A composite medium approximation for unsaturated flow in layered sediments

Saturated-unsaturated flow in strictly layered sediments proceeds via conductors in parallel in the direction parallel to bedding, and via resistors in series in the direction perpendicular to bedding. On sufficiently small scales of space and time, flow in such media will be subject to approximate capillary equilibrium locally, which provides a basis for approximating the effective hydraulic conductivity of a composite multi-layer medium in terms of the conductivities of the individual layers. Equations for the hydraulic conductivity tensor in "composite medium approximation" (COMA) are given in a coordinate system aligned with bedding. Hydraulic conductivity parallel to bedding is generally larger than in the perpendicular direction. The anisotropy depends on the spread of the conductivity distribution, and tends to increase for dryer conditions. The COMA model was implemented in a multi-phase flow simulator and tested by comparison with high-resolution simulations in which all layering heterogeneity is resolved explicitly. Under favorable conditions, COMA is found to accurately represent sub-grid scale flow and transport processes, providing a practical method for simulating field-scale flow and transport in layered media. The approximation improves when layers are thinner, and when flow rates are smaller.