Page 402 - Fundamentals of Reservoir Engineering

CHAPTER 10

IMMISCIBLE DISPLACEMENT

10.1 INTRODUCTION

This chapter describes how to calculate the oil recovery resulting from displacement by
an immiscible (non-mixing) fluid which is primarily taken to be water. After considering
several basic assumptions, the subject is introduced in the conventional manner by
describing fractional flow and the Buckley-Leverett equation. Since the latter is one
dimensional its direct application, in calculating oil recovery, is restricted to cases in
which the water saturation distribution is uniform with respect to thickness. In more
practical cases where there is a non-uniform saturation distribution, defined, for
instance, by the assumption of vertical equilibrium, then it is necessary to generate
relative permeabilities, which are functions of the thickness averaged water saturation,
for use in conjunction with the Buckley-Leverett theory. This has the effect of reducing
two dimensional problems to one dimension. The remainder of the chapter
concentrates on the theme of generating these averaged functions, for various
assumed flow conditions in homogeneous and layered reservoirs, and describes their
application in numerical reservoir simulation.

10.2 PHYSICAL ASSUMPTIONS AND THEIR IMPLICATIONS

Before undertaking to describe the mechanics of displacement, it is first necessary to
consider some of the basic physical assumptions which will later be incorporated in the
simple mathematical description of the process. The implications of each assumption
are described in detail.

a) Water is displacing oil in a water wet reservoir

When two immiscible fluids, such as oil and water, are together in contact with a rock
face the situation is as depicted in fig. 10.1. The angle Θ, measured through the water,
is called the contact angle. If Θ < 90° the reservoir rock is described as being water
wet, whereas if Θ > 90° it is oil wet. The wettability, as defined by the angle Θ, is a
measure of which fluid preferentially adheres to the rock.

The two dynamic situations shown in fig. 10.1 (a) and (b) are described as (a)
Imbibition; in which the wetting phase saturation is Increasing and (b) Drainage; in
which the wetting phase saturation is Decreasing. It has been determined
experimentally that the contact angle is larger when the wetting phase is advancing
over the rock face than when retreating and this difference is described as the
hysteresis of the contact angle.