Effective properties of multiphase flow in heterogeneous porous media

Abstract

The impact of heterogeneity on multiphase fl.ow is explored using a spectral perturbation technique employing a stationary, stochastic representation of the spatial variability of soil prop­erties. A derivation of the system's effective properties - nonwetting phase moisture content, capillary pressure, normalized saturation and permeability - was developed which is not specific as to the form of the permeability dependence on saturation or capillary pressure. This lack of specificity enables evaluation and comparison of effective properties with differing characterization forms. Conventional characterization techniques are employed to parameterize the saturation, capillary pressure, relative permeability relationships and applied to the Cape Cod and Borden aquifers. An approximate solution for the characteristic width of a dense nonaqueous phase liquid (DNAPL) plume or air sparging contributing area is derived to evaluate the sensitivity of system behavior to properties of input processes. Anisotropy is predicted for uniform, vertical flow in the Borden Aquifer consistent with both prior experimental observations and Monte Carlo simulations. Increases of the mean capillary pressure (increasing nonwetting phase saturation) is accompanied by reductions in nonwetting phase anisotropy. Similar levels of anisotropy are not found in the case of the Cape Cod aquifer; the difference is attributed largely to the mean value of the log of the characteristic pressure which is shown to control the rate of return to asymptotic permeability and hence system uniformity. A positive relation between anisotropy and interfacial tension was observed, consistent with prior numerical simulations. Positive dependence of lateral spreading on input fl.ow rate is predicted for Cape Cod Aquifer with reverse response at Borden Aquifer due to capillary pressure dependent anisotropy of Borden Aquifer. The effective permeability for horizontal fl.ow with core scale heterogeneity was found to be velocity dependent with features qualitatively similar to experimental observations and numerical experiments. Application of Leverett scaling as generally implemented in Monte Carlo simulations under represents aquifer hetero­ geneity and for the Borden Aquifer, van Genuchten characterization reduces system anisotropy by several orders of magnitude. Anisotropy of the effective properties proved to be less sensitive to Leverett scaling if the Brooks-Corey characterization was used due to insensitivity in this case to the variance of the slope parameter.