Page 174 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 112

B
(p , z )
A
A
+ z

ψ = p + ρg (z − z ) arbitrary datum plane (z=z) o
B
0
B
B
ψ = p + ρg (z − z )
A
0
A
A

(p , z )
B
B
B
Fig. 4.3 Referring reservoir pressures to a datum level in the reservoir, as datum
pressures (absolute units)

Suppose pressures are measured in two wells, A and B, in a reservoir in which an
arbitrary datum plane has been selected at z = z 0. If the pressures are measured with
respect to a datum pressure of zero, then as shown in fig. 4.3, the calculated values of
ψ A and ψ B are simply the observed pressures in the wells referred to the datum plane,
i.e.

ψ A = (absolute pressure) A + (gravity head) A

In a practical sense it is very useful to refer, pressures measured in wells to a datum
level and even to map the distribution of datum pressures throughout the reservoir. In
this way the potential distribution and hence direction, of fluid movement in the
reservoir can be seen at a glance since the datum pressure distribution is equivalent to
the potential distribution.

4.7 RADIAL STEADY STATE FLOW; WELL STIMULATION

The mathematical description of the radial flow of fluids simulates flow from a reservoir,
or part of a reservoir, into the wellbore.

For the radial geometry shown in fig. 4.4, flow will be described under what is called
the steady state condition. This implies that, for a well producing at a constant rate q;
dp/dt = 0, at all points within the radial cell. Thus the outer boundary pressure p e and
the entire pressure profile remain constant with time. This condition may appear
somewhat artificial but is realistic in the case of a pressure maintenance scheme, such
as water injection, in which one of the aims is to keep the pressure constant. In such a
case, the oil withdrawn from the radial cell is replaced by fluids crossing the outer
boundary at r = r e.