Page 508 - Petrophysics
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476 PETROPHYSICS: RESERVOIR ROCK PROPERTIES
Similarly, the total pressure drop is equal to:
(7.157)
Substituting Equations 7.156 and 7.157 into Equation 7.155, and canceling
the identical terms q, m, and A yields:
(7.158)
and the average reservoir permeability of n segments arranged in series is:
(7.159)
It is important to emphasize that the fluid properties are assumed to be
constant in the entire system.
Radial Flow Systems
A similar analysis can be made to determine the average permeability
when radial flow of fluids is through a series of homogeneous concentric
segments with different permeabilities, as shown in Figure 7.18. Using
the radial incompressible fluid flow Equation 7.57, the total pressure drop
between radii rw and re, where the pressures are pw and pe, respectively,
is equal to:
(7.160)
and the pressure drops in the individual segments are:
(7.161)
If Equations 7.155, 7.160 and 7.161 are combined, and the identical
term (qp/2nh) is canceled, one finds:
