Presentation on theme: "Petrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief Models Digital Formation,"— Presentation transcript:
Petrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief Models Digital Formation, Inc. November 2003 Title
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
Benefits – Seismic 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.
Benefits – Petrophysics Verifies consistency of petrophysical model. Ability to create reconstructed porosity logs using deterministic approaches.
Benefits – Engineering Reliable mechanical property profiles for drilling and stimulation design. Does not rely on empirical correlations, or neural network curve generation, for mechanical properties.
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.
Gassmann 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 rock M erf =Elastic modulus of the empty rock frame B erf =Bulk modulus of the empty rock frame B solid =Bulk modulus of the rock matrix and shale B fl =Bulk modulus of the fluid in pores and in clay porosity T =Total Porosity B =Bulk density of the rock fluid and shale combination V p =Compressional wave velocity
Gassmann 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.
Wyllie 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: t=Travel time = 1/V t ma =Travel time in matrix t fl =Travel time in fluid Matrix Contribution Fluid Contribution
Linking Gassmann to Wyllie Calculate t values from Gassmann using fluid substitution –Liquid filled i.e. Gas saturation S g =0 –Gas filled assuming remote (far from wellbore) gas S g –Gas filled assuming a constant S g of 80% From t values, calculate effective fluid travel times ( t fl ) Knowing mix of water and gas, determine effective travel time of gas ( t gas ) Relate t values to gas saturation, bulk volume gas
Gassmann S g vs. Ratio of Dt gas to Dt wet Color coding refers to porosity bins
Gassmann Bulk Volume Gas vs. Ratio Dt gas to Dt wet Color coding refers to porosity bins
Gassmann Bulk Volume Gas vs. Dt gas C1C1 Hyperbola = C 3 C2C2
Adding a Gas Term to Wyllie Equation Gas term involves C 1, C 2 and C 3 (constants) Equation reduces to traditional Wyllie equation when S g =0 If gas is present, but has not been determined from other logs, the acoustic cannot be used to determine reliable porosity values. Gas Contribution Matrix Contribution Water Contribution
Krief Equation – Part 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. V p =Compressional wave velocity V S =Shear wave velocity B =Bulk density of the rock fluids and matrix and shale =Shear modulus K=Elastic modulus of the shaley porous fluid filled rock K S =Elastic modulus of the shaley formation K f =Elastic modulus of the fluid in pores b =Biot compressibility constant M b =Biot coefficient T =Total Porosity
Krief 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.
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, 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 Rocks – Gassmann DTP Compressional shows significant slowing due to gas
Slow Rocks – Krief DTP Compressional shows significant slowing due to gas
Slow Rocks – Krief DTP & DTS Compressional shows very good comparison Ratio and Shear shows fair to good comparison
Fast Rocks – Gassmann DTP Actual compressional meanders between wet and remote Noticeable slowing due to gas
Fast Rocks – Krief DTP Actual compressional superimposes on both wet and remote Negligible slowing due to gas
Carbonates – Gassmann DTP Compressional shows slight slowing due to gas
Carbonates – Krief DTP Compressional shows negligible slowing due to gas
Fast Rocks – Gassmann DTP/DTS Good comparison with actual Shear Ratio shows slight slowing due to gas
Fast Rocks – Krief DTP/DTS Good comparison with actual Shear Ratio shows negligible slowing due to gas
Conclusions – Part I Pseudo acoustic logs (both compressional and shear) can be 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 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.
Conclusions – Part II Interpretation 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.