Page 84 - Geology of Carbonate Reservoirs

CAPILLARY PRESSURE AND RESERVOIR PERFORMANCE 65

P oB
B
P wB

h Oil

P oA
A P wA
Water

Figure 3.7 Illustration of pressure relationships in a capillary tube partly filled with water
surrounded by oil. The capillary pressure is zero at the oil – water interface where the pressures
of oil and water, respectively, are equal. The pressure difference across the oil – water interface

at point B defines capillary pressure. (Adapted from an illustration in Amyx, Bass, and
Whiting (1960) .)
interface at A to be a plane and that capillary pressure there is zero so that P oA =
P wA at the free - water surface in the beaker. For the pressure at point B, the density
of oil and water must be considered such that

P oB = P oA − ρ o gh
P wB = P wA − ρ w gh

The pressure difference across the interface is the capillary pressure, which must be
in equilibrium with gravitational forces if the fluids are in equilibrium and not

fl owing, or

P c = P oB − P wB = (ρ W − ρ O ) gh

The expression for capillary pressure in terms of surface forces can be obtained by
2

equating the expressions for the upward and downward forces, 2 π rA T = π r ( ρ w −
) gh , respectively, which simplifi es to
ρ o
h = gr ⎛ 2 A T ⎞ ⎟ ⎠
⎜
⎝ ρ
w − ρ o
If the expression for adhesion tension ( A T ) is substituted to obtain an alternative
expression for h , which is in turn substituted in the equilibrium capillary pressure
expression above, the expression for capillary pressure becomes

P c = (2σ wo cosθ wo r ) −1

Capillary pressure is a function of adhesion tension ( σ wo cos θ wo ) and the inverse of

− 1
the radius ( r ) of the capillary tube. In carbonate reservoirs, adhesion tension