Predicting Waterflood Performance by the Graphical Representation of Porosity and Permeability Distribution
Authors: Johnson Jarl P. 
Published: December 2007

Abstract
A simple tool for predicting the waterflood performance of stratified reservoirs has been developed using a variation of the familiar layer concept. The variation suggested allows consideration of non-uniform porosity, development and mobility ratio. The procedure involves predicting both cumulative water injected and cumulative oil production in terms of percent water cut using a permeability-porosity classification system. The simplicity of the graphical approach to the cumulative oil recovery vs water cut prediction provides a convenient means of evaluating the areal as well as the vertical aspects of flood performance.
Introduction
A prediction technique, to be applicable to a heterogeneous reservoir should provide a means for considering variation in volume as well as permeability. The presence of multiple rock types with different porosity-permeability relationships cause the common assumption of a uniform porosity to be impractical. Further, the number of projects being evaluated in the prospect of a unitized operation make it desirable that a convenient means be provided to evaluate the lateral as well as the vertical aspects of porosity and permeability development. A variation in the application of some familiar devices can provide the solution to both of these problems.
Premises
The premises necessary to the use of the procedure to be described are common to other methods with the following exceptions:1. It is not necessary to assume a uniform porosity distribution or uniform water saturation.2. It is assumed that in layers of equal permeability capacity, the advance of the flood front is inversely proportional to the mobile hydrocarbon volume of the layer.3. A changing mobility ratio during the fill-up period is assumed.
Procedure
Rock Classification
To evaluate the effect of stratification on vertical sweep efficiency, reservoir permeability data from core analysis are classified according to a system similar to that proposed by Law and demonstrated in Table 1. In addition to classifying the permeability data, the porosity of each sample is recorded. By listing both the porosity and permeability for each sample, it is possible to relate the porosity capacity and permeability capacity without the necessity of assuming that a uniform porosity exists or assuming a porosity-permeability relationship. If sufficient data are available to estimate the water saturation for each permeability range, it is possible to compute the hydrocarbon pore volume which can be substituted for the porosity capacity value, establishing a direct relationship between permeability and hydrocarbon volume. The data are summarized at the bottom of each column, with the cumulative permeability capacity and corresponding reservoir volume shown as a per cent of the total as indicated in Table 1. For convenience, values are added from the highest toward the lowest permeability range. The example in Table 1 includes water saturation data and the cumulative hydrocarbon pore volume. A plot of the cumulative permeability capacity vs the logarithm of the corresponding cumulative porosity capacity for four wells is shown in Fig. 1. Data from several wells in a single project were plotted on this graph to illustrate that more than one system is implied in each instance by the changing slopes and that there is some disparity between the plots representing different wells. Variations in rock type are responsible for the multiple systems, a common occurrence in carbonate reservoirs. Areal variation in porosity and permeability development account for the disparity between the curves. It is often possible to combine the data from several wells as shown in Table 2 to provide a composite representation of the reservoir permeability distribution. It is important that the selection of data for a composite curve describes the vertical classification of the rock.
JPT
P. 1285ˆ