Effect of Reservoir Description on Performance Predictions
Authors: Craig F.F. 
Published: December 2007

In predicting the performance of a stratified reservoir, the engineer frequently uses an arbitrary number of layers. Presented here is a guide for selecting the minimum number of layers to describe the reservoir.

Introduction
Some of the earliest work in reservoir analysis was attempts to predict the oil recovery performance of a reservoir under various types of fluid injection. In these attempts it was recognized that many reservoirs cannot be adequately described as a single uniform permeability system. One of the earliest measures of permeability system. One of the earliest measures of the effect of reservoir nonuniformity was termed "conformance". It was defined as the fraction of the reservoir contacted by the injected fluid. Later efforts introduced the concept of a reservoir's being composed of a number of horizontal layers, each of uniform permeability, porosity, and thickness, continuous from permeability, porosity, and thickness, continuous from well to well, and insulated from crossflow. This concept of a layered or stratified reservoir has become widely used in the industry. On the basis of this concept, some field waterflood performance can be adequately predicted. An engineer faced with this prediction problem must decide on a most critical factor - the description of the layers that constitute the reservoir. In a few reservoirs, dense, relatively impermeable intervals separate the pay into a number of discrete zones, identifiable from cores and logs at each well. In such a reservoir the engineer probably would decide to consider each zone a separate layer. In some few other reservoirs, geological studies may be available from which to select the number of zones together with their permeability and porosity. In most reservoirs, however, the engineer has available only a very few well cores. Though there may be logs from each well, it is a nearly impossible task to infer permeability distributions from these logs. Thus layer properties must be selected from the available core data. Several techniques are available for quantifying reservoir heterogeneity from core data. One method is to determine the Lorenz coefficient. A major limitation of this method is that the Lorenz coefficient is not uniquely related to the permeability distribution; that is, several different permeability distributions may have the same value of Lorenz coefficient. The statistical approach of Testerman is an unbiased method for defining the number and location of strata from the analysis of a well core. The most popular technique, that introduced by Dykstra and Parsons, involves the calculation of a coefficient of permeability variation, V. This coefficient expresses the spread of a set of permeabilities having a log normal distribution, and is defined as
(1)
where
= median permeability, (permeability valueat 50 percent probability); = permeability at 84.1 percent of thecumulative sample.
The value of permeability variation can range from zero to 1, a completely uniform system having a zero permeability variation, with the permeability permeability variation, with the permeability variation increasing toward 1 as the distribution becomes more nonuniform.
JPT
P. 1239