A New Approach for Obtaining J-Function in Clean and Shaly Reservoir Using In Situ Measurements
Authors: Elgaghah S.A. , Tiab D. , Osisanya S.O. 
Published: March 2010

Abstract
Leverett's capillary J-function has been widely used in the petroleum industry as an effective tool for correlating capillary pressure data with rock properties. The major goals of this study are: (1) to investigate the effect of stress on the calculated values of J-function, and (2) to develop new models capable of obtaining the J-function using in situ measurements in clean and shaly heterogeneous reservoirs.
Two models are developed, in which well-logging data, a good source of in situ measurements, are used to calculate the Jfunction. The first model was obtained using Tixier's permeability equation and Archie's equation for water saturation. The second model was derived using Tixier's permeability equation in combination with the Schlumberger shale model for water saturation determination. These models were validated using actual field data from two reservoirs in Oklahoma and Louisiana.

Introduction
Leverett's capillary pressure J-function has been widely used in the petroleum industry as an effective tool for correlating capillary pressure data with rock properties. Capillary pressure data is a very useful tool, since it reflects the pore size distribution, the radius of the largest pore, the rock wettability, and the interfacial tension of fluids in the system. Leverett(1) developed the basic theory for the behaviour of the flow of fluid mixtures in reservoir rocks. He used well established thermodynamic and physical principles in the development of his theory. He divided the problems into two groups:Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids (gravitational forces), andDynamic problems, involving analysis of the flow of immiscible fluids in porous media under the effect of gravity, capillary, and external differential pressure forces.
The J-function is a very useful tool for correlating capillary pressure data and rock properties. Hence, it is an effective tool for the better description of reservoir rock and the behaviour of the capillary retention of the wetting fluid.

The Concept of J-Function
Leverett conducted several experiments using unconsolidated clean and clayey sands for the development of a dimensionless group called the "Leverett J-function." He used the J-function to correlate capillary pressure (PC), interfacial tension (σ), in addition to permeability (K) and porosity (φ) of the porous rock. He found, from the results of his experiments, that a dimensionless group of the form [PC / σ* √ (K/ φ)] vs. water saturation (SW) gives two satisfactory but closed curves, one for imbibition of water and the other for drainage. Leverett's data showed that a plot of this dimensionless group vs. the wetting-phase saturation (SW) yielded a unique curve describing the capillary retention of the wetting liquid existing in the clean, unconsolidated sands, when capillary forces were at equilibrium, as shown in Figure 1.
Later, Leverett et al.(2) proved theoretically, using the dimensionless analysis technique, that capillary pressure is proportional to the interfacial tension, to the radical v(K/ φ), and to the dimensionless function of the water saturation J(SW).