An Improved Model For Estimating Three-Phase Oil-Water-Gas Relative Permeabilities From Two-Phase Oil-Water And Oil-Gas Data
Authors: Kokal Sunil , Maini Brij B. 
Published: March 2010

Abstract
Laboratory measurements of three-phase relative permeabilities are extremely time-consuming and are rarely obtained for reservoir systems. Therefore, computer simulations of reservoir processes involving three-phase flow have to rely on predictive techniques for supplying the three-phase relative permeability data. The empirical models developed by Stone(8,9) have been used extensively. As discussed by Aziz and Settari(15) the Stone models must be normalized to obtain a good match of the oil relative permeabilities at the oil-water and oil-gas two-phase ends for systems in which the relative permeability to oil at connate water saturation in an oil-water system and at zero gas saturation in an oil-gas system is not unity. Even after incorporating the normalization suggested by Aziz and Settari(15), the Stone models do not provide a satisfactory match of available three-phase data. This paper presents a new method for normalizing Stone's first model.
The method was tested against six different sets of experimental data reported in the literature as well as with a new set of experimental data. Considerably improved matches were obtained with this version of the normalization scheme compared to the conventional Stone's Methods I and II results. The new fits are excellent at the highest oil isoperms and deviate slightly as the residual oil saturation is approached.

Introduction
Displacement of oil in reservoirs generally involves the flow of oil, water and gas. Enhanced oil recovery methods such as wAG solvent flooding, steamflooding and in situ combustion involve multiphase flow. To simulate such processes by numerical modelling requires experimental data or prediction methods for threephase relative permeabilities.
There are only a limited number of studies which deal with threephase relative permeability measurements and correlations in the literature. The first study was conducted by Leverett and Lewis(1) in 1941. They measured the three-phase relative permeability of a water-oil-gas system in unconsolidated sands. Since their work in 1941 several other studies have been reported. Numerous review articles on three-phase relative permeability correlations and experimental studies have also appeared in the literature. Some of these are the work of Saraf and McCaffery(2), Honarpour et al.(3), Bakerter(4) Manjnath and Honarpour(5), Parmeswar and Maerfat(6), Maini et al(7). The interested reader is referred to these studies for an up-to-date literature review of three-phase relative permeabilities.
Measurement of three-phase relative permeability in the laboratory is a difficult and time-consuming task due to the complicationsof three-phase flow through porous media. Relative permeabilities are function of fluid saturation history which makes their measurement complicated. A detailed description of the methods and the problems involved in the measurement of threephase relative permeability is given by Saraf and McCaffery(2) and Honarpour et at.(3). Due to the problems associated with threephase flow experiments and the amount of time and effort needed for obtaining experimental data on three-phase relative permeabilities, use of a predictive model is an attractive alternative.

Stone Models
The models of Stone(8,9), designated as Methods I and II, have been used extensively in reservoir simulation studies in the absence of three-phase data.