from the in-line water rotameter.

Figure 5.10 Comparison of the NMR predicted average liquid flowrate to the independent rotameter

measurement of liquid flowrate. Experimental trials visually observed to be in the stratified (strat.)

flow regime are indicated by open markers whilst slug flow trials are indicated by closed markers.

The average liquid volumetric flowrate predicted by analysis of the individual NMR

scans agrees reasonably well with the rotameter measurement of liquid flowrate. The root

mean square error (RMSE) for the fifteen velocity measurements is 0.058 m3/h. The RMSE

obtained here (from analysis of non-time-averaged scans) is higher than the RMSE of 0.029

m3/h determined in Figure 5.4 (from analysis of the time-averaged scans). The reduction in

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8

NM

R p

red

icte

d q

l[m

3/h

]


Strat.flow

Slug flow

qg

[m3/h]

0.6

1.2

2.4

81

accuracy is anticipated due to the substantial reduction in SNR (e.g. for ql = 0.48 m3/h, qg =

1.2 m3/h the time-averaged SNR is 73 whilst the average SNR for non-time-averaged scans

is 9). Whilst the regularisation procedure is relatively robust, this significant reduction in

SNR will cause a loss of accuracy. However the slight loss of accuracy is an acceptable

compromise given the ability to track the liquid velocity and holdup with respect to time

when applying the interpretation procedure to analyse non-time-averaged scans.

5.4 Conclusions

In this chapter, the application of the EFNMR multiphase flow metering system to

monitor gas/liquid stratified and slug flow regimes is demonstrated. Appropriate signal

interpretation via the application of Tikhonov regularisation allows the determination of the

velocity probability distribution of the liquid phase in air-water flows. Signal analysis

applied to individual FID signal measurements allows tracking of the liquid holdup and

velocity with time (at 0.55 – 1.25 Hz). The NMR estimate of liquid holdup is quite

comparable with a video analysis of the holdup. Furthermore, the accuracy of the liquid

velocity distributions are validated by comparison with an independent rotameter

measurement of the liquid volumetric flowrate. Finally, the variation in the liquid flowrate

may be used to distinguish stratified and slug flow regimes.

82

Chapter 6. Developing a technique for simultaneous oil and

water flowrate measurement

6.1 Introduction

This chapter details the development of an appropriate measurement technique for in-

situ quantification of the oil and water component flowrates. The EFNMR flow loop is

extended to be capable of performing oil/water flows experiments. The appropriate fluid

distinguishing mechanism and the relevant signal sensitivity for NMR measurement of

oil/water mixtures is discussed. The measurement system and data analysis are appropriately

adapted and extended for simultaneous velocity measurement and component distinction (via

T1 relaxometry). The 1H NMR signal of the multiphase fluid stream is acquired at varying

pre-polarisation conditions using a dual polarisation mechanism. The acquired FIDs are

interpreted via a two-dimensional signal inversion in order to provide the joint velocity-T1

probability distribution. Subsequent analysis allows the determination of individual phase

flowrates. Finally the application of the developed two-phase measurement procedure is

validated against in-line fluid rotameters both for single-phase oil and water flows.


6.2.1. NMR fluid quantification of oil/water systems

NMR provides multiple measurement options in terms of quantifying the relevant

phase fractions of a two-component system (such as oil and water). NMR spectroscopy can

be applied to quantify phase fractions due to the chemical shift of oil and water components

(e.g Wagner et al., 2016). However it is not possible to achieve the spectral resolution for

distinguishing oil and water at the Earth’s magnetic field, or at any practical field strength

for multiphase flow metering. Therefore a different approach must be applied in order to

quantify the relevant phase fractions.

83

NMR fluid relaxometry (i.e. relaxation rate measurement) is used across a range of

applications to study material properties and to distinguish relevant phase populations. For

example, in NMR well-logging fluid volumes (clay bound, capillary bound and free water)

are characterised using petrophysical analysis of T2 distributions (Freedman and Heaton,

2004, Kleinberg, 2001b). The T2 distributions of flowing oil/water emulsions have been used

to quantify the emulsion phase fractions (Allsopp et al., 2001, Kantzas, 2004, Kantzas et al.,

2009). This has been achieved by sampling flow and analysing a stationary sample such that

there is sufficient acquisition time to accurately perform a relaxometry measurement. There

is difficulty applying T2 measurements in-situ (i.e. directly on the flowing sample), since the

acquisition time is limited by velocity and various flow effects can impact the acquired NMR

signal (Mueller et al., 1986).

In contrast to T2 relaxometry, analysis of T1 relaxation is a more robust and flexible

approach to differentiating oil and water. T2 measurements are achieved using multi-pulse

acquisition sequences (e.g. CPMG measurements), however T1 signal contrast can be

achieved in our instrumentation through variation of the pre-polarisation conditions and thus

is not limited in terms of acquisition time. Furthermore, T2 measurements are more sensitive

to internal magnetic field gradients arising from magnetic susceptibility differences between

phases in emulsified flows (Fridjonsson et al., 2014a). T1 differentiation will be used as the

fluid phase distinguishing mechanism in this work. Further development of signal contrast

mechanisms is discussed in sections 6.2.3 – 6.2.5.

6.2.2. Equipment for oil/water measurements

The EFNMR flow metering system presented in Chapter 4 is extended in order to be

capable of performing two-phase oil/water flow measurements. The advanced flow loop is

shown in a photo (Figure 6.1(a)) as well as a process and instrumentation diagram (Figure

6.1(b)). The EFNMR measurement system (i.e. the Halbach array and r.f. detection coil) are

the same as previously detailed in Chapter 4. A shorter separation distance (45 cm) relative

to the original separation distance (62 cm) for results presented in Chapters 4 and 5 was

achieved by using additional mu-metal shielding of the Halbach array as well as improved

shimming of the detection coil relative to the stray field. Shorter distances (less than 45 cm)

84

are not achievable due to the stray field from the Halbach array significantly interfering with

the detection coil. An upper limit of 150 cm is imposed on the Halbach separation distance

as larger distances are impractical for realistic flow metering system construction as well as

current practical lab constraints. The EFNMR detection system includes an electromagnetic

pre-polarising coil (a coaxial solenoid of diameter 10 cm, operating at 2.5 V and 6 A) which

can be used to provide a polarisation field to generate magnetisation at the detection coil.

The combined polarisation scheme (simultaneously using the Halbach and the

electromagnetic coil) is discussed in section 6.2.4. The EFNMR detection coil was also

modified to include a resistive Q-switch (Zhen et al., 2018). The application of the 90°

excitation pulse during NMR measurements results in residual stored energy causing

unwanted voltage oscillation (coil ring-down) in the r.f. probe. The Q-switch enhances the

rate of energy dissipation after the excitation pulse which allows reduction of the probe ring-

down time. This enables the acquisition delay time (time between excitation and initial signal

acquisition) to be reduced from 25 ms to 9 ms; allowing earlier acquisition of free induction

decay (FID) signals. This is essential for capturing the short relaxation behaviour of oil as

well as high velocity flows where the effect of fluid flush-out during the acquisition delay is

prominent.

Canola oil (purchased from Oil2U, Australia) and tap water are stored separately in

two intermediate bulk containers (1.0 m3 capacity). Canola oil was selected as an appropriate

oil for flow metering validation measurements primarily due its magnetic resonance

relaxation properties (T1 ~ 115 ms and T2 ~ 82 ms; see section 6.2.3) which allow the fluid

to be readily distinguished from water via NMR relaxometry. Furthermore canola oil has

physical properties (density of 920 kg/m3 and viscosity of 55 cP) which allow a range of

two-phase oil/water flow regimes (e.g. stratified flow, emulsions) to be achieved within the

flow metering system. Canola oil was transported via a close-coupled centrifugal pump

(Calpeda NM32-20A) and the individual phase flowrates monitored using an in-line

rotameter (Stubbe DFM350, 2.5 – 25 m3/h) prior to mixing. The tap water is concentrated

with sodium chloride (12 wt %) in order to reduce the separation time of oil-in-water

emulsions during two-phase flowing experiments (Klaus et al., 2012, Zolfaghari et al., 2016).

The addition of salt causes an increase in the water density (1.09 kg/m3) and viscosity (1.25

cP). Saline water is pumped using a centrifugal pump (Calpeda MXHLM803). The water

85

flowrate is monitored using a second in-line rotameter (Stubbe DFM350, 1.0 - 10 m3/h). Both

of the rotameters were re-calibrated using gravimetric measurement of fluid outflow in order

to account for the used fluid viscosities and densities. The individual phase flowrates are

adjusted using ball valves (V-02 for water and V-05 for oil in Figure 6.1(b)). During single-

phase experiments (i.e. only using water or only using oil alone), bypass lines are used such

that fluid returns directly to the appropriate tank after the NMR measurement section. During

two-phase flow (i.e. water and oil flowed simultaneously through the system) a gravimetric

oil/water separator (separation volume of 128 L) is used in order to split the two phases before

they return to their individual storage tanks.

86

Figure 6.1 Illustration of the experimental oil/water flow loop system. (a) A photo of the flow loop

apparatus with key system components indicated. The direction of flow through the NMR

measurement section is also indicated. (b) A process and instrumentation diagram of the flow loop.

((a)

EFNMR detection coil

Oil storage tank

Water storage tank

Water pump

Flow direction

Oil/water Separator

Pre-polarising Halbach magnet

Oil pump

(b)

87

6.2.3. T1 measurements of stationary fluids

The flow metering system will use T1 differentiation in order to quantify oil and water

(as discussed in section 6.2.1). Initial stationary T1 measurements of oil/water mixtures are

conducted to gain an understanding of the fluid magnetic relaxation properties prior to

flowing measurements. Experiments are conducted for eleven samples with the oil

volumetric fraction stepped from 0 – 100% (in 10 % increments). Each 500 mL sample is

placed in a bottle in the EFNMR detection coil. During stationary measurements of mixtures,

the liquids exist as stratified layers; the oil phase sits on top of a water layer in the bottle.

The mixture T1 distributions are measured using an excitation-delay method. FID signals are

acquired using multiple pulse and collect sequences (illustrated in Figure 2.3) with varying

polarisation-excitation delay time (i.e. tPE). Note that a minimum polarisation-excitation

delay of 60 ms is required due to instrument ring-down following the electromagnetic

polarisation pulse. For all mixtures except the 100 % oil sample; FID measurements are

acquired at 64 polarisation-excitation delay times logarithmically spaced from 65 ms to 6.5

s (with Nscans = 4). Improved accuracy was desired for the 100 % canola oil sample; therefore

the 64 polarisation-excitation delay times were logarithmically spaced between 65 and 600

ms (with Nscans = 16). Longer delay times are not necessary for canola oil due to the shorter

T1.

FID signals are back-extrapolated to determine the polarised signal prior to excitation

(SE). The measured polarised signal is modelled using the following equation;

𝑆𝐸(𝑡𝑃𝐸 , 𝑇1) = 𝑆𝑃 exp (−𝑡𝑃𝐸

𝑇1) (6.1)

where SP is the effective NMR signal after pre-polarisation. The measurement effectively

observes excited protons returning to their thermal equilibrium state in the Earth’s magnetic

field, thus is measuring T1 in the Earth’s field (further details regarding relaxation in variable

magnetic field strength is provided in appendix A.2). For each mixture; a T1 distribution is

fit to the measured signal decay with equation 6.1 using 1D Tikhonov regularisation

(described in section 2.3.1). Figure 6.2(a) shows the model fits to experimental signal data

88

and Figure 6.2(b) shows the resultant probability distributions for T1.

Figure 6.2 T1 measurements of oil/water mixtures. (a) the experimental signal decay as a function

of polarisation-excitation delay fit with the appropriate decay model (equation 6.1) using Tikhonov

regularisation, and (b) the T1 probability distributions for the oil water mixtures returned from

regularisation.

Figure 6.2(b) demonstrates that water exhibits a mono-exponential decay for T1 of

3.1 s. In comparison the canola oil exhibits bi-exponential T1 behaviour with the first peak

representing 64% of the sample with a log mean T1 of 81 ms and the second peak representing

0

20

40

60

80

0 1 2 3 4 5 6 7 8

NM

R S

ign

al [µ

V]

Polarisation - excitation delay [s]

Oil Fraction [%]0

102030405060708090100

Expt data

Model fit

(a)

0

1

2

3

4

5

0.01 0.1 1 10

P(T

1)

T1 [s]

0%10%20%30%40%50%60%70%80%90%100%

Oil fraction

(b)

89

36% of the sample with a log mean T1 of 217 ms. The bi-exponential relaxation behaviour

has been previously observed for canola oil (Luthria, 2004). Note that the two peaks of the

oil distribution are only effectively resolved for the 100 % sample where sufficient SNR is

achieved and more appropriate timing parameters are utilised (e.g. for the 90 % oil mixture

with Nscans = 4, the effective SNR of the oil is 35.8, whilst for the 100 % oil mixture with

Nscans = 16, the SNR is 74.5). Flowing measurements will observe a low SNR (similar to that

of the mixtures) such that the two canola oil peaks will in all likelihood merge into a single

peak. The overall distribution log-mean T1 (for the 100 % canola oil sample in Figure 6.2(b))

of 115 ms is thus a more useful comparison to results with lower SNR. The canola oil T1

relaxation behaviour measured in the EFNMR system is validated in appendix B.2 with

comparison to relaxometry measurements using a Magritek 2 MHz rock core analyser.

The relaxation distributions of oil/water mixtures presented in Figure 6.2(b)

demonstrate that the individual components can be readily differentiated via relaxometry.

All mixtures display two distinct peaks; the first peak at a short T1 of ~ 100 ms (associated

with canola oil) and a second peak at a higher T1 of ~ 3 s (associated with water). In Figure

6.2(a) the considerable difference in the initial signal amplitude between canola oil and water

(for single-phase samples) can be attributed to the initial signal delay between polarisation

and excitation (60 ms). The shorter T1 of canola oil results in a significant signal loss of 55

% during the initial delay (relative to the minor 1.9 % signal loss for water).

The accuracy of the T1 measurements of stationary mixtures in terms of quantifying

oil composition is now considered. The oil and water phases are distinguished using a T1

cut-off value (T1,C; similar to T2 cut-offs used to differentiate bound fluid and free fluid in

NMR analysis of rock cores (e.g. Hürlimann and Heaton, 2015)). For this work, a cut-off of

T1,C = 600 ms is used (calculated as the log-mean of the T1 relaxation rate for oil (115 ms)

and the T1 relaxation rate for water (3.1 s)). The signal contribution of each phase is

calculated by integrating over the relevant region of the T1 probability distribution;

𝑆𝑜 = ∫ 𝑃(𝑇1) 𝑑𝑇1𝑇1,𝐶

𝑇1,𝑚𝑖𝑛 (6.2)

𝑆𝑤 = ∫ 𝑃(𝑇1) 𝑑𝑇1𝑇1,𝑚𝑎𝑥

𝑇1,𝐶 (6.3)

90

where So and Sw are the oil and water signal contribution to the model fit respectively whilst

T1,min and T1,max define the bounds of the discretised T1 range. The individual phase fractions

are calculated from the relevant signal contribution of each phase in a mixture (Kleinberg

and Vinegar, 1996);

𝑥𝑤 =𝐻𝐼𝑜𝑖𝑙

𝐻𝐼𝑜𝑖𝑙+ 𝑆𝑜𝑆𝑤

(6.4)

𝑥𝑜 = 1 − 𝑥𝑤 (6.5)

where xw is the water phase fraction (water-cut), xo is the oil phase fraction and HIoil is the

hydrogen index for canola oil. The value for HIoil (0.96) has been experimentally determined

by comparing the measured signal intensity of canola oil and water samples obtained from

CPMG measurements in a Magritek 2 MHz NMR rock core analyser. The hydrogen index

is dependent on the atomic density of hydrogen in canola oil relative to water and is not

expected to be frequency dependent. Therefore, the value determined at 2 MHz is assumed

to be valid in the 2.29 kHz EFNMR system.

The NMR measured oil and water phase fractions are determined for each of the 9

stationary oil/water mixtures from 10 – 90 % (i.e. excluding the pure oil and pure water

samples). Figure 6.3 compares the NMR measured phase fractions to the volumetric cylinder

measurements of phase fractions (i.e. the fluid volume measurements obtained using a

volumetric cylinder during sample preparation) for both oil and water.

91

Figure 6.3 Phase fraction comparison for oil and water. The NMR measured component phase

fractions are validated against volumetric cylinder measurements obtained during sample preparation.

Equality lines are included for reference.

Figure 6.3 demonstrates good agreement between NMR and volumetric cylinder

measurements of phase fractions. The root mean square error for the nine mixtures is 2.3%.

This demonstrates that NMR T1 measurements can be used for accurate in-situ phase

quantification for oil/water mixtures. T1 measurements will now be incorporated into the

flow metering measurement procedure in order to quantify phase fractions of flowing

mixtures.

6.2.4. Measuring T1 of flowing fluids

The multi-exponential relaxation behaviour observed for the canola oil is useful for

demonstrating the applicability of the system to measuring complex multi-modal relaxation

behaviour anticipated for crude oils (Fridjonsson et al., 2014a). However the short relaxation

behaviour for oil introduces an additional difficulty in terms of obtaining measurements with

reasonable SNR. The signal attenuation during the intermediate decay (SPD) will be

significant for oil due to its low T1 (relative to water), particularly at low velocities (<1.0

m/s). In order to demonstrate the considerable signal decay, measurements of the SNR

(calculated as initial FID signal relative to average measured noise) obtained with canola oil

(alone) flowing through the system at velocities of 0.17 – 1.83 m/s are presented in Figure

6.4. FID measurements are obtained using 32 scan averages (Nscans = 32) at the shortest

separation distance used of 45 cm.

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

NM

R m

ea

su

red

fra

cti

on

Cylinder measured oil fraction

Oil

Water

92

Figure 6.4 SNR for FID measurements of canola oil flowing through the NMR flow meter with

signal pre-polarisation achieved using the Halbach array. The oil is travelling at velocities of at

velocities of 0.17 – 1.83 m/s and the polarisation-detection separation distance is 45 cm.

Figure 6.4 shows that at low canola oil velocities (<1.0 m/s) the SNR is poor (<5).

The low signal measured from the oil is a result of the significant intermediate signal decay

between polarisation and detection (SPD, as in Equation 4.3). Obtaining measurements with

such low SNR values was found to produce unreasonable solutions during signal processing

due to data inversion instability. Therefore, an alternative methodology must be considered

in order to obtain reasonable signal from the canola oil phase.

The electromagnetic pre-polarising coil (EPPC) which is associated with the EFNMR

detection coil (and used for stationary fluid measurements) was previously considered

unsuitable for flowing measurements (Fridjonsson et al., 2014b). The fluid flush-out effect

restricts the residence time in the coil such that the EPPC does not achieve sufficient

polarisation of flowing water. However the application of the EPPC can be considered useful

for fluids at low velocity and low T1. FID measurements of canola oil are obtained using

only the EPPC (i.e. without the upstream pre-polarising Halbach) with a pre-polarising time

of 600 ms. Figure 6.5 shows the measured SNR determined from FID measurements of

canola oil flowing at velocities of 0.17 – 1.83 m/s.

0

5

10

15

20

0 0.5 1 1.5 2

Me

as

ure

d S

NR

Velocity [m/s]

93

Figure 6.5 SNR for FID measurements of canola oil flowing through the NMR flow meter with

signal pre-polarisation achieved using the EPPC. The oil is travelling at velocities of 0.17 – 1.83 m/s

and the EPPC pre-polarising time is 600 ms.

Figure 6.5 demonstrates that the SNR is sufficient (>5) for low velocities (<2.0 m/s)

where the fluid outflow effect is reduced. At higher velocities, the outflow effect begins to

constrain the residence time of fluid in the pre-polarising region, therefore the measurable

signal is poorer (relative to low velocities).

By comparing Figures 6.4 and 6.5, it can be observed that the two polarising

mechanisms (i.e. the upstream Halbach array and the EPPC) are effective at different oil

velocity ranges. To further demonstrate this, the model for NMR signal polarisation of a

flowing fluid (which is fully defined below in section 6.2.5) has been used to calculate the

initial NMR FID signal (i.e. the first point of acquisition after the excitation-acquisition

delay) for the two separate polarisation conditions. The model is applied across a velocity-

T1 space of 0 – 3 m/s (for velocity) and 10 ms to 10 s (for T1). Figure 6.6 displays the model

output in terms of a 2D SNR map across the velocity-T1 space. Figure 6.6(a) shows the result

when using the Halbach array for pre-polarisation (at a minimum separation distance of 45

cm), whilst Figure 6.6(b) shows the result when applying the EPPC for pre-polarisation (with

a polarisation time of 600 ms). Figure 6.6(c) is the combined polarisation (i.e. the effective

sum of the two contributions). The model incorporates a noise value based on FID

measurements with 32 scan averages (Nscans = 32). Contour lines (in pink) for an SNR of 5

are included to indicate the appropriate regions where reasonable signal interpretation is

anticipated.

0

5

10

15

20

0 0.5 1 1.5 2

Me

as

ure

d S

NR

Velocity [m/s]

94

Figure 6.6 Model SNR of fluid phases in velocity-T1 space with application of two separate

polarising techniques in the EFNMR flow metering system. (a) The model SNR when applying the

Halbach magnet as the pre-polarising mechanism (with a separation distance of 45 cm), and (b) The

model SNR when applying the electromagnetic pre-polarising coil (with a polarisation time of 600

ms). (c) Combined polarisation incorporating the effective sum of the two contributions; however,

this is clearly dominated by the Halbach contribution. The pink lines are contours for SNR = 5;

highlighting the regions where reasonable interpretation of the measured signals can be anticipated.

From Figure 6.6 it can be observed that in general the Halbach permanent magnet

provides a much stronger signal across a broad range of velocities compared to the EPPC.

However the EPPC is successfully able to fill the void for low velocity (< 1.0 m/s) and low

T1 (50 – 600 ms) fluids (e.g. oil) where the Halbach polarisation has a poor SNR due to

intermediate signal decay between polarisation and detection. Therefore by combining the

polarising methods in a dual polarisation mechanism, the flow metering system can more

effectively measure signals across a range of velocities (0.1 – 3 m/s) and fluid T1 values (50

ms – 10 s). Considering that it is impractical to remove the Halbach array from the pipeline

during flow measurements, the combined measurements always incorporate Halbach array

pre-polarisation, with the option of additional re-polarisation using the EPPC once the fluid

reaches the EFNMR system.

Measurement of the fluid T1 under flow requires an independent variable to observe

signal contrast according to T1. For measurements obtained using the Halbach array alone;

the obvious independent variable is the separation distance which can easily be adjusted via

movement of the mobile Halbach magnet. Signal contrast with the EPPC can be observed

95

by varying the pre-polarisation time (tpolz). Thus variable separation distances (45 – 150 cm)

will be used to measure signal contrast for fluids with higher T1 (and/or at high velocities)

whilst the variable pre-polarisation time (10 – 600 ms) will be used to measure signal contrast

for low T1 fluids with low velocity. The selection of appropriate sequence parameters will

be discussed in more detail in section 6.3.1.

6.2.5. NMR flow model development for signal polarisation

The model of the NMR signal of a flowing fluid is now extended; focussing on the

incorporation of the secondary polarisation mechanism. The dual polarisation mechanism

involves the application of the EPPC in some of the FID measurements to provide additional

re-polarisation, whilst the permanent Halbach array will be applied for all experiments as it

is fixed around the pipeline. For experiments where the EPPC is not applied (i.e. the Halbach

magnet alone is used for pre-polarisation), the effective signal polarisation due to the Halbach

just prior to excitation (SPH), including the intermediate signal decay term, is:

𝑆𝑃𝐻(𝐿𝑃𝐷 , 𝑣, 𝑇1) = 𝑆0𝐻 (1 − exp (−𝐿𝑃𝐻

𝑣 𝑇1)) exp (−

𝐿𝑃𝐷

𝑣𝑇1) (6.6)

where S0H is the overall signal magnetisation after an infinite time in the Halbach field and

LPH is the length of the Halbach magnet. Therefore the fraction of fluid which is not polarised

(xNP) upon reaching the EFNMR detection coil is:

𝑥𝑁𝑃 = 1 −𝑆𝑃𝐻

𝑆0𝐻 (6.7)

This represents fluid which was either not polarised at the Halbach array or has decayed to

its original energy state during the residence time between polarisation and detection. The

effective signal polarisation of a stationary fluid (SPC) due to the EPPC can be described by

the T1 signal development (Pendlebury et al., 1979):

𝑆𝑃𝐶(𝑡𝑝𝑜𝑙𝑧, 𝑇1) = 𝑆0𝐶 (1 − exp (−𝑡𝑝𝑜𝑙𝑧

𝑇1)) exp (−

𝑡𝑃𝐸

𝑇1) (6.8)

where S0C is overall signal magnetisation after an infinite time in the EPPC field, tpolz is the

polarisation time and tPE is the polarisation-excitation delay (60 ms). For measurements

conducted on flowing fluids; the effective polarisation time is limited by the fluid residence

time in the polarising coil (Krüger et al., 1996, Krüger et al., 1984). A fluid element

96

travelling with velocity v will leave the EPPC region (with an effective length LPC of 27 cm)

after a residence time τPC = LPC/v, thus equation 6.8 is modified for flowing fluids:

𝑆𝑃𝐶(𝑡𝑝𝑜𝑙𝑧, 𝑇1) = 𝑆0𝐶 (1 − exp (−𝜏𝑃𝐶

𝑇1)) exp (−

𝑡𝑃𝐸

𝑇1)

where 𝜏𝑃𝐶 = min (𝑡𝑝𝑜𝑙𝑧,𝐿𝑃𝐶

𝑣− 𝑡𝑃𝐸) (6.9)

Note that the polarisation-excitation delay term is included in the minimisation expression to

account for fluid which would leave the coil during the delay time. The incorporation of the

minimisation term effectively restricts the range of useful polarisation times according to the

fluid velocity; larger pre-polarisation times (tpolz > 600 ms) are ineffective as the fluid will

flush through the coil before sufficient polarisation can be achieved. When combining the

dual effects of Halbach polarisation and the EPPC, only fluid which is not polarised upon

reaching the EFNMR (quantified by equation 6.7) can be re-polarised by the EPPC.

Therefore, the combined signal polarisation (SP) is modelled by:

𝑆𝑃 = 𝑆𝑃𝐻 + ൬1 −𝑆𝑃𝐻

𝑆0,𝐻൰ 𝑆𝑃𝐶 (6.10)

Note that if the pre-polarising coil is not applied (i.e. τPC = tpolz = 0) then SP = SPH, meaning

that the overall signal polarisation is just the signal polarisation due to the Halbach. The

overall model for the NMR signal of a flowing fluid (previously outlined in equation 4.5) can

now be considered as:

𝑆(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒 , 𝑣, 𝑇1) = 𝑆𝑃 (1 −𝑡𝑒𝑣


𝑡𝑒

𝑇2+ (𝑅𝐼𝑡𝑒)2)) for 𝑡𝑒 ≤

𝐿𝐷

𝑣, (6.11)

where SP is defined in equation 6.10.

The final FID component to be considered for flow measurements is the fluid T2

signal decay under flow. The effective T2 relaxation during flowing experiments will be a

function of the fluid composition considering the differing T2 relaxation rates for canola oil

and water. The measurement of fluid T2 distribution simultaneously with velocity and T1

under flow would be very difficult; therefore a T1/T2 ratio is introduced in order to link the

modelled T2 decay to the measured T1 decay. The T1/T2 ratio is defined as; RT = T1/T2 and is

specified about the oil/water T1 cut-off (T1,C = 600 ms, as discussed in section); with oil (T1

< 600 ms) having RT = 1.35 and water (T1 ≥ 600 ms) using RT = 1.63 (determined from

97

stationary fluid relaxation measurements). The T1/T2 ratio (RT) is introduced into the model

for NMR signal of a flowing fluid:

𝑆(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒, 𝑣, 𝑇1) = 𝑆𝑃 (1 −𝑡𝑒𝑣


𝑡𝑒∗𝑅𝑇


𝐿𝐷

𝑣 (6.12)

This effectively removes T2 from the model equation, leaving velocity (v) and spin-lattice

relaxation (T1) as the only dependent variables.

6.2.6. Velocity–T1 distribution determination via 2D inversion

The objective of the flow meter is to measure the phase flowrates of water and oil;

this will be achieved by measurement of the velocity distribution as well as phase fraction

determination via T1 differentiation. Therefore the velocity and T1 distributions must be

measured simultaneously as a joint 2D velocity-T1 distribution. This requires careful

consideration in the application of 2D inversion techniques.

The model for NMR signal of a flowing fluid (equation 6.12) now effectively

describes the relationship between the experimental parameters (i.e. LPD, tpolz and te) and the

measured parameters (i.e. v and T1) and is used as the model kernel function for 2D inversion.

The kernel function can be considered in terms of the “direct” and “indirect” dimensions; the

direct measurement is obtained from the single-shot FID signal which is detected (SD), whilst

the indirect measurement corresponds to variation in the pre-polarising conditions (SP). The

model kernel function is simplified as:

𝐊(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧 , 𝑡𝑒 , 𝑣, 𝑇1) = 𝑆𝑃𝑆𝐷

where 𝑆𝐷 = (1 −𝑡𝑒𝑣


𝑡𝑒∗𝑅𝑇


𝐿𝐷

𝑣 (6.13)

where SP has been previously described in equation 6.10. The kernel function is non-

separable as the measured parameters (v and T1) are present in both the direct and indirect

dimensions. Variable substitution is used in 2D regularisation inversions in order to allow

kernel separability; however this results in data truncation and back-extrapolation to fill

missing data which can cause the creation of artificial components in the resultant 2D

distribution (Leu et al., 2005, Mitchell and Fordham, 2011). Therefore a full kernel matrix

98

(i.e. non-separable matrix) is constructed to avoid such undesirable consequences during data

analysis (Mitchell et al., 2010a). A pseudo-1D inversion is applied (using appropriate matrix

manipulation) with the full kernel matrix in order to determine the 2D velocity-T1 probability

distribution. The relevant first-order Fredholm integral is now written as:

𝑆(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒) = ∫ ∫ 𝐾(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒 , 𝑣, 𝑇1)∞

0𝑃(𝑣, 𝑇1)

∞

0 𝑑𝑣 𝑑𝑇1 (6.14)

where S(LPD, tpolz, te) are the experimentally acquired NMR signals, K(LPD, tpolz, te, v, T1) is

the model kernel matrix described in equation 6.13 and P(v, T1) is the joint 2D probability

distribution to be determined. The NMR signals consist of FID measurements (with nF points

recorded for each FID) acquired at variable pre-polarising conditions. The FID

measurements are compressed using window-averaging (Mitchell et al., 2014) in order to

obtain signal matrices of reasonable size for inversion processing; the FID signals are divided

into nw equally sized windows or bins (FID signals are generally dominated by a linear

outflow effect; therefore using equally spaced windows is appropriate (Istratov and Vyvenko,

1999)). The data points within each bin are averaged to provide a compressed FID signal of

size nw (in this work nw = 32). If FID measurements are acquired at nL different separation

distances (for variable Halbach position measurements) and nT different polarisation times

(for additional pre-polarisation at the electromagnetic coil) then there are npp = nL + nT pre-

polarisation conditions. Thus the effective NMR measured signals will be of size nw×npp

(i.e. a 2D data matrix of npp compressed FIDs each of length nw). The signal matrix (S) is

unwrapped into a 1D signal column vector (s). If the solution matrix (P) for the probability

distribution is to be of size mv×mT1 then the relevant model kernel matrix (K) will be of size

n×m (where n = nwnpp and m = mvmT1). The row elements of the model kernel matrix describe

changes in signal with respect to the experimental parameters (i.e. LPD, tpolz and te) and

correspond to the signal vector components. The column elements of the model kernel matrix

describe changes in the measured signal with respect to the measured parameters (i.e. v and

T1) and correspond to the solution vector components. The measured signals (s) have now

been appropriately manipulated such that the signal vector is of length n = nwnp and the model

kernel (K) has been manipulated to provide a matrix of size n×m in order to solve the solution

vector (p) of length m with 1D Tikhonov regularisation (using equation 2.18). The vector

and matrix are also of appropriate size to ensure reasonable computational efficiency

(Mitchell et al., 2012). Note that the smoothing operation matrix (Q) must be carefully

constructed to calculate the finite second difference across 2D solution space. The resultant

99

solution is returned as a vector (p) is of length m and is reshaped into the final 2D distribution

(P of size mv×mT1). Useful graphical representations of the described matrix manipulation

procedures are presented by Mitchell et al. (2012). The 1D distributions (P(v) and P(T1))

may be determined by projecting the 2D distribution onto the relevant 1D axis (velocity axis

for P(v) and T1 axis for P(T1)).

6.2.7. Component flowrate calculations

The joint 2D velocity-T1 probability distribution can now be used to calculate

individual phase flowrates (of canola oil and water). The oil and water phases are

distinguished with a T1 cut-off value (T1,C = 600 ms, as described in section 6.2.3). The signal

contribution of each phase is calculated by integrating over the relevant region of the joint

2D probability distribution:

𝑆𝑜 = ∫ ∫ 𝑃(𝑣, 𝑇1)𝑣𝑚𝑎𝑥

0𝑑𝑣 𝑑𝑇1

𝑇1,𝐶

𝑇1,𝑚𝑖𝑛 (6.15)

𝑆𝑤 = ∫ ∫ 𝑃(𝑣, 𝑇1)𝑣𝑚𝑎𝑥

0𝑑𝑣 𝑑𝑇1

𝑇1,𝑚𝑎𝑥

𝑇1,𝐶 (6.16)

where So and Sw are the oil and water signal contribution to the model fit respectively, T1,min

and T1,max define the bounds of the discretised T1 range and vmax is the maximum value in the

discretised velocity range. The phase fractions (xw and xo) are calculated from the relevant

signal contribution of each phase according to equations 6.4 and 6.5. The individual velocity

distributions of each phase (P(vo) and P(vw) for oil and water respectively) are determined by

integrating the relevant regions of the 2D distribution:

𝑃(𝑣𝑜) = ∫ 𝑃(𝑣, 𝑇1) 𝑑𝑇1𝑇1,𝐶

𝑇1,𝑚𝑖𝑛 (6.17)

𝑃(𝑣𝑤) = ∫ 𝑃(𝑣, 𝑇1) 𝑑𝑇1𝑇1,𝑚𝑎𝑥

𝑇1,𝐶 (6.18)

The mean velocity for each phase (vM,o and vM,w for oil and water, respectively) is then be

determined by calculating the expected value for each phase velocity distribution:

𝑣𝑀,𝑖 = ∫ 𝑣𝑖𝑃(𝑣𝑖)𝑣𝑚𝑎𝑥

0𝑑𝑣𝑖 (i = oil or water) (6.19)

Finally, individual volumetric flowrates for each phase (qo and qw for oil and water

respectively) are calculated:

𝑞𝑖 = 𝑥𝑖𝑣𝑀,𝑖𝐴 (i = oil or water) (6.20)

100

where A is the internal cross-sectional area of the pipe. The phase flowrates which are

measured from the NMR signal analysis methodology are verified against independent

flowrate measurements from in-line rotameters of single-phase flow which are obtained prior

to mixing in the flow loop.

6.3 Experimental procedure

6.3.1. Choice of experimental parameters

Experimental NMR measurements require the selection of appropriate sequence

parameters for the independent variables relevant to signal polarisation (i.e. pre-polarisation

time and separation distance). The EPPC uses variable polarisation time in order to observe

signal contrast in flowing fluids; twenty FID measurements are conducted with

logarithmically spaced pre-polarising times ranging from (10 to 600) ms (at a fixed separation

distance of 70 cm). Polarisation times longer than 600 ms are not useful with current

hardware as the effective polarisation time is limited by the residence time of fluid within the

coil. A further twenty FID measurements are conducted at variable separation distances

logarithmically spaced between (45 and 150) cm (with zero pre-polarisation). Therefore, 40

FID measurements are conducted for each flowrate (20 with variable pre-polarising time and

20 with variable separation distance). Each FID is signal averaged with 32 scans (Nscans).

The FID acquisition time (ta) is varied from 0.205 – 0.819 s and the repetition time is varied

from 0.6 – 1.8 s depending on the flow velocity and pre-polarising time. The relevant

sequence parameters for the 40 FIDs are summarised in Figure 6.7.

101

Figure 6.7 Summarisation of the polarising conditions for the 40 FID measurements. For the first

20 measurements, both the Halbach and the EPPC are used for polarisation, with the Halbach position

held constant (70 cm separation distance) whilst the polarisation time is logarithmically varied from

10 – 600 ms. For the second 20 FID measurements, only the Halbach is used for polarisation with

separation distances logarithmically ranging from 45 – 150 cm.

The overall measurement procedure, which has not been ‘total acquisition time’

optimised, takes ~21 minutes to capture the required FID data. The above set of FID

conditions will be referred to as the “NMR flow measurement sequence” from here onwards.

6.3.2. Experimental measurement workflow

Figure 6.8 provides a flow chart outlining the key steps in the procedure applied to

measure the fluid flowrates using the NMR flow measurement sequence. The NMR flow

measurement sequence is applied with the EFNMR system using the associated Prospa

software (Magritek, New Zealand), capturing 20 FID measurements at varying separation

distance and 20 FID measurements at varying pre-polarisation time (as discussed in section

6.3.1). Once the data has been recorded, it is imported into Matlab R2017b for signal

processing and analysis. A series of pre-processing steps are applied to the imported FID

data such that they are suitable for inversion. A Gaussian noise filter is implemented on the

measured FID spectrums primarily to remove the influence of 50 Hz mains noise. Each FID

signal is then truncated at the point where the SNR reaches 1 (i.e. data with SNR < 1 is

removed); such that the baseline noise does not influence the signal and introduce artefacts

in the resulting 2D velocity-T1 distribution. The truncated signals are then window averaged

0

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Constant separation distance (70 cm)

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102

such that the data is of appropriate size for computationally efficient inversion (Istratov and

Vyvenko, 1999).

The processed FID data is then fit with the appropriate 2D velocity-T1 distribution

using the NMR flow model (equation 6.13) via Tikhonov regularisation inversion (equation

2.18). The 2D regions of the velocity-T1 distribution are appropriately integrated in order to

determine the relevant signal contribution of each phase (according to equations 6.15 and

6.16). The signal contributions are corrected for the oil hydrogen index in order to quantify

volumetric fluid fractions (according to equations 6.4 and 6.5). The expected value of each

of the individual phase velocity distributions are calculated to determine the mean velocity

(according to equation 6.19). Finally, the individual volumetric flowrates for water and oil

are calculated from the volumetric phase fractions and phase mean velocities (using equation

6.20).

103

Figure 6.8 Flow chart outlining the NMR flow measurement procedure.

Flowing measurements

Measure 20 FIDs with varying tpolz

Measure 20 FIDs with varying LPD

Record data

Import data into Matlab

Signal pre-processing

Experimental data fit with model using 2D Tikhonov inversion

2D velocity-T1

distribution measured

Integrate relevant regions to determine oil and water NMR signal

contribution

Correct for oil hydrogen index

Calculate volumetric flowrate of each phase

Validate against inline rotameters

Calculate mean velocity of each

phase

1. Filtering

2. Truncation

3. Window averaging

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Direction of increasing LPD

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Direction of increasing tpolz

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Expt. data

Model fit

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Model fit

104


6.4.1. Single-phase measurements – Water

The flow measurement procedure is first demonstrated for single-phase water flows.

An example result is shown for water flowing at 6.0 m3/h (corresponding to a velocity of

1.11 m/s). The pipe flow Reynolds number (Re = ρvMD/μ) is calculated as 54,600 for this

flowrate, indicating turbulent flow. The flow loop system (illustrated in Figure 6.1(a)) is

configured for single-phase water use (via appropriate valves) and then water is flowed

through the system with the rotameter set at 6.0 m3/h. The NMR flow measurement sequence

is applied to capture the 40 FID measurements (as outlined in section 6.3.1). Figure 6.9(a)

shows the 20 FID measurements with variable separation distance whilst Figure 6.9(b) shows

the 20 FID measurements with variable pre-polarisation time. For each FID measurement,

the effective polarisation is determined by back-extrapolating the measured FID signal to

zero time since excitation (i.e. te = 0). Figure 6.9(c) shows the effective polarisation as a

function of separation distance whilst Figure 6.9(d) shows the effective polarisation as a

function of pre-polarisation time. For each of the measured signal plots (i.e. Figure 6.9(a-d))

the relevant model fit determined by fitting equation 6.13 to the experimental data using

Tikhonov regularisation is also shown. Figure 6.9(e) displays the resultant 2D velocity-T1

probability distribution obtained from the inversion procedure as well as the projected 1D

distributions (P(v) and P(T1)).

105

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LPD

[cm]45485154586266707580859096

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Model fit


(a)

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Model fit


(b)

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Model fit

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Experimental data

Model fit

(d)

106

Figure 6.9 An example 2D velocity-T1 measurement for single-phase water. The water is flowing

at 6.0 m3/h (corresponding to a water velocity of 1.11 m/s). Measured experimental signals; (a) FID

measurements at variable polarisation-detection separation distance, (b) FID measurements at

variable electromagnetic coil pre-polarisation time, (c) effective polarisation as a function of

polarisation-detection separation distance and (d) effective polarisation as a function of pre-

polarisation time. For each of the measured signal plots (a-d) the model fit is also displayed. (e) The

resultant 2D velocity-T1 probability distribution as well as the 1D distributions (P(v) and P(T1)). The

dashed line indicates the oil-water T1 cut-off (600 ms).

Figure 6.9(a) and (c) illustrate the signal decay as a function of the polarisation-

detection separation distance; the effective polarisation exhibits an exponential decay as a

function of LPD according to exp(-LPD/(vT1)) (as in equation 6.6). Figure 6.9(b) and (d)

illustrate measured signal decay as a function of the EPPC pre-polarisation time; the effective

polarisation increases exponentially according to (1- exp(-τPC/vT1)). The limiting effect of

the fluid residence time in the coil (τPC = LPC/v – tPE = 0.27/1.11 – 0.06 = 183 ms) is

observable during pre-polarising time experiments; at tpolz > 183 ms the fluid residence time

is less than the pre-polarising time, thus the effective polarisation remains constant. Note

that the initial effective polarisation (e.g. tpolz = 10 ms) in the pre-polarising experiments (in

Figure 6.9(d)) is offset to 26.6 μV corresponding to the initial polarisation due to the Halbach

(at a separation distance of LPD = 70 cm). This will not exactly match the effective

polarisation at LPD = 70 cm in Figure 6.9(c) due to non-adiabatic signal attenuation during

application of the polarisation pulse (see Appendix A.3 for further detail). The 2D velocity-

Oil-water cut-off

(e)

107

T1 distribution displays a single 2D peak exhibiting measured properties anticipated for the

experiment; the mean velocity from the 2D distribution is 1.09 m/s whilst the log-mean T1 is

2.68 s. This demonstrates excellent agreement between the reference flowrate measurement

(6.0 m3/h) and the NMR water flowrate measurement (5.95 m3/h).

To further demonstrate the accuracy of the NMR flow measurement sequence, the

measurement procedure is conducted for ten different water flowrates of 1.0 – 10.0 m3/h

(corresponding to mean velocities of 0.18 – 1.83 m/s). The pipe flow Reynolds number range

for these flows is determined to be 9030 – 90300, therefore all ten flowrates are considered

to be turbulent. Figure 6.10(a) shows the effective polarisation as a function of separation

distance for each flowrate (the same as Figure 6.9(c)) whilst Figure 6.10(b) shows the

effective polarisation as a function of pre-polarisation time (the same as Figure 6.9(d)). For

each measurement, the acquired 2D velocity-T1 distribution has been separated into

individual 1D distributions (corresponding to the projected 1D distributions in Figure 6.9(e))

with the velocity distributions (P(v)) shown in Figure 6.10(c) and the T1 distributions (P(T1))

displayed in Figure 6.10(d).

108

Figure 6.10 Measured signal data and corresponding velocity and T1 distributions for single-phase

water measurements. Flow measurements are obtained at flowrates of 1.0 – 10.0 m3/h (corresponding

to mean velocities of 0.18 – 1.83 m/s). (a) Effective polarisation as a function of polarisation-

detection separation distance and (b) Effective polarisation as a function of pre-polarisation time. For

each of the measured signals in (a) and (b) the model fit is also displayed. (c) The 1D velocity

distributions and (d) 1D T1 distributions for each water flowrate obtained using the inversion

procedure.

Figure 6.10(a) demonstrates the effective polarisation as a function of polarisation-

detection separation distance; the exponential rate of decay is decreasing as velocity increases

as anticipated according to the relationship; exp(-LPD/(vT1)) (as in equation 6.6). Figure

6.10(b) shows the effective polarisation as a function of the pre-polarising time. The

effective polarisation becomes constant at earlier pre-polarising times as the velocity

increases (e.g. for 3.0 m3/h effective polarisation is constant at tpolz > 0.44 s whilst for 10.0

m3/h effective polarisation is constant at tpolz > 0.09 s). This is a consequence of the fluid

residence time in the coil reducing as velocity increases. In general, the larger fluid residence

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Model fit

(b)

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109

time observed for lower velocities results in higher effective polarisation (relative to flows at

higher velocities). This is not always the case (e.g. a flowrates of 1.0 and 2.0 m3/h) due to

complex flush-out effects observed due to the non-adiabatic signal diminishment (see

Appendix A.3 for further details).

The velocity distributions shown in Figure 6.10(c) each display a single peak. The

distributions exhibit a turbulent velocity distribution shape very similar to those measured

using the 1D FID analysis measurement discussed in section 4.3.2. The accuracy of the

means of the velocity distributions is validated via the flowrate comparison in Figure 6.11.

The T1 distributions in Figure 6.10(d) each display a mono-exponential peak at a similar

position. The average log-mean T1 across the ten distributions is 2.55 s. The T1 distributions

tend to broaden as the velocity increases. The rate of exponential decay with respect to the

separation distance decreases (as shown in Figure 6.10(a)) as the velocity increases which

results in the relative fraction of the observable effective polarisation decay being reduced.

The sensitivity of Tikhonov regularisation inversion to accurately fit the appropriate

dependent parameter distributions (i.e. v and T1) is influenced by the range and number of

each independent parameter (i.e. te, LPD and tpolz) (Istratov and Vyvenko, 1999, Mitchell et

al., 2014). For example; at a water flowrate of 1.0 m3/h (mean velocity of 0.18 m/s), the

effective polarisation decays from 61.6 μV at LPD = 45 cm to 7.9 μV at LPD = 150 cm

(corresponding to an 87 % signal decay) thus the inversion is sensitive to longer T1

components and a narrow T1 distribution is observed. However, at a water flowrate of 10.0

m3/h (mean velocity of 0.183 m/s), the effective polarisation decays from 26.9 μV at LPD =

45 cm to 19.6 μV at LPD = 150 cm (corresponding to a 27 % signal decay). This results in

the inversion being relatively less sensitive to the longer T1 components (compared to flows

at lower velocity) and a broad T1 distribution is observed. In order to be more sensitive to

longer T1 components at high velocities, the separation distance would need to be

substantially increased; however this results in an impractically large flowmeter. In any case,

the necessity of accurately measuring T1 is not strictly important if the relevant components

(e.g. oil and water) are distinguishable for two-phase flow measurements.

110

The accuracy of the NMR flow measurement procedure for single-phase water flows

can be validated against the rotameter flowrate measurements. The NMR measurement of

water flowrate is extracted from the 2D velocity-T1 distributions captured in Figure 6.10

using the component flowrate calculation procedure outlined in section 6.2.7. Figure 6.11(a)

shows a comparison of the NMR measured water flowrate (qw,nmr) to the rotameter measured

water flowrate (qw,rot). Figure 6.11(b) shows the deviations of the NMR measured flowrate

(i.e. qw,nmr - qw,rot).

Figure 6.11 Comparison of the NMR and rotameter measurements of water flowrate. (a) Direct

comparison of flowrates, and (b) Deviations of the NMR measured flowrate.

Figure 6.11 shows excellent agreement between the NMR measured flowrate and the

rotameter measured flowrate. The mean error (calculated using equation 3.6) is 0.011 m3/h

and the root mean square error (calculated using equation 3.7) is calculated as 0.068 m3/h for

the ten water flowrate measurements.

6.4.2. Single-phase measurements – Oil

Flowing measurements are now shown for single-phase canola oil flows. An example

result is demonstrated for canola oil flowing at 6.0 m3/h (corresponding to a velocity of 1.11

m/s). The pipe flow Reynolds number is determined as 820; therefore the flow is laminar.

The flow loop system is configured for single-phase oil use and then oil is flowed through

the system with the rotameter set at 6.0 m3/h. The NMR flow measurement sequence is

captured with the 40 FID measurements (as outlined in section 6.3.1). Figure 6.12(a) shows

the 20 FID measurements with variable separation distance whilst Figure 6.12(b) shows the

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20 FID measurements with variable pre-polarisation time. For each FID measurement, the

effective polarisation is determined by back-extrapolating the measured FID signal to zero

time since excitation (i.e. te = 0). Figure 6.12(c) shows the effective polarisation as a function

of separation distance whilst Figure 6.12(d) shows the effective polarisation as a function of

pre-polarisation time. For each of the measured signal plots (i.e. Figure 6.12(a-d)) the

relevant model fit determined by fitting equation 6.13 to the experimental data using

Tikhonov regularisation is also shown. Figure 6.12(e) displays the resultant 2D velocity-T1

probability distribution obtained from the inversion procedure as well as the 1D distributions

(P(v) and P(T1)).

0

2

4

6

8

10

0 0.02 0.04 0.06 0.08 0.1

NM

R S

ign

al

[µV

]


LPD

[cm]45485154586266707580859096

Expt. data

Model fit


(a)

0

2

4

6

8

10

0 0.02 0.04 0.06 0.08 0.1

NM

R S

ign

al

[µV

]


tpolz

[ms]1012151924293645567086107133165204253314390484600

Expt. data

Model fit


(b)

112

Figure 6.12 An example 2D velocity-T1 measurement for single-phase canola oil. The oil is flowing

at 6.0 m3/h (corresponding to an oil velocity of 1.11 m/s). Measured experimental signals; (a) FID

measurements at variable polarisation-detection separation distance, (b) FID measurements at

variable electromagnetic coil pre-polarisation time, (c) effective polarisation as a function of

polarisation-detection separation distance and (d) effective polarisation as a function of pre-

polarisation time. For each of the measured signal plots (a-d) the model is also displayed. (e) The

resultant 2D velocity-T1 probability distribution obtained from the inversion procedure as well as the

1D distributions (P(v) and P(T1)). The dashed line indicates the oil-water T1 cut-off (600 ms).

Note that not all variable separation distance trials are incorporated in inversion

analysis; FID signals with an initial signal below the minimum allowable SNR (SNR cut-off

of 1) are removed to essentially avoid fitting to noise. This can be observed in Figure 6.12(a)

0

2

4

6

8

10

12

14

16

40 80 120 160

NM

R S

ign

al [µ

V]


Experimental dataModel fit

(c)

0

2

4

6

8

10

12

14

16

0 200 400 600

NM

R S

ign

al [µ

V]


Experimental data

Model fit

(d)

(e)

Oil-water cut-off

113

and (c); only FIDs at a separation distances less than or equal to 96 cm are used in the

inversion. The FID measurements at variable separation distance in Figure 6.12(a) show that

the measurable signals are substantially lower relative to those from the water measurements

(shown in Figure 6.9(a)). For example; the maximum signal for the oil FIDs at varying

separation distance in Figure 6.12(a) is 3.5 μV, which is much less than the maximum signal

of 30.7 μV in Figure 6.9(a). This can be attributed to the considerable intermediate signal

decay when the fluid flows from the polarising Halbach array to the r.f. detection coil (as

discussed in section 6.2.4). This justifies the use of the EPPC for low T1 fluids; Figure 6.12(b)

demonstrates an improvement in the measurable signal (up to 7.0 µV for tpolz = 600 ms).

The rate of decay in the measured FIDs is faster for oil measurements relative to

water. The oil signal fully decays to the SNR cut-off after ~0.09 s at maximum polarisation

(for the FID at tpolz = 600 ms in Figure 6.12(b)). For the same FID measurement for water

with a velocity of 1.11 m/s (FID with tpolz = 600 ms in Figure 6.9(b)), the signal has decayed

to the SNR cut-off at ~0.16s. The difference in FID attenuation rates is a result of the

differing T2 decay constants for canola oil and water. The log-mean T2 for canola oil is 82

ms relative to measured water T2 of 1.96 s (see Appendix A.3). This illustrates how T2 decay

is much more influential on the FID for oil measurements relative to water. This will restrict

the ability of the inversion to accurately resolve the velocity distribution in flowing oil

measurements.

The measured 2D velocity-T1 distribution in Figure 6.12(e) displays a broad 2D peak

exhibiting measured properties anticipated for the experiment; the mean velocity from the

2D distribution is 1.11 m/s whilst the log-mean T1 is 0.88 s. The measured velocity

distribution is much broader than the corresponding distribution for water at the same

velocity (shown in Figure 6.9(e)). This can be attributed to the difference in the single-phase

flow regime. The water (Re = 54600 at 1.11 m/s) exhibits turbulent flow which will have a

flat radial velocity profile and therefore the velocity probability distribution will be

reasonably narrow close to the mean velocity. The much more viscous canola oil (Re = 820

at 1.11 m/s) exhibits laminar flow which is anticipated to have a Pouiselle radial velocity

profile. The corresponding velocity probability distribution for a Pouiselle radial profile is a

114

uniform probability density function with velocities ranging from 0 to 2vM. The theoretical

velocity distribution thus contains sharp (non-smooth) changes at the distribution boundaries

(i.e. 0 and 2vM). The Tikhonov penalty function (||Qp||2 in Equation 2.18) imposes

smoothness on the resulting distribution using the finite second derivative operator (Q).

Therefore the uniform velocity probability distribution for canola oil is very difficult to

capture experimentally as the non-smooth distribution will be penalised during inversion data

analysis. The laminar profile is reflected by the much broader velocity distribution (relative

to those of water) ranging from 0 to 2.5 m/s (~2vM). The measured T1 distribution does not

capture the bi-exponential behaviour of canola oil (as seen for the stationary oil measurement

in section 6.2.3). The two peaks are much more difficult to resolve for the flowing

experiments when considering the much lower SNR (~74 for the stationary measurement

compared to ~16 for flowing measurement at 6.0 m3/h) and the complex dual polarisation

model used to measure the T1 of flowing fluid.

The measurement procedure is conducted for ten different oil flowrates of 1.0 – 10.0

m3/h (corresponding to mean velocities of 0.18 – 1.83 m/s). Figure 6.13(a) shows the

effective polarisation as a function of separation distance for each flowrate, whilst Figure

6.13(b) shows the effective polarisation as a function of pre-polarisation time. For each

flowrate, the measured 2D velocity-T1 distribution has been separated into individual 1D

distributions with the velocity distributions (P(v)) shown in Figure 6.13(c) and the T1

distributions (P(T1)) displayed in Figure 6.13(d). Note that for flowrates of 1.0 and 2.0 m3/h,

none of the FID measurements at variable separation distance had an initial signal above the

SNR cut-off, therefore they are not used within the inversion and are not displayed in Figure

6.13(a).

115

Figure 6.13 Measured signal data and corresponding velocity and T1 distributions for single-phase

oil measurement. Flow measurements are obtained at flowrates of 1.0 – 10.0 m3/h (corresponding to

mean velocities of 0.18 – 1.83 m/s). (a) Effective polarisation as a function of polarisation-detection

separation distance and (b) Effective polarisation as a function of pre-polarisation time. For each of

the measured signals in (a) and (b) the model fit is also displayed. (c) The 1D velocity distributions

and (d) 1D T1 distributions for each oil flowrate obtained using the inversion procedure.

In Figure 6.13(a), the rate of exponential decay is much faster relative to the water

results in Figure 6.10(a) due to the much shorter T1 of canola oil relative to water. Only the

two highest flowrates (9.0 and 10.0 m3/h) have a measurable signal at the longer separation

distances (final measured point is 141 cm for measurements at 9.0 and 10.0 m3/h). In Figure

6.13(b); the influence of the FID measurements at varying pre-polarisation times is more

prominent for the oil measurements relative to water measurements. The FID measurements

observe a rapid polarisation according to the short T1 of oil (measured as ~81 ms under flow).

The velocity distributions in Figure 6.13(c) are relatively broad and typically range from ~ 0

0

2

4

6

8

10

12

14

16

40 80 120 160

NM

R S

ign

al

[µV

]


(a)

0

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8

10

12

14

16

0 200 400 600

NM

R S

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[µV

]


Flowrate[m3/h]

12345678910

Expt. data

Model fit

(b)

0

1

2

3

4

5

0 1 2 3 4 5

P(v

)

Velocity [m/s]

12345678910

Flowrate [m3/h]

(c)

0

1

2

3

4

5

0.01 0.1 1 10

P(T

1)

T1 [s]

12345678910

Flowrate [m3/h]

(d)

116

to twice the mean velocity indicating a laminar velocity profile (as discussed in relation to

the oil flow measurement example in Figure 6.12). Some of the velocity distributions display

two velocity peaks as a consequence of the data inversion; particularly at higher velocity (e.g.

at 7.0 and 9.0 m3/h). Furthermore, the T1 distributions each display a single peak with the

average log-mean T1 across the ten distributions being 81 ms. This is slightly shorter than

the log-mean T1 measured for stationary flow (115 ms – see section 6.2.3). The suggested

source of the discrepancy is inversion sensitivity and the model complexity. Using a complex

model in combination with the Tikhonov regularisation results in reduced inversion stability

and can lead to inaccurate measurement results (Mitchell et al., 2014). The incorporation of

complex calibration factors such as the T1/T2 calibration ratio (refer to section 6.2.5) and the

non-adiabatic signal loss (refer to Appendix A.3) can influence the position of the T1

distribution. The shorter oil T1 is much more sensitive to such parameters relative to the

longer water T1. The bi-exponential peak observed in the T1 distribution of stationary

measurements (see section 6.2.3) is not resolved for any of the flowing oil measurements;

this is attributed to the lower SNR and complex dual polarisation model as discussed in

relation to the oil flow measurement example at 6.0 m3/h in Figure 6.12.

The accuracy of the NMR flow measurement procedure for single-phase oil flows

can be validated against the rotameter flowrate measurements. The NMR measurement of

the oil flowrate is extracted from the 2D velocity-T1 distributions captured in Figure 6.13

using the component flowrate calculation procedure outlined in section 6.2.7. Figure 6.14(a)

shows a comparison of the NMR measured oil flowrate (qo,nmr) to the rotameter measured oil

flowrate (qo,rot). Figure 6.11(b) shows the deviations of the NMR measured flowrate (i.e.

qo,nmr – qo,rot).

117

Figure 6.14 Comparison of the NMR and rotameter measurements of oil flowrate. (a) Direct

comparison of the NMR measured oil flowrate to the rotameter measured oil flowrate. (b) Deviations

of the NMR measured flowrate relative to the rotameter measured oil flowrate.

Figure 6.14 shows excellent agreement between the NMR measured oil flowrate and

the rotameter measured oil flowrate. The mean error is -0.013 m3/h and the root mean square

error is calculated as 0.094 m3/h for the ten oil flowrate measurements. The accuracy

demonstrated for both single-phase oil and water flows gives confidence in applying the

measurement procedure to two-phase oil water flows as will be demonstrated in Chapter 7.

6.5 Conclusions

In this chapter the procedure for simultaneous measurement of the individual phase

flowrates in two-phase oil/water flows has been developed. The EFNMR flow meter is

extended to incorporate a dual polarisation scheme utilising the upstream Halbach array as

well as an electromagnetic pre-polarising coil which is integrated with the EFNMR detection

coil. The oil and water fractions are distinguished using the fluid spin-lattice relaxation time

(T1) which is captured using the polarised signal contrast. T1 relaxometry is demonstrated to

be an appropriate distinguishing mechanism; example measurements performed on

stationary oil/water mixtures accurately quantify the component phase fractions. The dual

polarisation system allows improved measurement sensitivity (relative to the initial EFNMR

system) with an effective velocity range of (0.10 to 3.0) m/s and effective T1 range of 50 ms

to 5.0 s. The corresponding NMR flow model has been developed simultaneously with the

apparatus in order to describe the NMR signal of fluid flowing through the upgraded flow

measurement system. An appropriate experimental measurement pulse sequence has been

0

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-0.1

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118

outlined which involves capturing FID signals at varying pre-polarising conditions. The

multi-FID signals are fit with a joint 2D velocity-T1 distribution using the developed NMR

flow model via a 2D Tikhonov regularisation algorithm. The performance of the NMR flow

measurement was examined for both single-phase water and oil flows and demonstrates

excellent agreement with in-line rotameter measurements. Furthermore; the velocity

distributions capture the appropriate single-phase flow classification; with laminar flows

(exhibited by oil) being distinguished from turbulent flow profiles (displayed by water) by

broader, sometimes bimodal, apparent velocity distributions.

119

Chapter 7. Quantitative characterisation of two-phase

oil/water flows

7.1 Introduction

In this chapter, the flow measurement methodology developed in Chapter 6 is applied

to simultaneously quantify phase flowrates for two-phase oil/water flows. Flow

measurements are performed across five different oil/water flow regimes. The 2D velocity-

T1 distributions are analysed in terms of two-phase flow characteristics such as the oil/water

velocity slip. The performance of the measurement system is analysed in each flow regime

via comparison against the individual phase flowrates.

7.2 Experimental methodology

7.2.1. Flow regimes

The measurement and analysis of two-phase oil/water flows requires consideration of

the range of possible liquid-liquid flow regimes. Details regarding the classification and

description of such flow regimes were discussed in section 3.1.3. For the experimental

oil/water flow loop used in this work (outlined in section 6.2.2), the visually observed flow

patterns have been classified into five different flow regime categories which are similar to

the regimes observed by Trallero et al. (1997). The flow regimes include; stratified flow

with mixing at the interface (St w/ mix), a dispersion of oil-in-water over a free water layer

(Do/w & w), a dual dispersion of water droplets in oil over oil droplets in water (Do/w &

Dw/o), a full oil-in-water emulsion (Eo/w) and a full water-in-oil emulsion (Ew/o). The oil

and water flowrates are not measurable (due to the rotameter metering range) at the low

flowrates required to achieve stratified flow (without mixing) thus this flow regime was not

incorporated in the experimental measurements performed. A summary of the five relevant

oil/water flow regimes (originally shown in Table 3.2) is presented here (in Table 7.1) for

reference with respect to the oil/water experiments conducted in this Chapter.

120

Table 7.1 Summary of the five relevant oil-water flow regimes.

Name Abbreviation Description Illustration

Stratified

flow with

mixing

St w/ mix. Fluids exist as segregated

layers with the presence of

small capillary waves at the

interface. Small quantities of

droplets of each fluid are

dispersed into the alternate

phase.

Dispersion

of oil-in-

water and

water

Do/w & w A dispersion layer exists at the

top of the pipe with oil

droplets entrained within a

continuous water phase. The

bottom layer consists of free

water alone.

Dispersion

of water-in-

oil and

dispersion

of oil-in-

water

Dw/o &

Do/w

A dual dispersion with; water

droplets dispersed into a

continuous oil layer (top)

above oil droplets dispersed

into a continuous water layer

(bottom).

Oil-in-water

emulsion

Eo/w A full emulsion of oil droplets

dispersed in a continuous

water layer.

Water-in-oil

emulsion

Ew/o A full emulsion of water

droplets dispersed in a

continuous oil layer.

An experimental matrix of oil and water superficial velocities to be used for

verification of the NMR flow measurement procedure is presented in Figure 7.1. The water

superficial velocities range from 0.18 – 2.03 m/s (corresponding to flowrates of 1.00 – 11.1

m3/h) and the oil superficial velocities range from 0.17 – 1.46 m/s (corresponding to flowrates

of 1.00 – 8.00 m3/h). The specified superficial velocities are chosen such the measurements

will cover a range of two-phase flow regimes. The visually observed flow regime for each

measurement point is indicated by the marker type and colour. A comparison to the flow

regime boundaries observed by Trallero et al. (1997) is provided (indicated with black lines);

121

this data is chosen for comparison due to the relatively similar experimental conditions;

experiments were conducted with tap water and mineral oil with a pipe diameter of 50.1 mm,

density ratio (ρo/ρw) of 0.85 and a viscosity ratio (μo/μw) of 29.6 (Trallero et al., 1997). In

this work, experiments are conducted with saline tap water and canola oil with a pipe

diameter of 44.0 mm, density ratio of 0.86 and a viscosity ratio of 44.0.

Figure 7.1 The experimental matrix of oil and water superficial velocities for two-phase flowing

measurements conducted in this work. The marker type and colour indicate the visually observed

flow regimes, whilst the flow regime boundaries from the work of Trallero et al. (1997) are indicated

by black lines.

The position of visually observed flow regimes (from this work) relative to the

observed flow regimes from Trallero et al. (1997) match relatively well. Exact agreement is

not anticipated as liquid-liquid flow regimes are dependent on a range of experimental

conditions (e.g. fluid densities, viscosities and wall wetting properties) (Angeli and Hewitt,

2000, Arirachakaran et al., 1989, Xu, 2007). The difference in flow regime transitions can

be attributed to the relative difference in viscosity ratios. In this work the high oil viscosity

(~55 cP) results in flow regime transitions at lower velocities (relative to the work of Trallero

et al. (1997)). For example, the transition from stratified flow with mixing (St w/mix) to a

dispersion of water droplets in oil over oil droplets in water (Do/w & Dw/o) occurs at vos ≈

0.10

1.00

0.10 1.00

Su

perf

icia

l w

ate

r ve

loc

ity,

vw

s[m

/s]

Superficial oil velocity, vos [m/s]

StratifiedStratified with mixing ()

Oil in water emulsion ()

Disp. o/w & w ()

Water in oil emulsion ()

Disp. w/o & Disp. o/w ()

122

0.50 m/s in this work compared to the transition at vos = 0.70 m/s observed by Trallero et al.

(1997).

The 34 experimental measurement points (shown in Figure 7.1) are categorised into

the five appropriate flow regimes according to visual observation. NMR measurements are

taken at each point according to the measurement procedure outlined in section 6.3. The

measured phase flowrates for oil and water are compared to in-line rotameter measurements

of the single-phase flowrates prior to mixing in the flow loop.

7.2.2. Fluid separation

The validation of experimental measurements requires reliable operation of the two-

phase flow loop; including adequate phase separation at the gravimetric separating tank.

Emulsion stability bottle tests were conducted in order to understand the separation behaviour

of the canola oil and water emulsions and are presented in Appendix C.1. The emulsions

(oil-in water as well as water-in-oil) were observed to be stable over a considerable timeframe

(~1 day). The formation of stable oil/water dispersions under flowing conditions prevents

adequate fluid separation at the gravimetric separator during measurements. This causes the

storage tanks to be contaminated with the alternate phase and thus the concentration of the

“pure fluids” discharged from the storage tanks changes throughout the duration of a

measurement. In general, the contamination is acceptable for the water storage tank as the

free water phase in the tank is denser than the emulsion and therefore free water will be

discharged from the bottom of the tank through the water side of the system (including the

water rotameter). However the presence of an emulsion is highly problematic for the oil

phase; the emulsion is denser than the free oil phase thus the emulsion sinks to the bottom of

the oil storage tank. The outlet at the bottom of the tank will discharge the emulsion (and

any water which has separated from the emulsion) when it should be discharging pure oil.

This means that water is contaminating the oil side of the system which is consequential for

both the rotameter and NMR flow measurement principles. The rotameter measurement is

dependent on the properties (e.g. density and viscosity) of the fluid being measured; thus it

is not suitable for measuring a fluid of changing composition. The NMR measurement

technique assumes constant fluid composition throughout the duration of the experiment.

123

Changing the fluid composition within the NMR measurement sequence will result in

unexpected changes (considering the assumed constant composition throughout a sequence)

in the NMR signals and the interpretation will yield incorrect flow measurement results.

The emulsion stability bottle tests (see results in Appendix C.1) observed significant

reduction in stability of oil-in-water emulsions in the presence of sodium chloride. Therefore

salt was introduced to the system (12 wt %) in order to enhance separation during trials with

oil-in-water emulsions. Measurements conducted in flow regimes with an oil-in-water

emulsion present (i.e. in the dispersion of oil-in-water & water flow regime as well as oil-in-

water emulsions) are anticipated to achieve sufficient phase separation. The NMR flowrate

measurements for such flow regimes may be confidently validated against the rotameter

measured flowrates.

Increasing salinity enhances the stability of water-in-oil emulsions (Ling et al., 2018).

Poor separation will be observed in flow regimes where water-in-oil emulsions are present

(i.e. the dispersion of water-in-oil and dispersion of oil-in-water flow regime, as well as the

water-in-oil emulsion flow regime). The fluid storage tanks will be contaminated leading to

changing fluid composition over the duration of an experiment (as discussed above). The

oil-side pump is designed to transport the canola oil; it provides a greater pressure head in

order to shift the more viscous canola oil. Therefore when water is inlet into the oil-pump,

the overall flowrate of the oil-side (and hence through the two-phase measurement section)

increases. As a result, the measurements cannot be reasonably validated when water-in-oil

emulsions are present. Furthermore, the emulsion contaminating the oil storage tank leads

to increasing water content as the experiment progresses.

For oil-in-water emulsions; reasonable separation can be achieved (on the order of

minutes), however oil-in-water emulsions are observed at high flowrates. The fluid

separation efficiency is dependent on the residence time of the mixture within the separator.

The separator residence time is inversely proportional to the total multiphase flowrate;

therefore the degree of fluid separation will be reduced as the flowrate increases. Partial

separation results in the composition in the multiphase pipeline measurement section

124

changing throughout the duration of a measurement. For example, for the measurement

presented in section 7.3.3, the overall fluid flowrate is 8.96 m3/h which means for a separation

volume of 128 L the separation residence time will be ~51s. Partial separation will result in

a slight increase in water concentration and thus small flowrate measurement errors are

anticipated.


In the following sections, example NMR measurement results are presented for each

flow regime. The overall performance of the technique across all measurements is then

discussed in section 7.3.6.

7.3.1. Stratified flow with mixing

Ten measurements were visually observed to be in the stratified flow with mixing

flow regime (St w/ mix); consisting of two segregated layers of fluid in the pipe cross section

with water on the bottom layer and oil on the top layer. Some mixing (droplets from each

layer dispersing into the alternate layer) is observed at the interface of the two layers. The

degree of mixing (quantity and size of bubbles) increases as the overall fluid flowrate

increases. Figure 7.2 illustrates an example 2D velocity-T1 probability distribution for a

water flowrate of 1.00 m3/h and an oil flowrate of 0.95 m3/h. A table providing information

of key resultant properties is also included.

125

Results Oil Water

Measured fraction [%] 69.8 30.2

Log-mean T1 [s] 0.094 1.85

Mean velocity [m/s] 0.25 0.60

Rotameter flowrate [m3/h] 0.95 1.00

NMR flowrate [m3/h] 0.96 0.99

Figure 7.2 An example 2D velocity-T1 distribution for a stratified with mixing flow regime. The

water flowrate is 1.00 m3/h and the oil flowrate is 0.95 m3/h. The vertical dashed pink line indicates

the oil/water cut-off (T1,C = 600 ms) used to distinguish the two components. The 1D velocity

distribution is separated into the individual components. The table to the right indicates key resulting

parameters for both the oil and water phases.

The 2D velocity-T1 distribution illustrated in Figure 7.2 clearly shows two separate

regions with distinguishable T1 relaxation. The 2D distribution is reflective of the stratified

with mixing flow regime; the oil region (T1,LM = 0.094 s, vM = 0.25 m/s) displays a lower

velocity relative to the water region (T1,LM = 1.85 s, vM = 0.60 m/s). The measured velocity

difference is capturing the velocity slip that exists between the two liquid phases in the

stratified flow regime. The canola oil has a much higher viscosity (55 cP) relative to the

saline water (~1.25 cP). The higher viscosity results in a higher fluid-wall frictional force

for the canola oil leading to a lower velocity relative to the water phase. Note that for the

similar flowrates of 1.00 m3/h and 0.95 m3/h for water and oil respectively, the higher water

velocity will correspond to a higher oil fraction. The accuracy of the measurement for this

example is excellent; the NMR measured oil flowrate (0.96 m3/h) deviates from the rotameter

measured oil flowrate (0.95 m3/h) by only 0.01 m3/h, whilst the NMR measured water

flowrate (0.99 m3/h) deviates from the rotameter measured water flowrate (1.00 m3/h) by -

0.01 m3/h.

Oil

Water

126

7.3.2. Dispersion of oil-in-water & free water layer

Three measurements were visually observed as a dispersion of oil droplets in water

layer above a continuous water layer on the bottom of the pipe. Figure 7.3 illustrates an

example 2D velocity-T1 probability distribution in the dispersion of oil-in-water and water

(Do/w & w) flow regime for a water flowrate of 5.59 m3/h and an oil flowrate of 3.06 m3/h.

Results Oil Water


Log-mean T1 [s] 0.135 3.81




Figure 7.3 An example 2D velocity-T1 distribution for the dispersion of oil-in-water and water flow

regime. The water flowrate is 5.59 m3/h and the oil flowrate is 3.06 m3/h.

The 2D velocity-T1 distribution in Figure 7.3 for the dispersion of oil-in-water above

a water layer measurement displays three distinct regions. The region at short T1 corresponds

to the dispersed oil droplets in the top layer (fraction = 31.0 %, T1,LM = 0.135 s, vM = 1.42

m/s). The large dispersing water region at the lower velocity (fraction = 55.3 %, T1,LM = 3.74

s, vM = 1.31 m/s) corresponds to water with oil droplets dispersed within it. The small “free

water” region at high velocity (fraction = 13.7 %, T1,LM = 4.30 s, vM = 2.42 m/s) is water from

the water only layer (at the base of the pipeline). The free water layer is relatively small

(13.7 % of total pipeflow volume) as the oil flowrate is relatively high for a dispersion of oil-

in-water and water flow; meaning that the two-phase flow is beginning to approach the flow

regime boundary and transition towards a dual dispersion flow. The measurement is able to

capture the anticipated velocity slip quite well for this example; the fluids within the

dispersion layer (i.e. the dispersed oil drops and the water phase containing the oil) both have

very similar velocities which is anticipated for a continuous dispersion layer. The water only

phase (on the bottom layer of the pipe) is observed to be at a higher velocity relative to the

Free water

Dispersing water

Dispersed Oil

127

dispersion phase. This is expected as the dispersion will be more viscous relative to the free

water phase. The NMR measured water flowrate (qw,nmr = 5.66 m3/h) matches the rotameter

measured water flowrate (qw,rot = 5.59 m3/h) very well. However the NMR measured oil

flowrate (qo,nmr = 2.40 m3/h) is under-predicted relative to the rotameter measured oil

flowrate. (qo,rot = 3.06 m3/h). This discrepancy can possibly be attributed to the poor SNR

of oil flows at intermediate velocities. The introduction of the EPPC has partially alleviated

the issue of sensitivity to short T1 components, providing reasonable SNR for flows at low

velocities < 0.4 m/s. However there is still difficulty in providing an accurate inversion (due

to a poor SNR < 6) at intermediate velocities (~0.4 – 1.1 m/s) as this is between regions of

effective operation for each polarisation mechanism. The Halbach array does not provide

significant polarisation as the intermediate decay is considerable relative to higher velocities

(> 1.1 m/s), whilst the EPPC does not provide significant polarisation as the fluid residence

time within the EPPC is restricted relative to lower velocities (<0.4 m/s).

7.3.3. Oil-in-water emulsion

Eight of the two-phase oil/water flow measurements were observed to be an oil-in-

water emulsion (Eo/w); consisting of oil droplets fully emulsified into the continuous water

phase. Figure 7.4 illustrates an example 2D velocity-T1 probability distribution for the oil-

in-water flow regime for a water flowrate of 7.43 m3/h and an oil flowrate of 1.53 m3/h.

128

Results Oil Water


Log-mean T1 [s] 0.104 3.45




Figure 7.4 An example 2D velocity-T1 distribution for the oil-in-water flow regime. The water

flowrate is 7.43 m3/h and the oil flowrate is 1.53 m3/h.

The 2D distribution in Figure 7.4 displays a small region at short T1 corresponding to

the emulsified oil (T1,LM = 0.104 s, vM = 2.11 m/s) and a large region at high T1 corresponding

to water (T1,LM = 3.45 s, vM = 1.79 m/s). The velocity slip ratio is determined to be 1.18 from

the measured velocity-T1 distribution; this agrees well with the results of Rodriguez and

Oliemans (2006) who observed oil in water dispersions to have a slip ratio close to or slightly

greater than 1 (Xu et al., 2008). For this measurement, the NMR measured water flowrate

(qw,nmr = 8.27 m3/h) is over-predicted relative to the rotameter measured flowrate (qw,rot =

7.43 m3/h). The NMR measured oil flowrate (qo,nmr = 1.79 m3/h) is reasonably close to the

rotameter measured flowrate (qo,rot = 1.53 m3/h). The suggested source of discrepancy for

the water flowrate measurement is inadequate residence time (~51 s) for separation of the

oil-in-water emulsion (discussed in section 7.2.2).

7.3.4. Dispersion of oil-in-water & Dispersion of water-in-oil

Ten of the two-phase oil/water measurements were observed to be a dual dispersion

with a top layer consisting of water droplets dispersed into oil and a base pipeline layer of oil

droplets dispersed into water. Figure 7.5 illustrates an example 2D velocity-T1 probability

distribution for the dispersion of water-in-oil and dispersion of oil-in-water flow (Dw/o &

Do/w) regime for a water flowrate of 1.00 m3/h and an oil flowrate of 3.06 m3/h.

Emulsified Oil

Emulsifying water

129

Results Oil Water


Log-mean T1 [s] 0.144 2.59




Figure 7.5 An example 2D velocity-T1 distribution for the dispersion of water-in-oil and dispersion

of oil-in-water flow regime. The water flowrate is 3.06 m3/h and the oil flowrate is 1.00 m3/h.

The 2D velocity-T1 probability distribution in Figure 7.5 shows four distinct regions

(a fifth artefact peak is discussed below); two at low velocity (~ 0.5 m/s) and two at higher

velocity (~1.1 m/s). The high velocity region has a lower water-to-oil-ratio (WOR = 0.41)

relative to the low velocity region (WOR = 0.54). The viscosity ratio (μemulsion/μoil) is

approximated using the following equation for a medium emulsion (Sjoblom, 2001);

𝜇𝑒𝑚𝑢𝑙𝑠𝑖𝑜𝑛

𝜇𝑜𝑖𝑙= 𝑒5𝑥𝑤(1 − 3𝑥𝑤 − 4.5𝑥𝑤

2) (7.1)

where xw is the water-cut. For the high-velocity region, the estimated viscosity ratio is 2.2,

whilst for the low-velocity region, the estimated viscosity ratio is 2.9. Furthermore, visual

observation of the dual emulsion found the top layer to occupy a larger fraction of the cross-

sectional area. The lower WOR, lower estimated viscosity and visual observation of larger

observed fraction indicate that the high velocity layer is likely to be oil continuous. Thus it

is suggested that the low velocity regions are the oil-in-water dispersion (i.e. water

continuous layer) and the high velocity components are the water-in-oil dispersion (i.e. oil

continuous layer). The four regions can then be described as; (i) dispersed oil droplets with

low velocity and low T1 (fraction = 23.5 %, T1,LM = 0.436 s, vM = 0.45 m/s), (ii) dispersing

water with low velocity and high T1 (fraction = 12.7%, T1,LM = 5.18 s, vM = 0.61 m/s), (iii)

dispersing oil with high velocity and low T1 (fraction = 45.3%, T1,LM = 0.092 s, vM = 1.14

m/s) and (iv) dispersed water droplets with high velocity and high T1 (fraction = 18.6 %, T1,LM

Dispersing water

Dispersed water

Dispersed Oil

Dispersing Oil

130

= 1.92 s, vM = 1.01 m/s). The suggested distribution of components indicates that the slip

ratio is greater than one (S = voc/vwc = 2.08; where voc is the mean velocity of the oil

continuous phase and vwc is the mean velocity of the water continuous phase). The viscosity

of dual emulsions is considerably complex (Farah et al., 2005); therefore it is difficult to

predict the slip of the two dispersed phases.

The NMR measured water flowrate (qw,nmr = 1.43 m3/h) is over-predicted relative to

the rotameter measured water flowrate (qw,rot = 1.00 m3/h). The NMR measured oil flowrate

(qo,nmr = 3.38 m3/h) is also over-predicted relative to the rotameter measured oil flowrate.

(qo,rot = 3.06 m3/h). The flow measurement errors as well as the relaxation rate (T1,LM) are a

consequence of inadequate separation of the water-in-oil dispersion layer which will lead to

contamination of water in the oil tank (as discussed in section 7.2.2). The complex

multiphase changes in fluid fractions and velocities will cause the measured FID signals to

unexpectedly change. This can help explain the inversion artefact peak (at low and moderate

T1; such artefact peaks are resolved during inversion in order to fit unanticipated changes in

FID signals (e.g. from changing fluid composition). In the measurement presented in Figure

7.5; increasing water content (with a longer T1 relative to oil) causes the degree of

intermediate signal attenuation (between polarisation and detection) to be reduced. This

leads to an increasing FID signal amplitude as the measurement sequence progresses.

Consequently, the measured T1 values under flow vary significantly from the anticipated T1

values from stationary measurements (e.g. the dispersed oil droplets have T1,LM = 0.436 s

relative to the stationary T1,LM = 0.114 s). The inversion (and associated NMR signal model)

has shifted the dispersed oil droplet contribution to higher T1,LM as well as introducing an

artefact contribution (at T1,LM ~ 1.0 s, vM ~ 0.1 m/s) in order to fit to the observed FID signal

measurements. This will lead to inaccurate phase fraction measurements (e.g. the dispersed

oil droplets fit at higher the T1,LM of 0.436 s will have a larger phase fraction than the real

droplets at T1,LM of 0.114 s). The oil-side contamination also leads to increased overall

flowrate (when water is transported by the oil pump) which is observable in the flowrate

measurement errors. The overall flowrate is relatively low (4.06 m3/h) which means the

inadequate separation will have a small impact on the flowrate measurements (relative to the

example presented in 7.3.5).

131

7.3.5. Water-in-oil emulsion

The final three measurements were visually observed to be in the full water-in-oil

emulsion flow regime (Eo/w); consisting of water droplets fully emulsified into the

continuous oil phase. Figure 7.6 illustrates an example 2D velocity-T1 probability

distribution for the oil-in-water flow regime for a water flowrate of 1.00 m3/h and an oil

flowrate of 6.13 m3/h.

Results Oil Water


Log-mean T1 [s] 0.087 4.51




Figure 7.6 An example 2D velocity-T1 distribution for the emulsion of water-in-oil flow regime.

The water flowrate is 6.13 m3/h and the oil flowrate is 1.00 m3/h.

The 2D velocity-T1 probability distribution in Figure 7.6 shows two distinct regions

which are distinguishable by the fluid T1 relaxation distribution. The region at low T1

corresponds to emulsifying oil (T1,LM = 0.087 s, vM = 2.06 m/s) whilst the region at high T1

corresponds to emulsified water droplets (T1,LM = 4.51 s, vM = 0.91 m/s). For the water-in-

oil emulsion, inadequate separation of phases (discussed in section 7.2.2) will cause

significant (given the degree of emulsification) and rapid (considering the overall flowrate

of 7.13 m3/h) changes in phase fractions. In this example, phase contamination is evident

from two major effects (discussed in further detail below); (i) over-predicted oil velocity, and

(ii) over-predicted water fraction. Minor artefact peaks are also present which is to be

expected considering the FID signals will not behave according to the NMR signal model

when the fluid composition is changing.

Emulsifying Oil

Emulsified water

132

The over-predicted oil velocity is a consequence of signal misinterpretation. The

changes to phase fractions and velocities results in adverse changes in the measured FID

signal similar to the results presented in section 7.3.4. In this example, the 2D inversion (and

associated NMR signal model) has fit an artificially high oil velocity in order to account for

the observed changes in measured FID signals. Consequently, the velocity slip ratio is

measured as to be 2.26; which is very high relative to the anticipated slip ratio of 1 for a fully

emulsified stream where all components are travelling in the same continuous phase.

The second impact of over-predicted water fraction (NMR measured fraction is 55.1

%, whilst the anticipated fraction (for an assumed velocity slip of 1) is ~14 %) is a physical

effect of the oil-tank contamination. The emulsified water entrained into the oil continuous

phase will result in water being outlet through the oil side of the system. This causes the

overall water fraction to considerably increase in the duration of the NMR measurement

sequence (~21 minutes). The water pumped through the oil-side of the system will also have

an enhanced flowrate (as it is transported by the oil pump). As a result, the NMR measured

water flowrate (qw,nmr = 2.74 m3/h) is considerably higher than the rotameter measured water

flowrate (qw,rot = 1.00 m3/h) whilst the NMR measured oil flowrate (qo,nmr = 5.06 m3/h) is

underpredicted relative to the rotameter measured oil flowrate (qo,rot = 6.13 m3/h). The

overall flowrate in this example (7.13 m3/h) is higher relative to the example presented in

7.3.4 such that the impact of inadequate separation is greater.

7.3.6. Summary and discussion of results

The overall performance of the NMR measurement technique is now considered with

respect to all 34 two-phase oil/water measurements. Figure 7.7 presents a comparison

between NMR measured flowrates to in-line rotameter measurements for both oil and water

flowrates. Figure 7.7(a) shows results for the stratified with mixing, dispersion of oil-in-

water and water, as well as the oil-in-water emulsion flow regimes. These are flow regimes

where the experiments were successfully performed (i.e. with reasonable fluid separation)

such that the NMR flowrate measurements may be confidently validated by rotameter

flowrate measurements. Figure 7.7(b) presents results for the dispersion of water-in-oil and

dispersion of oil-in-water, as well as the water-in-oil emulsion flow regimes. These are the

133

flow regimes where inadequate oil and water separation was observed such that experiments

cannot be validated as very poor agreement is expected between NMR and rotameter flowrate

measurements (as discussed in section 7.2.2).

Figure 7.7 Direct comparison of the NMR measured flowrates and rotameter measured flowrates

(for both oil and water) for two-phase oil/water flow measurements. (a) Flowrate comparison for the

stratified with mixing (St w/ mix), dispersion of oil-in-water and water (Do/w & w), as well as the

oil-in-water emulsion (Eo/w) flow regimes. (b) Flowrate comparison for the dispersion of water-in-

oil and dispersion of oil-in-water (Dw/o & Do/w), as well as the water-in-oil emulsion (Ew/o) flow

regimes.

Figure 7.7(a) shows the NMR measured flowrates compare very well to the rotameter

measured flowrates for both oil and water for the stratified with mixing, dispersion of oil-in-

0

2

4

6

8

10

12

0 2 4 6 8 10 12

NM

R m

ea

su

red

flo

wra

te [

m3/h

]


Oil Water

St w/ mix

Do/w & w

Eo/w

(a)

0

2

4

6

8

10

12

0 2 4 6 8 10 12

NM

R m

ea

su

red

flo

wra

te [

m3/h

]


Oil WaterDw/o & o/w

Ew/o

(b)

134

water and water, as well as the oil-in-water emulsion flow regimes. Figure 7.7(b) shows very

poor agreement between NMR measured flowrates and rotameter measured flowrates for

both oil and water in the dispersion of water-in-oil and dispersion of oil-in-water flow regime,

as well as the water-in-oil emulsion flow regime. The NMR measured oil flowrates are

underpredicted relative to the rotameter oil flowrates, whilst the NMR measured water

flowrates are overpredicted relative to the rotameter water flowrates. The source of error for

the results presented in Figure 7.7(b) is the inadequate separation of water-in-oil emulsions

(as discussed in section 7.2.2).

A statistical comparison between the flow measurement techniques is performed in

order to quantify the relative performance in each flow regime. Figure 7.8 presents (a) the

mean error and (b) the root mean square error of the NMR flowrate measurements relative to

the rotameter measurement (for both oil and water) across the five flow regimes.

Figure 7.8 Statistical summary of NMR flow measurement performance in the five different flow

regimes. (a) Mean error (ME) of the NMR measured flowrate relative to rotameter measured

flowrates for each flow regime. (b) The root mean square error (RMSE) of the NMR measured

flowrate relative to rotameter measured flowrates in each flow regime.

The quantitative statistics shown in Figure 7.8 further reinforce the results presented

in Figure 7.7. Good agreement is observed for the first three flow regimes (St w/ mix, Do/w

& w, and Eo/w); the mean error is less than 0.10 m3/h across these flow regimes; except for

the oil flowrate measurement in the dispersion of oil-in-water and water flow regime. This

flow regime only had three experiments, and the example presented in Figure 7.3 (with a

-5

-4

-3

-2

-1

0

1

2

3

4

5

St. w/mix

Do/w &w

Eo/w Dw/o &Do/w

Ew/o

NM

R m

ea

su

red

flo

wra

te

ME

[m

3/h

]

Flow regime

WaterOil

(a)

0

1

2

3

4

5

St. w/mix

Do/w &w

Eo/w Dw/o &Do/w

Ew/o

NM

R m

ea

su

red

flo

wra

te

RM

SE

[m

3/h

]

Flow regime

WaterOil

(b)

135

deviation of -0.66 m3/h) demonstrates the source of this discrepancy. For mid-range oil

velocities (~1.4 m/s) there is loss of measurement sensitivity due to the poor SNR measured

in this velocity-T1 range. The velocity is between the effective regimes of the two polarising

mechanisms; the Halbach array achieves improved polarisation at higher velocities, whilst

the EPPC achieves improved polarisation at lower velocities.

Very good agreement is observed in the stratified with mixing flow regime (RMSE <

0.20 m3/h for both oil and water) as the two-phase flow stream is not emulsified, and the low

overall flowrate gives the fluid sufficient residence time for the two phases to separate in the

gravimetric separation tank. The flowrate agreement is marginally poorer for the oil-in-water

emulsion, primarily due to the reduced separation efficiency observed at higher flowrates.

The oil-in-water emulsion flow regime results in an emulsified mixture and requires a shorter

residence time (typically 1 minute, depending on the overall flowrate) for fluid separation.

This results in poorer comparison errors (RMSE of 0.55 m3/h for water and 0.32 m3/h for oil)

in the oil-in-water emulsion flow regime relative to the stratified with mixing flow regime.

The mean errors and RMSEs are significantly worse (absolute errors are greater than

2 m3/h) for both oil and water flowrate measurements in the dispersion of water-in-oil and

dispersion of oil-in-water flow regime, as well as the water-in-oil emulsion flow regime. The

mean errors highlight that the water flowrate is substantially over-predicted whilst the oil

flowrate is under-predicted in these flow regimes. The key source of error is the inability to

separate water-in-oil emulsions in a reasonable timeframe (for full detail, see section 7.2.2).

Water-in-oil emulsions are much more stable (separation occurs after ~ 1 day) relative to oil-

in-water emulsions (which separate within a few minutes – see appendix C.1). Poor fluid

separation of water-in-oil emulsions results in water significantly contaminating the oil tank

during the experimental timeframe and adversely impacting NMR and rotameter flowrate

measurements. Therefore, the system is currently unsuitable for validating measurements

when a water-in-oil emulsion is present. Future work will consider overcoming this issue

(using demulsifying agents as well as a larger flow loop with increased separation volume)

such that NMR measurements within the dispersion of water-in-oil and dispersion of oil-in-

water flow regime, or the full water-in-oil emulsion flow regime may be validated.

136

7.4 Conclusions

The performance of the NMR flow measurement procedure (which was developed in

Chapter 6) is examined for two-phase oil/water flows which were visually observed to be in

five different flow regimes. The NMR flow measurement technique performed very well in

the stratified with mixing, dispersion of oil-in-water and water, and oil-in-water emulsion

flow regimes, with very good agreement in each of these flow regimes. Furthermore, the

NMR flow measurement technique was successfully able to capture two-phase flow

characteristics; for example the oil/water velocity slip in the stratified with mixing flow

regime or the presence of three distinct regions in the dispersion of oil-in-water and water

flow regime. The flow measurement performance was much poorer in the dispersion of

water-in-oil and dispersion of oil-in-water flow regime, as well as the full water-in-oil

emulsion flow regime. The measurement error is a result of inadequate separation of water-

in-oil dispersions; this problem will be rectified in future work.

137

Chapter 8. Conclusions and future work

8.1 Conclusions

This thesis presented the development of an Earth’s field nuclear magnetic resonance

(EFNMR) multiphase flow meter (MPFM). The flow meter consists of an EFNMR r.f. coil

positioned downstream of a mobile pre-polarisation permanent magnet. The system excites

a 1H NMR signal from fluid moving through the flow meter. The free induction decay (FID)

signal is then acquired and appropriate signal interpretation techniques allow determination

of the composition and flowrate of the measured fluid stream.

Initial system development focussed on establishing an appropriate velocity

measurement technique. Velocity probability distributions were determined by fitting the

measured FID signal of a flowing water stream with a NMR fluid model using Tikhonov

regularisation. The measured velocity distributions were determined to be accurate with

validation against in-line rotameter measurements of water flowrate. The measured velocity

distributions capture the appropriate single-phase flow behaviour with good comparison to

theoretical turbulent distributions. The NMR measurement technique also demonstrated

robust behaviour, with further validation of artificially constructed multi-modal (two-pipe)

velocity distributions.

The system was then applied to analyse two-phase gas/liquid flows in the stratified

and slug flow regimes. The velocity measurement procedure allows accurate measurement

of the liquid velocity distribution in air/water flows. The signal interpretation technique was

applied in a ‘single-shot’ analysis to provide real-time tracking of the liquid holdup and

velocity (at 0.55 – 1.25 Hz). The NMR estimate of liquid holdup is shown to be comparable

138

against a simultaneous video track of holdup. Temporal variation in the liquid flowrate can

be used as a metric to distinguish stratified and slug flow.

The flow metering apparatus and associated signal analysis techniques were then

extended towards the analysis of two-phase oil/water flows. A dual polarisation scheme was

detailed which utilised an electromagnetic pre-polarising coil as well as the mobile

permanent magnet. The oil and water fractions are distinguished using the fluid spin-lattice

relaxation time (T1) which is captured using polarised signal contrast. The multi-FID signals

are fit with a joint 2D velocity-T1 distribution using the developed NMR flow model via a

2D Tikhonov regularisation algorithm. The subsequent analysis of the measured 2D

distributions enables measurement of key phase flow properties, including phase velocities,

fractions and flowrate. The NMR measurement procedure was used to perform accurate

flowrate measurements in the stratified flow with mixing, dispersion of oil-in-water and

water, and oil-in-water emulsion flow regimes. Furthermore; the measured 2D velocity-T1

distributions captured multiphase flow characteristics such as velocity slip. The procedure

could not be accurately validated for the dispersion of water-in-oil and dispersion of oil-in-

water flow regime, or the water-in-oil emulsion flow regime; these regimes produced a water-

in-oil emulsion which could not be sufficiently separated during the total measurement time

which led to flowrate quantification errors.

In summary, the EFNMR MPFM has overall demonstrated very good flow

measurement performance for single-phase flows, two-phase gas/liquid flows and two-phase

oil/water flows. The work presented in this thesis provides an excellent platform for further

developing the measurement system towards a fully capable NMR MPFM.

8.2 Future work

Three aspects of potential future work for the EFNMR MPFM project will be

discussed; (i) improvements to the flow loop equipment, (ii) improvements to the NMR

magnetic hardware, and (iii) advancing the flow measurement procedures.

139

8.2.1. Improving the flow loop equipment

The current flow loop has provided a good experimental set-up for validation of the

multiphase flow measurements presented in this thesis. However to further progress the

measurement system an improved experimental apparatus is required. Firstly a

demulsification technique should be considered to provide adequate separation of water-in-

oil emulsions. A chemical demulsifier will provide the simplest solution; however emulsion

stability testing will be required in order to ensure sufficient destabilisation of emulsions

(Zolfaghari et al., 2016). The appropriate demulsifier should provide separation of water-in-

oil emulsions in a reasonable timeframe (several minutes). This will allow NMR

measurements to be validated across all flow regimes, including the dispersion of water-in-

oil and dispersion of oil-in-water flow regime, as well as the water-in-oil emulsion flow

regime. A larger flow loop system will also be designed with greater separation capacity

(e.g. 1000 L compared to the current 128 L). This will allow the fluids a much longer

residence time to achieve reasonable separation.

The second important upgrade for the flow loop is incorporating realistic three-phase

flow. Three-phase measurements should first be demonstrated for oil-water-air mixtures

(including further development of the associated signal processing). However to truly

demonstrate the capability of the system, three-phase measurements with methane as the gas

phase should be performed. Pressurised methane (unlike air) will produce a measurable

NMR signal and can in principle be distinguished from water and oil via T1 relaxometry.

However the hydrogen index (influencing signal contribution) and T1 of methane is

dependent on pressure and temperature (Gerritsma and Trappeniers, 1971). Therefore

appropriate measurements of oil-water-methane mixtures will be required to develop and

validate the appropriate NMR measurement techniques in three-phase flows under a variety

of conditions. This will require a flow loop with high-pressure flow-lines as well as three-

phase separation in order to validate experimental results.

8.2.2. NMR magnetic hardware improvements

The measurements conducted in this thesis demonstrate that the dual polarisation

scheme is not the optimal method for improving the sensitivity to short T1 components (T1 <

140

100 ms). The impact of the Halbach array stray field on the Earth’s field detection coil has

previously been presented in regards to the measured magnetic field deviation as a function

of separation distance (Fridjonsson et al., 2014b). Further analysis of this effect is presented

in Appendix C.2. The stray field interference is significant due to the relative magnitudes of

the two magnetic fields (Halbach field is 0.3 T whilst Earth’s field is ~54 µT). If the detection

field strength is increased; then the relative impact of the Halbach array stray field on the

detecting field is reduced. A detection frequency of ~200 kHz is suggested to allow reduction

of the separation distance to ~5cm (subject to future magnetic field simulations and

experimental validation). Furthermore, utilising a system with a permanent magnet

producing the detection field eliminates the need for the measurement system to be

perpendicular to the Earth’s magnetic field. Figure 8.1 presents a new model SNR at the

assumed detection frequency of 200 kHz for the Halbach polarisation alone (calculated using

equation 6.13) applied across a velocity-T1 parameter space of (0 to 3) m/s and (0.01 to 10)

s with an assumed minimum separation distance of 5 cm. The higher SNR achievable would

allow the number of scans to be reduced (Nscans = 8) in order to achieve a shorter pulse

sequence measurement time of ~ 5 minutes.

Figure 8.1 Model SNR of fluid components in velocity-T1 space using the Halbach array alone at a

separation distance of 5 cm. The pink lines are contours for SNR = 5; highlighting the region where

reasonable interpretation of the measured signals is anticipated.

Figure 8.1 demonstrates that the proposed system is more sensitive to the short T1

components relative to the current dual polarisation system. There is still a region at low

velocity and low T1 with poor SNR. However if the Halbach array was brought to such a

141

short separation distance (of 5 cm), then the spin-lattice relaxation behaviour is considerably

more complicated during the transition from the Halbach array (polarising field) to Earth’s

field (intermediate decay) to the r.f. coil (detection field) such that some of the NMR flow

model assumptions may no longer apply. Magnetic field simulations should be conducted to

provide appropriate guidelines for the future magnetic system design of the NMR multiphase

flow meter.

The modification of the detection coil frequency will introduce a range of additional

benefits. The introduction of the dual polarisation scheme has resulted in an overly complex

NMR flow model. Using a complex model in combination with the Tikhonov regularisation

results in reduced stability of the inversion and can lead to inaccurate measurement results

(Mitchell et al., 2014). Removing the dual polarisation method will simplify the model and

improve inversion stability. A higher detection frequency would allow reduced ring-down

acquisition delay (Andrew and Jurga, 1987, Hoult, 1984) allowing a considerable increase in

the maximum measurable velocity (Zhen et al., 2018). For example; with the current system

(ring-down delay of 9 ms and detector length of 14 cm) the maximum measurable velocity

is ~3.5 m/s. This is achieved with an initial signal loss of 22.5 % (Sloss = vtdelay/LD, i.e. the

flush-out effect for te = tdelay as modelled in Equation 4.4). For a modified system with further

reduction in ring-down delay (e.g. 1 ms) albeit with a reduced detector length (7 cm), the

maximum measurable velocity (at Sloss = 22.5 %) would be ~15.8 m/s. The reduced ring-

down delay would also allow CPMG pulse sequences to be captured with considerably

reduced echo spacing. This provides a considerable advantage relative to the current FID

measurements as CPMG experiments are less sensitive to the magnetic field inhomogeneity

which changes as the Halbach array is shifted.

8.2.3. Advancing NMR flow measurement techniques

One of the key advantages of NMR over other multiphase measurement techniques

is the ability to non-invasively detect fluid behaviour and dynamics. The improvements to

the magnetic system detailed in section 8.2.3 could also incorporate additional magnetic

hardware improvements such that more advanced NMR measurements can be performed on

multiphase pipelines. For example; a major problem in oil and gas pipelines is the formation

142

and treatment of oil and water emulsions (Stewart and Arnold, 2008). The appropriate

treatment of oilfield emulsions requires consideration of emulsion characteristics, such as

droplet sizes. The application of NMR towards oil/water emulsion characterisation has been

well demonstrated (Fridjonsson et al., 2014a, Johns, 2009, Ling et al., 2016) including the

application of the EFNMR system towards droplet sizing (Fridjonsson et al., 2012). The

potential combination of droplet sizing techniques (e.g. Ling et al., 2017) with flow

measurement techniques presented in this thesis would provide a MPFM with excellent

oil/water characterisation capabilities. The in-situ characterisation would then provide

valuable information for emulsion destabilisation and treatment in oilfield production.

The multiphase flow metering industry has previously highlighted the potential of

tomographic techniques (Chaouki et al., 1997). Current MPFMs have considerable

measurement uncertainty due to the flow regime dependence of many commercial techniques

(Sætre et al., 2012). Capturing real-time images of multiphase flows would provide flow

regime identification; reducing measurement uncertainty and providing a valuable

information for flow assurance purposes (Ismail et al., 2005). NMR imaging has previously

demonstrated the ability to characterise and accurately quantify multiphase flow behaviour

across a range of chemical engineering applications (Gladden and Sederman, 2013, Gladden

and Sederman, 2017). The current EFNMR system has an inherently poor SNR, results in

an unreasonable timeframe and resolution for image acquisition (Halse et al., 2008).

However modern developments in statistical analysis (e.g. Bayesian analysis) have enabled

spatially quantitative measurements to be achieved with EFNMR (Fridjonsson et al., 2015,

Ross et al., 2012). The future low-field NMR system (discussed in section 8.2.2) could be

designed to capture magnetic resonance images of reasonable SNR. This could provide

tomographic analysis of the pipe cross-section; giving the potential for flow regime

identification which provides considerable benefits for flow assurance and production

monitoring purposes (Thorn et al., 1999).

143

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Appendices

Appendix A. Calibrations for NMR flow measurements

A.1 Magnetic field inhomogeneity

Experimental measurements acquire the free induction decay (FID) signal from fluids

flowing through the flow metering system. The FID signal obtained from a flowing medium

consists of two components; (i) stationary FID behaviour, and (ii) a ‘flush-out’ effect as

excited fluid leaves the detection volume according to fluid velocity. The flush-out effect

has been addressed in section 4.2.2; further detail regarding the stationary fluid behaviour is

provided here.

The stationary FID consists of T2 decay (due to spin-spin relaxation of the fluid) and

signal dephasing due to magnetic field inhomogeneities. For the single-phase water flow

measurements conducted in Chapter 4; capturing a FID of water in the pipe is sufficient to

calibrate the stationary FID behaviour. However for the two-phase oil/water measurements

conducted in Chapter 6; the impact of spin-spin relaxation on the stationary FID behaviour

cannot be calibrated as the fluid composition is unknown. Therefore the spin-spin relaxation

and magnetic field inhomogeneity decay effects must be segregated and accounted for

separately. The FID signal was previously given in equation 2.14; this can be considered in

terms of the two relevant components as follows;

𝑆(𝑡) = 𝑆0exp (−𝑡

𝑇2) exp(−(𝑅𝐼𝑡)2) (A.1)

where the first component (exp(-t/T2)) describes spin-spin relaxation behaviour and the

second component (exp(-(RI t)2)) describes magnetic field inhomogeneity decay behaviour in

the Earth’s magnetic field (with RI describing the Gaussian relaxation decay rate).

Measurement of the magnetic field inhomogeneity function is achieved by

comparison of a FID measurement to a standard CPMG measurement for a given sample.

The T2 decay component of the FID can be measured via a CPMG experiment; using spin

echoes to refocus spins which have been dephased by field inhomogeneity (Carr and Purcell,

1954, Meiboom and Gill, 1958). A measured CPMG signal decay (SCPMG) is described by;

168

𝑆𝐶𝑃𝑀𝐺(𝑇𝐸) = 𝑆0𝑒−

𝑇𝐸𝑇2 (A.2)

where S0 is the initial CPMG polarisation and TE is the echo time of the acquired signals. By

substituting equation A.2 into equation A.1 and performing a simple rearrangement, the field

inhomogeneity function may be described by;

𝐼(𝑡) = exp(−𝑅𝐼𝑡2) = 𝑆𝐹𝐼𝐷(𝑡)

𝑆𝐶𝑃𝑀𝐺 (A.3)

The field inhomogeneity function is determined from measurement of a stationary water

sample (in the pipeline); a CPMG measurement is acquired with 64 echoes at 100 ms spacing

whilst a FID measurement is obtained for an acquisition time of 819.2 ms. Both

measurements use Nscans = 32 and tpolz = 5 s. A T2 distribution is fit via the CPMG model

equation A.2 to the measured CPMG signal decay using 1D Tikhonov regularisation. The

FID (with the T2 decay calibrated according to the measured CPMG) is then fit with equation

A.1 using the Gaussian relaxation rate RI as a fitting constant, and thus the field

inhomogeneity function is determined. Figure A.1 shows the results of field inhomogeneity

function determination; including the measured CPMG signal and model fit, the measured

FID signal and model fit as well as the determined inhomogeneity distribution. Signals are

normalised to the back-extrapolated fit at zero time. Note that only the first 10 echoes are

shown for the CPMG decay for clarity of the other plots; however the full CPMG

measurement is repeated in Figure B.1(a).

169

Figure A.1 NMR water measurements used for field inhomogeneity function determination. A

CPMG measurement fit with a T2 distribution via equation A.2, a FID measurement fit with equation

A.1 and the resultant inhomogeneity function.

Figure A.1 illustrates the half-Gaussian line shape for the inhomogeneity distribution

and demonstrates that the model decay for the FID (according to equation A.1) fits reasonably

well to the measured data. The Gaussian relaxation rate is determined as 0.973 s-2 from the

model fit to the measured FID.

The application of the field inhomogeneity function to the measurement of flowing

data is complicated by local and temporal variation in Earth’s magnetic field. The proposed

flow measurement procedure applies variable polarisation-detection separation distances in

order to observe signal contrast according to T1. The movement of the Halbach array is

observed to interfere with the field inhomogeneity. In order to partially alleviate this

problem, the EFNMR detection coil is shimmed at each of the separation distances. To fully

account for the variations in the field inhomogeneity caused by shifting the Halbach array;

the field inhomogeneity function must be measured at each relevant separation distance. This

is demonstrated in Figure A.2; FID measurements are acquired with stationary water in the

pipe, with each FID signal fit with equation A.1 in order to determine the relevant field

inhomogeneity function for the logarithmically spaced separation distances of 45 – 150 cm.

Signals are normalised to the maximum value obtained from the back-extrapolated fit at zero

time.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

No

rma

lis

ed

NM

R S

Ign

al


Measured CPMG Model Fit to CPMGMeasured FID Model Fit to FIDInhomogeneity function

170

Figure A.2 Experimentally acquired FID signals at varying separation distances of 45 – 150 cm.

FID measurements are acquired with stationary water in the pipe running through the EFNMR

system. Signals are fit with the model equation A.1

The results shown in Figure A.2 demonstrate variation in the decay rate of the FID

measurements. The FID signals are relatively similar at separation distances above 62 cm

where the impact of the Halbach is minimal. FID measurements at shorter separation

distances cause more stray field interference with the EFNMR detection region causing an

increase in the observed decay rate (as separation distance is reduced). FID measurements

at separation distances closer than 45 cm begin to show considerably faster decay as the

Halbach magnet interferes with the EFNMR detection coil such that the FID is dominated by

inhomogeneity decay.

A.2 Relaxation in variable magnetic field strengths

The proposed dual polarisation system introduces complication due to the presence

of multiple magnetic field strengths through the NMR measurement system. Figure A.3

illustrates how fluid flowing through the system is subject to three separate magnetic fields

(Larmor frequency (ω0) is indicated for 1H precession); the field of the pre-polarising

Halbach magnet (~300 mT / 12,800 kHz), the Earth’s magnetic field alone (~0.054 mT/2.29

kHz) and the field created by the electromagnetic pre-polarising coil (EPPC, 18.7 mT, 920

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

NM

R S

ign

al [µ

V]


LPD

[cm]45485154586266707580859096

103109116124132141150

Expt. data

Model fit

171

kHz). Following application of the EPPC, the coil is switched off and fluid will return to the

Earth’s magnetic field for excitation and detection.

Figure A.3 Illustration of the three separate magnetic field strengths present in the flow metering

system.

The spin-lattice relaxation rate (T1) of a fluid changes with field strength and therefore

fluid flowing through the system will experience variable T1 relaxation throughout different

sections of the system (Graf et al., 1980, Korb and Bryant, 2002). It is assumed that the T1

experienced due to the Halbach array’s magnetic field is the same as that measured for the

EPPC field. Despite the significant difference in field strength (300 mT for the Halbach

compared to 21.7 mT for the electromagnetic coil) this assumption appears reasonable; the

T1 of water is constant for higher field strengths (T1 of pure water at 250C is 2.89 s for B0 >

1.8 mT) (Graf et al., 1980) and whilst there is no data (to the author’s knowledge) of the T1

of canola oil at changing field strength, the T1 of olive oil is relatively constant between the

two field strengths (T1 of ~110 ms at 19 mT and T1 of ~125 ms at 300 mT) (Alessandri et al.,

2005).

In order to account for variable T1 relaxation, stationary fluid T1 measurements are

made at two different field strengths; in the Earth’s field and in the polarising field. T1

relaxometry measurements in the Earth’s magnetic field were previously presented in section

6.2.3 using an excitation delay sequence. The measurements demonstrated mono-

exponential relaxation behaviour for water with a T1,EF (the spin-lattice relaxation rate in the

earth’s magnetic field) of 3.1 s, whilst canola oil observes bi-exponential relaxation

behaviour with a log-mean T1 of 115 ms.

Pre-polarising Halbach Array (~300 mT / 12,800 kHz)

Intermediate section: Earth’s field (~0.054 mT / 2.29 kHz) Electromagnetic

pre-polarisation coil (18.7 mT / 920 kHz)

Detection: Earth’s field (~0.054 mT /

2.29 kHz)

172

A saturation recovery measurement is applied in order to measure the T1 for canola

oil and water in the polarising field. FID signals are acquired 64 polarisation times (i.e. tpolz)

which are logarithmically spaced from 10 ms – 10 s. The polarisation-excitation delay is

held constant (at the minimum of 60 ms). FID signals are back-extrapolated to determine the

pre-polarised signal (SP). The measured polarised signal is modelled using the following

equation;

𝑆𝑃(𝑡𝑝𝑜𝑙𝑧, 𝑇1) = 𝑆0 ൬1 − exp ൬−𝑡𝑝𝑜𝑙𝑧

𝑇1,𝑃𝐹൰൰ (A.4)

where S0 is the effective NMR signal after an infinite polarisation time in the electromagnetic

coil and T1,PF is the fluid spin-lattice relaxation constant in the polarising field. The

measurement is observing fluid magnetisation development in the polarising field, thus is

measuring T1 in the polarising field. A T1,PF distribution is fit with equation A.4 to the

measured polarised signal using the Tikhonov regularisation algorithm for both canola oil

and water. Figure A.4(a) shows the model signal fit to experimental data and Figure A.4(b)

shows the resultant probability distributions for T1,PF.

Figure A.4 Measuring T1 in the EPPC polarising field. (a) Regularised signal fit of equation A.4 to

measured signal data at variable polarisation times for canola oil and water. (b) Resultant T1,PF

probability distributions (P(T1,PF)) for both canola oil and water.

The polarising field T1 measurements show very similar results to the Earth’s field T1

measurement; with marginally higher relaxation rates. Water exhibits a mono-exponential

decay for T1,PF of 3.3 s, whilst the canola oil displays bi-exponential behaviour with the first

peak representing 62% of the sample with a log mean T1 of 71 ms and the second peak

representing 38% with a log mean T1 of 250 ms. The difference in the final polarised signal

0

20

40

60

80

100

0.01 0.1 1 10

NM

R S

ign

al

[µV

]

Polarisation time [s]

Water

Expt.data

Model fit

(a)

Oil

0

1

2

3

4

5

0.01 0.1 1 10

P(T

1,P

F)

T1,PF [s]

WaterOil

(b)

173

(95.0 µV for water and 51.9 µV for canola oil) can be attributed to the initial signal delay (60

ms) between polarisation and excitation.

In order to account for the complex relaxation behaviour in multiple fields during

flowing measurements, a ‘field calibration ratio’ is used. The model for NMR signal of a

flowing fluid (i.e. equation 6.12) is modified to account for the relevant T1 value in each field,

i.e. T1,PF is used for signal polarisation in the Halbach, whilst T1,EF is used for intermediate

signal decay in the Earth’s magnetic field. Hence equation 6.12 becomes;

𝑆(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒 , 𝑣, 𝑇1,𝐸𝐹) = 𝑆0𝐻 (1 − 𝑒−

𝐿𝑃𝐻𝑣𝑇1,𝑃𝐹) (𝑒

−𝐿𝑃𝐷

𝑣𝑇1,𝐸𝐹) ൬1 −𝑡𝑒𝑣

𝐿𝐷൰ 𝑒

−൬𝑡𝑒∗𝑅𝑇𝑇1,𝐸𝐹

+(𝑅𝐼𝑡𝑒)2൰

for 𝑡𝑒 ≤𝐿𝐷

𝑣 (A.5)

however considering the measurement system uses T1 to differentiate oil and water; only one

T1 value should be used. The detection coil operates in the Earth’s magnetic field; thus it is

more relevant to measure T1,EF for fluid differentiation. The field calibration ratio; RF =

T1,PF/T1,EF is introduced and T1,PF is replaced;

𝑆(𝐿𝑃𝐷 , 𝑡𝑝𝑜𝑙𝑧, 𝑡𝑒 , 𝑣, 𝑇1,𝐸𝐹) = 𝑆0 (1 − 𝑒−

𝐿𝑃𝐻𝑣 𝑅𝐹𝑇1,𝐸𝐹) (𝑒

−𝐿𝑃𝐷

𝑣𝑇1,𝐸𝐹) (1 −𝑡𝑒𝑣

𝐿𝐷) 𝑒

−൬𝑡𝑒∗𝑅𝑇𝑇1,𝐸𝐹

+(𝑅𝐼𝑡𝑒)2൰

for 𝑡𝑒 ≤𝐿𝐷

𝑣 (A.6)

Incorporating the calibration ratio introduces additional measurement complexity, however

it can successfully quantify for the multi-relaxation behaviour at different field levels. The

field calibration ratio is not constant; the T1 measurements demonstrate that the different

fluids exhibit different changes of T1 between fields. Therefore separate field calibration

ratios are used for oil and water. The field calibration ratios are defined about the oil/water

T1 cut-off (T1,C = 600 ms, as discussed in section); for oil (T1,EF < 600 ms), RF = 1.08

(averaged for both canola oil components) and for water (T1,EF ≥ 600 ms), RF = 1.06.

A.3 Signal diminishment during repolarisation

During NMR measurements of flowing streams, an unexpected signal drop was

observed with the introduction of the electromagnetic pre-polarising coil. This effect is

174

demonstrated in Figure A.5; FID measurements of single-phase water flows are acquired at

three different velocities (0.37, 0.73 and 1.10 m/s) with two FIDs acquired for each velocity.

The first FID acquired is with only Halbach polarisation (at a separation distance LPD = 70

cm) – i.e. no re-polarisation at the EPPC is applied. The second FID acquired has the same

Halbach polarisation (LPD = 70 cm), however EPPC is switched on (polarising current of 6

A) for just 1 ms. Each FID measurement uses 64 scan averages.

Figure A.5 Demonstration of the signal diminishment with introduction of the EPPC. FID

measurements are shown for three different velocities (0.37, 0.73 and 1.10 m/s) with two FIDs

acquired for each velocity; one with only Halbach polarisation (no EPPC re-polarisation indicated by

diamonds) and the second with the EPPC switched on for 1 ms (with EPPC re-polarisation indicated

by crosses).

The FID signals were anticipated to have negligible difference (with and without

using the EPPC) considering the minimal polarisation time of 1 ms should result in negligible

polarisation of water molecules (water T1,PF was measured as 3.3 s). However Figure A.5

shows the initial FID signal amplitude for the measurements with the EPPC switched on for

1 ms is observed to drop relative to the FID signal without the EPPC.

In order to further understand the observed signal diminishment, similar experiments

are repeated for a water flows at a range of velocities (0.18 – 1.83 m/s) and with different

polarisation-excitation delays (tPE) of 60 – 400 ms. The variable polarisation-excitation delay

is applied in order to examine the variation in signal diminishment with time, without

influencing the fluid polarisation (which would occur if the polarisation time was increased).

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5

NM

R S

ign

al [µ

V]


Velocity [m/s]

0.37

0.73

1.10

No EPPC re-polz.

With EPPC for 1 ms

175

For each velocity and delay time, two FIDs are measured (as in Figure A.5); the first without

the EPPC and the second with the EPPC switched on for 1 ms. The measured FID signals

are fit with velocity probability distributions (according to the methodology presented in

section 4.2.3) and the initial FID signal amplitude (SI) is determined by back-extrapolation

of the model fit such that time since excitation pulse is zero (i.e. te = 0). The signal

diminishment is quantified by the ratio of the FID signal amplitude with the EPPC switched

on (SI,EPPC) to the FID signal amplitude with only the Halbach (SI,Hal);

𝑆𝑑𝑖𝑚 =𝑆𝐼,E𝑃𝑃𝐶

𝑆𝐼,𝐻𝑎𝑙 (A.7)

Figure A.6 illustrates the signal diminishment at ten different water velocities (0.18 – 1.83

m/s) and four polarisation-excitation delays (60, 100, 200 and 400 ms).

Figure A.6 Experimental measurement of the signal diminishment as a function of velocity and the

polarisation-excitation delay (tPE).

The signal diminishment presented in Figure A.6 can be considered in terms of a

piecewise linear function of velocity and time segregated into three components. The first

piecewise component involves the signal ratio linearly decreasing as a function of velocity

(e.g. tPE = 60 ms, a linear decrease is observed for v < 1.5 m/s) until a transition point; this is

indicative of a flush-out effect from the detector region. Note that this component is not

observable for tPE = 400 ms as flush out has already occurred during the polarisation-

excitation delay. The transition point separates the first and second piecewise components

0.6

0.7

0.8

0.9

1

1.1

1.2

0 0.5 1 1.5 2

Sd

im

Velocity [m/s]

tPE

[ms]60100200400

176

and changes with the polarisation-excitation delay (e.g. for tPE = 60 ms, the transition velocity

is ~1.5 m/s, whilst for tPE = 100 ms, the transition velocity is ~0.9 m/s). The second piecewise

component observes the signal ratio linearly increasing with respect to velocity; this is

indicative of a flush-in effect into the detector region. The third and final component of the

piecewise function is a constant function of Sratio = 1; indicating that the diminishment is no

longer in effect and the FID signal amplitude with the EPPC switched on is the same as the

FID signal amplitude with only the Halbach. The suggested cause and a model to describe

observed signal variation is now considered.

The Magritek EFNMR system utilises a pre-polarising coil in order to achieve

reasonable signal sensitivity due to the increased polarising field strength (~18.7 mT

compared the Earth’s Field strength of ~ 54 μT) (Appelt et al., 2006, Blümich et al., 2009a,

Halse and Callaghan, 2008). One of the difficulties in using the pre-polarising field is

ensuring that the full pre-polarised magnetisation can be detected by allowing an adiabatic

field discharge (Conradi et al., 2017). The field discharge from the polarising field strength

to Earth’s field strength must be sufficiently slow to ensure an adiabatic field transition (e.g.

an adiabatic transition from a field of 0.05 T to Earth’s field requires a few milliseconds)

(Mohoric and Stepisnik, 2009). Whilst the transition is adiabatic for “switching off” (field

discharge) the pre-polarising coil, the transition is non-adiabatic for “switching on” the pre-

polarising coil. This is not a problem for the majority of measurements conducted using the

Earth’s field system as there is no significant pre-existing polarised signal which can be

disrupted when the polarising coil is switched on. However, the non-adiabatic transition

occurring for the polarisation coil “switch on” is important for the unusual set-up of the

EFNMR flow meter with a dual polarisation system. Fluid entering the EFNMR system will

have previously been magnetised or polarised by the upstream Halbach array and therefore

possess an initial magnetisation. The rate of polarising field accumulation is too fast (i.e. the

time for field “switch-on” is too short) and therefore the flowing fluid experiences a non-

adiabatic transition from Earth’s field to polarising field. This means that the pre-magnetised

signal (due to the Halbach) will not be able to fully re-orientate from the Earth’s field to the

pre-polarising field. Consequently, a signal loss is observable between experiments where

only the Halbach is used and experiments where both the Halbach and EPPC are used (as

177

demonstrated in Figures A.5 and A.6). The effect of the pre-polarising pulse on the

measurable signal in different experiments is illustrated in Figure A.7.

Figure A.7 Illustration of effective signal development during variable polarisation scenarios using

a pulse and collect experiment. (a) Signal variation for stationary fluid measurement (i.e. effectively

using the EPPC alone for pre-polarisation), (b) signal variation for a flowing measurement using the

Halbach alone (i.e. the EPPC is not applied), and (c) signal variation for flowing fluid measurements

Adiabatic “switch-off”

Non-adiabatic “switch-on” r.f. excitation

pulse

Measured FID

Signal polarisation

Polarising pulse

Intermediate decay

(a). Standard pulse and collect for stationary fluid.

Pulse sequence

Effective signal

r.f. excitation pulse

Incoming Halbach signal

(b). Pulse and collect for flowing measurements with Halbach only.

Pulse sequence

Effective signal

Measured FID

Measured FID

Adiabatic “switch-off”

Non-adiabatic “switch-on” r.f. excitation

pulse

Signal polarisation

Polarising pulse

Intermediate decay

(c). Pulse and collect for flowing measurements with Halbach and pre-polarising coil

Incoming Halbach signal

Pulse sequence

Effective signal

Signal loss

178

with the Halbach and the EPPC applied. The signal loss due to non-adiabatic field transition is only

relevant for the final scenario involving the dual polarisation mechanism.

Accounting for the non-adiabatic transition is complicated not only due to the fact

that the quantity of signal loss is unknown, but that the signal loss is a function of fluid

position within the coil. The EPPC and Earth’s field detection coil are both coaxial solenoid

coils and therefore have polarisation and detection field profiles (as a function of position

within the EFNMR apparatus) respectively. The transition from the polarisation field to

Earth’s field will therefore depend on the fluid’s position within the EFNMR apparatus.

Adiabatic transitions are more easily achievable near the centre of the coil where the signal

sensitivity is a maximum (Conradi et al., 2017). The direction of the polarising field (BP)

will nearly match the direction of the horizontal component of the Earth’s magnetic field at

the centre of the coil (Be). The direction of the polarising magnetic field will change as a

function of the position within the solenoid such that regions further away from the centre

will require larger reorientation from the polarising field to the Earth’s field. Therefore the

fluid further away from the centre of the coil will have a lower sensitivity and as a result the

non-adiabatic signal diminishment will be larger. The final consideration is the impact of

fluid outside the polarisation coil region which can flush through during detection. The

aforementioned signal effects are incorporated into the following simplistic model which

quantifies the signal variation due to the non-adiabatic transition. Fluid within the pipeline

is separated into regions of significance based on the fluid position relative to the polarisation

and detection zones. These regions are illustrated in Figure A.8 and a description of the

signal attenuation for each region is provided below the figure.

179

Figure A.8 Illustration of the impact of the non-adiabatic transition on different regions of fluid

within the pipeline. The length of the polarisation zone (LP), detection zone (LD) and intermediate

zones (LI) are indicated.

Figure A.8 highlights three regions of fluid within the pipeline; the initial fluid,

intermediate fluid and outside fluid. The “initial fluid” region (highlighted in blue) is fluid

in the detection region of the coil when the EPPC is switched on. The detection zone (of

length LD = 10 cm) reflects the sensitivity of the detection coil along the axis parallel to the

pipeline. The majority of the fluid in the detection region will experience an adiabatic

transition as the signal sensitivity is strongest towards the centre of the coil. However a full

adiabatic transition between fields is not possible due to the time of coil switch-on, thus a

small fraction of the polarised fluid (kP) will not transition from Earth’s field to the pre-

polarising field. This fraction of fluid which does achieve field transition will not be detected

following the excitation pulse (i.e. there is a partial impact causing signal loss). The

“intermediate fluid” region (highlighted in red) is fluid outside the detection zone of the

EFNMR apparatus but still within the polarisation zone (of length LP = 27 cm) of the EPPC.

This fluid is in two regions either side of the detection zone (both of length LI = 8.5 cm).

Note that the downstream intermediate region will not be detected (as fluid has already

passed through the detection region) however is incorporated into the model for consistency.

This region has significantly poorer sensitivity relative to the detection zone. The impact of

the non-adiabatic transition will result in a more significant fraction of fluid (kI) experiencing

a non-adiabatic transition. The “outside fluid” region (highlighted in green) is not impacted

by the non-adiabatic transition as the fluid is not within the polarising region of the coil. It

is assumed that this fluid which moves from outside the polarising region to within the

LD

LP

LI LI

Flow direction

Pipe

Signal regions Initial fluid – partial impact Intermediate fluid – significant impact Outside fluid – no impact

180

polarising region will effectively experience an adiabatic transition; the EPPC will have a

“polarisation profile” involving changing field strength with length. The velocity of the fluid

is low enough such that the moving fluid will experience a gradual change in field strength

as it moves into the polarising region. There is no signal change of the outside fluid initially,

however this fluid will become important as it moves into the detection zone replacing fluid

which has experienced a signal change.

The effect of the non-adiabatic transition will depend on the type of fluid (i.e. initial,

intermediate or outside) and the relative fraction of each fluid in the detector at a given time.

In order to aid the understanding of the signal loss model Table A.1 provides a description

of position, quantification of the relevant fluid fractions and a visual depiction of the regions

within the detection zone for five different cases at different times since the polarisation

switch on.

181

Table A.1 Movement of the separate signal variation regions at different times since the

polarisation switch on. The fraction of each region (initial, intermediate (interm.) and outside) in the

detection zone as well as a visual depiction of the effective region positions is also shown. The

detection region is indicated by dashed lines.

Table A.1 considers five different cases (A-E) at variable time since the polarisation

switch-on (tps). Case A is the initial position (i.e. tps = 0) where the “initial fluid” alone is

fully inside the detector zone. Note that this case is never applied as there is minimum

polarisation-excitation delay of 60 ms; however it is shown to assist understanding. Case B

shows the “intermediate fluid” flushing into the detection zone, whilst the “initial fluid” is

flushing out of the detector zone. Case C has the “intermediate fluid” fully within the

detection zone; note that this will only apply if LI ≤ LD. The “outside fluid” is beginning to

flush into the detection zone whilst the final fraction of the “initial fluid” is still flushing out

of the detector. In Case D the “initial fluid” has now completely left the detection zone and

the “intermediate fluid” is now flushing out of the detector. Finally in Case E, the

“intermediate fluid” has completely left the detection region and the “outside fluid” will

completely fill the detector. This means that the detector is now filled with fluid which was

Pipe

Detection region Pipe



Detection region

Pipe

Detection region

182

not impacted by the non-adiabatic transition and thus the signal will effectively be the same

as if the fluid was polarised by the Halbach alone.

In order to quantify the signal variation due to non-adiabatic field transition (SNA) at

a given time since polarisation pulse (tps), the following equation is applied;

𝑆𝑁𝐴(𝑡𝑝𝑠) = 𝑥𝑃(1 − 𝑘𝑃) + 𝑥𝐼(1 − 𝑘𝐼) + 𝑥𝑂 (A.8)

where xP is the fraction “initial fluid” within the detection zone, xI is the fraction of

“intermediate fluid” within the detection zone and xO is the fraction of “outside fluid” within

the detection zone. The values of xP, xI and xO are determined by selecting the relevant case

(according to the time since polarisation) from Table A.1, whilst kP and kI are fractions of the

“initial fluid” and “intermediate fluid” which observe non-adiabatic field transitions.

In order to validate the described model and estimate the values of the parameters kP

and kI, the experimentally measured signal diminishment ratios shown in Figure A.6 are fit

with equation A.8 using a least squares fitting method. The effective model fit is shown in

Figure A.9.

183

Figure A.9 Model fit of equation A.8 to experimentally measured signal diminishment ratios (SRatio)

as a function of fluid velocity and time since excitation pulse (tPE).

Figure A.9 shows good agreement between the experimental data and model fit; the

linear flush-in and flush-out effects are well captured by the model. During the application

of flow metering measurements and the signal loss model, the detector profile is described

by a super-Gaussian function (Parent et al., 1992). The super-Gaussian profile captures the

shape of the detection profile introduced by the detection solenoid coil much better than a

uniform profile of length LD. During the calculation of the signal loss model fractions (xP, xI

and xO); the detector profile is used instead of the single parameter LD in order to better

describe the signal loss as a function of fluid position. The super-Gaussian profile introduces

non-linearity into the model-fit which causes the slight curvature of the model-fit. The results

of the least squares model fit return parameter values of kP = 0.085 and kI = 0.253 indicating

8.5 % of the fluid in the “initial region” experiences a non-adiabatic transition, whilst 25.3

% of the fluid in the “intermediate region” experiences a non-adiabatic transition. Note that

in reality, the signal loss fractional parameters (i.e. kP and kI) will instead form a ‘signal loss

profile’ as a function of position with the detector (i.e. k(l) where l represents position within

the detector) and will depend on both the polarisation and detection profiles. However such

a ‘signal loss profile’ is too difficult to measure practically and therefore has been simplified

into the two signal loss parameters (kP and kI) in two discretised regions (the “inside” and

“intermediate” regions).

0.6

0.7

0.8

0.9

1

1.1

1.2

0 0.5 1 1.5 2

SR

ati

o

Velocity [m/s]

Expt data

Model fit

tPE

[ms]60

100200400

184

Appendix B. Fluid relaxometry

B.1 T2 measurements of canola oil and water

Measurements of the fluid T2 distributions (for stationary samples) are conducted in

order to assist understanding of the expected relaxation behaviour of oil and water. The T2

distribution of water is fit to measured CPMG data (64 echoes acquired at 100 ms spacing)

with equation A.2 using Tikhonov regularisation (as previously shown Figure A.1).

Determining the T2 distribution for canola oil is more complicated; due to considerable timing

delays, CPMG experiments in the EFNMR system are limited to echo times greater than 50

ms. Therefore for canola oil, which is anticipated to have a low T2 of ~100 ms (Luthria,

2004) the majority of observable signal decay will have occurred in the first few echoes (~6

echoes). Using such a small number of data points is unsuitable for regularisation analysis

in order to determine a distribution of relaxation parameters (e.g. the bi-exponential

distribution for canola oil) (Mitchell et al., 2014). Thus an alternative measurement and

analysis technique must be considered for determination of the T2 distribution for canola oil

in the EFNMR system.

A FID measurement has a much shorter acquisition delay (9 ms with the Q-switch)

and faster data spacing (dwell time of 50 µs) relative to a CPMG experiment in the EFNMR

system; allowing a reasonable number of points to be acquired for data analysis before the

observable signal decays. The magnetic field inhomogeneity function is first determined by

analysing the FID signal and CPMG measurement for a water sample (as shown in Figure

A.1). A canola oil sample is then placed in the system and a FID signal is acquired (Nscans =

32, tacq = 409.6 ms). The canola oil T2 distribution is fit to the measured FID signal with

equation A.1 using Tikhonov regularisation analysis. Figure B.1 displays the results of fluid

T2 analysis. Figure B.1(a) shows the measured CPMG signal data and corresponding fit for

the water sample as well as the measured FID signal and corresponding model fit for the

canola oil sample. Figure B.1(b) shows the resultant T2 probability distributions determined

via regularisation analysis.

185

Figure B.1 Measuring T2 of oil and water in the EFNMR system. (a) Regularised signal fit of

equation A.2 to measured CPMG signal data for water and the regularised signal fit of equation A.1

to measured FID signal data for canola oil. (b) The corresponding T2 distributions for water and

canola oil.

Figure B.1(b) shows similar results to the T1 measurements previously conducted

(both in the Earth’s field and the polarising field). The water exhibits a mono-exponential

decay with a T2 of 1.96 s. The canola oil displays bi-exponential behaviour with 50 % at 51

ms and 50 % at 139 ms. The difference in the initial signal in Figure B.1(a) can be attributed

to the initial signal delay (60 ms) between polarisation and excitation (the same effect as

observed in Figure A.4(a)). Note that for T2 measurements with lower SNR (e.g. during

flowing measurements), the two peaks can often be merged into a single peak. The overall

distribution (i.e. the bi-exponential distribution in Figure B.1(b)) log-mean T2 of 82 ms is a

more useful comparison to such results (with lower SNR).

The stationary T2 distributions are useful in understanding the expected decay

behaviour during flow; however such distributions will be difficult to measure under flow.

They will be particularly difficult to measure simultaneously with the T1,EF and velocity

distributions; therefore T1/T2 ratios are introduced in order to assist signal interpretation and

inversion. The T1/T2 ratio is defined around the oil/water T1 cut-off of T1,EF = 600 ms; with

oil (T1,EF < 600 ms) having RT = 1.35 (averaged for both canola oil components) and water

(T1,EF ≥ 600 ms) using RT = 1.63.

0

20

40

60

80

100

120

0.01 0.1 1 10

NM

R S

ign

al

[µV

]


Model fit

(a)Expt.data

Water (CPMG)

Oil (FID)

0

2

4

6

8

10

12

14

0.01 0.1 1 10

P(T

2)

T2 [s]

WaterOil

(b)

186

B.2 Comparative relaxometry measurements

Oil relaxation times (T1 and T2) were measured using an alternative NMR system (the

Magritek 2 MHz Rock Core Analyser (RCA)) in order to give confidence in the observed oil

relaxation behaviour in the EFNMR system. The RCA operates at a much higher frequency

(2 MHz relative to 2.29 kHz for the EFNMR system) and utilises a permanent magnet for the

polarising field (compared to the EPPC utilised in the Earth’s field system). This system

design means that the polarisation-excitation (tPE = 0.1 ms) and polarisation-acquisition delay

(tdelay = 0.1 ms) are much shorter relative to the EFNMR system (tPE = 60 ms and tdelay = 9

ms). The short system delays mean that it is possible to capture a much greater proportion

of the short relaxation behaviour during experimental measurements which gives greater

confidence in the measured relaxation distributions (relative to measurements in the EFNMR

systems). An inversion recovery measurement (Vold et al., 1968) was performed in order to

quantify the oil T1 distribution. The inversion recovery experiment (described in section

2.1.5) was performed with 32 logarithmically spaced inversion times from 0.1 to 5000 ms.

A T1 distribution is fit via the inversion recovery model (equation 2.9) to the measured signal

using Tikhonov regularisation. Figure B.2(a) shows the model signal fit to experimental data

and Figure B.2(b) shows the resultant probability distributions for T1.

Figure B.2 Measuring canola oil T1 in the Magritek 2 MHz Rock Core Analyser. (a) Normalised

signal fit of equation 2.9 to measured signal data for an inversion recovery measurement of canola

oil. (b) Resultant T1 probability distribution (P(T1)) for canola oil.

In Figure B.2(b) the bi-exponential relaxation behaviour is observed for the canola

oil with the first peak representing 60% of the sample with a log mean T1 of 70 ms and the

second peak representing 40% with a log mean T1 of 213 ms. This is consistent with the

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000 10000

No

rmalised

NM

R s

ign

al

[-]

Inversion time [ms]

ExperimentaldataModel fit

(a)

0

0.5

1

1.5

2

2.5

3

3.5

0.01 0.1 1

P(T

1)

T1 [s]

(b)

187

values observed with T1 analysis in the polarising field using the EFNMR system. Marginal

differences are anticipated; the measurement technique is slightly different (e.g. errors

introduced by the 60 ms delay between polarisation and excitation for the measurement using

the EFNMR system).

A CPMG measurement (Carr and Purcell, 1954, Meiboom and Gill, 1958) was

performed in order to quantify the oil T2 distribution. The CPMG measurement consists of

8192 echoes with an echo spacing (TE) of 0.1 ms. The CPMG is processed into 64

logarithmically spaced windows. A T2 distribution is fit via the model equation A.2 to the

measured signal using Tikhonov regularisation.

Figure B.3 Measuring canola oil T1 in the Magritek 2 MHz Rock Core Analyser. (a) Normalised

signal fit of equation A.2 to measured data for a CPMG measurement of canola oil. (b) Resultant T2

probability distribution (P(T2)) for canola oil.

Figure B.3(b) shows the bi-exponential T2 relaxation behaviour of canola oil with the

first peak representing 60% of the sample with a log mean T2 of 67 ms and the second peak

representing 40% with a log mean T2 of 197 ms. This is reasonably consistent with the values

observed with T2 analysis of canola oil using the EFNMR system. Some variation is

anticipated; the Earth’s field measurement utilises an FID measurement calibrated relative to

the inhomogeneity decay function (see appendix A.1 for further detail). Furthermore, the

SNR is higher in the RCA (SNR of 77 in the RCA relative to a SNR of 28 in the EFNMR

system) which allows improved resolution of the relaxation distribution components.

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000

No

rmalised

NM

R s

ign

al

[-]

Echo time [ms]

Experimental data

Model fit

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.01 0.1 1

P(T

2)

T2 [s]

(b)

188

Appendix C. Flow system design considerations

C.1 Separation of oil and water emulsions

The formation of emulsions (either oil-in-water, or water-in-oil) within production

pipelines is an ongoing problem in crude oil production and transportation (Alboudwarej et

al., 2007, Arnold et al.). In this work, canola oil and water flow simultaneously through

pipelines in the experimental apparatus which will result in the formation of emulsions at

appropriate flow conditions. The system is configured as a loop; therefore oil and water

mixtures require separation prior to returning to their individual storage tanks. A gravimetric

separator (with a separation volume of 128 L) is utilised to achieve mixture separation during

two-phase oil/water flowing experiments. The effectiveness of the separator is dependent on

the fluid residence time within the separator as well as the degree of emulsification of the

mixture. Emulsion stability bottle tests were conducted in order to understand the residence

time behaviour of the canola oil and water emulsions.

Emulsions were prepared in 80 mL batches using a high shear homogeniser (Miccra

D8, ART-moderne Labortechnik, Germany). Samples were mixed for 3 min at 16000 rpm

(determined as the mixing speed which is the pipe flow Reynolds number equivalent to the

maximum overall flowrate of 10.0 m3/h). Each sample is visually monitored, and

photographs are obtained over an hour to observe speed of phase separation. Figure C.1

shows photographs of an example emulsion stability test for a 50% canola oil/ 50% water

mixture at variable times since emulsion formation.

189

Figure C.1 Photographs of emulsion stability bottle tests for a 50% canola oil/ 50% water mixture.

Photographs are captured; (a) directly after, (b) 1 minute after, (c) 1 hour after, and (d) 1 day after

emulsion formation via mixing.

The emulsion in Figure C.1 was observed to be stable for the first 30 minutes. After

one hour the emulsion can be observed to have formed two distinct layers, albeit with each

phase appearing milky and opaque indicating the presence of the alternate phase within each

layer (i.e. the top layer is an emulsion of water droplets within oil and the bottom layer is an

emulsion of oil droplets within an water continuous phase). The emulsion is observed to

have fully separated into two clear layers (oil and water alone) after one day, indicating the

lack of droplets present within the layers.

The observed separation times are obviously inappropriate for application within the

flow loop system. For example, a flowrate of 10 m3/h would require an impractically large

10 m3 gravity separator to achieve the partial separation of fluids observed in Figure C.1(c).

A demulsification technique was required to enhance the separation and achieve separation

of emulsions in a reasonable timeframe (ideally on the order minutes for the separation

residence time). The simplest system modification would be the introduction of a chemical

demulsifier to the solution (Zolfaghari et al., 2016). The introduction of high concentrations

of sodium chloride (>10%) has been observed to reduce emulsion stability for crude oil and

water emulsions (Moradi et al., 2011, Wang et al., 2010) as well as canola oil and water

emulsions (Klaus et al., 2012). Therefore emulsion stability bottle tests were conducted with

12 wt % salt introduced to the mixture. Three emulsions were prepared; one with 25 % oil/

75 % water, a second with 50 % oil and 50 % water and a third with 75 % oil/ 25 % water.

The results of the bottle stability tests are summarised in Table C.1. Partial separation time

(a) Initial (b) 1 min (c) 1 hour (d) 1 day

190

indicates the time required to form two layers of approximately correct volume, whilst full

separation time indicates the time required for the individual layers to appear clear.

Table C.1 Summary of emulsion stability bottle test results.

Test Oil/water

[vol %]

NaCl

[wt %]

Partial

separation time

Full separation

time

A 50 / 50 0 ~ 1 hour ~ 1 day

B 25 / 75 12 < 1 min ~ 5 min

C 50 / 50 12 < 1 min ~ 5 min

D 75 / 25 12 ~ 1 hour ~ 1 day

The results of tests B and C indicate that sodium chloride can have a dramatic impact

on the stability of emulsions and effective phase separation. Sodium chloride is observed to

cause decreasing emulsion stability beyond a certain ionic strength value (which depends on

the emulsion system) (Perles et al., 2012). The sodium ions are suggested to interact with

the aqueous phase and alter the adsorption strength at the interface, thus impacting the droplet

stability. However sodium chloride is ineffective for test D where the mixture consists of 75

% oil and 25 % water; as water-in-oil emulsions show enhanced stability in the presence of

sodium chloride (Ling et al., 2018).

The results from the emulsion stability test lead to the introduction of 12 wt % sodium

chloride into the tap water storage tank of the flow loop system. The influence of salt on

emulsion stability is critical for the results of the two-phase oil water tests. For the flow

regimes where an oil-in-water emulsion forms (i.e. emulsion of oil-in-water and water as well

as full oil-in-water emulsions) the presence of the sodium chloride destabilises the emulsion

leading to phase separation in a reasonable time. For flow regimes where a water-in-oil

emulsion forms (i.e. dual emulsion of oil-in-water and water-in-oil as well as a full water-in-

oil emulsion) the sodium chloride is ineffective therefore the emulsion remains stable and is

unable to separate in a reasonable time.

C.2 Influence of the Halbach array stray field

The effect of the Halbach array stray field on the detection region is dependent on the

strength of the detecting field. In the case of the very low Earth’s magnetic field (~54 μT)

191

the impact of the Halbach array stray field is enough to significantly distort measurements at

separation distances lower than 45 cm. The impact of the Halbach array is quantified by

measuring the shift in Larmor frequency as a function of separation distance. The deviation

from the Earth’s magnetic field (ΔB0) can then be quantified using the following;

𝛥𝐵0(𝐿𝑃𝐷) = (𝜔(𝐿𝑃𝐷)− 𝜔0)

𝛾 (C.1)

where ω(LPD) is the measured Larmor frequency at a given separation distance, ω0 is the

Larmor frequency in the local Earth’s field (2294 kHz, when the Halbach array is not nearby)

and γ is the gyromagnetic ratio of 1H (42.58 MHz/T). Figure C.2 shows the change in local

magnetic field strength as a function of the polarisation to detection separation distance.

Figure C.2 Change in the local magnetic field strength as a function of the separation distance

between the polarisation and detection coil. The current measurement limit (at 45 cm) is indicated.

Figure C.2 shows the substantial impact of the Halbach array stray field on the Earth’s

field detection coil even at reasonably large separation distances (>45 cm). This can be

attributed to the considerable difference in magnitude between the two magnetic fields

(Halbach array field is 0.3 T whilst Earth’s field is ~54 µT). Figure C.2 shows that at the

current measurement limit of 45 cm, the magnetic field deviation is ~0.7 μT, corresponding

to a deviation of ~1.3 % relative to the local Earth’s magnetic field.

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80

ΔB

0[μ

T]


Currentmeasurement limit

192

If the detection field is higher, the relative impact of the Halbach array stray field will

be reduced. Upon back-extrapolation of the measured signals in Figure C.2; a detection field

of ~70 kHz is estimated to produce a relative deviation of 1 % at a 5 cm separation distance.

However this is a considerable back-extrapolation and more detailed magnetic field

simulations and experimental validation should be conducted to validate a reasonable

detection frequency. A detection coil in the range of 200-500 kHz will be considered for

future development of the low field NMR flow meter.

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