Abstract

Measurement of gas diffusivity in reservoir fluids is of great interest for a number of applications, and among different methods for the measurements, the pressure decay method has received special attention due to its simplicity. In this technique, a quiescent oil column is brought in contact with diffusing gas from the top and the rate of change of gas pressure in the gas cap is recorded. The interpretation of outcomes is based on a solution of a forward problem, which invokes a complicated boundary condition. In this work, an analytical solution is presented for the most general form of the boundary condition, which takes into account all parameters including gas solubility, diffusion and a possible interfacial resistance. Effect of resistance against mass diffusion at the interface is usually neglected in modeling. One objective of this paper is to better understand the role of the skin resistance, because its inclusion could increase the degree of freedom of the backward problem, and could lead to misleading results (despite a good match of the measurements).

Our mathematical solution reveals that depending on the relative magnitude of the resistance at the interface and the mass diffusion coefficient, the behavior of gas concentration at the interface and in the bitumen body may be different. It was found that when the film resistance is smaller, the concentration at the interface exceeds the final saturation concentration at the early time of diffusion and then it declines as gas diffuses into the bitumen body. When the resistance is large, the concentration at the interface remains lower than the final saturation concentration during the test. It is expected that this new analytical solution may lead to improved interpretation of pressure decay tests and more accurate estimation of mass transfer parameters.