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    Petrophysical Analysis of Fluid

    Substitution in Gas Bearing Reservoirs

    to Define Velocity ProfilesApplication

    of Gassmann and Krief Models

    Digital Formation, Inc.

    November 2003

    Title

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    Contents

    Benefits

    Introduction

    Gassmann Equation in Shaley Formation Wyllie Time Series Equation

    Linking Gassmann to Wyllie

    Adding a gas term to Wyllie Equation

    Krief Equation Examples

    Conclusions

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    BenefitsSeismic

    Reliable compressional and shear curves even if

    no acoustic data exists.

    Quantify velocity slowing due to presence of gas. Full spectrum of fluid substitution analysis.

    Reliable mechanical properties, Vp/Vs ratios.

    Reliable synthetics. Does not involve neural network or empirical

    correlations.

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    BenefitsPetrophysics

    Verifies consistency of petrophysical

    model.

    Ability to create reconstructed porosity logs

    using deterministic approaches.

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    BenefitsEngineering

    Reliable mechanical property profiles for

    drilling and stimulation design.

    Does not rely on empirical correlations, or

    neural network curve generation, for

    mechanical properties.

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    Introduction

    A critical link between petrophysics and seismic

    interpretation is the influence of fluid content on

    acoustic and density properties. Presented are two techniques which rigorously

    solve compressional and shear acoustic responses

    in the entire range of rock types, and assuming

    different fluid contents.

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    Gassmann Equation in

    Shaley FormationI The Gassmann equation accounts for the slowing of acoustic

    compressional energy in the formation in the presence of gas.

    There is no standard petrophysical analysis that accounts for theGassmann response and incorporates the effect in acoustic equations

    (e.g. Wyllie Time-Series). Terms in the Gassmann equation:

    M = Elastic modulus of the porous fluid filled rock

    Merf = Elastic modulus of the empty rock frame

    Berf = Bulk modulus of the empty rock frameBsolid = Bulk modulus of the rock matrix and shaleBfl = Bulk modulus of the fluid in pores and in clay porosityFT = TotalPorosityrB = Bulk density of the rock fluid and shale combinationVp = Compressional wave velocity

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    Gassmann Equation in

    Shaley FormationII In shaley formation, adjustments need to be made

    to several of the Gassmann equation terms,

    including porosity and bulk modulus of the solidcomponents.

    This allows a rigorous solution to Gassmann

    through the full range of shaley formations.

    Estimates of shear acoustic response are made

    using a Krief model analogy.

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    Wyllie Time Series Equation

    In the approach presented here, we have solvedthe Gassmann equation in petrophysical terms,and defined a gas term for the Wyllie Time-Series

    equation that rigorously accounts for gas. Original Time-Series equation:

    flemae ttt FF 1

    t = Travel time = 1/V

    tma = Travel time in matrix

    tfl = Travel time in fluid

    MatrixContribution

    FluidContribution

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    Linking Gassmann to Wyllie

    Calculate t values from Gassmann using fluidsubstitution

    Liquid filled i.e. Gas saturation Sg=0

    Gas filled assuming remote (far from wellbore) gas Sg Gas filled assuming a constant Sg of 80%

    From t values, calculate effective fluid travel times (tfl)

    Knowing mix of water and gas, determine effective traveltime of gas (t

    gas)

    Relate t values to gas saturation, bulk volume gas

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    Gassmann Sg vs. Ratio of Dtgas to Dtwet

    Color coding

    refers to porosity

    bins

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    Gassmann Bulk Volume Gas vs.

    Ratio Dtgas to Dtwet

    Color coding

    refers to porosity

    bins

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    Gassmann Bulk Volume Gas

    vs. Dtgas

    C1

    Hyperbola = C3

    C2

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    Adding a Gas Term to Wyllie Equation

    Gas term involves C1, C2 and C3 (constants)

    Equation reduces to traditional Wyllie equation when Sg=0

    If gas is present, but has not been determined from otherlogs, the acoustic cannot be used to determine reliable

    porosity values.

    mae ma water we

    tt Gas Term t t S

    F

    F

    Gas

    Contribution

    Matrix

    Contribution

    Water

    Contribution

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    Krief EquationPart I

    Krief has developed a model that is analogous to

    Gassmann, but also extends interpretations into the shear

    realm. We have similarly adapted these equations to

    petrophysics.

    Vp = Compressional wave velocity

    VS = Shear wave velocity

    rB = Bulk density of the rock fluids and matrix and shalem = Shear modulus

    K = Elastic modulus of the shaleyporous fluid filled rockKS = Elastic modulus of the shaley formationKf = Elastic modulus of the fluid in pores

    bb = Biot compressibility constant

    Mb = Biot coefficient

    FT = Total Porosity

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    Krief EquationPart II

    The Krief analysis gives significantly different results from

    Gassmann, in fast velocity systems (less change in velocity

    in the presence of gas as compared with Gassmann).

    In slow velocity systems (high porosity, unconsolidated

    rocks), the two models give closely comparable results.

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    Examples

    Slow Rocks

    Gassmann DTP

    Krief DTP

    Krief DTP & DTS

    Fast Rocks Gassmann DTP

    Krief DTP

    Carbonates

    Gassmann DTP

    Krief DTP Fast Rocks

    Gassmann DTP & DTS

    Krief DTP & DTS

    In all of these examples, thepseudo acoustic logs arederived from a reservoirmodel of porosity, matrix,clay and fluids.

    There is no informationfrom existing acoustic logsin these calculations.

    On all plots, porosity scaleis 0 to 40%, increasing rightto left.

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    Slow RocksGassmann DTP

    Compressional shows

    significant

    slowing due

    to gas

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    Slow RocksKrief DTP

    Compressional shows

    significant

    slowing due

    to gas

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    Slow RocksKrief DTP & DTS

    Compressional showsvery good comparison

    Ratio and Shear

    shows fair to

    good comparison

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    Fast RocksGassmann DTP

    Actual compressional

    meanders between

    wet and remote

    Noticeable

    slowing due to gas

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    Fast RocksKrief DTP

    Actual compressional

    superimposes

    on both wet andremote

    Negligible

    slowing due to gas

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    CarbonatesGassmann DTP

    Compressional

    shows slight

    slowing due to gas

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    CarbonatesKrief DTP

    Compressional shows

    negligible

    slowing due to gas

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    Fast RocksGassmann DTP/DTS

    Good comparison

    with actual Shear

    Ratio shows

    slight slowing

    due to gas

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    Fast RocksKrief DTP/DTS

    Good comparison

    with actual Shear

    Ratio shows

    negligible

    slowing due to gas

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    ConclusionsPart I

    Pseudo acoustic logs (both compressional and shear) canbe created using any combination of water, oil and gas,using either Gassmanns or Kriefs equations for clean and

    the full range of shaley formations. Comparison with actual acoustic log will show whether or

    not the acoustic log sees gas or not gives informationon invasion profile.

    Pseudo acoustic logs can be created even if no sourceacoustic log is available.

    Data from either model can be incorporated into the WyllieTime Series equation to rigorously account for gas.

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    ConclusionsPart II

    Interpretation yields better input to create syntheticseismograms and for rock mechanical properties.

    Methodology allows for detailed comparisons among well

    log response, drilling information, mud logs, well test dataand seismic.

    In fast velocity rocks and in the presence of gas, the Kriefmodel predicts less slowing effect than Gassmann.

    In slow velocity gas-bearing rocks, both models giveclosely comparable results.

    The techniques have been applied successfully to bothclastic and carbonate reservoirs throughout North America.