Variability of Point Source Infiltration Rates for Two-Phase Flow in Heterogeneous Porous Media

This study examines the influence of source release location, size, and strength on the infiltration rate and degree of lateral spreading of a dense nonwetting liquid infiltrating into an initially wetting liquid saturated, heterogeneous porous medium. It is demonstrated through numerical simulation in 25 realizations of a spatially correlated random hydraulic conductivity field that infiltration rates for point source releases are lognormally distributed with a variance equal to that of the underlying hydraulic conductivity distribution. The variability in infiltration rates is shown to decrease for sources larger than the correlation scale of hydraulic conductivity. In all cases, individual infiltration rates showed no tendency to converge to the ensemble average. A moment analysis demonstrates that the degree of lateral spreading of the nonwetting body for individual realizations varied greatly and also did not display a tendency to converge to an ensemble average. Numerical simulations carried out in an equivalent homogeneous porous medium incorporating large-scale anisotropy of intrinsic permeability provided infiltration rates below the ensemble average. For point source releases the degree of lateral spreading exhibited in the equivalent homogeneous porous medium was below the entire ensemble of heterogeneous results. A series of 10 simulations conducted in a single realization demonstrates that the degree of lateral spreading (second moment) along main drainage is a function of the average nonwetting phase saturation with greater degrees of lateral spreading at low capillary pressures. The practical implication of this study is that in addition to fluid and media properties the specific order of encounter of varying permeability lenses must be known in the immediate vicinity of a nonwetting phase release if infiltration rates are to be accurately predicted.