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.

在油气藏的生产寿命期间，多孔介质中的三相流可能出现在不同的场景中。不同相的同时流动由相对渗透率曲线建模，这是石油产量分析和预测的基础。实验室实验是相对渗透率曲线的主要数据来源。多孔介质中多相流的数学解是根据实验室数据确定相对渗透率曲线、检查数值储层模拟结果和筛选提高采收率技术的关键。储层建模的复杂性以及对历史与实验室数据相匹配的数值优化的使用表明了凹形相对渗透率曲线的重要性。在本文中，我们提出了多孔介质中一维不可压缩不混溶三相流的解析解，其中相对渗透率函数由凹曲线描述。由质量守恒产生的双曲方程组通过特征法求解。结果表明与数值解非常吻合。