Page 42 - Principles of Catalyst Development

Part I: Reservoir Engineering Primer 23

2 2
= force up I Tlr = force down / Tlr .
P c
Capillary Pressure and Pore Radius
Expressing capillary pressure in terms offeree up per unit area gives:

27crocos0
2ocos0
PC = _ - - = ----- (3>5)
n
71 r 4 r
where
r pore radius [cm]
a interfacial (or surface) tension [mN/m or dynes/cm]

6 contact angle [degrees]
Equation (3.5) shows that an increase in pore radius will cause a reduction in
capillary pressure while a decrease in IFT will cause a decrease in capillary
pressure.

Equivalent Height
Expressing P c in terms of force down leads to the expression

PC = - 2_- = h(r w - T air) (3.6)
Tir 2
where
h height of capillary rise [ft]
capillary pressure [psi]
P c
T w water, or wetting phase, density gradient [psi/ft]
air, or nonwetting phase, density gradient [psi/ft]
r ai>
Solving for h yields the defining relationship between capillary pressure and
equivalent height, namely

The equivalent height provides an estimate of the height of the transition zone
between immiscible phases. A more precise definition of transition zone is given