Petrophysical Analysis of Fluid Substitution in Gas Bearing Reservoirs to Define Velocity Profiles – Application of Gassmann and Krief Models Digital Formation,

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 inShaley 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 porosityT = Total PorosityB = Bulk density of the rock fluid and shale combinationVp = Compressional wave velocity

Gassmann Equation inShaley 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:

flemae ttt 1

t = Travel time = 1/Vtma = Travel time in matrixtfl = Travel time in fluid

MatrixContribution

FluidContribution

Linking Gassmann to Wyllie

• Calculate t values from Gassmann using fluid substitution– 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 travel

time of gas (tgas)• Relate t values to gas saturation, bulk volume gas

Gassmann Sg vs. Ratio of Dtgas to Dtwet

Color coding refers to porosity bins

Gassmann Bulk Volume Gas vs. Ratio Dtgas to Dtwet

Color coding refers to porosity bins

Gassmann Bulk Volume Gas vs. Dtgas

C1

Hyperbola = C3

C2

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 other logs, the acoustic cannot be used to determine reliable porosity values.

mae ma water w

e

tt Gas Term t t S

GasContribution

MatrixContribution

WaterContribution

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.

Vp = Compressional wave velocityVS = Shear wave velocityB = Bulk density of the rock fluids and matrix and shale = Shear modulusK = Elastic modulus of the shaley porous fluid filled rockKS = Elastic modulus of the shaley formationKf = Elastic modulus of the fluid in poresb = Biot compressibility constantMb = Biot coefficientT = 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 showssignificant

slowing due to gas

Slow Rocks – Krief DTP

Compressional showssignificant

slowing due to gas

Slow Rocks – Krief DTP & DTS

Compressional showsvery good comparison

Ratio and Shearshows fair to

good comparison

Fast Rocks – Gassmann DTP

Actual compressionalmeanders between

wet and remote

Noticeableslowing due to gas

Fast Rocks – Krief DTP

Actual compressionalsuperimposes

on both wet andremote

Negligibleslowing due to gas

Carbonates – Gassmann DTP

Compressionalshows slight

slowing due to gas

Carbonates – Krief DTP

Compressional showsnegligible

slowing due to gas

Fast Rocks – Gassmann DTP/DTS

Good comparison with actual Shear

Ratio showsslight slowing

due to gas

Fast Rocks – Krief DTP/DTS

Good comparison with actual Shear

Ratio showsnegligible

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 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.

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.