Mathematical Simulation of Two-Phase Flow with Interphase Mass Transfer in Petroleum Reservoirs
Authors: Tsutsumi Ginjiro , Dixon Thomas N. 
Published: December 2007

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Abstract
A two-dimensional, two-phase compositional reservoir model was constructed. In this model, the water movement was neglected. The fluid was divided into its hydrocarbon constituents and the state of phase equilibrium was assumed. The performance was represented by a set of performance was represented by a set of equations for the conservation of mass for all components. These equations were solved numerically with proper boundary and initial conditions. The phase equilibrium calculation was performed by a technique based on Rowe's definition of the convergence pressure.
A laboratory experiment was simulated by this model and good agreement between the calculated results and the laboratory data was obtained. A depletion drive of a volatile oil reservoir and a pressure maintenance of a volatile oil reservoir by dry gas injection were also simulated.
By comparing performances predicted by compositional models with those obtained by volumetric models, an effective range for the application of compositional models was obtained.

Introduction
The depletion drive of an oil reservoir or a gas-condensate reservoir, and the gas injection or water injection of an oil reservoir have been simulated mathematically. The most widely used models are volumetric models that assume the hydrocarbon fluid is made of two pseudocomponents (oil and gas) and that the pseudocomponents (oil and gas) and that the volumetric relation and physical properties of oil and gas are functions of the phase pressure only. The depletion drive process of oil reservoirs can be studied by these simulators with only small errors, but the simulation becomes inaccurate 2–4 when a transfer of intermediate components between phases occurs.
For example, in the process of pressure maintenance of a volatile oil reservoir by dry gas injection, the injected gas combines with the reservoir oil and changes the oil volume and its physical properties, while the gas itself also changes its volume and becomes richer in intermediate components. These changes occur even under a constant pressure; hence, this process cannot be simulated by a model that process cannot be simulated by a model that assumes no mass transfer between phases under constant pressure. This process can be simulated properly by subdividing the oil and gas into hydrocarbon components and solving the equation of conservation of mass for each component while simultaneously considering thermodynamic equilibrium between phases. This model is called a compositional model.