Application of NMR Logging for Characterizing Movable and ......The multifrequency MREX SM tool is...

SPWLA 47th

Annual Logging Symposium, June 4-7, 2006

1

Application of NMR Logging for Characterizing Movable and Immovable Fractions of

Viscose Oils in Kazakhstan Heavy Oil Field

Chen, S.

1, Munkholm, M.S.

1, Shao, W.

1, Jumagaziyev, D.

1, and Begova, N.

2

1Baker Atlas and

2Karazhanbasmunai

Copyright 2006, held jointly by the Society of Petrophysicists and Well Log

Analysts (SPWLA) and the submitting authors.

This paper was prepared for presentation at the SPWLA 47th Annual Logging

Symposium held in Veracruz, Mexico, June 4-7, 2006.

ABSTRACT

Estimating both the producible and total heavy oil

volumes is always a challenging issue with

conventional logs and is particularly difficult for shaly

sand reservoirs having variable clay content and

mineralogy. NMR-based analysis can potentially

overcome the difficulty but it also needs to address its

own challenges regarding the poor sensitivity of

diffusion and the overlapping T2 between heavy oil and

bound water. We successfully integrated NMR and

conventional logs to interpret heavy oil reservoirs in a

pilot study involving nine wells. We demonstrate that

the integrated approach overcomes the shortcomings of

the individual techniques, and is particularly applicable

to the Buzachi heavy oil fields.

INTRODUCTION A significant amount of oil reserves in Buzachi

Peninsula in Kazakhstan are heavy or viscose oils. In a

shallow heavy-oil reservoir, the in-situ viscosity

reaches or exceeds 400 cP; yet commercial quantity of

oils is produced by spontaneous flow, even at low

reservoir temperatures and pressures. The challenge is

to discern the flowable heavy oil zones from the

immobile zones and quantify the movable oil.

Conventional resistivity-based analysis at best provides

the quantity (saturation) but not the quality (viscosity

and viscosity distribution) of heavy oil. Moreover, the

varying clay properties and water salinity increasingly

cause the uncertainty of conventional saturation

models. Thus, NMR is added to the logging program.

The multifrequency MREXSM

tool is capable of

collecting multiple echo trains in a single logging pass

(Chen et al, 2003). The NMR pilot study in this oil field

includes nine heavy oil wells; most of them were

logged with Poroperm + Heavy Oil sequence (Sun et al,

2006). Quantification of permeability, oil saturation and

viscosity are the main objectives for acquiring NMR

logs. The shallow reservoir mainly consists of

unconsolidated to poorly consolidated sands with

significant and variable amounts of clays. The heavy oil

T2 distribution overlaps with the CBW and BVI T2

distributions, making the quantification of irreducible

water and heavy oil difficult and subsequently affecting

the permeability estimation. Thus, the primary issue is

to quantify the oil saturation.

We used two approaches to interpret the NMR log data.

In the first approach, we used the SIMET (Sheng et al.,

2004) processing method, which is a fluids and

formation forward-modeling-based inversion method

that simultaneously processes all echo trains. To reduce

the uncertainty arising from the insensitivity of the

diffusion and relaxation time between CBW and heavy

oil, we used standard open-hole shale volume

estimation such as that based on gamma ray (GR) to

quantify the most viscose component of the heavy oil,

which is most likely the immobile part, while the

movable oil estimated from SIMET is not constrained

by GR. In the second approach, we applied 2D NMR

inversion to visually separate heavy oil from CBW and

BVI. When non-NMR based CBW constraint is needed,

the constraint is built into the 2D inversion process.

Consistent results are obtained from the SIMET and 2D

NMR interpretations. Furthermore, permeability is

estimated based on SIMET results, excluding the heavy

oil volume from BVI and CBW. We completed our

petrophysical analysis by integrating NMR-based

saturation analysis with our conventional, resistivity-

based method. Moreover, with 2D NMR, we can truly

observe the viscosity variations with depth and the oil

constitutional changes from T2 and diffusivity

information without the assistance of other logs.

The comprehensive study was first conducted on one

well. The procedure was then applied to all other wells

in the same field without requiring further modification

of the interpretation models.

NMR LOGGING TECHNIQUE FOR HEAVY OIL

DETECTION

Special Data Acquisition Features for Heavy Oils The mechanism of relaxation decay of fluids in porous

rock can be expressed as the collective contributions of

the bulk, surface, and diffusion-induced relaxation

rates,

SPWLA 47th


2

( )12

1

1111

2

2

2222

DTEG

V

S

T

TTTT

B

DSB

⋅⋅++=

++=

γρ (1)

The surface relaxation term, ,VSρ originates from the

fluid-rock surface molecular interaction and is

significant only for wetting fluids. The combined bulk

and surface relaxation rates are often called the intrinsic

relaxation rate, 1/T2int, i.e.,

SB TTT 22int2

111+= , (2)

because both are the intrinsic properties of fluid and

formation, rather than controllable by experiments.

Thus, for non-wetting phase, ∞→ST2 , and

BnwTT 2int2

11≈ . (3)

Equation (3) is also valid for wetting fluid phase when

the bulk relaxation time is much shorter than the

surface relaxation time, .22 SB TT << Heavy oils have

extremely low relaxation times, and thus Eq. (3) is

always valid even though some heavy oil reservoirs

may be oil- or mixed-wet.

The third term in the right side of Eq. (1) is the

diffusion-induced decay term. It is experiment-

dependent and can be manipulated to enhance the

diffusion effect by monitoring interecho spacing, TE,

and the magnetic field gradient strength, G. For MREX

logging tool, varying operating frequency results in

different sensitive volumes, each corresponds to a well-

defined magnetic field strength B0,

γ

πfB

20 = , (4)

and a field gradient

drdBG 0= . (5)

For the MREX tool, the frequency dependence is

approximated by

5.1

fGMREX ∝ . (6)

Discerning oil and water by NMR logging techniques is

based on their apparent relaxation time, intrinsic

relaxation time, or diffusivity contrast, or a combination

thereof. Both heavy oil and bound water relax quickly,

even though the mechanisms of the fast relaxation rate

for the two fluids are different. The bulk relaxation is

dominant for heavy oil and surface relaxation for bound

water. Although the diffusivity contrast between the

two fluids is profound, it is difficult to detect because

any diffusivity-contrast-based technique must first

overcome the dominant intrinsic relaxation mechanism.

To achieve this, we constructed a PoroPerm + Heavy

Oil pulse sequence, which acquires 29 echo trains in

one logging pass. Among these echo trains, G varies

from about 15 Gauss/cm to nearly 40 Gauss/cm; the TE

range varies from 0.4ms to 10ms. The practical TE

upper bound is limited by the intrinsic relaxation time

of bound water and heavy oil, thus further increase of

TE is not desirable. Because of the extremely low

diffusivity of heavy oil, the use of a large G·TE contrast

is insufficient to quantify the heavy oil diffusivity but

qualitatively trends down the oil signal towards the

lower diffusivity range on a 2D map, thereby departing

from the water diffusivity line. In contrast, water has a

much larger diffusivity, thus is more sensitive to

respond to the G·TE variation.

Although a long TE is favored for enhancing the

diffusion sensitivity, the rapid decay due to a large

G·TE is detrimental to the overall SNR, because only a

few echoes have the signal amplitudes above the noise

level. The disadvantage is counteracted in the PoroPerm

+ Heavy Oil sequence by the following two aspects.

First, since the echo train acquired with a larger G·TE

decays much faster, only a small data acquisition

window is needed. Consequently, an echo train data

acquisition window is designed to be G·TE dependent

with the smallest window for the largest G·TE echo

train. Second, short wait times are used for the large

G·TE echo trains since the rapid relaxing heavy oil and

bound water signals do not require a long time to reach

full polarization. The time saved by decreasing the echo

train window and TW is used to increase the number of

repetitive measurements of the short echo trains for

improving the SNR of the fast decay components. More

detailed discussion is described in Sun et al. (2006).

Introduction to 2D NMR Processing Method The PoroPerm + Heavy Oil sequence produces multiple

echo trains with different wait times (TW) and interecho

time (TE) at up to six frequencies. 2D NMR maps (Sun

et al, 2003&2006, Hursan et al, 2005) were used to

view the diffusivity and intrinsic relaxation time

simultaneously.

The 2D inversion model,

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( )

( ) ,,...,2,1 and 3,3,1

12

exp

exp1),(

,

2

int2

3

1 1 1 int2,

,,0

TEKtR

tTEGD

T

t

TR

TWMTWtM

kjn

kl

n

k

j

N

n

L

l njn

njlk

⋅==

⋅⋅−−×

⋅−−=∑∑∑

= = =

γ (7)

requires no prior knowledge of fluid types and

properties prior to inversion process. The interpretation

of fluids is based on the location of signal intensities on

the 2D map. Since different TW data are included in the

data processing, the inversion model takes into account

the longitudinal relaxation time, T1, transverse

relaxation time, T2int, and diffusivity, D. In order to

reduce the size of the inversion matrix, we replaced the

T1 parameter with the ratio parameter .int21 TTR =

Since T1 is the same or slightly greater than T2int for any

type of fluids, R is generally a number greater than and

approximately unity. Thus, we can discretize R to no

more than three bins instead of discretizing the whole

T1 range that would involve 20-30 bins. The three 2D

maps corresponding to different R values are summed

up to construct a single 2D map:

[ ]∑=j

jRTDmapTDmap ),,(),( int2int2 . (8)

A 2D map can be further reconstructed to a 1D T2

spectrum by summing over different D components:

[ ]∑=

k

k TDmapTP ),()( int2int2 . (9)

Interpretation with NMR and Conventional Log Although the data acquisition and processing methods

described in the previous sections improve the

sensitivity of discerning heavy oil and bound water

from NMR data alone, there are circumstances where

quantitative separation of heavy oil from extremely fast

decaying bound water components is difficult.

Examples of such situations include (1) highly

conductive boreholes which reduce NMR SNR

significantly, and (2) formation rock minerals which

cause high internal gradient and consequently, the

smeared intensity distribution on T2 and diffusivity

map. When the heavy oil and bound water can not be

separated well, integrating NMR log with another log

or logs can significantly improve interpretation

quantitatively.

In such cases, an NMR–independent clay bound water

estimate can be very useful. The non-NMR CBW

estimate should be based on a shale indicator

appropriate for the formation. Examples of logs used

for shale volume determination include gamma-ray

(GR), spontaneous potential (SP), a combination of

neutron and density porosity, resistivity, or a

combination of the above. The choice is often based on

their sensitivity to the particular formation; in this

section we use a generic symbol, 2CBW , to represent

the non-NMR-based CBW estimate.

In the following, we consider two methods for

integration of a non-NMR-based CBW with an NMR

log.

Heavy oil usually has a broad T2 spectrum. SIMET

and/or 2D NMR may have the sensitivity to estimate

the longer T2 components of the heavy oil T2 spectrum

but may not have the sensitivity for the shortest T2

components in the heavy oil spectrum. Therefore, our

strategy in the first approach consists of the following

steps:

(1) Perform SIMET processing with the heavy oil T2

range set to be above the CBW cutoff. Thus, all the

shortest heavy oil T2 components are lumped to the

pseudo-CBW, denoted :'CBW

∑=

=

CBWcoutoffT

Ti

iTPCBW

,2

1,2

)(' int,2 . (10)

The heavy oil volume obtained from SIMET

inversion contains the lighter components in the

crude heavy oil. This light component is denoted as

LHOV , .

(2) Compute the difference between CBW’ and the

non-NMR log derived CBW2. The over-estimation

of NMR-based clay-bound water is part of the

heavy oil that overlaps with CBW on the T2

spectrum.

2, ' CBWCBWV HHO −= . (11)

(3) The NMR-based porosity estimate is compared to

another porosity estimate, such as a density-based

porosity. If MREXφ underestimates porosity

compared to density porosity ZDENφ , by more than

the random error margin, the difference represents

the extra-viscose components that are not

observable by the MREX tool when using TE =

0.4ms:

MREXZDENMHOV φφ −=, (12)

and, thus, should be included in the total heavy oil

volume:

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MHOHHOLHOHO VVVV ,,, ++= . (13)

Obviously, the validity of Eqns. (11) and (12) relies on

the robustness of the non-NMR log information.

Practically, a non-negative constraint is always applied

on HHOV , and MHOV , . In the subsequent sections, the

above approach is referred to as “SIMET-based

integrated petrophysical analysis.”

For a reservoir that exhibits significant lithology

variations, the second approach, described below, may

be more preferable.

The second approach uses the non-NMR-based CBW

estimate as a constraint built into the inversion process.

The detail of the second approach is given in Appendix

A. Here, only an outline is described. For notation

simplification purposes, a matrix form is used for

describing the inversion problem:

,md A= (14)

where d is the experimental data, m is the unknown

vector, and A is the inversion model matrix. The

inversion process is the least squares solution of Eq.

(14) with the inclusion of a regularization term that

stabilizes the solution

min,2

2

2

2=+− mdAm mWα (15)

subject to (1) the non-negative constraint,

0 ≥m , (16)

and the CBW constraint,

22,12

int2

0 torCBWmtorCBW

cutoffydiffusivitwaterDcutoffCBWT

ji +≤≤−≤ ∑>

<

where the two tolerances, 1tor and ,2tor are set by the

user and can be field specific and depend on the

robustness of CBW2.

FIELD EXAMPLES In the pilot study in a heavy oil field in the Buzachi

Peninsula of Kazakhstan, MREX logs data have been

acquired in nine wells. The key objectives for acquiring

NMR data in this field are to obtain permeability

estimates and to quantify the heavy oil saturations.

Knowing that NMR relaxation time or diffusivity

estimates correlate with the oil viscosity, we also want

to determine whether NMR has the sensitivity to

distinguish different grade oils. Since heavy oil T2

overlaps with bound water (capillary bound water

(BVI) and clay bound water (CBW)), correctly

estimating bound water and permeability requires

separating the oil and water volumes first. Thus, the

essential NMR data analysis is to discern the heavy oil.

These objectives are successfully met by applying the

2D NMR and the SIMET-based integrated

petrophysical analysis methods as described in the

previous sections.

Geology The field was discovered in the 1970’s. Production

drilling began in 1980; since then, thousands of wells

have been drilled in the field.

The reservoir formations contain unconsolidated sands,

poorly-cemented sandstones, and aleurolites

interlayered with shale. Overall clay content and

mineralogy show large variation over the field with

significant amount of chlorite, smectite, hydromica and

kaolinite. From the many wells drilled in the field, the

reservoir rocks are known for their high variability

vertically and laterally, which compromises the

reliability of density and neutron-based porosity

estimation. For this reason, the mineralogy- and

lithology-independent NMR porosity is useful in this

field.

The crude oil in the field is a low-GOR, heavy oil with

fluid densities in the range of 914.5 – 926.5 kg/m3 and

viscosities in the range of 240-400 cP under reservoir

conditions. The oil often contains highly resinous

components (up to 20 %) but relatively lower amounts

of paraffin. Resins in general have short T1 and T2

times, rendering the resins signal particularly

challenging to separate from bound water in the NMR

data. Furthermore, the non-Newtonian fluid nature of

resins may cause the resin-rich crude oil not to obey the

known relaxation time-viscosity correlations (Vinegar,

1995, Morris, 1997, Zhang et al., 1998, Chen et al.,

2004) in which case these known correlations may not

be applicable for characterization or quantification of

the oil volume and quality.

SIMET-Based Integrated Data Analysis In addition to the MREX log, wireline gamma ray,

density, neutron, acoustic and resistivity logs were also

included in the logging program for these wells. In the

initial analysis, a volumetric shaly sand analysis was

carried out based on the conventional open hole log

data alone, plotted in the first track of Fig. 1, and the

resultant Vsh is subsequently integrated with the MREX

data.

For BVI and CBW estimates, the simple approach of

applying T2 cutoff values to the NMR T2 spectrum for

separation of the fractional porosities does not work for

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the heavy-oil reservoir intervals. Shown in Track 2 of

Fig. 1 are the standard wellsite MREX deliverables for

Well #1 based on the use of default CBW and capillary

bound water T2 cutoff values. Because these standard

wellsite deliverables are based on the partition of

apparent T2 spectrum which does not separate oil from

water, the BVI and CBW volumes are potentially

contaminated with heavy oil signals. Consequently, the

Coates permeability computed from these BVI and

BVM values is not reliable. Track 3 compares the

wellsite permeability estimate with two different post-

processing permeability estimates. The wellsite

permeability corresponds to the effective permeability

for the case that none of the heavy oil can be produced.

However, it is much too small for the poorly

consolidated, high-porosity sands in the reservoir.

Furthermore, the permeability curve derived from the

wellsite shows only a weak correlation with the sand

volume computed from the conventional shaly sand

analysis, suggesting that those are heavy oil-bearing

sands. The permeability curve, marked as Perm without

VHO,H in Track 3 and derived from the SIMET analysis

(Track 4), shows much higher permeability in the

reservoir sand zone. Since SIMET first separates heavy

oil from water and then includes the heavy oil volume

into BVM such that

LHOVMBVMWBVM ,+= (17)

the SIMET-based permeability analysis represents the

effective permeability of the reservoir for the case that

the lighter components of the heavy oil is movable. In

the permeability track, the third permeability curve

corresponds to the situation where both LHOV , and

HHOV , should be movable, which is unrealistic for the

reservoir situation but would be compatible to the

cleaned formation rock absolute permeability. In fact,

this permeability estimate is in the same range as the

core permeability reported from historical core data and

well tests. The details of the SIMET analysis and the

determination of heavy vs. extra heavy oil volumes are

discussed in the subsequent paragraphs.

In the post-processing analysis, the Vsh is determined

based on conventional log analysis (Track 1). The

reservoir shale properties have been studied extensively

in the field in the past. Therefore, the variation of the

shale properties are well understood and incorporated in

the analysis to obtain reliable Vsh estimates. However,

as all the reservoir sands contain dispersed shale with

high variability in clay mineralogy, the electrical effects

from clay are challenging to a resistivity-based

saturation analysis. Furthermore, uncertainty in

saturation exponent and reservoir water salinity also

add to the complexity of the saturation analysis for the

field as a whole. In that aspect, an independent

saturation analysis from NMR is desired for cross-

validation.

We applied the SIMET-based integrated petrophysical

analysis, described in the previous section, to MREX

and Vsh data. Because there is no porosity

underestimation occuring, namely all heavy oil signals

are detectable by MREX with TE = 0.4ms, only the first

two steps of the analysis methods are used. The

SIMET-based integrated analysis result is shown in

Track 4. Except for the vertical resolution difference,

the shale intervals of the conventional and NMR data

are in general agreement. In the reservoir shaly sand

intervals, the field bound water volume (MVBW+MBVI)

is much too high. Specifically for clay bound water,

which reaches an unrealistic 22 pu for an interval with

15-20% total shale volume at approximately xx26-xx28

m. SIMET-based integrated analysis yielded much

improvement in the interpretation of the reservoir fluids

and has identified much of the apparent MCBW as

heavy oil.

In Track 4, the oil volumes directly obtained from the

SIMET without integrating Vsh is shown in light green

color, representing LHOV , . Extra heavy oil components,

shown in dark green color and represented by ,,HHOV

are obtained from the integrated analysis. The LHOV ,

oil has a longer relaxation time than that of ,,HHOV thus

is likely to produce. Note that the relaxation time range

of LHOV , oil is consistent with the typical resinous

hydrocarbon component. Adding resin to heavy oil

helps to produce; therefore, this oil volume is

considered to be ultimately producible. The oil

associated with HHOV , is not expected to be producible

but is part of the total oil-in-place and quantification of

this oil volume is important for the construction of an

accurate water saturation model.

Comparison of SIMET and 2D NMR-Based Analysis In this section we illustrate the results of using the two

integrated approaches to obtain the heavy oil and extra

heavy oil volumes. Figure 2 shows the result also for

Well#1. The resistivity logs and SIMET-based

permeability are shown in the 3rd

track. The NMR and

neutron-density porosities are shown in the 4th

track.

We see MREX porosity is in good agreement with the

density porosity in the sand zone. In the shale-rich

zones, however, density porosity is incorrect when the

sand matrix density value is used. On the other hand,

MREX porosity is not affected by the clay densities.

Shown in the 5th

and 6th

tracks are the T2int distributions

of water and heavy oil, respectively, derived from

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SIMET with the oil T2 range restricted to be above 3

ms. Any heavy oil signals below 3ms are included in

the clay bound water and subsequently determined by

integration with Vsh. Consequently, the SIMET-based

total oil saturation estimate is shown in the 7th

track and

the volumetrics, including the breakdown of VHO,L and

VHO,H, are plotted in Track 8.

In order to verify the SIMET result, 2D NMR analysis

is also performed on Well#1 and the Vsh constraint is

applied during the inversion. The 2D NMR-based

volumetrics are plotted in Track 9 and the

corresponding 2D NMR maps are shown in Track 10.

With the application of Vsh constraints, the 2D maps

show clean distinction between CBW (e.g., xx30) and

heavy oil (xx10-28). Moreover, among the heavy oil

depths, 2D NMR is able to distinguish oil that has more

of the heaviest components (e.g., xx26-xx27) from oil

that contains only small amounts of the heaviest

components (e.g., xx32-xx35) and these estimations are

in good agreement with SIMET-based integrated

interpretation (Track 8). The heaviest components are

observed at the lowest T2int end of the heavy oil signal.

Note that because 2D maps occupy more plotting space

than 1D curves, the exact depth that each 2D map

corresponds to should be considered a close

approximation.

The analysis shows some movable water over the oil-

filled sands. Considering that MREX has a depth of

investigation of 2.4-4 inches, that may be due to

invasion of the water-based mud in the MREX

investigative volume. The resistivity-based saturation

analysis of the open hole analysis is based on the deeper

reading induction log, which should see less, if any,

invasion. Overall, we find that for relatively thick oil

sands, the resistivity based Sw is in good agreement

with MREX-based BVI, supporting the argument that

the movable water seen by MREX is in fact due to

invasion.

The SIMET estimate of movable water and oil

corrected through integration with the conventional

analysis is considered the best estimate provider of

hydrocarbon storage capacity for the reservoir.

Qualification of Clay Types

Figure 3 shows a section from Well#2 of a shaly sand

formation with heavy oil intervals separated by shale

barriers. If we compare the depth intervals that are

dominated by shale, we find some shale intervals over

which the density and NMR porosities match very well

(depths marked by I) and other intervals over which

NMR porosity is significantly higher than density

porosity. In the absence of a tool problem, the

difference must originate from the variations in clay

types with different densities. When the sand matrix

density is used to plot the density porosity, clays with

higher matrix densities appear to have lower shale

porosities.

The difference between MREX and density porosities is

useful information that may qualitatively reveal the

dominant clay types. For shale intervals over which

NMR and density porosities agree well (Marked I in

Fig. 3), the clay density is close to 2.65, thus the

dominant clay type may be illite. On the other hand, for

intervals with NMR and density porosity mismatch, we

can estimate the shale matrix density using

)1()1( densanddenwNMRshNMRw φρφρφρφρ −⋅+⋅=−⋅+⋅

where NMR porosity in the shale is considered to be the

true porosity and denφ is the apparent density porosity

computed by assuming shale matrix density to be the

same as the sand matrix density. Thus,

( ) ( )

NMR

denNMRwdensandsh

φ

φφρφρρ

−

−−−=

1

1 (18)

For example, the zone marked C2 has

,24.0 and 18.0 ≈≈ NMRden φφ

using 1 and 65.2 == wsand ρρ we obtain

,78.2=shρ which may indicate that the dominant clay

type is chlorite. We intend to further investigate the

possibility of using this approach for qualification of

clay types in other wells.

CONCLUSIONS We developed methodology of integrating conventional

logs with NMR logs to improve the heavy oil reservoir

quantification. The conventional log-based shale

estimate can be integrated in either T2 domain or during

the echo train inversion process with SIMET or 2D

NMR approaches. We applied the new approaches to

heavy oil fields in Buzachi Peninsula in Kazakhstan.

The integrated analysis and standard open hole

volumetric analysis provides reliable irreducible water,

movable water, movable hydrocarbon and effective

porosity from MREX PoroPerm + Heavy Oil

acquisition. Furthermore, we have attempted utilizing

the difference between the apparent density porosity

and NMR porosity in shale intervals to qualify

dominant clay types.

ACKNOWLEDGEMENTS

We thank Arpad Mayer, Darcy Dorscher and Ed

Kueber of Karazhanbasmunai and Geoff Page, Gabor

SPWLA 47th


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Hursan, Weidong Li, and Jason Chen of Baker Atlas for

support, discussions and assistance. We would also like

to thank Karazhanbasmunai and Baker Atlas for

permission to publish this paper.

ABOUT THE AUTHORS

Songhua Chen is a senior staff scientist and project

manager for NMR interpretation development at Baker

Atlas Houston Technology Center. Prior to joining

Baker Atlas in 1996, he was a research scientist for 5

years with Texas Engineering Experiment Station in

College Station, Texas, where he worked in the area of

NMR and MRI applications to flow in porous media.

Songhua earned a BS from Nanjing Institute of

Technology in China and a PhD from University of

Utah, both in Physics.

Mette Munkholm is a staff petrophysicist with Baker

Atlas in Copenhagen, Denmark, presently with a

special focus on NMR geoscience applications. Prior to

the Copenhagen assignment, she worked as

petrophysicist for Z&S Geology, Stavanger and Baker

Atlas, Milan. She holds a BS degree in physics and

chemistry and MS and PhD degrees in geophysics from

the University of Aarhus, Denmark.

Wei Shao is a scientific software engineer for NMR

interpretation development at Baker Atlas Houston

Technology Center. Wei Shao earned a PhD from the

University of South Carolina in applied mathematics. Dossan Jumagaziyev is a senior petrophysical engineer

with Baker Atlas in Aktau, Kazakhstan. Prior to joining

Baker Atlas in 2002, he worked as GIS analyst for

Tengizchevroil and as senior geologist for

Karazhanbasmunai, Kazakhstan. He holds a BS degree

in oil and gas geology from the Kazakh National

Technical University of Almaty, Kazakhstan.

Nina Aleksandrovna Begova is the Principal

Geologist of Geology & Engineering Department of

Karazhanabsmunai JSC, experienced in classic

technologies of oil well designing, up-to-date

techniques of oil reservoirs development and simulation

of HC deposits. She graduated from Gubkin Petroleum

Institute, Faculty of Geology, Moscow in 1979. Her

major scientific interests include the integration and

application of geological and geophysical data for

digital simulation of geological objects and the analysis

of subsurface geology and evaluation of current state of

deposits using various software packages.

NOMENCLATURES

A inversion model matrix

B vector for CBW2 constraint

B0 static field strength

B1 RF field strength

CBW Clay bound water

CBW2 Clay bound water estimate from non-NMR log

CBW’ pseudo clay bound water signal which includes

True CBW and overlapping heavy oil

Components

CBWGR CBW estimate derived from GR

D diffusivity

e,E Echo amplitude with and without noise

included

f frequency

G RF field gradient strength

GR Gamma ray

GRsh Gamma ray reading from shale zone

GRsd Gamma ray reading from sand zone

L echo length, EE TN ⋅

M Echo magnetization amplitude

NE number of echoes in an echo train

P T2 distribution function

R ratio of T1/T2int

SE Sum of echoes

T1 longitudinal relaxation time

T2 transverse relaxation time

BT2 bulk fluid transverse relaxation time

T2cutoff dividing time between BVI and BVM

T2diff extra decay time factor due to diffusion

T2int intrinsic relaxation time

T2surf surface relaxation time

TE interecho time

TW wait time

W Regularization (stabilizing) matrix

VHO Volume of heavy oil

VHO,L Volume of lighter components of heavy oil

VHO,H Volume of heavier components in heavy oil

VHO,M Volume of extra-heavy components of heavy

oil that can not be sensed by NMR logging

tool

α Regularization parameter

φ porosity

APPENDIX

A. Description of the Inversion Problem

NMR echo signal amplitudes for fluids in porous media

can be expressed by a multi-exponential decay model.

The general multi-exponential model can be divided

into two categories. The first category assumes no prior

knowledge of fluid properties in the subject porous

rock, thus the broadest possible ranges of the key NMR

properties, intrinsic relaxation time iT int,2 and

diffusivity jD , are used in the inversion model. That is,

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the model does not tag fluid types, water, oil, or gas, to

the protons that contribute to the measured NMR

signal. The task of finding the fluid types and quantities

is done in the parameter domain after the parameters

are obtained from inversion. An example is 2D NMR

inversion. The second category assumes the fluid types

and properties are known or predictable; therefore, the

inversion models included the prior information to

reduce the parameter space. SIMET is an example of

the second category. In this appendix, we limit our

discussion to the first category approach.

The echo amplitude is

( )( )

∑∑∑= = =

⋅⋅+−

×

⋅−−

=

L

l

N

j

M

i

k

qj

i

il

p

ji

qpk

tTEGD

T

TR

TWm

TETWtd

1 1 12

int,2

int,2,

)12

1(exp

exp1

),,(

γ

(A1)

where ( ) TEKtk ⋅= ,...,2,1 is the time associated with

the kth

echo.

MREX PoroPerm + Heavy Oil sequence acquires data

with an assortment of wait times TW and interecho

times TE, which may also have different echo train

lengths K. Inverting the echo trains described by Eq.

(A1) yields the signal intensity jim , . For simplicity,

Eq. (A1) is often expressed in a linear matrix equation

format

,md A= (A2)

where d is the experimental data and m is the unknown

and

( )( )

⋅⋅+−

×

⋅−−=

k

qj

i

il

p

ijl

tTEGD

T

TR

TWA

)12

1(exp

exp1

2

int,2

int,2

γ (A3)

is the matrix element. The direct inversion of this

equation is ill-conditioned, thus a regularization term is

often used,

0. subject tomin2

2

2

2≥=+− mmdAm mWα (A4)

In the above expression, the condition 0≥m is known

as the non-negative constraint. It means that all

molecules must either positively contribute or do not

contribute to the total echo signal, but cannot contribute

it as a negative amplitude.

B. Non-NMR-Based CBW Constraint A non-NMR CBW estimate can be derived from

gamma-ray (GR), resistivity, spontaneous potentials

(SP) log, neutron and density porosity log, a resistivity

log, or a combination of them. For example, we can use

GR as the non-NMR CBW2 estimate. Practically, one

can use the GR measured at 100% shale and 100% sand

depths, and a porosity log to construct a clay-bound-

water curve, GRCBW :

sh

sdsh

sd

GRGRGR

GRGRCBW φ⋅

−

−= . (A5)

In this appendix, we use a generic symbol, 2CBW , to

represent the non-NMR-based CBW estimate. Most of

the non-NMR-based CBW2 estimates are based on the

mineralogy effects distinctive or weighted more to

clays. NMR-derived CBW is based on the strong

surface relaxivity, a significant amount of surface

water, and the extra-fine particle sizes associated with

clay. Therefore, directly equating the NMR and non-

NMR-based clay estimates sometimes may not be

practical. Instead of forcing CBW = CBW2, we allow

user-defined tolerances in the constraint,

22,12

int2

0 torCBWmtorCBW

cutoffydiffusivitwaterDcutoffcbwT

ji +≤≤−≤ ∑>

<

(A6)

where the two tolerances, tor1 and tor2 are set by the

user and can be field specific.

C. Inversion By combining Eqns. (A4) and (A6), the inversion

problem is equivalent to the following minimization

problem:

min2

2

2

2=+− mdAm mWα

subject to

0≥m

and

.0 22,12

int2

torCBWmtorCBW


ji +≤≤−≤ ∑>

<

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To implement the CBW2 constraint, two new variables,

u and v, are introduced so that we can convert the CBW2

inequality constraint to the following constraints:

,22,

int2

torCBWum


ji +=+∑>

<

(A7)

,12,

int2

torCBWvm

cutoffydiffusivitwaterDcCBWcbwT

ji −=−∑>

<

(A8)

subject to .0,0 ≥≥ vu

The details of the algorithm are documented in Chen et

al. (2006).

Eqns. (A7-A8) can be combined with Eq. (A2) to form

a new equation

111 dmA = (A9)

where where

,

2

11

−

+=

torcbw

torcbw

d

d

GR

GR (A10)

,1

=

v

u

m

m (A11)

and

−

=

10

01

00

1

B

B

A

A . (A12)

In Eq. (A12), B is a vector corresponding to the CBW2

constraint. Using these notations, Eqns. (A4) and (A6)

can be expressed in the following matrix form:

min,|||||||| 22

22111 =+− mWdmA mα (A13)

with the positive constraints of

.0,, ≥vum (A14)

LITERATURE CITED

Chen, S., Beard, D.R., Gillen, M., Fang, S., and Zhang, G.,

MR Explorer Log Acquisition Methods: Petrophysical

Objective-Oriented Approach., paper presented at the 2003

SPWLA Annual Symposium and Exhibitions, Galveston,

Texas.

Chen, S., Kwak, H., Zhang, G., Edwards, C., Ren, J.,

and Chen, J.: “Laboratory Investigation of NMR Crude

Oils and Mud Filtrates Properties in Ambient and

Reservoir Conditions,” paper SPE 90533, presented at

2004 SPE ATCE, Houston, Texas, Sept 26-28.

Chen, S., Shao, W., Fang, S., Munkholm, M., and Gillen, M.,

Method and Apparatus for Characterizing Heavy Oil

Components in Petroleum Reservoirs, U.S. patent pending,

2006.

Fang, S., Chen, S., Tauk, R., Philippe, F., and Georgi, D.,

Quantification of Hydrocarbon Saturation in Carbonate

Formations Using Simultaneous Inversion of Multiple

NMR Echo Trains,” SPE paper 90569, presented at 2004

ATCE, Houston, TX.

Hursan, G., Chen, S., and Murphy, E., “New NMR

Two-Dimensional Inversion of T1/T2app vs. T2app Method

for Gas Well Petrophysical Interpretation,” Paper GGG

presented at 46th

SPWLA Annual Symposium , New

Orleans, June 26-29, 2005.

Morriss, C.E., Freedman, R., Straley, C., Vinegar, H.,

and Tutunjian, P.N.: "Hydrocarbon Saturation and

Viscosity Estimation from NMR Logging in the

Belridge Diatomite," The Log Analyst (1997) March-

April, 44-59.

Sun, B. and Dunn, K-J., “Characterization of Porous

Medium Properties Using 2D NMR,” presented at Am.

Phys. Soc. 2003 Annual March Meeting.

Sun, B.Q., Olson, M, Baranowski, J., Chen, S., Li, W.,

and Georgi, D., Direct Fluid Typing and Quantification

of Orinoco Belt Heavy Oil Reservoirs Using 2D NMR

Logs, to be presented in 2006 SPWLA Annual

Symposium and Exhibition, Veracruz, Mexico, June 4-

7, 2006.

Vinegar, H.: "NMR Fluid Properties," SPWLA Short

Course on Nuclear Magnetic Resonance Logging, D.T.

Georgi (ed.), SPWLA, Paris (1995), Section 3.

Zhang, Q., Lo, S-W., Hirasaki, G.: "Some Exceptions

to Default NMR Rock and Fluid Properties," SPWLA

39th Annual Logging Symposium, Keystone, June,

(1998).

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Figure 1. Comparison of BVI, CBW, and permeability estimates derived from the overall apparent T2

distribution and from SIMET based analysis. The latter separates the heavy oil from bound water first, then

includes the heavy oil in the movable fluid volume for permeability estimation. The movable water shown in

the log is most likely from invaded water-based mud filtrate.

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Figure 2. 2D NMR and SIMET-based integrated interpretation for Well#1. Track 1: GR, SP, Caliper and Bit

size. Track 2: Measured depth in meter. Track 3: Resistivities. Coates permeability. Track 4: Density-

Neutron on sandstone matrix. Total and effective MREX porosity. Track 5: T2 fluid distribution for CBW,

BVI and BVMW with CBW cutoff at 3.3 ms and T2 cutoff at 33 ms. Track 6: T2 fluid distribution for heavy

oil. Track 7: Total water saturation from SIMET-based integrated interpretation. Track 8: Fractional

porosity for CBW, BVI, moveable water and oil from SIMET. Pore volume filled by CBW in brown, BVI in

pale blue, moveable water in blue, VHO,L in light green, and VHO,H, in dark green. Track 9: Fractional porosity

for CBW, BVI, moveable water and oil from 2D NMR. Pore volume filled by CBW in brown, BVI in pale

blue, moveable water in blue, VHO,L in light green, and VHO,H, in dark green. Track 10: 2D NMR diffusivity

versus T2 maps.

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Figure 3. SIMET-based integrated interpretation for Well#2. Zones I show good agreement between density

and MREX porosity. Zones C1 and C2 show higher MREX porosity than apparent density porosity. Track 1:

GR, SP, Caliper and Bit size. Track 2: Measured depth in meter. Track 3: Resistivities. Coates permeability.

Track 4: Density- Neutron on sandstone matrix. Total and effective MREX porosity. Track 5: T2 fluid

distribution for CBW, BVI and BVMW with CBW cutoff at 3.3 ms and T2 cutoff at 33 ms. Track 6: T2 fluid

distribution for heavy oil. Track 7: Total water saturation from SIMET-based integrated interpretation.

Track 8: Fractional porosity for CBW, BVI, movable water and oil. Pore volume filled by CBW in brown,

BVI in pale blue, movable water in blue, VHO,L in light green, and VHO,H, in dark green.

I

I

C1

C2

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