Foam placement for soil remediation: scaling foam flow models in heterogeneous porous media for a better improvement of sweep efficiency

Abstract

If injected with a large gas fraction, foam reduces mobility more in high-permeability layers and diverts flow to low-permeability layers. Here is a qualitative statement that has been claimed many times in many works related to environmental remediation and oil recovery. It is so true and relevant for foam flow in porous media and yet so little quantified and even less exploited in Darcy-scale numerical simulation. After briefly reviewing opportunities and challenges related to the use of foams in porous media and its Darcy-scale implicit-texture and population-balance modelling, we make a detour out of the strict framework of mathematical models by revisiting with a fresh eye the physics of foams on the large scale of heterogeneous natural porous media in terms of scaling laws. Specifically, it has been recently shown experimentally and theoretically that foam mobility reduction scales approximately as the square root of rock permeability within the framework of Darcy-type implicit-texture foam flow models [Douarche et al. (2020) Scaling foam flow models in heterogeneous reservoirs for a better improvement of sweep efficiency (Paper ThB04), in:17th European Conference of the Mathematics of Oil Recovery (ECMOR), Edinburgh, Scotland, 14–17 September; Gassara et al. (2020) Trans. Porous Media 131, 1, 193–221]. This also appears to hold for population-balance models under the local steady state assumption. This quantitative scaling law for the effect of permeability on foam properties was inferred from an analogy between foam flow in porous media and foam flow in capillary tubes and was found consistent with the modelling of available experimental data. We demonstrate by varying the permeability contrast and anisotropy of a stack of porous layers how foam regulates the flow and leads to flow diversion from high- to low-permeability layers. The threshold in permeability heterogeneity for which such a foam-driven diversion becomes effective is quantified through a sensitivity study accounting for foam injection type, permeability heterogeneity and anisotropy, heterogeneity structure, and scaling procedure. The simulations carried out clearly indicate that ignoring mobility reduction dependence on permeability in the foam process assessment of heterogeneous formations leads to an underestimation of mobility reduction benefits to improve flow conformance. The question of cores selection, as this rock-typing strategy in relation to the porous medium characterization may guide a smart and optimal design of pre-feasibility laboratory campaign for foam evaluation, and the generalization of the findings to multi-facies geological formations are also discussed. As such, the use of physical foam mobility reduction scaling law is highly recommended for foam process evaluation.