Page 386 - Petrophysics 2E

354 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

As indicated in Figure 5.23, the pore throat size distributions can have
considerable influence on the residual oil saturation, but the critical
capillary number remains at approximately lo-*. Small variations in the
critical value are to be expected because of the wide variability of experi-
mental procedures, rocks, and fluids. The direct influence of wettability
on the critical value has not been explored because the experiments
conducted thus far have been concentrated on strongly water-wet
systems. Oil-wet systems will exhibit a lower displacement efficiency
and probably will shift the critical capillary number to a higher value.
The capillary number is generally varied by increasing the flow rate and
lowering the interfacial tension. The displacing-phase flow rate can be
increased to a value near the inception of turbulent flow; turbulent flow
produces eddy currents that create cross flows that are not accounted
for in the capillary number. A large number of experiments have been
conducted by lowering the interfacial tension, which can be precisely
controlled for a given system, but for effective response it must be
lowered to a value less than 0.1 mN/m.
Using Darcy’s law, the capillary number can be rearranged by
substitution for the velocity to obtain:

This equation can be used to obtain the relationship between the
capillary number and the pressure gradient for a given system, or it can be
used to calculate the capillary number if all other conditions are known
for the system being analyzed.

EXAMPLE

Given the following data for a fluid-flow system, calculate the capillary
number and the pressure gradient for the flow of the fluid at the velocity
given: viscosity = 120 cP, interfacial tension = 36 mN/m, velocity =
0.68 m/D, porosity = 0.18, absolute permeability = 60 pm, and relative
permeability = 0.2 1.
SOLUTION

1.16 x lo-* x 120 x 0.68
n.. =
0.18 x 36
-1
1.46 x x 0.18 x 36 x
Pressure gradient
0.21 x 60 x
= 0.751 x lo6 Pa/m = 109 psi/m = 33 psi/ft