fluid substitute
TRANSCRIPT
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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.