A New Approach For Obtaining J-function In Clean And Shaly Reservoirs Using In Situ Measurements

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: to investigate the effect of stress on the calculated values of J-function, andto develop new models capable of obtaining J-function using in-situ measurements in clean and shaly heterogeneous reservoirs. Two models are developed in which well-logging data good source of in-situ measurements are used to calculate J-function. 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 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. Leverett1 developed the basic theory for the behavior 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 better description of reservoir rock and the behavior 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 a dimensionless group called "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)] versus water saturation (Sw) gives two satisfactory but closed curves, one for imbibitions of water and the other for drainage. Leverett's data showed that a plot of this dimensionless group versus 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, Fig. 1. Later, Leverett et al2 proved theoretically, using dimensionless analysis technique, that capillary pressure is proportional to the interfacial tension, to the radical √(K/ φ), and to the dimensionless function of the water saturation J(Sw). The term √(K/ φ) according to the equalization of Poiseuille and Darcy equations, can be proven to be equal to the "average pore radius" of porous rock.