Transp Porous Med (2011) 89:63–73
DOI 10.1007/s11242-011-9752-7
Capillary Pressure Curve for Liquid Menisci in a Cubic
Assembly of Spherical Particles Below Irreducible
Saturation
Jacob Bear · Boris Rubinstein · Leonid Fel
Received: 6 October 2010 / Accepted: 2 March 2011 / Published online: 30 March 2011
© Springer Science+Business Media B.V. 2011
Abstract The capillary pressure–saturation relationship, P
c
( S
w
), is an essential element
in modeling two-phase flow in porous media (PM). In most practical cases of interest, this
relationship, for a given PM, is obtained experimentally, due to the irregular shape of the void
space. We present the P
c
( S
w
) curve obtained by basic considerations, albeit for a particular
class of regular PM. We analyze the characteristics of the various segments of the capillary
pressure curve. The main features are the behavior of the P
c
( S
w
) curve as the wetting-fluid
saturation approaches zero, and as this saturation is increased beyond a certain critical value.
We show that under certain conditions (contact angle, distance between spheres, and satura-
tion), the value of the capillary pressure may change sign.
Keywords Porous media · Two-phase flow · Wetting fluid · Capillary pressure curve
List of Symbols
d Distance between spheres
n Number of spheres per unit cell
H Mean curvature of meniscus
P
c
Capillary pressure
P
w
, P
n
Pressures in wetting and non-wetting fluids
R Radius of sphere
S
w
, S
n
Saturations of wetting and non-wetting fluids
S
wr
, S
nr
Irreducible w-fluid and residual n-fluid saturations
This article is dedicated to the memory of Prof. Walter Rose (1920–2009), a friend, engineer and scientist,
who did pioneering work on the capillary pressure curve in reservoir engineering.
J. Bear (B ) · L. Fel
Department of Civil Engineering, Technion, 32000 Haifa, Israel
e-mail: cvrbear@techunix.technion.ac.il
B. Rubinstein
Stowers Institute for Medical Research, Kansas City, MO 64110, USA
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