Development of optimization program for estimation of three-phase relative permeability from unsteady-state coreflood experiments

It is essential to estimate the three-phase (oil-gas-water) relative permeability accurately for the numerical simulation of reservoir performances. The most common approach currently used in modeling a three-phase flow is to estimate the three-phase relative permeability using empirical correlations, based on the set of two-phase relative permeability data measured in a laboratory. The relative permeability model thus estimated, however, may lead to highly erroneous simulation results. On the other hand, it is unrealistic to rigorously acquire the three-phase relative permeability data directly from steady-state three-phase flow experiments because of a lot 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, gas and water saturation, through automatic history matching of unsteady-state core flooding experimental results. In this study, the program for optimizing three-phase relative permeability was developed, adopting the combination of several optimization methods such as Gauss-Newton method and iterative Latin hypercube sampling (ILHS) method. This program enables the estimation of oil-phase relative permeability in the three-phase condition by automatically history matching the calculation results with experimental results, incorporating a black oil type simulator as an engine of this program. First, the hypothetical unsteady-state core flooding experimental results (effluent rates of each phase and differential pressure) were prepared by numerical simulation mimicking core flooding experiments. The relative permeability to oil was then tuned so as to rigorously reproduce these hypothetical experimental results. By appropriately combining the optimization methods and referring to a variety of unsteady-state core flooding experiments, the relative permeability to oil was successfully estimated. This program is also expected to be extended to the estimation of the relative permeability in steam-water system and micro emulsion-oil-water system in which the rigorous measurement of relative permeability is difficult due to the complex phase behavior.