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l Contributed Paper

Magnetic Resonance Imaging, Vol. 14, Nos. 7/8, pp. 847-851, 1996 Copyright 0 1996 Elsevier Science Inc. Printed in the USA. All tights reserved

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QUANTITATIVE 1D SATURATION PROFILES ON CHALK BY NMR

DAN OLSEN,* SIMON TOPP,~ ANDERS STENSGAARD,? JENS VINTHER N@RGAARD,$

AND JAN REFFSTRUPS

*Geological Survey of Denmark, Thoravej 8, 2400 Copenhagen NV, Denmark, TDanish Research Centre of Magnetic Resonance, KettegLd Alle 30, 2650 Hvidovre, Denmark,

and $Technical University of Denmark, Lundtoftevej 100, 2800 Lyngby, Denmark

Quantitative one-dimensional saturation profiles showing the distribution of water and oil in chalk core samples are calculated from NMR measurements utilizing a 1D CSI spectroscopy pulse sequence. Saturation profiles may be acquired under conditions of fluid flow through the sample. Results reveal that strong saturation gradients exist in chalk core samples after core floods, due to capillary effects. The method is useful in analysis of corefloods, e.g., for determination of capillary pressure functions. Copyright 0 1996 Elsevier Science Inc.

Keywords: Porous media; Fluid saturation determination; 1D CSI.

INTRODUCTION

Petrophysical parameters are an integrated part of ev- ery simulation study concerning displacement pro- cesses in porous media. A prerequisite for meaningful modelling is reliable petrophysical data. Simulations and models rapidly evolve in the direction of more details and greater precision, and the underlying petro- physical data should evolve accordingly. The present paper describes a quantitative NMR method, which produces one-dimensional saturation profiles on sam- ples containing a water-oil fluid system. The back- ground for developing this method was a need for detailed saturation profile data in a new method for the calculation of capillary pressure functions.’ How- ever, the method presented here is equally suited to other situations where the fluid system may be ade- quately described in one dimension, e.g., dynamic or static experiments on suitable water-oil saturated po- rous systems.

Enwere and co-workers 253 used NMR for measuring qualitative saturation profiles during displacement ex- periments. 1D and 2D CSI pulse sequences with slice selection were used to obtain a spatial resolution of 0.94 mm on 1” core plugs. Echo time, TE, was 40 ms, and no correction was, made for relaxation.

Gamma ray attenuation and CT techniques may both be used for measuring saturation profiles.4-7 How- ever, these techniques require that the core be mea- sured two or three times while saturated with different fluid systems, resulting in problems with sample repo- sitioning and instrumental drift. Doping with reservoir incompatible chemicals is usually necessary.

EQUIPMENT AND METHODS

The objective of the NMR measurements was to obtain a succession of spatially resolved spectra along a selected direction. Each spectrum should represent the average spectrum of a slice through the sample.

A 4.7 T (200 MHz) SISCO scanner was used in the study. The scanner was equipped with a 13 cm insert gradient set, capable of producing magnetic gra- dients up to 100 mT/m. The RF coil used, was a slotted tube resonator, optimized for Bl homogeneity in the Z-direction.

A simple CSI sequence, containing one spatial and one chemical shift dimension was developed (Fig. 1) . Spatial information was obtained entirely by phase en- coding, and no slice selection was used. The full echo was sampled. To minimize off-resonance effects, the carrier frequency was chosen to be at the midpoint

Address correspondence to D. Olsen, Geological Survey of Denmark, Thoravej 8, 2400 Copenhagen NV, Denmark.

847

848 Magnetic Resonance Imaging 0 Volume 14, Numbers 7/8. 1996

RF

Phase encodlng

,mTE‘

Fig. 1. Timing diagram for the CSI pulse sequence.

between the water and oil peaks, and the shortest achievable hard pulses were used ( 100 /.Ls).

This pulse sequence fulfils the objective of the NMR measurements. It allows acquisition of spectra from the selected slices free of the chemical shift induced slice offsets that would result from the use of slice selection gradients. It also allows the use of hard pulses in order to minimize TE. The shortest practicable TE on the SISCO scanner is 3.5 ms, which enables mea- surement of samples having T2 time constants above approximately 2 ms.

A requirement of the measurement is that the water and oil peaks are spectrally well resolved. At 200 MHz the separation of the water and oil peaks is 700-800 Hz, depending on the oil used. In the investigated chalk samples the line widths (FWHM) of both peaks range from 60 Hz to several KHz. For line widths below approximately 300 Hz, interference between the peaks is negligible. As line widths increase above approxi- mately 600 Hz, measurement becomes futile.

Quantitative treatment of the data requires that the water and oil peaks are located at constant frequencies, and good homogeneity of the BO field across the whole sample volume is, therefore, important.

The time requirement for measurement of a 256 pixel saturation profile on a sample with T1 = 600 ms is 2 h, implemented with five different TEs and TR = 3 s. Compliance on TR, resolution, number of TEs, and phase cycling may bring the acquisition time down to 20 min, and still retain a fair signal to noise ratio.

DATA MANIPULATION

Figure 2 shows a grey tone rendering of a CSI data set. It represents a stack of spectra at consecutive spa-

tial positions. Several manipulations are necessary to transform the data set to a quantitative saturation pro- file.

Frequency Dimension Elimination For each spatial position the water and oil signal

intensities are determined by integration of the modu- lus spectrum.

Correction for Relaxation Repetition time, TR, is selected to be five times T, ,

to avoid differential saturation of the water and oil signals. The initial magnetization, M, , for each fluid in a selected slice is proportional to the amount of fluid in the slice. The transversal magnetization decays according to a complex multiexponential behaviour, which in this work is approximated by a single-expo- nential decay. Therefore, the signal intensity at time TE follows:

Z(TE) = Zie(-TE’T2), (1)

where Zi is the signal intensity corresponding to the initial magnetization Mi, and T2 is the spin-spin relax- ation constant. The effect of relaxation is corrected by acquiring CSI data at four to six different TEs, and at each spatial position, Z, by modelling according to Eq. ( 1) to obtain the initial signal intensity Ii (Z ) .839 Figure

-6bO0 6 60bO Frequency dimension (Hz)

Fig. 2. Example of a CSI data set. Lighter shade indicates higher signal intensity.

Quantitative 1D saturation profiles on chalk by NMR 0 D. OLSEN ETAL. 849

Single exponential fit of signal intensities vs TE (pixel 78)

0.2

0.2

.s

t 0 0.1

C

a jjl 0.1 v)

0.0

0. lImY!.?;;,,', 5 0 10 T&ls 20 25 a0

Fig. 3. Example of CSI data for a single pixel in a profile, and the calculated model functions. The profile is measured on sample MUD at 1 ml/h.

3 exemplifies the modelling of signal intensity vs. time for a single pixel in a typical profile. The measured water and oil signal intensities are plotted together with the model function. Examination of similar plots indicates that the single exponential model is an ade- quate description of the relaxation in the investigated chalk samples. The standard deviation on the calcu- lated Zi is generally 4-6% relative, but is dependent on the experimental setup. Relaxation correction ac- cording to biexponential and stretched exponential models has been attempted, but was inferior to the single-exponential model. Application of these models would require CSI data for a larger number of TEs, and a better signal to noise ratio.

Correction for Proton Density The intensity profiles are corrected for the proton

densities of the fluids. These are calculated from chem- ical analyses, or measured on pure fluids.

Calculation of Saturation Saturation profiles are calculated from the corrected

intensity profiles according to

s,(z) = 7, zi,w,com(z) wv,co*(Z) + L,o,com(Z)

(2)

so(z) = L.,,(z) + L,,,*(z) ’ (3)

where S,,,(Z) and S,(Z) are saturations of water and oil, respectively, at position 2 in the profile. Ii,,,,,(Z) and zi,o,corr (Z > are signal intensities of water and oil, respectively, at position 2 in the profile, corrected for relaxation and proton density. Equations (2) and (3)

are valid if the pore space of the sample does not contain a free gas phase.

FLOODING EXPERIMENTS

The fluid saturation gradient observed at the end of a flooding process is governed by the capillary forces in the structure and is, thus, an indirect measure of the capillary pressure function. In a new technique’ this is utilized to obtain the capillary pressure function by back-calculation from the measured steady state satura- tion distributions after flooding processes.

To obtain a steady-state saturation distribution, a core is first fully saturated with water and then flooded with oil until an equilibrium situation is reached, leaving part of the water retained by capillary forces in the core. To preserve the saturation gradient it is essential that the saturation profile is measured while flow is maintained. Flooding experiments were further planned to investigate the sensitivity of saturation profiles to variations in flood- ing rate, degree of sample homogeneity, and the stability of saturation profiles with time. Care was taken to elimi- nate free gas from the sample to produce a fluid system consisting solely of brine and oil.

The experiments were made on chalk samples from the Danish sector of the North Sea. All samples were 1.5 ” plug samples, which had been cleaned in a Soxhlet extractor using methanol and toluene. Basic parameters are given in Table 1. The phase-encoding direction was chosen to be along the length of the sample.

In one type of flooding experiment, a core was satu- rated with brine and then flooded down with oil until a stable saturation distribution was reached. In this situation the pressure difference across the sample was constant, and brine production had ceased. Flooding rate ranged from 1 ml/h to 8 ml/h. The duration of the flooding period was usually 7-12 days to assure saturation equilibrium. The flooding took place in a mobile flooding unit, ’ which enabled maintenance of continuous flow through the core during transportation, and, therefore, allowed the time-consuming flooding process to take place outside the NMR scanner. A conventional Hassler core holder manufactured from nonmagnetic materials was used.

Table 1. Petrophysical and NMR parameters

Sample id. M717 M15D M722

Length (mm) Diameter (mm)

WV ::-;5, Tl (ms) at S, = 100% T2 (ms) at SW = 100% Line width FWHM (Hz)

73.2 74.6 71.9 37.8 37.7 37.9

1.12 1.74 0.90 32.1 37.2 29.1

620 659 770 10.0 12.7 11.1

124 84 118

850 Magnetic Resonance Imaging 0 Volume 14, Numbers 7/8, 1996

To test the effect of varying the flow rate, a multirate experiment was performed on sample M15D. The core was flooded in three steps with flow rates 1 ml/h, 2 ml/h, and 4 ml/h, respectively, using a total period of 33 days to ensure equilibrium at each step. Flow was maintained during NMR measurement. The equilib- rium saturation profiles corresponding to the three flow rates are shown in Fig. 4. In all cases the capillary end effect is pronounced resulting in a water saturation at the outlet end of approx. 90%. A systematic change in profile shape is seen as flow rate increases. The 2 ml/h profile was acquired with a different setup, re- sulting in more noise in the profile. A capillary pressure function may be calculated from the profiles.’ Figure 5 shows a quantitative map of the water distribution in the sample at the time of the 1 ml/h saturation profile, calculated from images acquired with a CHESS pulse sequence.” The buildup of water caused by the end effect is clearly seen. In the lowest part of the sample a hairline fracture with high water saturation extends through the sample. Several faint structures are visible.

Another flooding experiment was made to test the change in the saturation profile during a prolonged flooding experiment (Fig. 6). In this experiment flow was stopped before the NMR measurements. The first profile was acquired after 7 days of flooding at 1 ml/ h. The sample was then rested for 51 days, preserved in laboratory oil, whereafter flow was restarted at 1 ml/h. After 18 days of flooding the second profile was acquired. Note that the saturation profile never recovers to the initial saturation at the outlet end, though the rest of the two profiles are very similar.

To test the effect of flooding on an inhomogeneous sample, a flooding was conducted on sample M722,

Fig. 4. Saturation profiles from multirate experiment, sam- ple MUD.

Fig. 5. 2D image of water distribution in sample MUD at the time of the 1 ml/h saturation profile. Lighter shade indi- cates higher water saturation.

which contains two transverse stylolites and several transverse laminations (Fig. 7). Contrary to the other examples, flow was perpendicular to the structures of the sample, resulting in a much more irregular satura- tion profile.

LIMITATIONS AND ACCURACY

Spin-spin relaxation and resolution of spectral peaks restrict the choice of samples suitable for NMR satura- tion profiling. Though the method is only demonstrated for chalk samples, it is estimated to be suitable for many samples of limestone and clean sandstone.

The accuracy of the produced NMR profiles is dif- ficult to assess because no comparable method was available for calibration. Comparison of profile mean saturations with conventional bulk saturation determi- nations indicates an accuracy of 2.0%-points on the mean saturations. The accuracy of the pixel saturations

80

0 10 20 30 40 50 60 70 80 90 100 Distance along sample (mm)

//I Inlet end - Exp. time 8 days - Exp. time 77 days /)i

Fig. 6. Change of saturation profile with time, sample M717.

Quantitative 1D saturation profiles on chalk by NMR 0 D. OLSEN ETAL. 851

Fig. 7. Inhomogeneous sample M722.

is inferior, perhaps around 5%-points, but dependent on the setup.

Saturation profiles are typically 256 pixels long, re- sulting in a spatial resolution of 0.39 mm for a 100 mm profile.

CONCLUSIONS 7.

Detailed saturation profiles on chalk samples were generated by a 1D CSI technique. The technique is at present restricted to rock material with T2 time con- stants above 2 ms, and susceptibility contrasts low enough to allow resol.ution of spectral peaks.

8.

Flooding experiments were conducted; these in- volved repeated NMR measurements of saturation pro- files during periods of up to 5 wk of sustained fluid flow through the sample.

9.

10. Acknowledgment-The Danish Ministry of Environment and En-

ergy is acknowledged for its funding of the present work through the EFP-93 programme.

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