Effective parameters for multiphase flow in layered soils

Abstract

This paper examines whether practical and useful effective parameters can be developed and used in the complex case of multiphase flow in heterogeneous porous formations. Strong nonlinearities in the governing flow equations make exact evaluation of effective parameters difficult, and several shortcomings in the published work to date are identified. In particular, an important multiphase flow phenomenon, fingering, has yet to be properly treated. This may be a severe limitation because, as demonstrated in two-dimensional laboratory experiments, the presence of heterogeneities will provide conditions suitable for the generation of fingers. The development of fingers introduces a new length scale into the hierarchy of heterogeneity scales exhibited by natural porous formations, the finger diameter. Experimentally, it is observed that finger development allows fluid to by-pass a significant fraction of the porous media, increasing the front velocity and reducing the degree of large-scale entrapment. As explicit consideration of fingering has yet to be included in the evaluation of effective parameters for multiphase flow, including unsaturated flow, such phenomena may not be accurately represented in the approaches developed thus far. The experimental observations suggest that when the scale of an oil plume is much larger than the heterogeneity length scale then a large-scale flow model based on the local flow equations should describe the overall flow, even in the presence of local fingering. Nevertheless, the challenging problem of deriving the appropriate effective properties remains.