Page 450 - Petrophysics

4 18 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

(7) the flow is laminar, i.e., negligible turbulence effects; and
(8) gravity forces are negligible.

With these restrictions in mind, the apparent velocity is

where q is the volumetric flow rate (cm3/sec) and A is the cross-sectional
area perpendicular to flow direction (an2). The actual velocity (va) is
determined by dividing the apparent velocity (v) by the porosity of the
rock (Q). If an irreducible water saturation, Siw, is present, the actual
velocity in a water-wet reservoir is:

(7.3)

Combining Equations 7.1 and 7.2 yields:

(7.4)

Separating variables and integrating between limits 0 and L, and p1 and
p2, one obtains the following expression for the volumetric flow rate:

Equation 6.5 is the conventional linear flow equation used in fluid flow
calculations. This expression is written in the fundamental units that
define the Darcy unit. Transforming it into the commonly used oilfield
units, such that q = bbl/D, A = fi2, p = psi, L = ft, and k = mD, gives:

( 5*615 30*483) = A(30.482) k(10-3) - (1/14.7)
Ap
' 24 ~60x60 ~1 L 30.48
or:

In SI units, a flow rate of 1 m3/s will result for a fluid flowing through
a porous medium with a permeability of 1 pm2, a cross-sectional area
of 1 m2, and fluid viscosity of 1 Pa x s under a pressure gradient of
Pa/m.