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.

在许多工业过程和自然现象中，重力被认为是导致多组分化学物质混合物组成变化的最重要因素之一。已经通过实验和数值模型对此进行了大量研究，尤其是在化学过程和石油储层工程中。在重力作用下组成变化的动力学过程的建模和仿真对于理解石油储层形成和初始状态的演化过程具有根本的重要性。这项工作提出了修改后的亥姆霍兹自由能与现实状态方程耦合的框架中组成变化的动力学模型。针对动力学模型，提出了一种高效，易于实现，热力学上一致且鲁棒的数值方案。严格证明该方案是无条件稳定的。基于单组分系统的实现非常简单，不需要为多组分流体选择参考物质。对于种类繁多的多组分系统，所提出的方案允许以随机顺序对偏微分方程组进行数值计算，在本工作中称为“无偏方案”。当前方案在计算上是有效的，并节省了计算机内存。设计了几个数值示例来验证该方案的性质。对于种类繁多的多组分系统，所提出的方案允许以随机顺序对偏微分方程组进行数值计算，在本工作中称为“无偏方案”。当前方案在计算上是有效的，并节省了计算机内存。设计了几个数值示例来验证该方案的性质。对于种类繁多的多组分系统，所提出的方案允许以随机顺序对偏微分方程组进行数值计算，在本工作中称为“无偏方案”。当前方案在计算上是有效的，并节省了计算机内存。设计了几个数值示例来验证该方案的性质。