Appraisal of Marsal's Extrapolation Method for Establishing Oil Recovery
Authors: Hooykaas H. 
Published: December 2007

Abstract
A few years ago Marsal published a method of predicting oil recovery as a function of time for an edge-water-drive reservoir with several rows of wells. The method is based solely on oil- and water-production data obtained during a short period for the first row of wells and the gross productions (past and future) of all wells. This paper presents a streamlined version of the original publication and experimental evidence showing the reliability of this version. For this purpose scaled experiments were performed in a large model (750 X 500 X 23 cm, 24.4 ft X 16.2 ft X 8.9 in.) in which edge-water-drive reservoirs with three rows of production wells were simulated. From the results of the experiments it is concluded that the method gives a fairly accurate prediction of the future production behavior of the reservoir and enables us to select the most profitable production plan. Results obtained with the method were always slightly conservative.
Introduction
The calculation method developed by Marsal aims at forecasting future reservoir behavior. It can be applied to floods in which a number of down-dip wells are rapidly going to water. Essentially it is a method for predicting the future behavior of the up-structure wells on the basis of the observed behavior of the down-structure wells. As such, the method is especially useful for predicting behavior of edge-water drives toward several rows of wells. The requirement to be met for justifying the approach is identity of production mechanism in all regions of the reservoir. The attraction of the method then lies in the fact that it applies even when we have no complete description of the prevailing production mechanism. The original publication was in the German language and for this reason, perhaps. did not attract widespread attention. In our opinion it deserves to do so because it does offer in a simple way results which are in fair agreement with observed data. The aim of the present paper is to bring the method to the attention of a wider audience. The method in its most simplified form is reviewed and experimental data in support of it are presented.
PRINCIPLES
To show Marsal's principle. we will first write the continuity equation for very simple conditions, linear flow (in the positive x-direction) in an incompressible porous body [cross-section A(x), porosity (x)], saturated with incompressible fluids (oil saturation S).When the oil in this formation is displaced by water, injected at x = 0 (inlet face), we get
S f(x)A(x) + q(t) = 0, ............(1)t x
where q(t) is the total gross displacement rate and f the fractional oil flow. The equation can be solved if we make the assumptions:
that the fractional oil flow (f) is a univalent function of saturation (S); and that the function is the same throughout the porous medium.
Then:
f = f(S)
f df S= x dS x
S df S(x) A(x) + q(t)= 0.t dS x
Solving this equation with the method of characteristics, we obtainx t
df(x)A(x) dx = q(t)dt,.............(2)dSo o
for a constant saturation,
dS= 0.dt
To simplify the formulas, we write
x(x)A(x)dx = Vp(t),......................(3)
o
and
dfg(f) = f[f(S)] = g{f[S(x, t)]} =, .......(4)dS
so that
Vp(x)g (x, t) =, ..........................(5)We(t)
JPT
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