Oil displacement by multicomponent slug injection: An analytical solution for Langmuir adsorption isotherm

Abstract

Injection of water containing dissolved chemical components is one of the most important enhanced oil recovery (EOR) techniques. This problem can be modeled by an (n+1)×(n+1) system of hyperbolic partial differential equations representing the conservation of water and chemical components. In this paper we present the solution to the problem of oil displacement by a water slug containing n dissolved chemicals driven by pure water. It is considered that the chemicals can be adsorbed by the rock following Langmuir adsorption isotherm. The solution for any number of dissolved chemicals was obtained from a generalization of the case where three polymers are dissolved in the slug. To build the solution we first introduced a potential function replacing time as an independent variable. This procedure splits the original system of equations into a one-phase purely chromatographic problem and a scalar hyperbolic equation. The one-phase problem was solved using multicomponent chromatography theory, and its solution was used to solve the scalar equation. Both solution procedures are based on the method of characteristics. Finally, the solution of the scalar equation was mapped onto the space-time plane. The concentration solution shows the development of a complete chromatographic cycle in the porous media, and due to the separation of the chemicals, water banks appear in the water saturation solution. These results are new and present important insights for two-phase multicomponent flows in porous media.