sonic-magnetic resonance method a sourceless porosity evaluationgasbearing

7/28/2019 Sonic-Magnetic Resonance Method a Sourceless Porosity EvaluationGasBearing

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Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference andExhibition held in Houston, Texas, 36 October 1999.

This paper was selected for presentation by an SPE P rogram 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 paper

for 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 300words; 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.

AbstractFor environmental reasons, there are times when the use ofradioactive chemical sources for density and neutron loggingis not possible. The inability to use these logging toolsseriously affects porosity determination in gas-bearingreservoirs. Several tools, such as the nuclear magneticresonance (NMR) tool, the sonic tool or a minitron-based tool,determine porosity without using a radioactive source. These

tools, however, are influenced by many effects and, when usedalone, cannot deliver an accurate gas-independent porosity.

A new methodology that combines sonic and NMR logs forimproved porosity evaluation in gas-bearing reservoirs isproposed. The first variant of the method uses the soniccompressional transit time and the total NMR porosity(TCMR) to determine the total porosity, corrected for the gaseffect, and the flushed zone gas saturation. In this approach, alinear time-averaged equation corrected for compaction isapplied to the sonic compressional log. The simplicity of thesolution (much like the previously published DMR1 Density-Magnetic Resonance Interpretation Method) allows fast, easycomputation and a complete error analysis to assess the quality

of the results.

In the second variant of the method, we show that the rigorousGassman equation has a very similar response to the Raymer-Hunt-Gardner (RHG) equation for a water-gas mixture. Thisallows substitution of the complex Gassman equation by themuch simpler RHG equation in the combined sonic-NMR

(SMR) technique to estimate total porosity and flushed zonegas saturation in gas-bearing formations.

The technique is successfully applied to an offshore gas wellin Australia. In this well, the porosity in the well-compactedsands is in the 20-25 p.u. range and the compaction factor isaround 0.77. The sonic-magnetic resonance results compared

favorably to the established density-magnetic resonanceresults and also to core data. In another offshore gas well fromthe North Sea, the porosity in the highly uncompacted sands isin the 35-40 p.u. range and the compaction factor is around1.85. The SMR technique was able to produce a very goodporosity estimate comparable to that estimated from thedensity-neutron logs.

IntroductionMany authors have discussed the applications of Sonic logs ingas-bearing formations.2-4 Stand-alone sonic techniques thatuse Wyllie equation or Raymer-Hunt-Gardner equation arebased on empirical observations on water-saturated samples

that are extended to water-gas mixtures.5, 6 Stand-alone sonictechniques alone that involves Gassman theory are generallytoo complex for the petrophysicist to consider the effects ofmany moduli parameters on the sonic measurements and tosolve for porosity 7- 9.

Other authors have discussed the applications of NMR logs ingas-bearing formations.10, 11 Porosity logs derived from NMRalone suffer from the low hydrogen index of the gas and thelong T1 polarizationtime of the gas when the data is acquiredwith insufficient wait time. To provide a robust estimate oftotal porosity in gas-bearing formations, a combined density-NMR technique has been proposed. However, density logginguses a radioactive chemical source, and in certain

environments, it is not used because of fears of the radioactivesource being lost in the hole. The sonic-magnetic resonancetechnique has been developed to provide an accurate porosityin these situations.

This paper will demonstrate thata) The Gassman and RHG methods predict very similar

SPE 56767

Sonic-Magnetic Resonance Method: A Sourceless Porosity Evaluation in Gas-BearingReservoirsChanh Cao Minh, SPE, Greg Gubelin, SPE, Raghu Ramamoorthy, SPE, SchlumbergerStuart McGeoch, SPE, Shell Company of Australia


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2 C. CAO MINH, G. GUBELIN, R. RAMAMOORTHY, S. MCGEOCH SPE 56767

sonic responses.b) Both Gassman and RHG sonic porosities are quite

insensitive to fluid type, and hence to water saturation.c) The solution of the Gassman approach is more complex,

requiring five parameters compared to only one for theRHG method. RHG is therefore more practical.

d) Combining TCMR and RHG provides a good estimate ofporosity in gas bearing formations.

e) Combining TCMR and a modified Wyllie scheme gives asimple analytic solution analogous to the DMR method.

The TCMR/RHG and TCMR/Wyllie schemes are applied totwo field examples. The results are compared to those fromDMR, core data and density/neutron analysis.

Sonic Porosity EquationsThe three methods (in order of increasing complexity) tocompute sonic porosity from the compressional slowness arebased on the Wyllie, Raymer-Hunt-Gardner and Gassmanformulae. In this section, each approach is analyzed, and thepredictions from each compared.

Wyllie Method

The Wyllie equation is

=tc tmatf tma

1

Cp. (1)

Eq. 1 can be re-arranged into

tc =(1 )tma + tf* (2a)

with

tf*

= Cp (tf tma )+ tma. (2b)

In these equations,is porosity,

tc is the sonic compressional slowness,tma is the matrix compressional slowness,tfis the fluid compressional slowness,Cp is the compaction factor needed to correct the sonicporosity to true porosity.

Raymer-Hunt-Gardner Method

The Raymer-Hunt-Gardner equation is

1tc

= (1 )2

tma+

tf. (3)

If the fluid is a mixture of gas and water at a saturation Sxo,then its slowness is computed from

tf = 304.8f

Kf. (4)

n Eq. 4, fis the composite fluid density of water ( w) and gas( g):

f =Sxo w + (1 Sxo ) g . (5)

Kfis the composite fluid bulk modulus of water (Kw) and gas(Kg), given by Woods law:

13

1

Kf=

SxoKw

+1Sxo

Kg. (6)

Gassman Method

The third method involves Gassman theory and requires moreparameters:

tc = 304.8

K +4

3G

. (7)

G is the shear modulus of the rock. The composite bulkdensity ( ) can be obtained from the density log. Thecomposite rock bulk modulus (K) is at the core of theGassman theory:

K = Kdf +

(1Kdf

Kma)2

Kf+

1

Kma

Kdf

Kma2

. (8)

In Eq. 8, the dry-frame bulk modulus (Kdf) varies withporosity. The shear modulus (G) in Eq. 7 also varies withporosity. For quartz samples, it has been shown that

Kdf = Kma (1 3.39 +1.952

) (9)and

G = Gma(1 3.48 + 2.192) (10)

where the subscriptmadenotes the matrix properties.3, 9

Applicability of the above equations to sandstones can beachieved by calibrating the matrix properties in a known waterzone.

The moduli of the matrix and the fluid are constant for a givenrock and fluid type. Some typical values are shown in table 1.For the fluid mixture, the shear modulus is zero at lowfrequency. For complex lithology, the effective matrix modulican be estimated from the average of the generalized Hashin-Shtrikman bounds.12


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SPE 56767 SONIC-MAGNETIC RESONANCE METHOD: A SOURCELESS POROSITY EVALUATION IN GAS-BEARING RESERVOIRS 3

The shear slowness (ts) is defined by

ts = 304.8G

. (11)

Eqs 1 to 11 allow the compressional slowness of a water-gasmixture in a porous system to be modeled.

Predictions fr om All Sonic Models

Fig.1 shows the model predictions for three porosity cases: 15p.u., 22 p.u. and 30 p.u.The parameters used in the modelingare listed in table 2. Three observations can be made. First, theWyllie result varies considerably with the water saturation anddiffers drastically from the RHG or Gassman results. Second,the RHG and Gassman results are quite insensitive to thewater saturation when the water saturation is less than 95%.

Third, in average-to-high porosity, the RHG result is almostidentical to the Gassman result.

Fig. 2 shows that the fluid mixture slowness as predicted byEq. 4 is responsible for the behavior of the Wyllie response

curves in Fig. 1.

Fig. 3 shows the RHG porosity variations with tc for two tfvalues that correspond to a 100% water case and a mixedwater-gas case. There is little error in the porosity estimationeven if tf of water is used instead of tf of a water-gasmixture.

Fig. 4 shows the Wyllie porosity variations with tc for thesame two tf cases above. It is apparent that an error in tfleads to a large error in the porosity estimation.

It is instructive to study the sensitivity of the sonic porosity

determination totfandtma.Fig. 5 shows the RHG and Wyllie porosity variations with tfassuming tc =90 s/ft. It confirms that the RHG results arelittle affected by tf whereas the Wyllie results are stronglydependent ontf.

Fig. 6 shows the RGH and Wyllie porosity variations withtma assuming tc = 90 s/ft. The plot suggests that bothmodels are sensitive to tma.

The above observations lead to a strategy to combine the sonicRHG porosity (which is insensitive to gas but sensitive tomatrix) and the NMR total porosity (which is sensitive to gas

but insensitive to matrix) for the determination of totalporosity in gas-bearing formations. The relative insensitivityof the RHG porosity to gas also alleviates the problem ofdifferent depths of investigation (10 in. for the sonic and 1.1in. for the CMR) which could cause the two tools to seedifferent gas volumes.

Sonic Magnetic Resonance Method Using RGHThe total CMR porosity (TCMR), from the CMR* CombinableMagnetic Resonance tool, is defined by

TCMR = SxoHIw(1 eWT

T1w ) + (1 Sxo)HIg (1 eWT

T1g) (12)

where

WT is the wait time,HIw, HIg are the hydrogen index of water and gas respectively,

T1w, T1g are the longitudinal relaxation time of water and gasrespectively.

In gas-bearing formations logged with insufficient wait time,the long T1 and the low hydrogen index of the gas cause

TCMR to read too low.

The modeling above suggests that the RHG model can be usedinstead of the Gassman model to determine porosity.However, when tc exceeds about 120 s/ft, the RHG modelgives unrealistic porosity as shown in Fig. 7. In this case, amore realistic modification of the RHG is the Cyberlook*

equation:

= 0.625tc tma

tc(13)

or the first order approximation of the RHG equation:

1

tc=

(1 1.9 )

tma+

tf. (14)

Both Eq. 13 and Eq. 14 are plotted in Fig. 7 together with theoriginal RHG equation. The coefficients 0.625 and 1.9 mightbe changed to suit the local conditions.

Sonic Magnetic Resonance Method Using WyllieThe modeling results also suggest that the Wyllie modeldependence on the gas-water mixture can be minimized byintroducing an equivalent gas slowness (tg) given by theequation:

tg = 300 +185 (15)

and recasting Eq. 2b with a linear fluid mixture law :

tc =(1 )tma + Sxotw

+ (1Sxo )tg . (16)

Eq. 15 is specific to the modeling and the case studiesdiscussed in this paper. The superscript indicates that bothtw of water (generally mud filtrate) and tg of gas need to becorrected for compaction as per Eq. 2b. The compaction factor

* Mark of Schlumberger


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can be determined in a known porosity zone, or in a water-bearing zone whereTCMR is equal to total porosity. If none ofthe above conditions applies, the compaction factor might beestimated from a nearby shale astshale/100.

Eq. 16 is attractive because it has the same functional form asthe density equation. Hence the DMR equations fordetermining a gas-corrected porosity and flushed-zone water

saturation can be readily used in the sonic-magnetic resonancemethod by merely substituting the density parameters by theircorresponding sonic parameters.1

=tw tg

tma tw

Pg = 1 -e-

WT

T1 g

SMRP =

SPHI (1-HIgPg

HIw) +TCMR

HIw

+ ( 1 -HIgPg

HIw

)

Sxg=

SPHI -TCMR

HIw

SPHI (1-HIgPg

HIw) +TCMR

HIw

. (17)

In the above equations, SPHI is the sonic porosity assuming100% water and corrected for compaction, SMRP is the totalporosity corrected for the gas effect, and Sxg is the flushed-zone gas saturation.

Fig. 8 shows the modeling results of Eq. 16. Compared toFig. 1, the variation of the recasted Wyllie equation withrespect to water saturation is greatly reduced. Note that Eq. 15provides an estimate oftgfor the expected porosity range andis not to be used to solve for porosity. For example, if theexpected porosity is around 40 p.u., then tg=300*0.4+185 =305 s/ft for Cp=1. If the expected porosity is around 20 p.u.then tg =300*0.2+185 =245s/ft for Cp =1. It follows thatas porosity decreases, the estimated tgconforms to frequentfield observations that the gas effect on the compressionalslowness becomes negligible.14 The estimation needs not bevery accurate since for a given error in the sonic porosityequation, the final error in the gas-corrected porosity (SMRP)is reduced by roughly half after combining withTCMR.

Examples

Aust ral ia well compacted sands

Fig. 9 shows the openhole logs. The top reservoir from 360 ftto 320 ft is gas-bearing, separated from the water zone near

the bottom at around 690 ft by a long shale sectioninterspersed with some tight streaks and shaly sands sections.Note that gas identification from the T2 distribution displayedin track 4 is impossible. Gas identification is much moreobvious from the large density-neutron separation (and largetc -TCMR separation) displayed in track 3. The soniccompressional slowness (tc) is scaled to read 0 p.u. whentc =55 s/ft (matrix) and the correct porosity in the waterzone, yielding a full scale of 30 p.u. when tc =85 s/ft. Itfollows from Eq. 1 that the compaction factor is Cp =(85-55)/(184-55)/0.3 =0.77, where the fluid slowness estimatedfrom the mud salinity, temperature and pressure is 184 s/ft.(As a comparison, the compaction factor determined from thenearby shale is ~0.78.)

The expected porosity is around 20 p.u., hence the estimatedgas slowness as per Eq. 15 is tg =300*0.2+185 =245 s/ft.SinceCp =0.77, the gas slowness corrected for compaction asper Eq. 2b is tg =0.77*(245-55)+55 =201 s/ft. Similarly,the water slowness corrected for compaction is tw =0.77*(184-55)+55 =154 s/ft. The SMR (Wyllie) equations

17 can then be solved to give the gas-corrected total porosityand the flushed zone gas saturation.

If the RHG equation is used, there is no need to determine Cpand tg. The mathematics to solve simultaneously theTCMRand RHG equations is more complicated and has beenimplemented in the ELAN* Elemental Log Analysis programas the SMR (RHG) method. Fig. 10 shows the results of theSMR (RHG) method. Tracks 1 to 4 show the measured logs(dash) and the reconstructed logs (solid). Track 5 shows thevolumetric results. As expected, SPHI (RHG) is little affectedby the gas and reads only a few p.u. higher thanSMRP.

Fig. 11 shows the comparison of SMRP (RHG), SMRP

(Wyllie) and DMRP with core porosity. For clarity, the sonicporosity and density porosity are limited to TCMR in theshales. All three methods give excellent results. Furthermore,a simple rule of thumb can be derived at this point: DMRP is60% DPHI +40%TCMR, SMRP (Wyllie) is 50% SPHI +50%TCMR, and SMRP (RHG) is 80% SPHI +20%TCMR.

The above rules of thumb assume full polarization of theliquids in the pore space.

Fig. 12 shows the comparison of Timur-Coates permeabilitiesusing SMRP andTCMR respectively with core permeability.

The results show that underestimating the correct porosity canlead to an order of magnitude error in the computedpermeability in gas-bearing formations.

Fig. 13 shows the comparison of the volume of water in theflushed zone computed from the SMR (RHG) method, SMR(Wyllie) method and DMR method respectively with thevolume of water computed from the Rxo tool. All are in goodagreement.


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Fig. 14 shows the ELAN results with different set of loggingmeasurements. Track 1 shows the ELAN withTCMR, RxoandGR. Theoretically, the gas-corrected porosity can bedetermined from theTCMR (Eq. 12) if Sxo, in turn, can beestimated from the Rxo log. In practice, this result is quitesensitive to an error in Sxo or the input NMR gas parameters asseen in track 1. CombiningTCMR and tc has the benefit ofcompensating the individual errors in the final result, thereby

providing a robust estimation of the gas-corrected porosity(track 2). Track 3 shows the ELAN result withTCMR, tc, Rxoand GR. It is essentially the same as the ELAN result withonly TCMR, tc and GR. The parameters used in theprocessing are listed in table 3.

North Sea well uncompacted sands

Fig. 15 shows the openhole logs. The gas-bearing section isunmistakably shown by the large separation between density-neutron or TCMR-tc separation. The sonic compressionalslowness (tc) is scaled to read 0 p.u. when tc =55 s/ft(matrix) and the correct porosity in the water zone, yielding afull scale of 60 p.u. when tc=205s/ft. It follows from Eq. 1

that the compaction factor is Cp = (205-55)/(190-55)/0.3 =1.85. (As a comparison, the compaction factor determinedfrom the nearby shale is ~1.7.)

The expected porosity is around 40 p.u., hence the estimatedgas slowness as per Eq. 15 is tg=300*0.4+185 =305 s/ft.SinceCp =1.85, the gas slowness corrected for compaction asper Eq. 2b is tg =1.85*(305-55)+55 =517 s/ft. Similarly,the water slowness corrected for compaction is tw =1.85*(190-55)+55 =305 s/ft. These values are quite differentfrom the values used in the first well. The SMR (Wyllie)equations 17 can then be solved to give the gas-corrected totalporosity and the flushed zone gas saturation.

Fig. 16 shows the ELAN results of the SMR (RHG) techniquein track 1 and SMR (Wyllie) technique in track 2. Both agreewell with the total porosity estimated from the density-neutronlogs. The quick rule of thumb whereby SMRP (Wyllie) is 50%SPHI +50%TCMR, and SMRP (RHG) is 80% SPHI +20%

TCMR can also be verified. Again, full polarization of theliquids is required for these thumb rules. The parameters usedin the processing are listed in table 4.

ConclusionsCombining sourceless sonic and NMR measurementsimproves the petrophysical evaluation of gas-bearing

formations in cases where no density log is available. Twoapproaches have been demonstrated, using the Raymer-Hunt-Gardner formula and a modified Wyllie scheme.

It has been shown that the RHG equation gives a similarresponse to the Gassman equation. Therefore, therecommended procedure to combine sonic and NMR logs is tosolve for the RHG equation and theTCMR equation. This

procedure requires the least sonic input parameters but doesnot have a simple analytical solution. A quick approximationof total porosity is 80%SPHI +20%TCMR.

Alternatively, the sonic Wyllie equation with the compactionfactor and the fluid parameters chosen as explained in thepaper can also be used in conjunction with the TCMRequation. The linear equations give simple analytical solutions

analogous to the DMR technique. A quick approximation oftotal porosity is 50%SPHI +50%TCMR.

Both methodologies have been tried successfully on two wellswith very different porosity and compaction history.

AcknowledgementsWe are grateful to the operators for releasing the data used inthis paper. We would like to thank Dylan Davies ofSchlumberger for reviewing the manuscript, Nick Heaton ofSchlumberger and Joel Turnbull of Fina (U.K.) for helpingwith the field data.

References

1 Freedman, R., Cao Minh, C., Gubelin, G., Freeman, J., Terry, R.,McGinnes, Th., Combining NMR and Density Logs forPetrophysical Analysis in Gas-Bearing Formations, Paper II,SPWLA Symposium Transaction, 1998.

2 Brie, A., Pampuri, F., Marsala, A.F., Meazza, O., Shear SonicInterpretation in Gas-Bearing Sands, paper SPE30595,presented at the SPE Annual Technical Conference &Exhibition, Dallas, 1995.

3 Ramamoorthy, R., Murphy, W.F., Fluid Identification ThroughDynamic Modulus Decomposition in Carbonate Reservoirs,paper Q, SPWLA Annual Logging Symposium, 1998.

4 Murphy, W.F., Acoustic Measures of Partial Gas Saturation inTight Sandstones, Journal of Geophysical Research, n. 89, pp.11549-11559, 1984.

5 Wyllie, M.R.J ., Gregory, A.R., Gardner, L.W., Elastic WaveVelocities in Heterogeneous and Porous Media, Geophysics, n.21, pp. 41-70, 1984.

6 Raymer, L.L., Hunt, E., Gardner, J ., An Improved Sonic TransitTime-to-Porosity Transform, Technical Review, vol. 28 - n.28., also in SPWLA Annual Logging Symposium, Lafayette,La., 1980.

7 Gassman, F., ber die Elastizitat Porozer Medien, Vierteljahrder Naturforschenden Gessellschaft in Zrich, n. 96, pp. 1-23,1951.

8 Dutta, N.C., Od, H., Attenuation and Dispersion ofCompressional Waves in Fluid-Filled Rocks with Partial Gas-

Saturation (White Model) Part I:Biot Theory Part II: Results,Geophysics, n. 44, pp, 1777-1805, 1979.

9 Ramamoorthy, R., Murphy, W.F., Coll, C., Total PorosityEstimation in Shaly Sands from Shear Modulus, SPWLAAnnual Logging Symposium, paper H, 1995.

10Akkurt, R., Vinegar, H.J ., Tutunjian, P.N., Guillory, A.J., NMRLogging of Natural Gas Reservoirs, SPWLA Annual LoggingSymposium Transactions, paper N, 1995.


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11Flaum, C., Kleinberg, R.L., Hrlimann, M.D., Identification ofGas with the Combinable Magnetic Resonance (CMR),SPWLA Annual Logging Symposium Transactions, paper L,1996.

12 Berryman, J.G., Mixture Theories for Rock Properties, in AHandbook of Physical Constants, Ahrens, T.J., ed., AmericanGeophysical Union, Washington, 236 pp., 1995.

13Wood, A.W., A Textbook of Sound, The MacMillan Co., NewYork, 360 pp., 1955.

14Suau, J., Boyeldieu, C., A Case of Very Large Gas Effect on theSonic, Technical Review, vol. 26 - n. 3, 1980.

Table 1Bulk and shear modulus of some minerals and fluids.K(Gpa) G (Gpa)

Quartz 38 42Calcite 77 32Dolomite 95 45Water 2.2-3.2 -Oil 1.7-2.7 -Gas 0.01-0.1 -

Table 2Parameters used in the modeling of sonic responses(g/cc) tc(s/ft) K(Gpa) G (Gpa)

Rock 2.65 55.5 38 42Water 1 190 2.6 -Gas 0.15 1180 0.01 -

Table 3Parameters used in the Australian well(g/cc) tcRHG

(s/ft)tcWyllie(s/ft)

HI T1(s)

Rock 2.65 55 55 - -Water 1.04 184 154 (Cp=0.77) 0.97 -Gas 0.15 - 201 (Cp=0.77) 0.5 4

NMR pulseparameters

Wait time: 4 (s) 5000 echoes TE: 0.2 (ms)

Table 4Parameters used in the North Sea well(g/cc) tcRHG

(s/ft)tcWyllie(s/ft)

HI T1(s)

Rock 2.65 55 55 - -Water 1.0 190 305 (Cp =1.85) 1 -Gas - - 517 (Cp =1.85) 0.5 2.5

NMR pulse

parameters

Wait time: 4 (s) 3000 echoes TE: 0.2 (ms)

NomenclatureTCMR Total NMR porosity (v/v)DMRP Gas-corrected total porosity using DMR method (v/v)SMRP Gas-corrected total porosity using SMR method (v/v)DPHI Density porosity assuming 100% water (v/v)SPHI Sonic porosity assuming 100% water (v/v) Porosity (v/v)tc Sonic compressional slowness (s/ft)ts Sonic shear slowness (s/ft)tma Matrix compressional slowness (s/ft)tf Fluid compressional slowness (s/ft)tshale Shale compressional slowness (s/ft)Cp Compaction factor (unitless)Sxo, Flushed-zone water saturation (v/v)

f Composite fluid density (g/cc)w Water density (g/cc)g Gas density (g/cc)

Kf Composite fluid bulk modulus (Gpa)Kw Water bulk modulus (Gpa)Kg Gas bulk modulus (Gpa)G Rock shear modulus (Gpa)

Gma Matrix shear modulus (Gpa) Rock bulk density (g/cc)K Rock bulk modulus (Gpa)Kdf Dry-frame bulk modulus (Gpa)Kma Matrix bulk modulus (Gpa)WT Wait time (s)HIw Water hydrogen index (unitless)HIg Gas hydrogen index (unitless)

T1w Water longitudinal relaxation time (s)T1g Gas longitudinal relaxation time (s)T1 Longitudinal relaxation time (s)T2 Transverse relaxation time (s)


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Fig 1A. Sonic responses for a water-gas mixture in a 15 p.u.sandstone.

Fig 1C. Sonic responses for a water-gas mixture in a 30 p.u.sandstone.

Fig 1B. Sonic responses for a water-gas mixture in a 22 p.u.

sandstone.

Fig. 2 Slowness of the composite water-gas mixture. It affectsstrongly the Wyllie equation, but has little effect on the RHGor Gassman equation.

0 0.2 0.4 0.6 0.8 160

80

100

120

140

160

180

200 =0.15

Sxo

Wyllie

RHG

Gassman

A

tc-s/ft

0 0.2 0.4 0.6 0.8 150

100

150

200

250

300=0.22

Wyllie

RHG

Gassman

Sxo

B

tc-s/ft

0 0.2 0.4 0.6 0.8 150

100

150

200

250

300

350 =0.30

Wyllie

RHG

Gassman

Sxo

C

tc-s/ft

0 0.2 0.4 0.6 0.8 1100

200

300

400

500

600

700

800

900

1000

Sxo

tf-s/ft


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Fig. 3 The RHG sonic porosity is little affected by the fluidslowness.

Fig. 5 Porosity responses of the RHG and the Wyllie equationsas a function of the fluid slowness for tc =90s/ft.

Fig. 4 The Wyllie sonic porosity is strongly affected by thefluid slowness.

Fig. 6 Porosity responses of the RHG and the Wyllieequations as a function of the matrix slowness.

tc - s/ft

40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

Porosity

RHG

tf=190 s/ft

tf=380 s/ft

60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

Porosity

Wyllie

tf=190 s/ft

tf=380 s/ft

tc - s/ft

400 600 8000

0.05

0.10

0.15

0.20

0.25

tf - s/ft

Por

osity

RHG

Wyllie

tc=90, tma=55.5

50 60 700.10

0.15

0.20

0.25

0.30

0.35

0.40

tma - s/ft

Porosity Wyllie

RHG

tc=90, tf=190


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Fig. 7 The RHG porosity is abnormally high whencompressional slowness exceeds about 120 s/ft. In this case,both the simplified RHG Eq. 13 and RHG Eq. 14 give morerealistic porosity estimation.

Fig. 8B Response of the Wyllie equation with the proposed

fluid mixture law and gas slowness in a 22 p.u. sandstone

Fig. 8A Response of the Wyllie equation with the proposedfluid mixture law and gas slowness in a 15 p.u. sandstone.

Fig. 8C Response of the Wyllie equation with the proposedfluid mixture law and gas slowness in a 30 p.u. sandstone.

50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

tc - s/ft

RHG

simplified RHG 1simplified RHG 2

0.2 0.4 0.6 0.8 150

100

150=0.22

Wyllie

RHG

Gassman

Sxo

tc-

s/ft

B

0 0.2 0.4 0.6 0.8 150

100

150 =0.15

Sxo

Wyllie

RHG

Gassman

A

tc-s/ft

0.2 0.4 0.6 0.8 150

100

150 =0.30

Wyllie

RHG

Gassman

Sxo

C

tc-s

/ft


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850.1 1000

0.3 0

GR

0 200

300

400

500

600

T2

0.3 3000

Depth(ft)

ms

Rt

Rxo

tc

NPHI

DPHITCMR

700

Fig. 9 Australian well openhole logs. The gaszone is shaded and separated from the waterzone by a long shale section interspersed withtight streaks and shaly sands.

55

300

400

500

600

GRraw-reco

0 200

Rxoraw-reco

0.2 20

Vpraw-reco

10 20

TCMRraw-reco

00.25

TCMRSPHI (RHG)SMRP (RHG)

SMR VxoFlushed Gas

Shale

Sand

01

Depth(ft)

700

Fig. 10 Australian well ELAN results fro

combining TCMR, Vp (1/tc) using RHG

equation, GR and Rxo logs.


11/13


.

600

500

400

300

DPHIDMRP

TCMRCore Porosity0.25 0

SPHI (Wyllie)SMRP (Wyllie)

TCMRCore Porosity 00.25

SPHI (RHG)SMRP (RHG)

TCMRCore Porosity 00.25

Depth(ft)

700

600

500

400

300

SMRP KTCMR KCore K

0.1 10000(md)

Depth(ft)

700

Fig. 11 Comparison of SMRP(RHG), SMRP(Wyllie), DMRP and core porosity. Thesonic porosity SPHI was limited to TCMR in the shales.

Fig. 12 Comparison of permeabilityderived from SMRP, fromTCMRand core permeability.


12/13


600

500

400

300

SMR (RHG) VxoDepth(ft)

SMR (Wyllie) Vxo DMR Vxo

0.25 00.25 00.25 0

Archie (Rxo)Vxo Archie (Rxo)Vxo Archie (Rxo)Vxo

700

ELAN with t-TCMR-Rxo-GRELAN with t-TCMR-GRELAN with TCMR-Rxo-GR

TCMR

SPHI (RHG)SMRP (RHG)SMR VxoGas

Shale

Sand

01

Gas

Shale

Sand

01

Gas

Shale

Sand TCMR

PHI ELANELAN Vxo

01

TCMR

SPHI (RHG)SMRP (RHG)SMR Vxo

Fig. 13 Australian well Comparison of the flushed-zonewater volumes from the SMR (RHG) technique, the SMR(Wyllie) technique, the DMR technique and the watervolume determined from the Rxo log.

Fig. 14 Australian well Comparison of theELAN results using different subset of logs.

The ELAN results with TCMR-Rxo-GRshows unstable results. The ELAN resultswitht-TCMR-GR are practically the same

as the ELAN results witht-TCMR-Rxo-GR.

Depth(ft)

300

400

500

600

700


13/13


106 16

0 1200.6 0

205 55

750

800

850

Depth

(ft)

GR

Cali

Rt T2

0.3 3000

msRxo

tc

NPHI

DPHITCMR

Oil

Water

Gas

1 0

Oil

SPHI (Wyllie)Phi D-N (dash)

SMRP (Wyllie)TCMR (dot)Vxo SMR (Wyllie)

Water

Gas

1 0

Fig. 15 North Sea well openhole logs. The gas zoneis identified by the large separation between thedensity-neutron logs. It is separated from the waterzone below by a heavy oil zone.

Fig. 16 North Sea well ELAN results withSMR (RHG) and SMR (Wyllie). Both SMRPporosities agree with porosity estimated fromdensity-neutron logs (Phi D-N).

SPHI (RHG)Phi D-N (dash)SMRP (RHG)

TCMR (dot)Vxo SMR (RHG)

750

800

850

Depth

(ft)

sonic-magnetic resonance method a sourceless porosity evaluationgasbearing

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