Analysis of mass transfer processes with reaction in heterogeneous porous media

The study is devoted to the analysis of reactive mass transfer in a two-layer porous medium with a spatially inhomogeneous distribution of porosity. The paper considers a system consisting of two regions: the left one with constant porosity and the right one with variable porosity described by a given distribution. Under the condition of a low rate of mineral dissolution, the system is reduced to a stationary statement, which allows us to obtain analytical solutions for the concentration and its derivative at the interface between the media. Particular attention is paid to the influence of key dimensionless parameters – the Peclet (Pe) and Damköhler (Da) numbers, which determine the dynamics of the process. It is found that at Pe ≫ 1, the system enters a stationary mode, at which the concentration tends to the limit 1/(1+Da), and its derivative – to the value -Da ∙ Pe/(1+Da). In the case of Da ≪ 1, the concentration and its derivative become independent of the mass transfer parameters which indicates a change in the transfer mechanism in this limiting mode. An important role is also played by the inverse relationship between the Da number and the parameter α, characterizing the distribution of porosity, which emphasizes the influence of the heterogeneity of the medium on the stability of the dissolution front. The obtained analytical solutions are confirmed by numerical calculations, demonstrating a high degree of consistency. The results of the work are of practical importance for modeling the processes of acid treatment of formations, filtration control in oil and gas fields and forecasting hydrogeological processes in heterogeneous porous media.

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