Page 409 - Fundamentals of Reservoir Engineering

IMMISCIBLE DISPLACEMENT 344

c) The displacement is considered as incompressible

This assumption implies that steady state conditions prevail in the reservoir with the
pressure at any point remaining constant. There must, of course, be a pressure
differential between injection and production wells but the variation in the pressure
dependent variables, viscosities and densities, resulting from this differential is ignored.
This type of displacement will occur if

q = q + q = q i (10.7)
t
o
w
where
q t = total flow rate (r.vol/time)

q o = oil " " "

q w = water " " "

q I = water injection rate

The assumption is quite realistic since the engineer has control over the displacement
process to a much greater extent than, say, during the volumetric depletion of a
reservoir. Therefore, the wells and surface facilities are usually designed for constant
rate injection/production for it makes little sense to do otherwise. In addition, from a
reservoir engineering point of view, there are definite advantages in maintaining the
pressure at a constant level above that at which the solution gas first becomes mobile
(refer Chapter 3, sec. 5). Because of this assumption the methods described in this
chapter will be equally appropriate for the description of the displacement of oil by gas
at constant pressure with no mass transfer between the phases.

d) The displacement is considered to be linear

Throughout the chapter displacement will be considered exclusively in a linear
prototype reservoir model, as shown in fig. 10.6.

Production

q t
w
h

L
q i

Injection y x
θ Z

(a) (b)

Fig. 10.6 Linear prototype reservoir model, (a) plan view; (b) cross section