Unstable flows in Soil and Fractured Rock – Similarities and Differences

Unstable flow phenomena in the vadose zone are known to occur in soils as well as in unsaturated fractured rock, well established examples involve flows bypassing porous matrix such as fingering in fractures and macropore flow in soils. Traditionally, processes in these two natural porous media received different theoretical and experimental treatments based on the agro-hydrological focus in soils, and waste isolation or deep recharge for fractured rock. Additionally, typical low porosity, small pore sizes, and limited impact of plant roots within rock matrix result in different flow regimes than found in loose and unconsolidated soils. Nevertheless, we propose a theoretical framework for unifying flow regimes and conditions within these unsaturated domains by quantifying interplay between capillary, gravity and viscous forces. Application of force balance within simplified pore spaces found in soils and rock yields simple scaling relationships for motion of liquid elements where gravitational force in excess of capillary pinning force scales linearly with viscous force. The results are extended to fluid-fluid displacement front morphologies using dimensionless force ratios expressed as Bond and Capillary numbers that enable certain generalizations. Considering available experimental data, we define conditions for onset of unstable and intermittent flows leading to baypass flows and enhanced liquid and gas entrapment. The results provide a basis for delineation of a tentative value of Bond number ~0.05 as an upper limit of applicability of the Richards equation and related continuum-based models for unsaturated flow in both soil or fractured rock.