gtecorrectionformultigte_spe84481

8/11/2019 GTECorrectionforMultiGTE_SPE84481

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SPE 84481

GTECorrection for Processing Multigradient, Multiple-TENMR Log DataS. Chen, SPE, G. Hursan, SPE, D. Beard, and D. Georgi, SPE, Baker Atlas, Houston, Texas, USA

Copyright 2003, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE Annual Technical Conference andExhibition held in Denver, Colorado, U.S.A., 5 8 October 2003.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300

words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

AbstractWe have developed a data processing method that allows a

valid integration, in the time domain, of echo trains acquiredin different field gradients, G, and different interecho times,

TE. The combined echo train can be used to obtain clay bound

water (CBW), bulk volume irreducible (BVI), and total

porosity information with improved vertical resolution. The

same data, in the uncombined form, are used for fluid propertyestimation. Thus, the data are used more economically.

As an added benefit, the combined echo train allows the

use of a single T2cutoff, consistent with the laboratory core-NMR derived T2cutoff. Although using a zero-gradient,

laboratory core-NMR derived T2cutoffto calibrate NMR logs

acquired in a gradient field is a common practice, the

discrepancy cannot be ignored for NMR logs acquired with alarge GTEproduct. With the new method, this discrepancy is

minimized. Field examples are provided to show the benefit

with the new method.

IntroductionThe new generation, multi-frequency NMR logging

instruments, such as the Magnetic Resonance ExplorerTM(MREX) from Baker Atlas, are capable of acquiring data

useful for characterizing both the formation rock properties

(e.g., bound and movable fluids, porosity, and permeability)

and reservoir fluid properties. However, these differentproperties often require an assortment of NMR acquisition

parameters and sequences. High-resolution formation rock

characteristics require acquisition schemes that generate

repetitive echo trains to reduce the vertical stacking

requirement. In contrast, fluid properties usually vary moreslowly with depth than rock properties and require acquisition

methods that can maximize the fluid contrasts, achievable with

variable magnetic field gradients (G), interecho times (TE),and wait times (TW) in the acquisition scheme. Currently,

multiple G, TE, and TW data are not combined in the time

domain to obtain formation rock properties because echo

trains having different GTE cannot be simply stackedCommon practice is to log either multiple passes, each for a

separate objective or a single, slow, comprehensive acquisition

pass. Either way the data are not used economically.

Baker Atlas global NMR logging service records reveal

that a high percentage of NMR logging job requests are forformation rock property characterization. These properties

include total and effective porosities, clay and capillary bound

water volumes, movable fluid volume, and permeability. Ligh

hydrocarbon typing and flushed-zone gas or oil saturationscomprise the next largest group of logging job requests. There

are also less commonly exploited techniques of NMR logging

such as those used in heavy oil formations, which haveexperienced some success in various geological areas

worldwide. This global picture roughly reflects the relative

robustness of the NMR logging techniques available to-date

Based on this assessment, we have developed a small-numberof objective-oriented acquisition sequences that coincides with

this global picture.1 These single-pass, comprehensive

sequences all include an objective of formation rock property

estimation.

Ideally, the multifrequency, multiple echo trains generatedfrom a single acquisition pass are processed using a

comprehensive inversion method with a forward model basedon the knowledge of fluid and rock properties, thereby

providing all petrophysical information in a single processing

step.1,2 Such an approach, however, is more suitable for

postprocessing because it may require interpretation input, for

example, known fluid properties. For well-site deliverablesoften the rock property information is sufficient for wel

completion decisions. An automated, rapid processing method

for obtaining rock properties, requiring no interpretation input

from the log engineer, is essential. One frequently usedapproach is to invert individual echo trains separately. The

porosity is derived from just one of the inversion results. Thusa great amount of data is not used. Another approach is tostack all echo trains together that are acquired with the same

TEand are fully polarized, even though they are not acquired

at the same frequency and field gradient. The second approach

is valid only if the frequency and the corresponding field

gradient differences do not affect the overall decay ratesubstantially. Otherwise, a smeared T2 spectrum is obtained

which, in some cases, can affect the BVI interpretation. We

propose a method to correct for the effect using a time

dependent weighting function to stack all pertinent echo trains

ETG


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2 SPE 84481

together, thereby improving the data quality and reducing the

requirement for vertical stacking.

Features of the MREX ToolBaker Atlas MREX tool possesses several important features.

Figure 1 illustrates the MREX tools static and RF field

distributions for one representative cross section. The tool has

a vertical aperture of 24 in. Extended magnets on both ends ofthe antenna are used to provide prepolarization of the nuclei

under investigation. The details of the tool will be published ina subsequent paper. In this paper, a brief summary of the tool

features is provided.

The MREX is a side-looking tool with a sensitive volume

that penetrates into the formation from 2.5 in. to 4.5 in.depending on the operating frequency. This penetration depth

is selected to be tolerant of borehole irregularities and less

affected by invasion. The side-looking configuration does not

sense the borehole signal from behind the tool (Figure 1 and 2)

and, thus, it can be used for almost all borehole sizes.Furthermore, centralization is not an issue for the MREX in

deviated and horizontal wells.The side-looking MREX is a gradient tool. The gradient

strength decreases with frequency. The gradient feature makes

it possible to excite multiple sensitive volumes in one single

polarization time using a frequency interleaving method. The

operating frequency band ranges from mid-400kHz to upper-800kHz with sufficient frequency separation between

frequencies to avoid interference from the excitations in

neighboring sensitive volumes. Because the magnitude of the

MREX tools field gradient varies with frequency, the echotrains acquired with different frequencies may exhibit different

apparent decay, even if they are acquired with identical

acquisition parameters, such as interecho time, TE, and waittime, TW. The longer the echo-train length is, the greater the

difference in apparent T2decay.

Figure 1. Illustration of one cross section of the B0 and B1 fielddistribution from the MREX tool. The arrows in the squaresindicate the B0 and B1 directions in the center of the sensitivevolume range.

Multiple Echo Train Acquisition by MREXThe multi-frequency capability of the MREX tool allows us to

acquire a large number of echo trains in a single pass, yieldingboth formation rock and fluid properties. For example, a six-

frequency version of the PoroPerm package and a three-

frequency PoroPerm + Oil package each acquire more than ten

echo trains. These echo trains all satisfy the followingexpression, but the parameters are different:

=

compN

i

fluidEjEi

Eii

Ej

DTGkT

T

TkMp

TkfE

mm

m

_ 222

2 12expexp

),,(

(1)

where i,j, k, mare indices for ithT2component,jthfrequency

kthecho, and m

thTE, respectively, and

iWi TTp l 1exp1 = (2)

is the polarization factor for the ithT1component and lthwai

time,T . The spread of frequencies, TlW

E, TW, and the number

of echoes, NE, among these echo trains make their apparent

decay times significantly different. In this section, we describe

these two acquisition packages and their purposes. In the nextsection, we describe a method for the time-domain integration

of these echo trains.

MREXMREXMREX

borehole

formation

B1B0

Figure 2. Illustration of the side-looking MREX tools sensitivevolume (the red-colored area). Signals are contributed only fromthe front of the tool over an aperture extending approximately120.

FiberglassSleeve

The PoroPerm package is designed to obtain basic

formation rock properties, such as effective and total porosity

permeability, clay-bound and capillary-bound water volumes

movable fluid volume, and the T2distribution.

Antenna

The left side of is a three-frequency version of the

PoroPerm acquisition package (PoroPerm3). The basicacquisition scheme includes 7 echo trains (ET), which are

acquired with the same TE, typically 0.6 ms, but vary in

frequency, f, echo train length, NE, and TW. ET #1 is a fully

polarized, long echo train, typically with 500 ms of data. ETs

#2 and #7 are each a series of echo trainlets (ETL). Each has a

10-ms length ( EE TNL = ) and a 30 ms wait time. During a 1s

acquisition window, 12 phase-alternating pairs of ETLs are

acquired and these ETL data are stacked in the acquisition

software. ETs #3 and #4 are fully polarized echo trains bu

Figure 3


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SPE 84481 3

with a data acquisition length of only 30 ms. These two ETs

can be combined with ET #1 to reduce the random noise in the

initial decay of the ET, which is critical to BVI estimation.ETs #5 and #6 are partially polarized echo trains having the

same NE as #3 and #4. Combining ETs #1, 3, 4, 5, and 6

provides an alternative approach for BVI estimation.

Normally, ET #1 is acquired with the highest frequency and,

thus, its sensitive volume will be the closest to the borehole. Inthe case of severe borehole rugosity, causing contamination in

the sensitive volume corresponding to the highest frequency,ETs #3 and #4 will still provide the uncontaminated total

porosity, and the combined ET #3, 4, 5, and 6 will provide the

BVI estimate.

Figure 3. Illustration of PoroPerm acquisition package.

The three-frequency version of the PoroPerm acquisition is

used only when the resulting wait times for ETs #1, #3, and

#4 are sufficient to reach the complete polarization of all

signals. If the formation requires longer wait times for fullpolarization, the six-frequency version (PoroPerm6), which is

shown on the right-hand side of Fig. 4, is used. We see thatPoroPerm6 simply repeats PoroPerm3; thus, the data

processing does not become more complicated. This approach

can be theoretically extended to 3nfrequencies where nis an

integer; however, six frequencies usually suffice. Clearly, with

this implementation the number of echo trains acquired in aunit time is independent of the number of frequencies.

There are advantages of implementing the variable

frequency number version instead of using a fixed, maximum

number of frequencies. First, the SNR is frequency dependent:

variable frequency implementation, we take advantage of the

higher frequencies and use the minimum number o

frequencies that can satisfy the need for continuous dataacquisition, while achieving full polarization. Second, when

fewer frequencies are used, the time between the two

consecutive phase-alternating pairs (PAPs) is reduced. This

results in a more flexible acquisition and delivers the data with

better vertical resolution.

AdjustableTimegap

3A

3C

3E

3F

3D

1A

1B

2A

2C

2B

1C

1C

2C

TWL

T

WL

TWL

TWS

TWS

AdjustableTimegap

3A

3C

3E

3F

3D

AdjustableTimegap

3A

3C

3E

3F

3D

1A

1B

2A

2C

2B

1C

1C

2C

TWL

T

WL

TWL

TWS

TWS

F1 F2 F3

2

3

4

5

6

1

2

1

time

F1 F2 F3

1

3

45

6

2

1

2

2

3

4

5

6

1

2

1

time

F1 F2 F3 F4 F5 F6

2

1

2

1

1

2

1

2

7 7

7

2 9

1 8

10

1112

13

14

2

3

4

5

6

1

2

1

2

3

4

5

6

1

2

1

2

3

4

5

6

1

2

1

time

F1 F2 F3

1

3

45

6

2

1

2

1

3

45

6

2

1

2

1

3

45

6

2

1

2

2

3

4

5

6

1

2

1

2

3

4

5

6

1

2

1

2

3

4

5

6

1

2

1

time

F1 F2 F3 F4 F5 F6

2

1

2

1

2

1

2

1

2

1

2

1

1

2

1

2

7 7

7

2 9

1 8

10

1112

13

14

the higher the frequency, the higher the SNR. By using a

igure 4. Three-frequency version of PoroPerm + Oil package.

The PoroPerm + OIL package (Figure 4) is designed for

log

trains. Table 1

sum

er usually requires adequate

polarization contrast and/or diffusion contrast. In the

F

n, a single-p

from fre

ging oil-bearing formations. Agai ass concept is

used with sufficient variations of TE, TW, and field gradient toevaluate the formation and to perform hydrocarbon typing

The acquisition is designed for wells having light and mediumgrade oils with low to moderately high GOR.

The acquisition package yields 13 echo

marizes the default values of the key acquisition

parameters for each ET with the echo train IDs defined inFigure 4. There are two pairs of dual-TW ETs (1A and 1B

quency #1 and 2A and 2B from frequency #2). The

implementation uses the highest frequency for frequency 1 (f1)

which couples with the longest TE(2.1 ms) for acquiring ET

1A and 1B. At this frequency, the tool gradient is

approximately 34 gauss/cm.Discriminating oil and wat


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4 SPE 84481

Por Effect of Multiple GTEon T2cutoffand BVIoPerm+OIL package, polarization contrast can be obtainedwith two long echo trains having different TWs and can also

be obtained from a multi-component T1 analysis. Diffusion

contrast is obtained using multiple ETG data. The maximum

ETG is chosen to make the diffusion-induced decay,

( ) ( )22 DTG

D E

=

, (3)

One of the important petrophysical parameters that can be

derived from NMR logs is the irreducible bound watervolume, BVI. A commonly used method for estimating BVI is

to use a T2cutoffsuch that

12

12diffT

d laxation decay of the wate

substantially over the operating frequency range, we canchoose to use the highest frequency (thus, the highest

gradient) to match the longest TE, thereby maximizing the

diffusion contrast.

Alternatively, maximizing the ETG contrast results in a

great difference in t

=cutoffT

T

dTTPBVI

2

min2

22 )( (4)ominate the overall re r phase.

Because the MREX tools magnetic field gradient varies

he observed ong individual echo

trai

whereP(T2) is the apparent T2distribution with individual Tcomponents given by:

1diff2

12

12

++= TV

STT B . (5)

decay am

dins. From Table 1 we see that three fferent TEs are used to

acquire the full-length (default value: ms5001 ==ii

EE NTL ),

fully-polarized echo trains, 1A, 2A, and 3A. Theircorresponding GT values are approxim

[ ] [ ] [ ] .2:1:4:: 321 EEE TGTGTG

The extra decay due to diffusion, , expressed in Eq

(3), depends on (a) the field gradient, G, which is associated

with the acquisition frequency, (b) the inter echo time, T

1diff2

T

E, an

acquisition parameter, and (c) the diffusivity, D, a fluidproperty. Obviously, data that is acquired with a different GTEcombination results in a different apparent T2 distribution

P(T2). If the same T2cutoffvalue is used to compute the BVI o

the same formation, the results are gradient and TEdependent

If the T2diffis significantly larger than both T2Band ( )SV , the

dependency may be negligible. However, if the GTEproduc

is large, T becomes dominant and the diffusion effect may

not be negligible.

1diff2

E ately

These differences must be corrected for be re the echo trainsan be integrated in the time-domain.

equency PoroPerm + OILpackage

(kHz) (ms) (s) (ms) group

foc

Table 1. Default parameters for the 3-fr

ET

ID

Freq TE TW NETE NS/

1A 880 2.1 4+* 500 11B 880 2.1 1 500 1

1C 880 0.6 0.03 10 12

2A 790 0.6 4+ 500 12B 790 0.6 1 500 12C 790 0.6 0.03 10 12

3A 695 1.5 4+ 500 13C 695 0.6 0.03 10 12

3D 695 0.6 0.05 10 8

3E 695 0.6 0.1 30 4

3F 695 0.6 0.2 50 4

: Acqu ead ti lus ad le d

Without considering the tool and acquisition dependencies

the value of the T2cutoff depends on the rocks surface

mineralogy. Therefore, a common practice is to calibrate the

T2cutoff with laboratory NMR measurements. These lab

measurements are often performed in a uniform magnetic fieldwithout an external gradient and, thus, a negligible

contribution from . To calibrate NMR logs using a

laboratory core-NMR derived T

1diff2

T

2cutoff, one sometimes has to

consider the disparity of the field gradient between NMR

laboratory and logging data.Figure 5 shows the gradient effect on the T2cutoffshift with

and without an external field gradient. All plots assume that

the BVI contains water only, at 200-F temperatureenvironment. The gradient strength is approximately 18

Gauss/cm for MRIL operating at 750 kHz and 26 Gauss/cm

for MREX at the same frequency. The intercepts of the

horizontal lines with the T2cutoffcurves represent the apparen

T2cutoff values that should be used on the log data. Clearly,there will be a dependence for carbonates if the GTEis large

On the other hand, for a small GTE, a slight shift in the T2cutofmay not result in a significant BVI discrepancy.

* isition overh me p justab elay.

ffective

orosity, together with the ETLs for CBW, the total porosity

can

additional field-gradient induced decay differences.

quisition

ackages and log examples are described in Ref. 3.

The three fully polarized ETs are used for e

p

be obtained. There are five sets of short echo trainlets with

a length of 10 ms acquired with three frequencies (2 of 1C, 2of 2C, and 1 of 3C), totaling 60 trainlets per sample. These

short, partially polarized trainlets are stacked together for

CBW estimation without the ETG correction because

their EE TN only equals 10ms, resulting in negligible

More details of PoroPerm and Properm+Oil ac

Although it is possible to adjust the T2cutoffaccording to thegradient and TE, in practice it is confusing to use multiple

T2cutoff values for the same formation. Even if a T2cutofadjustment is applied, individual echo trains still must beinverted independently, missing the opportunity of combining

the multiple frequency data to obtain one single, high-quality

echo train.

p


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SPE 84481 5

Figure 5. The discrepancy between T2cutoffvalues derived in the labwith no applied gradient, and the apparent T2cutoff in the gradienttool environment. All data are computed based on a 200-F

temperature environment.

Justification for GTECorrectionIn this section we describe a method to reasonably integrateecho trains acquired with different GTE combinations to

improve the BVI and total porosity estimation. The movable

fluid volume can be estimated once the porosity, BVI, and

CBW are known:

BVICBWBVM T = . (6)

Thus, as long as CBW and BVI can be estimated accurately, it

is not essential to have an accurate T2distribution to obtain an

accurateBVM.Generally, BVI contains only a water phase and water

diffusivity, Dw, is known if the formation temperature andpressure are known. Borehole temperature is a routine logging

measurement, but pressure is usually not measured directly

during logging. However, formation pressure computed fromsparsely measured and interpolated pressures, or from the

pressure gradient, is usually sufficient for Dw estimation

because water diffusivity depends only weakly on the

pressure. The BVM fluid diffusion is unknown as it depends

on the fluid constituents. However, approximating the BVM

fluid diffusivity, , with DBVMD w will not significantly affect

the BVI estimate if any of the following apply:

a. BVM contains water only. Obviously the assumptionabove is exact. WBMF invasion also belong to thiscase.

b. BVM contains light oils with or without water. Asoil is the non-wetting phase, the light oil T2dependslittle on the surface relaxation and the bulk T2 is in

the range of several hundred ms to several seconds.

The diffusivity of light oil,Do, is usually in the rangeof 0.1-1 timesDw. The corresponding T2diff,ois on the

order of several hundred milliseconds. Thus,

replacing an unknown DBVM by Dw does not

substantially shift the oil T2spectrum and, thus, BVM

will not be misinterpreted as BVI. OBMF invasion

also belongs to this case.

c. BVM contains medium viscosity oil, in which case

the bulk oil, T2B, is in the vicinity of 40100 ms areservoir conditions. For a typical T2diff,w= 100500ms, and T2diff,O >> T2diff,w. As long as

),min( ,diff2,diff22cutoff2 woB TTTT


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( )

=

12exp

221

22

2wE

E

DTGGkT

, (8)

to E2 echo-by-echo, using the Dwand Gvalues derived from

the corresponding reservoir temperature, pressure, and

activation frequencies. The result approximates the predicted

E2atf1.

( ) ( ) ( 212212 ,,,,,,, ffDTTkfETkfE wEEE ) . (9)

Step 3. Compare the summation of echoes, ( )12 fSE and

, as before. If the difference is larger than tolerance,

proceed to step 4.

( )11 fSE

Step 4. If this indicates an

overcorrection. When this occurs, reduce the gradient factor,

, by a multiplication factor between 0.5 and 1 and

reiterate the process. If then an

undercorrection is indicated. When this occurs, increase the

factor by a multiplication factor between 1 and 2 and

reiterate the process. Although rarely needed, this step

provides a means to handle the over- or undercorrections that

may arise from the uncancelled portion of the internal gradient

effect described in Appendix A or from an incorrectD.

( ) ( ) ,11 21 tolerancefSfS EE >

( ) ( 11 12 fSfS EE

22

22

21 GG

21G

) ,tolerance>

G

The above steps are applicable strictly to those echo trains

that are acquired with the same TEbut different frequencies

(and, thus, gradient). This is the case of MREX PoroPerm

acquisition. The second case is more general: it involves twoecho trains that can differ inG, TE, and the echo train length,

L. In this case, a minor generalization of replacing SE with

SE/TEand replacing the multiplication factor,, by

( ) ( )

==

12exp

222

221

2

21

11

wEEEE

DTGTGkTkTt

(10)

for the kthecho in an E2echo train at time t. For such cases, we

typically choose to correct the echo train with the largest

to be consistent to the one with the smallestETG ETG ,

because the latter is closest to the common laboratory NMR-

measured results taken from a zero external gradient.

Time-Dependent Echo WeightsAfter the correction is completed, a weighted averaging

is applied to the corrected echo trains with the weightsdepending on the noise and T

ETG

Eof the individual echo trains.The TEdependency is straightforward. The standard deviation

of noise for any echo in an echo train is a constant before

the G correction is applied. Because the correction is a

time-dependent factor, the noise becomes time dependent,

, after the multiplication factor,or , is applied:

ET

ETkt=

( ) ( ) ( ) ( ) ( ) ( ) ( )ttNttettEtM +== , (11)

where eis the NMR signal without noise and Nis the noise.

The second term shows that the noise is also amplified (or

reduced) by the same time-dependent correction factor

To average, the corrected echo trains, a time-dependen

weight,

ETG

( ) 2)( = ttw , is introduced:

( )

( ) ( )

( )

=

ll

l

ll

t

ttM

tM2

2

, (12)

where l is the echo train index. If increases with t, the

noise of the later echoes increases, while the amplitudes of

these later echoes are small. Because the same

( )tl

( )tl factor is

used to construct the weighting factor, the larger the ( )tl , the

smaller the weight. Hence, the time dependent weight reducesthe importance of the noisy later echoes in the data integration

process.

The frequency-dependence of the noise in the origina

echo trains are also taken into account with the time

dependent weight by multiplying and then replacing with

lll tt *)()( = (13)

where is the standard deviation of noise for the llth echo

train.Further, the difference in the data sampling rate due to the

different TEis also built in by replacing Eq. (13) with

lElll Ttt = )()( . (14)

Equation (14) indicates that in the absence of the GTEcorrection, high-frequency and short-TE data are weightedmore than the low-frequency and long-TEdata. The integrated

echo train has the S/N better than either of the constituent echo

trains.

ExamplesA. Comparison of BVI and BVM from Individual and

GTE-corrected Echo Train Processing

Figure 6 shows a comparison of BVI and BVM estimated

from the three fully-polarized echo trains, labeled 1A, 2A, and

3A in ,from the three-frequency version PoroPerm +

Oil package. The three ETs have the same acquisitionwindow, L,but the TE values are different so the NEs are

adjusted accordingly. Because the data were acquired with

different frequencies (See ), the corresponding Gs

differ. Thus, the additional decay ( T ) due to diffusion in

the gradient field is strongest in 1A and weakest in 2A

causing the corresponding T

diff,2

2spectra to shift differently. Whena fixed T2cutoff(33 ms in this example) is used to compute BVI

and BVM using individual ETs, the resulting three sets of BVI

exhibits Consequently, the BVM

estimates are also affected. The trend is opposite

Thus, to obtain consistent BVI

estimates from these three ETs, one either has to discard the

ETs with the larger , such as 1A and 3A in this case, or

integrate these ETs in the time-domain before inversion.

.132 AAA BVIBVIBVI >

ETG

2ABVM

Figure 4

Table 1


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SPE 84481 7

In the simplest approach, we can integrate the ETs simply

by computing a weighted average; this ignores the

difference. In this case, the weights are not time

dependent and are simply proportional to

ETG

( ) 22 =lEll

Tw .

Because 2A has the shortest TE, it carries the largest weight.Therefore, the resulting integrated ET is most similar to 2A

ET. In the next example, we demonstrate that the difference inBVI estimates between the GTE-corrected and uncorrected

integrated echo trains is negligible only with a very small

T2cutoff, but is non-negligible for a long T2cutoff.

B. Comparison of BVI from GTE corrected and non-

corrected, Integrated Echo Trains

Figure 7 shows a comparison of the BVI estimates obtained

with and without the GTEcorrection to the same ETs used in

.The same T2distributions were used to calculate the

BVI shown in the four tracks but the nominal T2cutoffvalue is,from left to right, 33 ms, 40 ms, and 50 ms, respectively. As

the nominal T2cutoff increases, so does the discrepancy of the

results because the longer T2components are more affected bythe decay due to the T2diff.

Figure 6

Figure 6. Comparison of BVI and BVM estimated from the threeecho trains, 1A, 2A, and 3A in Figure 4, in the three-frequencyversion of PoroPerm+Oil package. The difference is attributed tothe GTEdifference among these ETs.

Note that in the processing protocol described above, the GT

correction is applied to the ETs with respect to

, where is the minimal GT

combination among all acquired ETs. Ideally, the correction

should be applied with if one wants to compare

log and core data in the same condition. Usually, the

discrepancy is insignificantly small. Furthermore, if one

desires to consider the remaining small difference, one canchoose to shift the T

E

E( ) ( )2min2 EEi GTTG i ( )minEGT

( ) 0min

=EGT

2cutoff accordingly after inverting the

integrated ET. In a later example, we demonstrate that such an

additional correction is often unnecessary. The desired T2cutoffshift can be computed easily with the known Dw. The T2cutoff

shift is more desirable if the GTEcorrection is applied with

respect to an ET that has its corresponding GTEvalue greater

than ( )minEGT .

Figure 7. Comparison of BVI estimates obtained with and withoutthe GTEcorrection. The same T2distributions are used in the foutracks but the T2cutoffvalue is, from left to right, 33 ms, 40 ms, and50 ms, respectively. As the T2cutoff increases, so does thediscrepancy of the results because the longer T2components aremore affected by the decay due to the T2diff.

C. GTECorrection for PoroPerm Data

The next example includes the analysis of a data set acquiredwith the six-frequency version of the PoroPerm acquisition

sequence. The integrated ET includes the contribution from al

fully polarized ETs, either with a long acquisition window (L

= 500 ms) or a short one (L = 30 ms). The long ETs are

acquired with the highest frequencies which correspond to thehighest gradients; the short ETs, designed to improve the

quality of the early echoes, are acquired with lower

frequencies and, thus, the corresponding gradients are smaller

With a typical Dw = 810-9 m2/s, the gradient difference

between the highest and lowest frequencies in the PoroPerm6

results in no more than 4.7% of the decay amplitude at t=30

ms. Therefore, it is not necessary to consider this differencebefore integrating the short and long L echo trains together

This is particularly true if most of the fluid constituents in the

formation correspond to short T2components such as CBW or

BVI.Figure 8 illustrates the six fully polarized echo trains

acquired with the PoroPerm6 sequence from Baker AtlasAustin Test well. The leftmost plot shows all six echo trains

The short and long echo trains have 30 ms and 500 msacquisition windows, respectively, but for clarity, only the firs

60 ms of data are plotted from the long echo trains and all 30

ms of data for the short echo trains are plotted. The middlepanel includes the weighted average ET based on (a) only the

two long echo trains and (b) all six, long and short, echo

trains. We see that for only 30 ms of data and a TEof 0.6 ms

there is no difference in the decay rate, so no GTEcorrection

is needed. The rightmost plot shows the inversion results fromthe corresponding two integrated echo trains displayed in the


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8 SPE 84481

center plot. A slight improvement of the spectrum

resolvability is observed by including all echo trains.

Figure 8. Illustration of PoroPerm echo train integration with andwithout the GTEcorrection.

D. T2cutoff: Laboratory vs. PoroPerm Log

In our processing protocol, when two echo trains with

different L are integrated, the GTE correction is always

applied to the shortLecho trains. For the PoroPerm sequence,the shortLecho trains are acquired with lower frequencies and

thus correspond to lower GTE

values. Correcting these shortL

echo trains increases the GTE effect. In contrast, all echo

trains in the PoroPerm sequence are acquired with a TEof 0.6

ms so that the maximum (GTE)max for any echo train in thePoroPerm acquisition is smaller than the (GTE)max in

PoroPerm + Oil acquisition. To assess the significance of the

(GTE)maxon the effective T ,logcutoff2

( )( )PTDTGTTT EG ,,,111

diff2,0

lab2cutoff

logcutoff2

+==

, (15)

and, consequently, the BVI estimates, we show a limestone

well example in Figure 9; the PoroPerm6 data were acquiredfrom Baker Atlass Austin test well.

In Figure 9a, from left to right, the first track shows thetotal porosity, the second track shows the comparison of BVI

using the 90-ms nominal T2cutoff and the effective T ,

using the actual well temperature of 100 F. The BVIdifference estimated from the twoT

logcutoff2

2cutoffs is negligible. Even

if the well temperature were 300 F, the difference would stillbe very small (Fig. 9b). The modification of the T2cutoff

becomes desirable only if both the laboratory-derived T2cutoffand the well temperature are high. To illustrate this point, we

plot in Fig. 9c BVI and Perm with a modified lab-derived

T2cutoff of 120 ms and a well temperature of 300 F. Underthese conditions, the effect due to the T2cutoffshift on BVI and

permeability estimates is more noticeable. Even when it is

needed, it is a simple step to modify the T using Eq.

(15).

logcutoff2

E. Improvement of Repeatability

Figure 10 illustrates the improvement of BVI repeatability forthe Austin Test well using data acquired with the three-

frequency PoroPerm+Oil sequence. Three passes were

acquired in the same interval to evaluate the BVI repeatability.

The left track shows the BVI estimated from the lowest GTEand the fully-polarized echo train, acquired at 795 kHz. The

right track plots the BVI estimated using all long echo trains

(L=500ms) acquired at various frequencies and TEs. The GTEcorrection and weighting is applied to these data beforeintegration.

(a)

(b) (c)

Figure 9. Comparison of BVI and Permeability estimated with thenominal T2cutoff and those computed from the GTE-corrected dataThe nominal T2cutoffis used here as the laboratory-derived value

(a)T

2cutoff(lab) = 90 ms,T

= 100 F, (b) (a)T

2cutoff(lab) = 90 ms,T

=300 F, and (c) (a) T2cutoff(lab) = 120 ms, T= 300 F.

The data shown in both tracks of Figure 10 have been averageover 2 levels. The repeatability is better with the integrate

echo trains, especially for depths where the BVI is smal

demonstrating the benefit of integrating echoes trains witdifferent GTEs.


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SPE 84481 9

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

TE interecho timeTW wait time

V pore volume

Greek letters

time-dependent G correction factorET

gyromagnetic ratio the difference of magnetic susceptibility surface relaxivity standard deviation of noise time-dependent weighting factor time-dependent G correction factorET

T total porosity

subscripts

ext external

int internal

i,j,k,l dummy indices

o oilFigure 10. Comparison of repeatability using the best quality echotrains (left track) and the integrated, GTEcorrected echo train.

w water

AcknowledgmentsConclusions

Numerous individuals at Baker Atlas have contributed to thedevelopment of the MREX tool and data acquisition and

processing software. We thank Baker Atlas for permission to

publish the results.

We have presented a method that considers the gradient and

interecho time differences between the MREX echo trainsacquired in a single-pass acquisition and thereby allows us to

integrate these echo trains in the time-domain before

inversion. The integrated echo train is used to obtain porosity,BVI, and BVM for real-time processing without requiring real

time interpretation input from the log engineer. Furthermore,we have discussed the T2cutoffdiscrepancy between laboratory-

based, zero-gradient NMR data and NMR log data acquired in

a gradient field. Finally, we have demonstrated that for theMREX PoroPerm acquisition with TE = 0.6 ms, the

discrepancy poses negligible effect for the majority of real,

non-extreme situations.

References1. Fang, S., Chen, S., and Georgi, D., SIMET for Fluid

Characterization: Processing Algorithms and Implementation,BA Internal Report, 2002.

2. Slijkerman, W. F. J., Looyestijn, W. J., Hofstra, P., and HofmanJ. P.,: Processing of Multi-Acquisition NMR Data, paperSPE56768 presented at the 65th (Month 1999) ATCE of SPE

New Orleans, Louisianna.

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

MR Explorer Log Acquisition Methods: PetrophysicalObjective-Oriented Approaches, Paper ? presented a

44th (June 2002) SPWLA Logging Symposium and

Exhibitions, Galveston, Texas.

NomenclaturesB0 static field strength

B1 RF field strength

D diffusivity Appendix: Internal Gradient Effecte,E Echo amplitude with and without noise includedIn general, fluids filling the pore space of formation rocks are

subjected to the total magnetic field gradient:f frequency

G RF field gradient strength

intGGG exttotal

rrr

+= , (a1)

which is the vector sum of the external and internal gradients

The internal gradient arises from the differences in magnetic

susceptibility between the matrix and the saturating fluidGenerally, it depends on both pore geometry and the type of

rock chemical constituents (mineralogy). The internal gradien

can, in principle, be significant. It is proportional to theexternal field strength:

L echo length, N EE T

M Echo magnetization amplitude

NE number of echoes in an echo train

porer pore radius

S pore surfaceSE Sum of echoes

t time

T temperature


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10 SPE 84481

The effect of the internal gradient inEq. (a4) can be embedded

into the rest of terms:pore

0int ~

r

BG

, (a2)

1ext2diff,

1int2diff,

12

12

+

++= TT

V

STT B . (a5)thus, it is frequency dependent and represents the

difference in the magnetic susceptibility between the fluid and

the solid matrix, and rporerepresents the effective radius of thepores). Variation in the operating frequency of the current

NMR logging tools, the variation ofB0is less than a factor of

2 and so does the internal field gradient. The variation of theexternal gradient is greater. More importantly, the time and

ensemble averaging of the randomly orientated Ginteliminates

the term extint GG . The phase displacement is proportional

to the sum of the squares of the internal and external gradients

The term in the brackets in Eq. (5a) is independent of theexternal gradient. The internal gradient strength variation is

linearly proportional to the frequency variation as

fBG 0int ,while the external gradient variation is greater than the linear

proportionality off. For most cases where on the average

intGGext >>

and T does not dominate the term in the square bracket

we approximate that the quantity in the square bracket of Eq

(a5) is frequency independent. Thus, if all the data to be

combined have the same T

1int2diff,

E, the term in brackets is regarded tobe approximately the same for all echo trains. If TEvalues o

these echo trains are different, the term in the bracket is

approximately valid only if the decay term due to internagradient is much smaller than that of the bulk and surface

relaxation terms combined or is much smaller than theexternal gradient term. These conditions are practically and

approximately valid in many cases.

( ) 2ext2intextint2ext2int2

2 GGGGGGGtotal +++=r

. (a3)

Thus, the diffusion decay rate, Eq. (a3), which is a function of

the gradient, can be separated into the internal and external

gradient, respectively:

1212

22ext

222int

21

ext2diff,1

int2diff,1diff2,

fluidEfluidE DTGDTGTTT

+=+= .

(a4)

gtecorrectionformultigte_spe84481

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