Mathematical Modelling of Diffusion and Dispersion Mechanisms in Miscible Gas Injection Process

Diffusion and dispersion are considered as the two fundamental mechanisms for the miscible gas injection process in the oil reservoirs, which unfortunately are mostly disregarded in the reservoir simulators. In fact, these two phenomena tend to control the miscibility of the injected fluid with oil in the porous media. Neglecting theses (existing) phenomena in reservoir simulators may bring about erroneous results, which may subsequently role an unreliable basis to be applied into the gas injection projects. The aim of this work is to exhibit the error that should be emerged in case of neglecting these phenomena, in a quantitative manner. Initially, the effects of diffusion and dispersion are shown during a miscible gas-injection process using a one-dimensional model under different scenarios. Such scenarios include both considering and neglecting the diffusion and dispersion terms. A comparison between the results from each scenario should demonstrate if a considerable error should arise in the simulation results by neglecting these effects. It would also show if such neglecting will result in inaccurate estimation of gas composition change, oil recovery factor, and the gas breakthrough time. Based on the expected results, an appropriate dispersion coefficient for accurate design of miscible gas injection processes will be estimated and introduced.