Virtual Soil Simulator - unsaturated pore media water transport model including film flow and isothermal vapor transport phenomena

Simulation of unsaturated water movement in porous media has conventionally been based on the Richards equation (RE), coupled with hydraulic conductivity functions that account solely for capillary-driven liquid flow. This approach, however, overlooks the presence of thin water films adsorbed on solid surfaces, which may contribute appreciably to transport processes under moderately dry to dry conditions. Recent advances, particularly the Peters–Durner–Iden (PDI) framework, enable a physically consistent representation of film flow and isothermal vapor diffusion within formulations of unsaturated hydraulic conductivity.

In this work, we introduce the Virtual Soil Simulator, a finite-volume, OpenFOAM-based implementation of the RE augmented with the PDI model to explicitly represent capillary, film, and vapor transport processes. Model performance was assessed using a suite of benchmark tests with analytical or well-established numerical reference solutions, including one-dimensional infiltration, infiltration under steep hydraulic gradients, and two-dimensional nonlinear infiltration scenarios. The results demonstrate high numerical accuracy and robust mass conservation.

The applicability of the model is further demonstrated through two case studies. In the first, inverse simulation of a 12-day soil core drying experiment showed that the classical RE formulation reproduced measurements only during the early, wet stage, whereas the PDI-enhanced model remained consistent with observations over the entire drying period and accurately represented regimes dominated by film and vapor flow. In the second case, a synthetic desaturation analysis conducted across 467 soil types indicated that film flow markedly accelerates drainage, with significant effects persisting even at comparatively high pressure heads (−10 m). These findings indicate that neglecting film flow leads to systematic underestimation of unsaturated hydraulic conductivity and distorted predictions of drying and drainage behavior. Moreover, simulations at very low pressure heads emphasize that reliable representation of transport processes requires the combined consideration of both film and vapor fluxes.

Acknowledgments

This research was founded by the National Science Centre within contract 2021/43/B/ST10/03143.