Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for 3 x 3 hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to 2 x 2 system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.
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机译：多孔介质中一维两相多组分流的解析解描述了提高采收率，废物处置的环境流以及地下储层中污染物传播和含水层中水管理的过程。我们推导了3 x 3双曲守恒律系统的精确解，该解对应于多孔介质中的两相四组分流，其中第三组分的吸附取决于其自身在水中的浓度以及第四组分的浓度。使用势函数作为自变量而不是时间，可以将初始系统划分为2 x 2的浓度系统和一个标量双曲线方程式的相饱和度，从而可以将非自相似问题与波相互作用完全集成。
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