Interpreting 4D Seismic Response to Changes in Effective Pressure with Rock Physics Modeling
Authors: Smith Brackin A. , Lane F. David , Danudjaja Sugiharto 
Published: October 2008

Abstract
We present a case study that contributes to understanding changes in seismic amplitudes associated with production induced pressure variations. We find that as reservoir pressure decreases, and effective pressure increases, far-stack seismic amplitudes brighten. This is contrary to expectations, since we know that increasing effective pressure increases velocity, consequently a low-impedance reservoir sand should exhibit diminished amplitude. Modeling based on Hertz-Mindlin- Hashin-Shtrikman contact theory shows that even though both compressional and shear velocities increase with increasing effective pressure, shear velocity increases more than compressional velocity, so the resulting Vp/Vs ratio decreases. This helps explain an initially confusing observation made during a 4D study of an oil field in offshore Indonesia in which far-offset amplitudes brighten and near-offset amplitudes dim.

Introduction
Interpretation and modeling of the 4D seismic response to production processes plays a prominent role in current applications of reservoir and development seismic analysis. Among the production processes that have generally wellunderstood effects on 4D seismic data are increases in water saturation due to injection or natural water drive, and increases in gas saturation due to injection or reduction of reservoir pressure below the bubble point of the in-situ oil. These effects are routinely modeled in a variety of software packages using Gassmann fluid subsitution, Batzle-Wang-Han fluid equations, and Zoeppritz reflectivity.
The effect of production-related stress variations on seismic amplitudes could potentially contribute substantially to the 4D signature. Unfortunately, these effects are not always thoroughly considered in typical 4D modeling and interpretation exercises. Landro and Kvam1 use 4D time differences associated with changes in P-wave velocity to interpret reservoir pressure changes. Tura and Lumley2 show how changes in acoustic impedance and shear impedance can be used to interpret reservoir pressure changes in conjunction with water saturation changes. Our study focuses on developing a rock physics model for predicting seismic amplitude response to pressure changes. We find this approach is useful for interpreting 4D seismic observations in an oil field that has undergone substantial pressure drawdown.

Development of Modeling Approach
We use Hertz-Mindlin-Hashin-Shtrikman (HMHS) contact theory for modeling the effect of pressure changes on seismic amplitudes. This methodology was adopted because of its ability to accurately model a large range of pressure variations for a variety of lithologies. The method we developed eliminates the need for specifying individual petrophysical parameters required to compute modulus values with the traditional formulas. Our formulation simplifies to two expressions for the change in bulk and shear moduli as a function of pressure3 :(1a)Knew/Kold=(Pnew/Pold)?(1b)Gnew/Gold=(Pnew/Pold)?
Knew and Gnew are the bulk and shear moduli of the dry rock at critical porosity with effective pressure Pnew, and Kold and Gold are the bulk and shear modulus of the dry rock at critical porosity with effective pressure Pold. The exponent,?, should be derived by a fit to laboratory core measurements of compressional and shear velocity under varying confining pressure and pore pressure.