A multi-scale numerical framework for the simulation of reactive solute transport in highly non-stationary porous media

Laboratory of Applied Sciences, ENSAH Al Hoceima, Abdelmalek Essaâdi University, Morocco

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Published online: 13 May 2026

Abstract

This work introduces a new multi-scale method that reduces numerical issues in reactive solute transport computations in highly nonstationary heterogeneous geological media. The new method is based on scale-decomposition to express reaction-advection terms as well-posed problems, in contrast to conventional simulation approaches which become problematic when mass exchange at different scales is considered. By using a stochastic model of small-scale heterogeneity, the model can represent tailing phenomena (which are normally ignored by stationary models) more accurately. A numerical simulation of nonlinear reactive solute transport in complex, highly heterogeneous permeability fields demonstrates that this new multi-scale method can reduce mass balance errors by 14.7% and speed up convergence by 22.8% over conventional multi-scale methods. Based on these results support the effectiveness for using these methods as a better tool in environmental risk assessments of heterogeneous aquifers over a long time, along with enhanced capability of tracking dynamic plume evolution.