Equilibrium or Nonequilibrium Models: A Critical Issue in Determination of Gas Diffusivity in Oil

Abstract

Abstract Accurate simulation, design and implementation of any gas injection and solvent-based oil recovery processes requires a thorough understanding of a gas diffusion coefficient. This parameter is usually determined by monitoring gas pressure in a PVT cell during a pressure-decline test and analyzing the data by developing mathematical models that are different in imposed boundary conditions at a gas-liquid interface (the so-called equilibrium or nonequilibrium boundary conditions). Classically, the equilibrium boundary condition was applied at the gas-oil interface with the assumption of saturated interface at all times. But, recently in a number of researches it has been claimed that some time is required before establishment of the equilibrium state at the interface. These researchers considered existence of the non-equilibrium state and used a Robin-type boundary condition to account for the effect of resistance at the gas-oil interface on gas diffusion into oil. This paper considers these boundary conditions and investigates the effects of taking into account nonequilibrium nature of a diffusion process on estimation of mass transfer parameters using a lot of literature pressure-decay data of CH4, C2H6, CO2 and N2 dissolution in Athabasca bitumen at two different temperatures (50 and 90 °C) and an initial pressure of 8 MPa. Mass transfer parameters (a diffusion coefficient and a mass-transfer coefficient) are individually determined for each test by means of the equilibrium and non-equilibrium models and compared with each other. It is concluded that the values of the diffusion coefficient calculated by the equilibrium and non-equilibrium models are in an excellent agreement, indicating sufficiency of the classical mass transfer models to estimate the diffusion coefficient. On the other hand, although the non-equilibrium effects exist during gas dissolution in oil, applying a Robin-type boundary condition at the two-phase interface is not significant enough to affect the gas diffusion process.