Analytical solution for one-dimensional three-phase incompressible flow in porous media for concave relative permeability curves

Abstract

Three-phase flow in porous media may appear in different scenarios during the production life of a hydrocarbon reservoir. The simultaneous flow of different phases is modeled by relative permeability curves which are fundamental to petroleum production analysis and forecast. Laboratory experiments are the main source of data for relative permeability curves. Mathematical solutions for multiphase flow in porous medium are key for determining relative permeability curves from laboratory data, to check numerical reservoir simulation results and for screening an enhanced oil recovery technique. The complexity of reservoir modeling and the use of numerical optimization to history match the laboratory data have shown the importance of concave relative permeability curves. In this paper we present the analytical solution for one-dimensional incompressible immiscible three-phase flow in porous media, where the relative permeability functions are described by concave curves. The hyperbolic system of equations that results from mass conservation is solved by the method of characteristics. The results show close agreement to numerical solutions.