Page 472 - Petrophysics

440 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

where the pressures are pw and Pe, respectively, and assuming r:/$ = 0,
one obtains:

0.00708kh(pe - pw)
qsc = (7.66)
pB,[ln(r,/r,) - 0.50(1 - f)]

It is evident from Equation 7.66 that:

(a) f = 0 represents no-flow condition at re, because for this value off,
Equation 7.66 becomes similar to Equation 7.62, which is specifically
derived for the case of bounded reservoirs under pseudosteady state.
(b) f = 1 represents a full active water drive reservoir, and Equation 7.66
becomes similar to Equation 7.57. f = 1 also represents a balanced
five-spot water injection pattern with unit mobility ratio.
(c) f > 1 indicates that the fluid volume entering a reservoir at re is greater
than the fluid volume entering the well bore at r,, such as under
excess fluid injection. Equation 7.66 provides away to determine the
strength of water drive f, if the producing rate and pressure drop are
known. The parameter f can be determined more accurately from
transient well test analysis [22].

If the average reservoir pressure, p , is used instead of the external
pressure, pe which is practically impossible to establish in such a mixed
boundary system, Equation 7.66 becomes:

0.00708kh(p - pw)
qsc =
pB,[ln(r,/r,) - 0.75 + 0.25fl

This expression is similar to Equations 7.60 and 7.64 for f = 1 and
f = 0, respectively, and can easily be derived by substituting p into
Equation 7.58 and integrating. p is obtained from Equation 7.66 by
assuming re > r, and replacing pe with p and re with r. Combining
Equation 7.66 and 7.67 yields a very useful relationship for determining
the external pressure of a mixed boundary system:

(7.68)

For a well in a closed outer boundary reservoir f = 0, and because at t = 0
the external pressure, pe, is equivalent to the initial reservoir pressure, pi,