Page 183 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 121

Although the above description of the concept of relative permeability has been
restricted to a two phase oil-water system, the same general principle applies to any
two phase system such as gas-oil or gas-water.

4.9 THE MECHANICS OF SUPPLEMENTARY RECOVERY

Supplementary recovery results from increasing the natural energy of the reservoir,
usually by displacing the hydrocarbons towards the producing wells with some injected
fluid. By far the most common fluid injected is water because of its availability, low cost
and high specific gravity which facilitates injection.

The basic mechanics of oil displacement by water can be understood by considering
the mobilities of the separate fluids. The mobility of any fluid is defined as

kk
λ = r (4.35)
µ

which, considering Darcy's law, can be seen to be directly proportional to the velocity of
flow. Also included in this expression is the term k r /µ, which is referred to as the
relative mobility.

The manner in which water displaces oil is illustrated in fig. 4.10 for both an ideal and
non-ideal linear horizontal waterflood.

IDEAL
1− S or

S w (a)

S wc
x

1− S or NON-IDEAL

(b)
S w

S wc

x

Fig. 4.10 Water saturation distribution as a function of distance between injection and
production wells for (a) ideal or piston-like displacement and (b) non-ideal
displacement

In the ideal case there is a sharp interface between the oil and water. Ahead of this, oil
is flowing in the presence of connate water (relative mobility = k ro (S w=S wc )/µ o = k′ /µ o),
ro
while behind the interface water alone is flowing in the presence of residual oil (relative
mobility = k rw(S w=1 - S or)/µ w = k′ /µ w). This favourable type of displacement will only
ro
occur if the ratio