Development of optimization program for estimating three－phase relative permeability from unsteady－state core flooding experiment by genetic algorithm and iterative Latin hypercube sampling

It is essential to estimate the three-phase (oil-water-gas) relative permeability accurately in the numerical simulation for the three-phase flow behavior in porous media. The most common approach currently used in modeling the three-phase flow is to calculate the three-phase relative permeability, from the set of two-phase (oil-water and oil-gas) relative permeability data measured in a laboratory, using the empirical correlations such as Stone and Baker. However, these existing three-phase relative permeability models may lead to highly erroneous simulation results. On the other hand, it is unrealistic to obtain the three-phase relative permeability data directly from three-phase core flooding experiments in the steady-state condition, because they take a great deal of cost and time. The objective of this research is to develop a new method to estimate the three-phase relative permeability as functions of oil, water and gas saturation, through automatic history matching of unsteady-state core flooding experiment results. In this research, the programs for estimating three-phase relative permeability were developed, applying the Genetic Algorithm (GA) and the Iterative Latin Hypercube Sampling (ILHS), which are non-gradient optimization methods, as optimization tools. These programs enable the estimation of the oil phase relative permeability in the three-phase condition, and the relative permeability to water and gas phases as functions of water and gas saturation respectively, by automatically matching the calculation results with experimental results. The black oil type simulator was modified so that it could read the oil relative permeability as a complicated function of oil, water and gas saturation, which was adopted as an engine of these optimization programs. The hypothetical unsteady-state core flooding experiment results (oil, water and gas production rates and inlet/outlet pressure) were prepared by numerical simulation instead of actually conducting experiments. Three-phase relative permeability was then tuned so as to strictly reproduce these hypothetical experiment data by numerical calculation. In all the trial cases with different conditions, three-phase relative permeability was successfully estimated using the above optimization programs. These programs are also expected to be extended to the estimation of the relative permeability in the steam-water system, gas hydrate-gas-water system and micro emulsion-oil-water system in which the rigorous measurements of relative permeability in the steady-state condition are difficult due to the complex phase behavior.