Page 476 - Petrophysics

444 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Dimensionless Pressure
Steady-state and pseudosteady-state radial flow equations previously
presented are strictly applicable to the case where the well is located at
the center of a circular drainage area. For other well locations, drainage
area shapes, and external boundary conditions, the dimensionless form
of these flow equations is given by:

kh
qsc = ( 1*1.2pB,) (&) (7.78)

In reservoir systems where the pressure change with time is negligible
and the assumption of steady-state radial flow is applicable, the dimen-
sionless pressure drop, p~, is:

(7.79)

As producing time increases the pressure decline throughout the
reservoir becomes a linear function of time, and the assumption of
pseudosteady-state flow becomes applicable. When this flow regime
occurs, and Ap is equal to (pe - p,) or (pi - p,), the dimensionless
pressure, PD, is:

1 2.2458A
PD = 2ntD,4 + -In ( r$cA ) (7.80)
2

CA is a dimensionless shape factor whose value depends on reservoir
shape and well location as shown in Table 7.1. The dimensionless time,
tDA, is defined by:

0.000263713
tDA = ( QpCtA )t

where the drainage area, A, is expressed in ft2 and producing time, t, is
in hours.
For pseudosteady state and Ap = p - pw , the dimensionless pressure
PD in Equation 7.78 is given by:

1 2.2458A
PD = -In( 2 r$CA ) (7.82)