Measurement of gas diffusivity in reservoir fluids is of interest for numbers of applications, and among different methods, 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 the results 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 surface resistance. Effect of resistance against mass diffusion 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). Diffusion coefficients are needed for analysis and design of solvent based and gas injection recovery techniques. This parameter improves the prediction of compositional reservoir simulators.

Our mathematical solution reveals that depending on the permeability of the interface and magnitude of mass diffusion coefficient; the behavior of gas concentration at the interface and bitumen body changes. It was found out that once the film resistance is larger, the concentration at the interface exceeds the saturation concentration at the early time of diffusion and then it gets back to it as diffusion proceeds into the bitumen body.

It is expected that this new analytical solution would lead to improved interpretation of pressure decay tests and more accurate estimation of mass transfer parameters.

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