A Method for Extrapolation of Cut vs Recovery Curves

Abstract

JPT Forum articles are limited to 1,500 words including 250 words for each table and figure, or a maximum of two pages in JPT. A Forum article may present preliminary results or conclusions of an investigation that the present preliminary results or conclusions of an investigation that the author wishes to publish before completing a full study; it may impart general technical information that does not warrant publication as a full-length paper. All Forum articles are subject to approval by an editorial committee. Letters to the editor are published under Dialogue, and may cover technical or nontechnical topics. SPE-AIME reserves the right to edit letters for style and content. Introduction For a fully developed waterflood with no major operational changes planned, a plot of fractional water cut vs total recovery is used often to obtain a quick estimate of ultimate recovery at a given economic water cut. Extrapolation of past performance on the "cut-cum" plot is a complicated task. The difficulty arises mainly because curve fitting by simple polynomial approximation does not result in satisfactory answers in most cases.This paper presents an equation that is a fair representation of the waterflood process, based on the concepts of fractional flow and the Buckley-Leverett recovery formula,* which may be written as (1) ER = over-all reservoir recovery, volume of hydrocarbon recovered divided by oil in place, place, fw= fractional water cut, where m and n are constants. Derivation of the Equation The fractional flow equation (after neglecting the capillary pressure and gravity terms) may be written as (2) The main portion of the ko/kw curve vs Sw plotted on semilog paper is quite linear and may be expressed as (3) where a and b are constants. On substitution, Eq. 2 may be written as (4) where As shown by Welge,* the water saturation at the producing end (S,.) may be expressed as producing end (S,.) may be expressed as(5) where Sav = average water saturation throughout thesystem. Since (6) In these equation, Swi is the initial water saturation. JPT P. 203