Investigating pore network models as numerical tools to solve steady saturated groundwater flow

In this paper, a novel procedure is introduced and employed to transform the partial differential steady saturated flow equation in porous media into a system of linear equations using Pore Network Models (PNMs). At first, a simple Square Pore Network Model (SPNM) is introduced and then this model is improved by increasing node connectivity (Square-Diagonal PNM; S-DPNM) and modification in handling impermeable boundaries by introducing imaginary nodes and pipes (S-DPNMi). Finally, a generalized formulation for unstructured discretization (Unstructured PNM; UPNM) of the domain is given and the effect of handling impermeable boundaries (UPNMi) on model accuracy is investigated. To explore the capabilities of these models as numerical tools, three examples are solved. Application of these models without modifications for impermeable boundaries (SPNM, S-DPNM, and UPNM) yields comparable results to those of traditional Finite Difference (FD) and Finite Element (FE) methods. Modification in handling impermeable boundary nodes not only yields results that are everywhere more accurate than FD and FE, but also benefits the simplicity of formulations.