A New Displacement Capillary Pressure Model
Authors: Bentsen Ramon G. , Anli Jun 
Published: March 2010

Abstract
A capillary pressure function for porous media (commonly known as the J-function) was postulated by Leverett and has been widely used for correlation purposes. It is generally accepted) however, that the J-function correlates satisfactorily only the data from unconsolidated sands and from the same formation. It is the purpose of this study to formulate a new drainage capillary pressure function which would overcome this restriction.
The proposed model is a function of saturation and involves three parameters which have to be obtained experimentally. The model has been experimentally verified using data obtained from relatively homogeneous, water-wet, artificially consolidated silica cores, and using several different fluid combinations. This limited amount of experimental data suggests that the correlation may prove to be universal for relatively homogeneous and isotropic materials.

Introduction
Although the absolute magnitude of the capillary pressure in most petroleum reservoirs is not large, knowledge of the effects of capillary forces is extremely important in understanding fluid displacement in porous media. Firstly, the original distribution of fluids in the reservoir rock is controlled by gravitational and capillary forces(1, 2). Secondly, during the displacement process, the relative freedom of movement and distribution of fluids are primarily influenced by these forces. Finally. capillary forces are responsible for trapping a large portion of non-wetting fluid within the interstices of the rock. For these reasons, the study of capillary forces is essential in order to understand how one fluid displaces another in a porous medium.
It is of interest, therefore, to develop an equation which describes capillary effects in porous media. It is also of interest to express such an equation in a universal form so that all of the drainage capillary pressure data, for example, could be reduced to a single correlation.
Leverett(3) I gave the essential concepts of capillary pressure in a porous medium. He defined the term "capillary pressure" and proposed a capillary pressure function, commonly called the J-function, which correlates the physical properties of a porous medium and ts fluids with capillary pressure. It has been noted(4), however, that the J-function is not truly satisfactory when data are taken from rock samples with various lithologic properties rather than from samples of similar lithologic types.
This study was undertaken at the University of Alberta(5) to devise a widely applicable function for the drainage capillary pressure fluid saturation relationship which could be used to analyze a recentlyformulated displacement equation. One of the parameters involved in the proposed capillary pressure model incorporates the effects of interfacial tension, wettability and pore-size distribution. Thus, it should be possible to reduce the drainage capillary pressure curves obtained using various rock-fluid combinations to a single curve.

Drainage Capillary Pressure Model
Analysis of the differential equation describing the displacement of one fluid by another(6), together with an appreciation of the physics involved(3), suggests several mathematical criteria which any model of drainage capillary pressure should meet. These criteria include the following.
1. The slope of the drainage capillary pressure curve must tend to minus infinity as the water saturation approaches the irreducible saturation.