Effects of Pore Structure On Capillary And Flo\v Phenonlena In Sandstones
Authors: Dullien A.K.L. 
Published: March 2010

Abstract
The importance of pore structure in determining capillary and flow phenomena in porous media is pointed out in a number of examples, mostly involving outcrop sandstones. The use of two kinds of bivariate pore size distributions is shown to be a versatile approach to characterizing pore structure. They together describe capillary hysteresis for both independent and interacting domains, and one of them correlates tertiary oil displacement efficiencies with pore structure; it also results in good predictions of the permeabilities and electric resistivity factors of tightly consolidated porous media such as sand- stones.

Introduction
CAPILLARY AND FLOW PHENOMENA in porous media are determined by the pore structure of the medium and the physico-chemical properties of the solids and the fluids. As is generally known, barring the presence of special effects, the flow of homogeneous fluids through porous media, under conditions of relatively low velocity follows Darcy's law:
(Equation in full paper)
Where v is the filter or seepage velocity, k is the permeability, VP is the pressure gradient and P the viscosity of the fluid. At higher flow rates, the Forchheimer equation has gained important theoretical and experimental support(1–3).
(Equation in full paper)
The permeability, k = 1/a, and the inertia coefficient, B are uniquely determined by the pore structure. The resistivity factor, F, of porous media(4–5)
(Equation in full paper)
where p u is the resistivity of an electrolyte and pO the
(Figure in full paper)
FIGURE 1 – Menisci in a conical capillary.
resistivity of the porous medium saturated with the electrolyte is also uniquely determined by the pore structure (where it has been taken for granted that the solid matrix of the porous medium does not conduct electricity).
It is well known(7-P) that the permeability k, of most porous media is a symmetric tensor which can be written in diagonal form:
(Equation in full paper)
where the principal permeabilities, k 1, k2 and ka, and thus the variation of permeability with the flow direction is determined solely by the pore geometry.
In the case of multi-phase phenomena in porous media, it is convenient to distinguish between immiscible and miscible phases. In the former case, the various fluids which co-exist in the pores have only limited miscibility and therefore are separated from each other by interfaces having non-zero interfacial tension. Whenever the interface has a non-zero curvature, in equilibrium there is always a pressure difference between the two sides of the interface, the so-called capillary pressure, Pc, given by Laplace"s equation
(Equation in full paper)
where the pressure is always greater in the fluid on the concave side of the meniscus; rm is the mean radius of curvature and CT is the interfacial tension. The value rm is determined jointly by the pore geometry and the value of the contact angle, 8, as shown for the simple case of the conical capillary in Figure 1 Immiscible displacement phenomena in sandstones involve capillary pressures in pores of a wide range of sizes and configurations.