Page 470 - Petrophysics

438 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

at any radius r of the bounded reservoir is obtained from Equation 7.62:

2w-l
p=pw+- [W/rw> - O.5(r/r,l2 + 0.5(rw/r,)2] (7.63)
kh

If Equation 7.63 is used in Equation 7.58 and the integration carried out,
the following expression is obtained for qsc (in oilfield units), assuming
re >> TW:

O.O0708kh(P - pw) O.O0708kh(P - pw)
-
qsc = - (7.64a)
pBo[ln(r.Jrw) - 0.751 pB,ln(0.472re/rw)

For other well locations, drainage area shapes, and external boundary
conditions, the general form of Equation 7.64a is:

(7.64b)

where T', is an effective drainage radius that includes the effect that a well
placement in a given drainage area will have on the performance of the
well. The effective radius can be written as:

(7.64~)

where A is the drainage area (ft2), and CA is the shape factor, as shown
in Table 7.1 [20, 251.
When external reservoir boundaries are mixed, the methods of
obtaining flow equations become more complex, especially during
unsteady state. During steady-state flow, however, this system can be
approximated by a radial cylindrical reservoir where only a fraction f of
the reservoir periphery is open to water encroachment. The fraction f is
referred to here as the drainage boundary index. This partial water drive
reservoir is produced by two processes:

(a) expansion of the reservoir fluid, and
(b) displacement of the reservoir fluid by water.