A Prediction Technique for Immiscible Processes Using Field Performance Data (includes associated papers 13392, 13793, 15146 and 19506 )
Authors: Ershaghi Iraj , Abdassah Doddy 
Published: December 2007

Summary
A prediction method based on the use of performance history of a waterflood proposed in 1978 by Ershaghi and Omoregie is scrutinized here. Using a reservoir simulation approach, performance data for some hypothetical waterfloods are generated to test the application of the proposed technique to various floodpatterns, reservoir properties, and field operating conditions. Recently published results on the behavior of relative permeability curves for immiscible processes areused to substantiate the assumptions inherent in the proposed technique. The limitations of the technique are discussed and applications to some actual case studies are presented.

Introduction
Conventional waterfloods and modified waterfloodsusing various additives still constitute the bulk of the fluid injection projects active in the U.S. and elsewhere. During the history of a water injection project, reservoir engineers are expected to predict performance using the past response data. A literature review shows that over the last 40 years, there have been many techniques proposed for such prediction purposes. These techniques range from empirical correlations to various analytical models. In addition to these techniques, the advent of reservoir simulation has resulted in the availability of a very powerful tool for performance prediction.
Many operators are still reluctant to use reservoir simulators because of inadequate reservoir data or insufficiently trained personnel to conduct simulation studies. Simple models often fail because of the inherentassumption as to the nature of the displacement mechanism or the misrepresentation of the real reservoir conditions.
Many years of field and laboratory research by the petroleum industry and the academia has resulted in abetter understanding of the multitude of parameters influencing the efficiency of fluid injection projects. It is well established that for immiscible displacements, reservoir heterogeneity, relative permeability characteristics, fluid viscosities, and flood pattern are the most important factors.
No prediction method can be used successfully in afield where the real reservoir is represented by laboratory-derived data and inadequately defined reservoir heterogeneity. A successful prediction technique requires input from the real reservoir performance. Alumped-parameter model that would embody all properties of the reservoir and the operating conditions can lead us to a realistic prediction of performance.
In 1978, Ershaghi and Omoregie presented a technique for extrapolation of water-cut vs. recovery curvesin waterflood operations. The technique allows one togenerate a field composite relative permeability ratiocurve that includes reservoir properties as well as operational problems. The main assumptions were (1) the plot of log (krw/kro) vs. Sw is a straight line and (2) the leaky-piston displacement concept of Buckley and Leverett is applicable.
Since Ref. 1 was published, many operators have contacted the authors with questions and comments about applying the technique to their specific cases-ranging from natural bottomwater drive to modified waterflood. Two additional papers about the technique haveappeared in the literature by others.
This paper is aimed at clarifying ambiguities about the technique and providing guidelines for its application.

Review of the Technique
Assuming that log (krw/kro) vs. Sw is a straight line, the concepts of fractional flow and the frontal advance theory proposed by Buckley and Leverett may be used toderive the following relationship between the recovery and the fractional water cut:
ER = (m . X) + n,
where
ER = recovery, X = ln[(1/fw) - 1] - (1/fw)fw = fractional water cut, m = 1/[b(1 - Swi)], n = -1/(1 - Swi)[Swi + 1/b ln(A)], A = a(mu w/mu o), and
a and b from
kro/krw = a ebSw.
JPT
P. 664^