Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen

Molecular diffusion has been considered to be an underlying mechanism for many of oil recovery processes like miscible and immiscible gas injection projects. Reliable estimation of the molecular diffusion coefficient as a transport property is therefore important in studying the performance of such systems. Interpretation of pressure-decay data has been traditionally used to estimate the molecular diffusion coefficient and usually to simplify the interpretation, its concentration dependency has been neglected. A pressure-decay model with concentration-dependent diffusion coefficient leads to a non-linear problem in which an analytical solution is difficult if not impossible to obtain. In this study, we used the Heat Integral Method (HIM) to solve the non-linear diffusion problem as a forward model. Using that forward model, we have developed a simple methodology for estimating the diffusion coefficient regardless of the form of function used for the concentration dependency of the molecular diffusion. Three different forms of functions for diffusion coefficient were considered. In its simplest form, the diffusion coefficient is set to be a constant value. In the two other forms, the diffusion coefficient was evaluated as a concentration-dependent two parameter equation using exponential and power-law functions, respectively. The proposed methodology is verified and tested using direct numerical solutions of the non-linear diffusion problem. Many numerical examples with a wide range of input parameters demonstrate the effectiveness of the proposed approach.

► Pressure-decay data is treated with concentration dependent diffusion coefficient.
► Heat Integral Method is used to solve the related non-linear diffusion problem.
► A simple backward model is developed to estimate the molecular diffusion coefficient.
► The model is verified using numerical solution of the non-linear diffusion problem.