Page 37 - Principles of Applied Reservoir Simulation 2E

22 Principles of Applied Reservoir Simulation

atmosphere. Laboratory fluids should also be at reservoir conditions to obtain
the most reliable measurements of wettability. Based on laboratory tests, most
known reservoirs have intermediate wettability and are preferentially water wet.

3.2 Capillary Pressure

Capillary pressure is the pressure difference across the curved interface
formed by two immiscible fluids in a small capillary tube:

PC = P m - P w (3.4)

where
capillary pressure [psi]
P c
P nw pressure in nonwetting phase [psi]
pressure in wetting phase [psi]
P w

Capillary Pressure Theory
Equilibrium between fluid phases in a capillary tube is satisfied by the
relationships/ores up = force down. These forces are expressed in terms of the
radius r of the capillary tube, the contact angle 6, and the interfacial tension 0,
The forces are given by
force up - IFT acting around perimeter of capillary tube
= O cos 0 x 2Kr

and
x
force down = density gradient difference cross-sectional
area x height h of capillary rise in tube
The density gradient F is the weight of the fluid per unit length per unit cross-
sectional area. For example, the density gradient of water T w is approximately
0.433 psia/ft at standard conditions. If we assume an air-water system, the force
down is
2
force down = (T w - T air)Ttr h
2
where the cross-sectional area of the capillary tube is Tlr . Capillary pressure
P. is defined as the force/unit area, thus