Multi-gene genetic programming expressions for simulating solute transport in fractures

In lieu of process-based models, evolutionary artificial intelligence techniques can yield accurate expressions describing complex phenomena. In the current study, closed-form expressions are developed to predict solute transport in a fracture-matrix system as a function of the parameters that describe relevant physical and chemical processes. The study adopts a multi-gene genetic programming approach to approximate a solution of the classical advection–dispersion equation for reactive transport in single, parallel-plate fractures. The approach is employed to obtain an accurate relationship between the hydraulic, geological, and chemical parameters of the fracture-matrix system as inputs and an ensemble of breakthrough curves as outputs. Solutions generated by the developed model showed good agreement with those of corresponding analytical and numerical models. Computationally, the developed approach is highly efficient, particularly when compared with the analytical solution, which typically requires relatively fine discretization to calculate the long-tailed breakthrough curves. Therefore, future work could extend the developed model to simulate field-scale networks and include additional and more complex transport phenomena. This approach advances solute transport behavior predictions through being simpler and computationally more efficient than currently adopted techniques, which is important as the scale of simulation increases from that of a single fracture to a network.