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Some consideration about fluid substitution without shear wave velocityFuyong Yan De-Hua Han Rock Physics Lab University of Houston
Summary
When S-wave velocity is absent approximate Gassmannequation using P-wave modulus is recommended by Mavko(1995) to calculate the fluid saturation effects Using bothlab data and log data our study shows that the approximateGassmann equation might introduce significant error influid saturation effect prediction except for unconsolidatedrocks Using S-wave velocity estimated by existingtechniques with same input parameters the exactGassmann equation should provide more reliableestimation of fluid saturation effect than that predicted byapproximate Gassmann equation
Introduction
Gassmann equation is regularly used to predict fluidsaturation effect in the industry but it needs input of bothcompressive wave velocity and shear wave velocity tocalculate shear modulus and bulk modulus Gassmannequation is often applied on log data to model the seismicresponse due to pore fluid variation But in practice quiteoften the shear wave sonic log is missing for variousreasons especially for old log data To handle this problemMavko (1995) brought up an approximation of Gassmannequation
( )f
f
dry
dry
sat
sat
MM
M
MM
M
MM
M
minus
+
minus
asymp
minus000 φ
(1)
Where M represents the P-wave modulus and Msat M0Mdry Mf are P-wave modulus of the saturated rock themineral the dry rock and the pore fluid respectively
Using lab rock physics data measured by Han (1986) wefound the absolute velocity error of the predicted P-wavevelocity indeed is very small several percent of the valuepredicted by exact Gassmann equation But the velocitychange caused by pore fluid change (the fluid saturationeffect) might also be only several percent of originalvelocity before fluid substitution So this error estimation ismisleading instead we should compare the fluid saturationeffects predicted by exact Gassmann equation and
approximation Gassmann equation By doing so we foundthat the approximate Gassmann equation systematicallyover estimated the fluid saturation effects and most oftenthe velocity error introduced by approximate Gassmann ismuch bigger than the fluid saturation effect predicted byexact Gassmann equation
Alternatively we can estimated the shear velocity usingexisting technique (Greenberg and Castagna 1992 Xu andWhite 1994) and then use exact Gassmann to predict fluidsaturation effects Using both lab data and log data wefound that as long as the the estimated shear wave velocityis not unreasonably unacceptable it will always providemore reliable estimation of fluid saturation effect than theapproximate Gassmann equation
Fluid substitution with approximate Gassmannequation
In order to check the validity of the approximate Gassmannequation we first applied it to Hanrsquos data Here we donrsquot
consider effects of dispersion differential pressurehydration of clay minerals and et al Thus we choose thedata measured at confining pressure of 50 MPa and at100 water saturation and then assume 50 of the porefluid is replaced by gas The approximate Gassmannequation using only P-wave velocity and exact Gassmannequation using both P-wave and S-wave velocities areapplied to calculate the fluid saturation effects respectivelyParameters used in the calculation are listed in Table 1
Table 1 Parameters used in fluid saturation effectcalculation
K water 225 GPa K quart 37 GPa
ρ water 101 gcc μ quart 44 GPa
K gas 0081 GPa K clay 21 GPa
ρ gas 0197 gcc μ clay 7 GPa
Figure 1 shows the comparison of P-wave velocity (atSw=05) calculated by the approximate and exactGassmann equations The velocity computed by exactGassmann equation is assumed to be correct and used asreference The velocities error is defined the differencebetween the P-wave velocities calculated by exact andapproximate Gassmann equation respectively The meansquare error relative to the correct velocity is about 223From Figure 1 it seems that the approximate Gassmannequation did a good job in estimating the velocity after thesaturation has been changed In Figure 2 we make a blindguess that the P-wave velocity does not change after 50
of the water is replaced by gas Comparing Figure 1 and 2we can see that generally our blind guess performs betterthan the approximate Gassmann equation in estimating thevelocity after pore fluid saturation change Thus Figure 1 ismisleading in evaluating the validity of the approximateGassmann equation
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Fluid substitution without S-wave velocity
Except for unconsolidated rock the fluid saturation effectof common reservoir rock also lies usually in range of several percent of its original velocity Thus to check thevalidity of the approximate Gassmann equation we shouldcompare the fluid saturation effects In Figure 3 we plottedthe fluid saturation effect predicted by approximateGassmann equation against the fluid saturation effectcalculated by exact Gassmann When the saturation ischanged from 100 to 50 for most of the rock samplesthe velocity will decrease The velocity increases slightlyfor several rock samples because of density effect All thedata points lie below the perfect line which means that theapproximate Gassmann systematically exaggerate the fluidsaturation effect For most of data points which lie belowthe green line the approximate Gassmann at least doublesthe fluid saturation effect If the actual fluid saturationeffect is -005 kms while the estimated fluid saturationeffect is -020 kms this is a big mistake in fluid saturationeffect prediction although the relative velocities error mightbe small (several percent of the original velocity)
In Figure 4 we plotted the ratio of velocity error (caused byapproximation) to fluid saturation effect (calculated byexact Gassmann equation) against porosity and the colorbar shows the original velocity before saturation variationAmong the 70 rock samples the velocity error introducedby approximation Gassmann equation is bigger than thefluid saturation effect for 743 of rock samples So in
term of fluid saturation effect estimation the approximateGassmann does not work for most of the rock samplesFrom Figure 4 it might be said the approximate equationworks best for loose sandstones of high porosity and lowvelocity
Fluid substitution with estimated S-wave velocity
In stead of using the approximate Gassmann equation wecan also use exact Gassmann and estimated shear wavevelocity to predict saturation effect when shear wavevelocity is not available There are two commonly usedmethods to estimate the shear velocity (Greenberg andCastagna 1992 Xu and White 1994) and here we selectthe technique introduced by Greenberg and Castaganarsquos
Figure 2 Cross plot between P-wave velocity estimatedby exact Gassmann and that by blind guess (assumingno velocity change after saturation is changed to 50)
Figure 4 Relation between porosity and relativevelocity error by approximate Gassmann equation
Figure 1 Cross plot between P-wave velocity estimatedby exact Gassmann and that estimated by theapproximated Gassmann equation (Original watersaturation Sw=10)
Figure 3 Comparison of fluid saturation effectsestimated by exact Gassmann and approximateGassmann equation
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Fluid substitution without S-wave velocity
(1992) since it requires exactly the same input informationas the approximated Gassmann equation (lithologyporosity saturation density elastic moduli andconcentrations of constituent minerals and pore fluids) Theregression coefficients for pure lithologies used in thisstudy are default and as given by Castagna et al (1993)
Same as previous study we assume the water saturation ischanged from 100 to 50 then we use exact Gassmannequation with the estimated shear wave velocity for 100water saturated rock to compute the P-wave velocitieswhen water saturation is changed to 50 The result isshown in Figure 5 Comparing with Figure 1 using exactGassmann and estimated S-wave velocity the predicted VP after saturation variation has a much smaller error than thatpredicted by the approximate Gassmann equation In termof fluid saturation effect estimation which we care mostthe result (Figure 6) is also much improved as compared toprevious study (Figure 3) From Figure 6 the estimated
fluid saturation effect rarely double the fluid saturationeffect calculated by exact Gassmann equation withmeasured S-wave velocity except when fluid saturationeffect is negligible
Inversion of S-wave velocity
The approximate Gassmann equation estimates fluidsaturation effect without using shear wave velocityinformation The same fluid saturation effect can becalculated using exact Gassmann equation the same P-wave velocity and a certain shear wave velocity This shearwave velocity is the implicit shear velocity used by theapproximate Gassmann equation The process of findingthis shear wave velocity is an inversion process and can bedescribed by the following equation system
( ) ( )20
2
20
2
10
1
10
1
f
f
sat
sat
f
f
sat
sat
K K
K
K K
K
K K
K
K K
K
minus
minus
minus
=
minus
minus
minus φ φ
(2)2
1 1 1
4
3sat PK Vμ ρ + = (3)
22 2 2
4
3sat PK Vμ ρ + = (4)
where subscript 1 and 2 represent original water saturationand changed water saturation respectively K sat K 0 K f arebulk modulus of saturated rock mineral and pore fluidrespectively μ and ρ are shear modulus and bulk density
respectively VP1 is the original P-wave velocity andVp2 isthe P-wave velocity after the saturation change and isestimated by the approximate Gassmann equationBasically there are three unknowns (K sat1 K sat2 μ ) in three
independent equations so we can solve for μ and calculatethe implicit shear wave velocity
Figure 6 Comparison of fluid saturation effectsestimated by exact Gassmann with measured andestimated S-wave velocities respectively
Figure 5 Cross plot between P-wave velocitiesestimated by exact Gassmann with measured andestimated shear wave velocities (Original watersaturation Sw=10)
Figure 7 Cross plot between estimatedinverted S-
wave velocity and measured S-wave velocity at 100water saturation
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Fluid substitution without S-wave velocity
In Figure 7 we plot the measured shear-wave velocityagainst the shear-wave velocity estimated using method of Greenberg and Castagna (1992) and the shear-wavevelocity inverted from fluid saturation effect predicted byapproximate Gassmann equation This plot explains whythe approximate Gassmann equation doest not work verywell in fluid saturation effect prediction it implicitly and
systematically use shear wave velocity much higher thanthe actual shear-wave velocity For this data set as long asthe average relative error of the estimated shear-wavevelocity is not higher than 94 it will provide morereliable result of fluid saturation effect estimation
Fluid substation of log data
Figure 8 shows example of fluid substitution of a tight gasreservoir The porosity of the gas reservoir lies around 20 The gas saturation is not high and is mostly lower than 25We assume that the gas are all replaced by brine and wantto see the saturation effect on P-wave velocity The fluidproperties are calculated using FLAG program with in-situpressure and temperature The blue curves are supplied log
data The estimated shear wave velocity (green curve) iscalculated by method of Greenberg and Castagna (1992)with regression coefficients for pure lithologies given byCastagna et al (1993)
With estimated S-wave velocity supplied P-wave log datausing exact Gassmann equation we can calculate P-wavevelocity (VP1) when water saturation is changed to 100for the whole gas reservoir interval With supplied S-wavelog and P-wave log data using exact Gassmann equationthe calculated P-wave velocity at 100 water saturation is
VP2 Using P-wave log data only and the approximateGassmann equation the calculated P-wave velocity at100 water saturation is VP3 Comparing VP2 with theoriginal P-wave log data we can see that fluid saturationeffect is mostly negligible to small The saturation effectestimated by estimated shear wave velocity is very close tothat predicted by using exact Gassmann equation and
supplied P-wave and S-wave log data The approximateGassmann equation always magnifies the saturation effectFor example at depth interval of 4542-4546 m the fluidsaturation effect is almost negligible but the approximateGassmann equation predicts a noticeable fluid saturationeffect The overall saturation effect of this gas reservoirinterval might be negligible but with approximateGassmann you might predict a significant fluid saturationeffect and thus provide false information for seismicforward modeling
As introduced in previous section we can invert the S-wave velocity implicitly used by approximate Gassmannequation As shown in the Figure 8 the inverted S-wavelies far away from the measured S-wave log data the
average error is more than 10 percent as long as theestimated S-wave velocity lies within the error bar definedby the inverted S-wave it will give more reliable fluidsaturation effect prediction than the approximate Gassmannequation
Conclusion
Based on analysis of both lab data and log data our studyshows that the approximate Gassmann equation (equation 1)is not a proper approximation of Gassmann to predict fluidsaturation effect except for unconsolidated rocks Using S-wave velocity estimated by existing techniques with sameinput parameters the exact Gassmann equation should
provide more reliable estimation of fluid saturation effectthan that predicted by approximate Gassmann equation
Acknowledgements
This work was supported by the FluidsDHI consortiumsponsors and we thank them for their continuous andgenerous support
Figure 8 Comparison of fluid saturation effectpredictions (1) VP1 calculated by exact Gassmannwith estimated VS (2) VP2 calculated by exactGassmann with measured VS and (3) VP3 calculatedby approximate Gassmann
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EDITED REFERENCES
Note This reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 2010
SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web
REFERENCES
Castagna J P 1993 AVO analysis-tutorial and review in J P Castagna and M Backus eds OffsetDependent Reflectivity-Theory and Practice of AVO Analysis Investigations in Geophysics No 8SEG 3-36
Greenberg M L and J P Castagna 1992 Shear-wave velocity estimation in porous rocks Theoreticalformulation preliminary verification and application Geophysical Prospecting 40 no 2 195ndash209doi101111j1365-24781992tb00371x
Han D-H 1986 Effects of Porosity and Clay Content on Acoustic Properties of Sandstones andUnconsolidated Sediments PhD dissertation Stanford University
Mavko G C Chan and T Mukerji 1995 Fluid substitution Estimating changes in Vp without knowingVs Geophysics 60 1750ndash1755 doi10119011443908
Xu S and R E White 1994 A physical model for shear-wave velocity prediction 56th
Meeting and
Technical Exhibit EAGE Expanded Abstracts
27EG Denver 2010 Annual Meetingcopy 2010 SEG
Main Menu
7292019 6 Papr849 Yan
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Fluid substitution without S-wave velocity
Except for unconsolidated rock the fluid saturation effectof common reservoir rock also lies usually in range of several percent of its original velocity Thus to check thevalidity of the approximate Gassmann equation we shouldcompare the fluid saturation effects In Figure 3 we plottedthe fluid saturation effect predicted by approximateGassmann equation against the fluid saturation effectcalculated by exact Gassmann When the saturation ischanged from 100 to 50 for most of the rock samplesthe velocity will decrease The velocity increases slightlyfor several rock samples because of density effect All thedata points lie below the perfect line which means that theapproximate Gassmann systematically exaggerate the fluidsaturation effect For most of data points which lie belowthe green line the approximate Gassmann at least doublesthe fluid saturation effect If the actual fluid saturationeffect is -005 kms while the estimated fluid saturationeffect is -020 kms this is a big mistake in fluid saturationeffect prediction although the relative velocities error mightbe small (several percent of the original velocity)
In Figure 4 we plotted the ratio of velocity error (caused byapproximation) to fluid saturation effect (calculated byexact Gassmann equation) against porosity and the colorbar shows the original velocity before saturation variationAmong the 70 rock samples the velocity error introducedby approximation Gassmann equation is bigger than thefluid saturation effect for 743 of rock samples So in
term of fluid saturation effect estimation the approximateGassmann does not work for most of the rock samplesFrom Figure 4 it might be said the approximate equationworks best for loose sandstones of high porosity and lowvelocity
Fluid substitution with estimated S-wave velocity
In stead of using the approximate Gassmann equation wecan also use exact Gassmann and estimated shear wavevelocity to predict saturation effect when shear wavevelocity is not available There are two commonly usedmethods to estimate the shear velocity (Greenberg andCastagna 1992 Xu and White 1994) and here we selectthe technique introduced by Greenberg and Castaganarsquos
Figure 2 Cross plot between P-wave velocity estimatedby exact Gassmann and that by blind guess (assumingno velocity change after saturation is changed to 50)
Figure 4 Relation between porosity and relativevelocity error by approximate Gassmann equation
Figure 1 Cross plot between P-wave velocity estimatedby exact Gassmann and that estimated by theapproximated Gassmann equation (Original watersaturation Sw=10)
Figure 3 Comparison of fluid saturation effectsestimated by exact Gassmann and approximateGassmann equation
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Fluid substitution without S-wave velocity
(1992) since it requires exactly the same input informationas the approximated Gassmann equation (lithologyporosity saturation density elastic moduli andconcentrations of constituent minerals and pore fluids) Theregression coefficients for pure lithologies used in thisstudy are default and as given by Castagna et al (1993)
Same as previous study we assume the water saturation ischanged from 100 to 50 then we use exact Gassmannequation with the estimated shear wave velocity for 100water saturated rock to compute the P-wave velocitieswhen water saturation is changed to 50 The result isshown in Figure 5 Comparing with Figure 1 using exactGassmann and estimated S-wave velocity the predicted VP after saturation variation has a much smaller error than thatpredicted by the approximate Gassmann equation In termof fluid saturation effect estimation which we care mostthe result (Figure 6) is also much improved as compared toprevious study (Figure 3) From Figure 6 the estimated
fluid saturation effect rarely double the fluid saturationeffect calculated by exact Gassmann equation withmeasured S-wave velocity except when fluid saturationeffect is negligible
Inversion of S-wave velocity
The approximate Gassmann equation estimates fluidsaturation effect without using shear wave velocityinformation The same fluid saturation effect can becalculated using exact Gassmann equation the same P-wave velocity and a certain shear wave velocity This shearwave velocity is the implicit shear velocity used by theapproximate Gassmann equation The process of findingthis shear wave velocity is an inversion process and can bedescribed by the following equation system
( ) ( )20
2
20
2
10
1
10
1
f
f
sat
sat
f
f
sat
sat
K K
K
K K
K
K K
K
K K
K
minus
minus
minus
=
minus
minus
minus φ φ
(2)2
1 1 1
4
3sat PK Vμ ρ + = (3)
22 2 2
4
3sat PK Vμ ρ + = (4)
where subscript 1 and 2 represent original water saturationand changed water saturation respectively K sat K 0 K f arebulk modulus of saturated rock mineral and pore fluidrespectively μ and ρ are shear modulus and bulk density
respectively VP1 is the original P-wave velocity andVp2 isthe P-wave velocity after the saturation change and isestimated by the approximate Gassmann equationBasically there are three unknowns (K sat1 K sat2 μ ) in three
independent equations so we can solve for μ and calculatethe implicit shear wave velocity
Figure 6 Comparison of fluid saturation effectsestimated by exact Gassmann with measured andestimated S-wave velocities respectively
Figure 5 Cross plot between P-wave velocitiesestimated by exact Gassmann with measured andestimated shear wave velocities (Original watersaturation Sw=10)
Figure 7 Cross plot between estimatedinverted S-
wave velocity and measured S-wave velocity at 100water saturation
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Fluid substitution without S-wave velocity
In Figure 7 we plot the measured shear-wave velocityagainst the shear-wave velocity estimated using method of Greenberg and Castagna (1992) and the shear-wavevelocity inverted from fluid saturation effect predicted byapproximate Gassmann equation This plot explains whythe approximate Gassmann equation doest not work verywell in fluid saturation effect prediction it implicitly and
systematically use shear wave velocity much higher thanthe actual shear-wave velocity For this data set as long asthe average relative error of the estimated shear-wavevelocity is not higher than 94 it will provide morereliable result of fluid saturation effect estimation
Fluid substation of log data
Figure 8 shows example of fluid substitution of a tight gasreservoir The porosity of the gas reservoir lies around 20 The gas saturation is not high and is mostly lower than 25We assume that the gas are all replaced by brine and wantto see the saturation effect on P-wave velocity The fluidproperties are calculated using FLAG program with in-situpressure and temperature The blue curves are supplied log
data The estimated shear wave velocity (green curve) iscalculated by method of Greenberg and Castagna (1992)with regression coefficients for pure lithologies given byCastagna et al (1993)
With estimated S-wave velocity supplied P-wave log datausing exact Gassmann equation we can calculate P-wavevelocity (VP1) when water saturation is changed to 100for the whole gas reservoir interval With supplied S-wavelog and P-wave log data using exact Gassmann equationthe calculated P-wave velocity at 100 water saturation is
VP2 Using P-wave log data only and the approximateGassmann equation the calculated P-wave velocity at100 water saturation is VP3 Comparing VP2 with theoriginal P-wave log data we can see that fluid saturationeffect is mostly negligible to small The saturation effectestimated by estimated shear wave velocity is very close tothat predicted by using exact Gassmann equation and
supplied P-wave and S-wave log data The approximateGassmann equation always magnifies the saturation effectFor example at depth interval of 4542-4546 m the fluidsaturation effect is almost negligible but the approximateGassmann equation predicts a noticeable fluid saturationeffect The overall saturation effect of this gas reservoirinterval might be negligible but with approximateGassmann you might predict a significant fluid saturationeffect and thus provide false information for seismicforward modeling
As introduced in previous section we can invert the S-wave velocity implicitly used by approximate Gassmannequation As shown in the Figure 8 the inverted S-wavelies far away from the measured S-wave log data the
average error is more than 10 percent as long as theestimated S-wave velocity lies within the error bar definedby the inverted S-wave it will give more reliable fluidsaturation effect prediction than the approximate Gassmannequation
Conclusion
Based on analysis of both lab data and log data our studyshows that the approximate Gassmann equation (equation 1)is not a proper approximation of Gassmann to predict fluidsaturation effect except for unconsolidated rocks Using S-wave velocity estimated by existing techniques with sameinput parameters the exact Gassmann equation should
provide more reliable estimation of fluid saturation effectthan that predicted by approximate Gassmann equation
Acknowledgements
This work was supported by the FluidsDHI consortiumsponsors and we thank them for their continuous andgenerous support
Figure 8 Comparison of fluid saturation effectpredictions (1) VP1 calculated by exact Gassmannwith estimated VS (2) VP2 calculated by exactGassmann with measured VS and (3) VP3 calculatedby approximate Gassmann
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EDITED REFERENCES
Note This reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 2010
SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web
REFERENCES
Castagna J P 1993 AVO analysis-tutorial and review in J P Castagna and M Backus eds OffsetDependent Reflectivity-Theory and Practice of AVO Analysis Investigations in Geophysics No 8SEG 3-36
Greenberg M L and J P Castagna 1992 Shear-wave velocity estimation in porous rocks Theoreticalformulation preliminary verification and application Geophysical Prospecting 40 no 2 195ndash209doi101111j1365-24781992tb00371x
Han D-H 1986 Effects of Porosity and Clay Content on Acoustic Properties of Sandstones andUnconsolidated Sediments PhD dissertation Stanford University
Mavko G C Chan and T Mukerji 1995 Fluid substitution Estimating changes in Vp without knowingVs Geophysics 60 1750ndash1755 doi10119011443908
Xu S and R E White 1994 A physical model for shear-wave velocity prediction 56th
Meeting and
Technical Exhibit EAGE Expanded Abstracts
27EG Denver 2010 Annual Meetingcopy 2010 SEG
Main Menu
7292019 6 Papr849 Yan
httpslidepdfcomreaderfull6-papr849-yan 35
Fluid substitution without S-wave velocity
(1992) since it requires exactly the same input informationas the approximated Gassmann equation (lithologyporosity saturation density elastic moduli andconcentrations of constituent minerals and pore fluids) Theregression coefficients for pure lithologies used in thisstudy are default and as given by Castagna et al (1993)
Same as previous study we assume the water saturation ischanged from 100 to 50 then we use exact Gassmannequation with the estimated shear wave velocity for 100water saturated rock to compute the P-wave velocitieswhen water saturation is changed to 50 The result isshown in Figure 5 Comparing with Figure 1 using exactGassmann and estimated S-wave velocity the predicted VP after saturation variation has a much smaller error than thatpredicted by the approximate Gassmann equation In termof fluid saturation effect estimation which we care mostthe result (Figure 6) is also much improved as compared toprevious study (Figure 3) From Figure 6 the estimated
fluid saturation effect rarely double the fluid saturationeffect calculated by exact Gassmann equation withmeasured S-wave velocity except when fluid saturationeffect is negligible
Inversion of S-wave velocity
The approximate Gassmann equation estimates fluidsaturation effect without using shear wave velocityinformation The same fluid saturation effect can becalculated using exact Gassmann equation the same P-wave velocity and a certain shear wave velocity This shearwave velocity is the implicit shear velocity used by theapproximate Gassmann equation The process of findingthis shear wave velocity is an inversion process and can bedescribed by the following equation system
( ) ( )20
2
20
2
10
1
10
1
f
f
sat
sat
f
f
sat
sat
K K
K
K K
K
K K
K
K K
K
minus
minus
minus
=
minus
minus
minus φ φ
(2)2
1 1 1
4
3sat PK Vμ ρ + = (3)
22 2 2
4
3sat PK Vμ ρ + = (4)
where subscript 1 and 2 represent original water saturationand changed water saturation respectively K sat K 0 K f arebulk modulus of saturated rock mineral and pore fluidrespectively μ and ρ are shear modulus and bulk density
respectively VP1 is the original P-wave velocity andVp2 isthe P-wave velocity after the saturation change and isestimated by the approximate Gassmann equationBasically there are three unknowns (K sat1 K sat2 μ ) in three
independent equations so we can solve for μ and calculatethe implicit shear wave velocity
Figure 6 Comparison of fluid saturation effectsestimated by exact Gassmann with measured andestimated S-wave velocities respectively
Figure 5 Cross plot between P-wave velocitiesestimated by exact Gassmann with measured andestimated shear wave velocities (Original watersaturation Sw=10)
Figure 7 Cross plot between estimatedinverted S-
wave velocity and measured S-wave velocity at 100water saturation
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Fluid substitution without S-wave velocity
In Figure 7 we plot the measured shear-wave velocityagainst the shear-wave velocity estimated using method of Greenberg and Castagna (1992) and the shear-wavevelocity inverted from fluid saturation effect predicted byapproximate Gassmann equation This plot explains whythe approximate Gassmann equation doest not work verywell in fluid saturation effect prediction it implicitly and
systematically use shear wave velocity much higher thanthe actual shear-wave velocity For this data set as long asthe average relative error of the estimated shear-wavevelocity is not higher than 94 it will provide morereliable result of fluid saturation effect estimation
Fluid substation of log data
Figure 8 shows example of fluid substitution of a tight gasreservoir The porosity of the gas reservoir lies around 20 The gas saturation is not high and is mostly lower than 25We assume that the gas are all replaced by brine and wantto see the saturation effect on P-wave velocity The fluidproperties are calculated using FLAG program with in-situpressure and temperature The blue curves are supplied log
data The estimated shear wave velocity (green curve) iscalculated by method of Greenberg and Castagna (1992)with regression coefficients for pure lithologies given byCastagna et al (1993)
With estimated S-wave velocity supplied P-wave log datausing exact Gassmann equation we can calculate P-wavevelocity (VP1) when water saturation is changed to 100for the whole gas reservoir interval With supplied S-wavelog and P-wave log data using exact Gassmann equationthe calculated P-wave velocity at 100 water saturation is
VP2 Using P-wave log data only and the approximateGassmann equation the calculated P-wave velocity at100 water saturation is VP3 Comparing VP2 with theoriginal P-wave log data we can see that fluid saturationeffect is mostly negligible to small The saturation effectestimated by estimated shear wave velocity is very close tothat predicted by using exact Gassmann equation and
supplied P-wave and S-wave log data The approximateGassmann equation always magnifies the saturation effectFor example at depth interval of 4542-4546 m the fluidsaturation effect is almost negligible but the approximateGassmann equation predicts a noticeable fluid saturationeffect The overall saturation effect of this gas reservoirinterval might be negligible but with approximateGassmann you might predict a significant fluid saturationeffect and thus provide false information for seismicforward modeling
As introduced in previous section we can invert the S-wave velocity implicitly used by approximate Gassmannequation As shown in the Figure 8 the inverted S-wavelies far away from the measured S-wave log data the
average error is more than 10 percent as long as theestimated S-wave velocity lies within the error bar definedby the inverted S-wave it will give more reliable fluidsaturation effect prediction than the approximate Gassmannequation
Conclusion
Based on analysis of both lab data and log data our studyshows that the approximate Gassmann equation (equation 1)is not a proper approximation of Gassmann to predict fluidsaturation effect except for unconsolidated rocks Using S-wave velocity estimated by existing techniques with sameinput parameters the exact Gassmann equation should
provide more reliable estimation of fluid saturation effectthan that predicted by approximate Gassmann equation
Acknowledgements
This work was supported by the FluidsDHI consortiumsponsors and we thank them for their continuous andgenerous support
Figure 8 Comparison of fluid saturation effectpredictions (1) VP1 calculated by exact Gassmannwith estimated VS (2) VP2 calculated by exactGassmann with measured VS and (3) VP3 calculatedby approximate Gassmann
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EDITED REFERENCES
Note This reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 2010
SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web
REFERENCES
Castagna J P 1993 AVO analysis-tutorial and review in J P Castagna and M Backus eds OffsetDependent Reflectivity-Theory and Practice of AVO Analysis Investigations in Geophysics No 8SEG 3-36
Greenberg M L and J P Castagna 1992 Shear-wave velocity estimation in porous rocks Theoreticalformulation preliminary verification and application Geophysical Prospecting 40 no 2 195ndash209doi101111j1365-24781992tb00371x
Han D-H 1986 Effects of Porosity and Clay Content on Acoustic Properties of Sandstones andUnconsolidated Sediments PhD dissertation Stanford University
Mavko G C Chan and T Mukerji 1995 Fluid substitution Estimating changes in Vp without knowingVs Geophysics 60 1750ndash1755 doi10119011443908
Xu S and R E White 1994 A physical model for shear-wave velocity prediction 56th
Meeting and
Technical Exhibit EAGE Expanded Abstracts
27EG Denver 2010 Annual Meetingcopy 2010 SEG
Main Menu
7292019 6 Papr849 Yan
httpslidepdfcomreaderfull6-papr849-yan 45
Fluid substitution without S-wave velocity
In Figure 7 we plot the measured shear-wave velocityagainst the shear-wave velocity estimated using method of Greenberg and Castagna (1992) and the shear-wavevelocity inverted from fluid saturation effect predicted byapproximate Gassmann equation This plot explains whythe approximate Gassmann equation doest not work verywell in fluid saturation effect prediction it implicitly and
systematically use shear wave velocity much higher thanthe actual shear-wave velocity For this data set as long asthe average relative error of the estimated shear-wavevelocity is not higher than 94 it will provide morereliable result of fluid saturation effect estimation
Fluid substation of log data
Figure 8 shows example of fluid substitution of a tight gasreservoir The porosity of the gas reservoir lies around 20 The gas saturation is not high and is mostly lower than 25We assume that the gas are all replaced by brine and wantto see the saturation effect on P-wave velocity The fluidproperties are calculated using FLAG program with in-situpressure and temperature The blue curves are supplied log
data The estimated shear wave velocity (green curve) iscalculated by method of Greenberg and Castagna (1992)with regression coefficients for pure lithologies given byCastagna et al (1993)
With estimated S-wave velocity supplied P-wave log datausing exact Gassmann equation we can calculate P-wavevelocity (VP1) when water saturation is changed to 100for the whole gas reservoir interval With supplied S-wavelog and P-wave log data using exact Gassmann equationthe calculated P-wave velocity at 100 water saturation is
VP2 Using P-wave log data only and the approximateGassmann equation the calculated P-wave velocity at100 water saturation is VP3 Comparing VP2 with theoriginal P-wave log data we can see that fluid saturationeffect is mostly negligible to small The saturation effectestimated by estimated shear wave velocity is very close tothat predicted by using exact Gassmann equation and
supplied P-wave and S-wave log data The approximateGassmann equation always magnifies the saturation effectFor example at depth interval of 4542-4546 m the fluidsaturation effect is almost negligible but the approximateGassmann equation predicts a noticeable fluid saturationeffect The overall saturation effect of this gas reservoirinterval might be negligible but with approximateGassmann you might predict a significant fluid saturationeffect and thus provide false information for seismicforward modeling
As introduced in previous section we can invert the S-wave velocity implicitly used by approximate Gassmannequation As shown in the Figure 8 the inverted S-wavelies far away from the measured S-wave log data the
average error is more than 10 percent as long as theestimated S-wave velocity lies within the error bar definedby the inverted S-wave it will give more reliable fluidsaturation effect prediction than the approximate Gassmannequation
Conclusion
Based on analysis of both lab data and log data our studyshows that the approximate Gassmann equation (equation 1)is not a proper approximation of Gassmann to predict fluidsaturation effect except for unconsolidated rocks Using S-wave velocity estimated by existing techniques with sameinput parameters the exact Gassmann equation should
provide more reliable estimation of fluid saturation effectthan that predicted by approximate Gassmann equation
Acknowledgements
This work was supported by the FluidsDHI consortiumsponsors and we thank them for their continuous andgenerous support
Figure 8 Comparison of fluid saturation effectpredictions (1) VP1 calculated by exact Gassmannwith estimated VS (2) VP2 calculated by exactGassmann with measured VS and (3) VP3 calculatedby approximate Gassmann
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EDITED REFERENCES
Note This reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 2010
SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web
REFERENCES
Castagna J P 1993 AVO analysis-tutorial and review in J P Castagna and M Backus eds OffsetDependent Reflectivity-Theory and Practice of AVO Analysis Investigations in Geophysics No 8SEG 3-36
Greenberg M L and J P Castagna 1992 Shear-wave velocity estimation in porous rocks Theoreticalformulation preliminary verification and application Geophysical Prospecting 40 no 2 195ndash209doi101111j1365-24781992tb00371x
Han D-H 1986 Effects of Porosity and Clay Content on Acoustic Properties of Sandstones andUnconsolidated Sediments PhD dissertation Stanford University
Mavko G C Chan and T Mukerji 1995 Fluid substitution Estimating changes in Vp without knowingVs Geophysics 60 1750ndash1755 doi10119011443908
Xu S and R E White 1994 A physical model for shear-wave velocity prediction 56th
Meeting and
Technical Exhibit EAGE Expanded Abstracts
27EG Denver 2010 Annual Meetingcopy 2010 SEG
Main Menu
7292019 6 Papr849 Yan
httpslidepdfcomreaderfull6-papr849-yan 55
EDITED REFERENCES
Note This reference list is a copy-edited version of the reference list submitted by the author Reference lists for the 2010
SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web
REFERENCES
Castagna J P 1993 AVO analysis-tutorial and review in J P Castagna and M Backus eds OffsetDependent Reflectivity-Theory and Practice of AVO Analysis Investigations in Geophysics No 8SEG 3-36
Greenberg M L and J P Castagna 1992 Shear-wave velocity estimation in porous rocks Theoreticalformulation preliminary verification and application Geophysical Prospecting 40 no 2 195ndash209doi101111j1365-24781992tb00371x
Han D-H 1986 Effects of Porosity and Clay Content on Acoustic Properties of Sandstones andUnconsolidated Sediments PhD dissertation Stanford University
Mavko G C Chan and T Mukerji 1995 Fluid substitution Estimating changes in Vp without knowingVs Geophysics 60 1750ndash1755 doi10119011443908
Xu S and R E White 1994 A physical model for shear-wave velocity prediction 56th
Meeting and
Technical Exhibit EAGE Expanded Abstracts
27EG Denver 2010 Annual Meetingcopy 2010 SEG
Main Menu