acoustic properties

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Generating Continuous

Im

Copyright 2010

This paper was prepared for presentation at the 2010held in Denver, Colorado October 17-22, 2010.

Introduction

In previous publications (Holmes andRock Physics models of Gassmann (19(1990) were combined with petrophysito derive pseudo acoustic logs both cand shear from other standard open-h

Rock Physics, when linked with PetropModeling, has a wide range of applicati

Figure 1: Examples of Rock Physics anmodeling applications

The conceptspresented in this

paper are anintegration of

petrophysics andgeophysics

SEG 2010 Annual Meeting, Denver, Colorado,

1

Logs of Matrix and Shale Acoustic Pr

roved Formation Evaluation

Michael HolmesAntony Holmes

EG annual meeting,

olmes, 2005)51) and Kriefal modeling,mpressional

ole logs.

hysicalions:

Petrophysical

A procedure is described wherebofsolids thematrixandshalec can be generated for :

Compressional acoustic

Shear acoustic data DT

Density log data RhoB

The deterministic calculations arrock physics modeling procedureto the Gassmann approach. Valican be verified by reconstructing

comparing with original data.

Output from the calculations areshowing variation with depth of:

DTPmatrix

DTPshale

DTSmatrix

DTSshale

RhoBmatrix

RhoBshale

From these curves, it is possible t

depth, each of the three log respo Shale

Matrix

Porosity

ctober 17-22, 2010

perties for

continuous curvesomponents of rocks

data DTP

based on Kriefs, which are similarity of the resultspseudo logs and

series of curves,

o calculate, by

nses contributed by:


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SEG 2010 Annual Meeting, Denver, Colorado, October 17-22, 2010

2

Method

Equations used in the Krief model are includedbelow. For a petrophysical solution, VPand Vsarereplaced by reciprocal velocity interval transit time,or acoustic slowness DTP and DTS:

The Biot model equations are written as follows:

While substituting:

Where:

and making use of the following relations:

Table 1: Listing of symbols used in the Kriefequation, and their definitions

Symbol DefinitionDTP Interval transit time of

compressional waveDTS interval transit time of shear

waveRhoB, b density of the formation

e effective porosity of the

formation, exclusive of thepore-space water associated

with the shale fractiont total porosity, including pore-

space water associated withthe shale fraction

Sxo

water saturation of the filtrate-flushed zone

Sw water saturation of the

uninvaded zone shear modulus (S wave

propagation)K elastic modulus (body waves)

B Biot compressibility constant

Vsh volume shale

MB Bulk elastic modulusSubscript Definition

Xma matrix (solid phase exclusiveof clay fraction)

Xmf mud filtrateXhc Hydrocarbons


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In our petrophysical solution to the Kriporosity, shale, and saturations are calcnon-acoustic logs. Then, using the Kritogether with published information onshear moduli, pseudo DTP and DTS cugenerated for a full range of fluid substoil/water and gas/water systems. Assumodeling procedure is perfect, the pseucurves should match the measured logssaturation values that exist in the reservmight speculate that, for the DTP and dsatuation is Sxo, whereas for the deeperlogs it is Sw.

A generalized model of porous rock is

Figure 2: Generalized model of porous r

As defined here,shaleis composed ofwith associated bound water, and silt.of very fine grained clastic and/or calcoften about 50% of the shale volume.petrophysical viewpoint, silt is difficultquantitatively from clay. Shaleshavegamma ray responses. Matrixis defin

clay mineral grains and probably inclumaterial similar to the silts associatedshales.

SEG 2010 Annual Meeting, Denver, Colorado,

3

f equations,ulated usingf equations,bulk andrves areitution

ing the entiredo acousticfor theoir. Oneensity logs thereading DTS

hown:

ck

lay minerals,ilt is made upreous materialrom ato distinguishostly high

d as the non-

es silt-sizedith clays in

Effective Porosity and containedremainder of the rock. The contaof water and other fluids, mostly

As defined in this paper,shales+

One of the important results of thability to define, for each of thecurves, the contribution of each ocomponents to the total log respo

Figure 3: Example of porous rockdata from the Bakken oil reservoir

An important observation is thatcontribution of acoustic responsemuch higher than for the densityshaleresponse is about the same

Percentagematrix

response is hilog as compared with acoustic lo

ctober 17-22, 2010

fluids make up theined fluids consistil and/or gas.

matrix=solids.

is study is theTP, DTS and RhoBf the 3 majornse.

odel with actual

the porosityto total response is

og. Percentageor all 3 logs.

her for the densitys.


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SEG 2010 Annual Meeting, Denver,

Calculation Procedures

Initial petrophysical processing consistdeterministic calculations:

Shale Volume frequently

ray log, or from a

combination (but not in gas Total Porosity be

density/neutron combinatresults are least affected b

and changing matrix proper

Effective porosity by subound water from total poro

Water saturation fromnumber of equations.

calculation that is the least r

The second stage involves solutionmodel, to calculate pseudo acoustic anBy comparing the pseudo logs withzone parameters of the solids canminimize differences.

A third procedure, again involving this employed to generate continuoussolids. Using zone values as a startina level-by-level basis, an initial matrito predict a shale value, to minimibetween pseudo and actual data. Thisin turn used to predict the matrixprocedure is iterated until differences

The end result is continuous curvesshale.

To avoid the problem of nopermissible curve ranges for the solidto 50% of the original input. The finthis procedure are recognized asreconstructed.

A final check on validity of the recthrough calculations of reconstructporosity logs.

olorado, October 17-22, 2010

4

of standard

from a gamma

ensity/neutron

reservoirs)st from aion, because

fluid content

ies

btracting claysity

any one of aOften the

eliable

to the Kriefd density logs.

easured data,e adjusted to

Krief model,curves of thepoint, and onvalue is used

ze differencesshalevalue is

value. There minimized.

of matrix and

-convergence,are restricted

al curves fromthe Krief

nstructions isd volumetric

Figure 4: Flow chart of calculation/i

As an independent checDT and RhoB from vol

compare with original DTfluid input as necessary t

Using an iterative approacalculate matrixand shaAdditional refinement of o

and shalemig

Compare pseudo logsmatrixand shalezone

improve

Run Krief model to calculDTS and ps

Deter

DTma, DTsh, Rhoma, Rhos

Basic petrophysi

e,t, Vsh

teration procedure

k, determine theoreticalmetric equations andnd RhoB curves. Adjust

o obtain the best match.

h within the Krief model,leas continuous curves.riginal zone input matrixt be required.

ith actual logs. Adjustinput as necessary tomatch.

te pseudo DTP, pseudoudo RhoB.

ine:

, and Krief components

al calculations:

, Sw, Shc


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5

Examples

1. Oil reservoir: Teapot Dome, Wyoming2. Oil Reservoir: Bakken Formation, Montana3. Shale Gas Reservoir: Western Canada4. Tight Gas Sand: Piceance Basin, Colorado

The following template is used for data presentation of all examples:

Figure 5: Description of template used for examples:Track 1: Petrophysical e, Vsh, Sw, Soor SgTracks 2 and 3: DTP and DTS original and pseudo curves (Krief Modeling)

Tracks 4 and 5: DTP solids and DTP comparisons volumetric modelingTracks 6 and 7: DTS solids and DTS comparisons volumetric modelingTracks 8 and 9: RhoB solids and RhoB comparisons volumetric modeling

1 83 4 5 6 7 92


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6

Figure 6: Example from an oil reservoir, Teapot Dome, Wyoming


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Figure 7: Oil reservoir, Bakken Formation, Montana


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Figure 8: Example from a shale gas reservoir in Western Canada


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Figure 9: DTP shale vs. resistivity from a shale gas reservoir in Western Canada

Figure 10: DTS shale vs. resistivity from a shale gas reservoir in Western Canada


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Figure 11: Example from tight gas sand in the Piceance Basin, Colorado


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Figure 12: DTP shale vs. DTP matrixfrom tight gas sand in the Piceance Basin, Colorado

Figure 13: DTS shale vs. DTS matrixfrom tight gas sand in the Piceance Basin, Colorado


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Conclusions

The technique allows for distinction betweenshale,matrix, and free porosity, together with their fluidcontent, in contribution to log responses for:

DTP DTS RhoB

Examination of changes with depth ofshaleandmatrixproperties helps in understanding changingrock properties with depth.

The reconstructed logs, when compared with originallog measurements, will indicate whether or not thesolids curve calculations are correct. Mismatches canmean one of three possibilities:

Incorrect calibration of properties whichinfluence log responses

An incorrect basic model Inconsistencies among logs used in the

calculations

A suggested geophysical application is to use thesolidscurves as a starting point, and then addporosity and contained fluids at specified levels togenerate a series of theoretical acoustic and densityprofiles. This procedure could be used to modeldifferent degrees of porosity development, and then

apply to defining seismic signatures.

References

1. Holmes, et al Petrophysical Rock PhysicsModeling: A comparison of the Krief andGassmann Equations, and applications toverifying and estimating compressional andshear velocities Presented at the SPWLA46thAnnual Logging Symposium, 2005

2. Holmes, et al Pressure Effects on Porosity-Log Responses Using Rock PhysicsModeling: Implications on Geophysical andEngineering Models as Reservoir PressureDecreases Presented at the SPE AnnualTechnical Conference and Exhibition , 2005.

3. Crain, E.R., The Log AnalysisHandbook1986, Penn Well Books.

4. Gassmann, F., ber Die Elastizitt porserMedien 1951, Vier. der Natur. Gesellschaftin Zrich, 96 1-23.

5. Krief, M., Garar, J., Stellingwerff, J., andVentre, J.,A petrophysical interpretationusing the velocities of P and S waves (full-waveform sonic) The Log Analyst, 31,November, 1990, 355-369.

6. Mavko, G., Mukerji, T., Dvorkin, J., TheRock Physics Handbook 1998, CambridgeUniversity Press.

About the Authors

Michael Holmeshas a Ph.D. from the University ofLondon in geology and a MSc. from the ColoradoSchool of Mines in Petroleum Engineering. Hisprofessional career has involved employment withBritish Petroleum, Shell Canada, Marathon OilCompany and H.K. van Poollen and Associates. Forthe past 20 years he has worked on petrophysicalanalyses for reservoirs worldwide under the auspicesof Digital Formation, Inc.

Antony M. Holmeshas a BS in Computer Sciencefrom the University of Colorado. He has beeninvolved with the development of petrophysicalsoftware for 20 years with Digital Formation, Inc.,particularly with regards to the implementation ofpetrophysical analyses.

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