Unconditionally stable, efficient and robust numerical simulation of isothermal compositional grading by gravity

The gravitational force has been considered as one of the most important factors leading to composition variation of multicomponent chemical species mixture in many industrial processes and natural phenomena. This has been largely studied through experimental and numerical modeling, especially in chemical processes and petroleum reservoir engineering. The modeling and simulation of dynamical process of composition variation under gravity is fundamentally important to understand the evolutionary process of petroleum reservoir formation and initial state. This work presents the dynamical modeling of composition variation in the framework of the modified Helmholtz free energy coupling with the realistic equations of state. An efficient, easy-to-implement, thermodyanmically consistent, and robust numerical scheme is proposed for the dynamical model. This scheme is rigorously proved to be unconditionally stable. The implementation is straightforward based on the single-component system and it is not required to choose a reference species for multicomponent fluids. For the multicomponent system of huge number of species, the proposed scheme allows to numerically compute the system of partial differential equations in a random order, which is called an “unbiased scheme” in this work. The current scheme is computationally efficient and saves computer memory. Several numerical examples are designed to verify the properties of the scheme.