Estimating Pressure and Saturation Changes From Time-Lapse AVO Data
Authors: Tura Ali , Lumley David E. 
Published: October 2008

Abstract
In current industry practice, angle-averaged (stacked or migrated) P-wave reflection seismic images, approximating Pwave impedance changes, are used in time-lapse (4D) seismic analysis. Introduction of angle dependency in P-wave reflection data allows one to estimate both P-wave and S-wave impedance changes over the reservoir. Utilizing time-lapse Pwave and S-wave impedance, we show how to invert for multiple reservoir properties such as changes in fluid saturation and pressure. Estimates of saturation and pressure change are useful for integration of time-lapse seismic data with reservoir engineering models to improve reservoir fluidflow prediction and enhance reservoir management decisions.

Introduction
Time-lapse seismic is a procedure where a reservoir is imaged with reflected seismic energy at several time steps while being depleted1,2. This technology is successful when changes in dynamic reservoir properties, such as pressure, fluid saturation and temperature produce an observable change in the seismic impedance contrast of the medium in 3-D space3. A careful analysis combining rock physics measurements, reservoir simulation and forward seismic modeling is required to identify if changes in reservoir properties can produce seismically observable impedance changes, and if so, how they are related to dynamic fluid flow in the reservoir4.
Here, we extend conventional post-stack time-lapse seismic analysis to pre-stack seismic data. With this extension we are able to estimate regions of separate saturation and pressure changes in an oil reservoir.

Inversion for Pressure and Saturation
The inverse problem we address here is to invert for changes in dynamic reservoir properties such as pressure and fluid saturation, given reflection angle dependent time-lapse seismic, or 4D AVO (amplitude variation with offset), data. Here, we consider the isothermal case.
The first step in this procedure is to invert the AVO data for relative changes in P-wave and S-wave impedance5. A second optional step would be to use log data to obtain absolute P-wave and S-wave impedances from the relative changes. Finally, time-lapse changes in impedances are related to time-lapse changes in dynamic reservoir properties using impedance crossplotting6,7. We illustrate this method and discuss the principles in an example.

Waterflood Example
A synthetic data example consisting of a 3D spatially heterogeneous reservoir model based on actual field data from a Chevron field in the Gulf of Mexico is considered. Flow simulations were performed in this reservoir model to simulate water injection recovery. Fig. 1 shows the simulated water saturation difference and pore pressure difference between the start of injection time in Jan/1992, and four years later in Feb/1996. In this portion of the model, a single water injector is located in the upper left corner, and a single oil producer is located in the lower right corner. Note that reservoir heterogeneity in porosity and permeability has caused the injected water to preferentially channel along the left side of the model, on its path from the injector to the producer. The pressure is higher at the injector location, and lower at the producer where fluid is being withdrawn from the reservoir.