Presentation on theme: "Title Petrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief Models Digital."— Presentation transcript:
1TitlePetrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief ModelsDigital Formation, Inc.November 2003
2Contents Benefits Introduction Gassmann Equation in Shaley Formation Wyllie Time Series EquationLinking Gassmann to WyllieAdding a gas term to Wyllie EquationKrief EquationExamplesConclusions
3Benefits – SeismicReliable 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.
4Benefits – Petrophysics Verifies consistency of petrophysical model.Ability to create reconstructed porosity logs using deterministic approaches.
5Benefits – Engineering Reliable mechanical property profiles for drilling and stimulation design.Does not rely on empirical correlations, or neural network curve generation, for mechanical properties.
6IntroductionA 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.
7Gassmann Equation in Shaley Formation – I 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 the Gassmann 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 rockMerf = Elastic modulus of the empty rock frameBerf = 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 = Total PorosityrB = Bulk density of the rock fluid and shale combinationVp = Compressional wave velocity
8Gassmann Equation in Shaley Formation – II In shaley formation, adjustments need to be made to several of the Gassmann equation terms, including porosity and bulk modulus of the solid components.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.
9Wyllie Time Series Equation In the approach presented here, we have solved the 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:MatrixContributionFluidContributionDt = Travel time = 1/VDtma = Travel time in matrixDtfl = Travel time in fluid
10Linking Gassmann to Wyllie Calculate Dt values from Gassmann using fluid substitutionLiquid filled i.e. Gas saturation Sg=0Gas filled assuming remote (far from wellbore) gas SgGas filled assuming a constant Sg of 80%From Dt values, calculate effective fluid travel times (Dtfl)Knowing mix of water and gas, determine effective travel time of gas (Dtgas)Relate Dt values to gas saturation, bulk volume gas
11Gassmann Sg vs. Ratio of Dtgas to Dtwet Color coding refers to porosity bins
12Gassmann Bulk Volume Gas vs. Ratio Dtgas to Dtwet Color coding refers to porosity bins
13Gassmann Bulk Volume Gas vs. Dtgas C2Hyperbola = C3C1
14Adding a Gas Term to Wyllie Equation ContributionMatrixContributionWaterContributionGas term involves C1, C2 and C3 (constants)Equation reduces to traditional Wyllie equation when Sg=0If gas is present, but has not been determined from other logs, the acoustic cannot be used to determine reliable porosity values.
15Krief Equation – Part IKrief 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 velocityVS = Shear wave velocityrB = Bulk density of the rock fluids and matrix and shalem = Shear modulusK = Elastic modulus of the shaley porous fluid filled rockKS = Elastic modulus of the shaley formationKf = Elastic modulus of the fluid in poresbb = Biot compressibility constantMb = Biot coefficientFT = Total Porosity
16Krief Equation – Part 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.
17ExamplesIn all of these examples, the pseudo acoustic logs are derived from a reservoir model of porosity, matrix, clay and fluids.There is no information from existing acoustic logs in these calculations.On all plots, porosity scale is 0 to 40%, increasing right to left.Slow RocksGassmann DTPKrief DTPKrief DTP & DTSFast RocksCarbonatesGassmann DTP & DTS
18Slow Rocks – Gassmann DTP Compressional showssignificantslowing dueto gas
19Slow Rocks – Krief DTP Compressional shows significant slowing due to gas
20Slow Rocks – Krief DTP & DTS Compressional showsvery good comparisonRatio and Shearshows fair togood comparison
21Fast Rocks – Gassmann DTP Actual compressionalmeanders betweenwet and remoteNoticeableslowing due to gas
22Fast Rocks – Krief DTP Actual compressional superimposes on both wet andremoteNegligibleslowing due to gas
23Carbonates – Gassmann DTP Compressionalshows slight slowing due to gas
24negligible slowing due to gas Carbonates – Krief DTPCompressional showsnegligible slowing due to gas
25Fast Rocks – Gassmann DTP/DTS Good comparison with actual ShearRatio showsslight slowingdue to gas
26Fast Rocks – Krief DTP/DTS Good comparison with actual ShearRatio showsnegligibleslowing due to gas
27Conclusions – Part IPseudo acoustic logs (both compressional and shear) can be created using any combination of water, oil and gas, using either Gassmann’s or Krief’s 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 information on invasion profile.Pseudo acoustic logs can be created even if no source acoustic log is available.Data from either model can be incorporated into the Wyllie Time Series equation to rigorously account for gas.
28Conclusions – Part IIInterpretation yields better input to create synthetic seismograms and for rock mechanical properties.Methodology allows for detailed comparisons among well log response, drilling information, mud logs, well test data and seismic.In fast velocity rocks and in the presence of gas, the Krief model predicts less slowing effect than Gassmann.In slow velocity gas-bearing rocks, both models give closely comparable results.The techniques have been applied successfully to both clastic and carbonate reservoirs throughout North America.