Effect of spreading coefficient on three-phase relative permeability of nonaqueous phase liquids

Three-phase flow conditions are encountered regularly, for example, during migration of released NAPL through the vadose zone, certain stages of soil vapor extraction, bioslurping, or generation of gases by microbes. To model three-phase flow, a common approach is to construct three-phase relative permeabilities based on a combination of two-phase relative permeabilities. Although this circumvents a lack of experimental data, it can lead to serious underprediction or overprediction of residual NAPL saturation. This can mislead decision makers that need to predict whether a particular spill will reach the water table or predict the speed of a NAPL front or conduct an assessment of the performance of remediation actions. Experimental data to estimate three-phase relative permeabilities is sparse. A study by DiCarlo et al. [2000a] generated significant experimental information. Their analysis focused on the high NAPL saturation region, given their emphasis on oil reservoir engineering. For environmental applications the low saturation region is of more interest. Using this data set, we derived a set of empirical relations that relate NAPL three-phase relative permeability km to NAPL saturation Sn and spreading coefficient C_s for S_n less than about 0.1, such that k_rn= A₁S_n^A2, where A₁ = 0.012 exp (-1.3C_s) and A₂ = 2.1 - 0.60C_s + 0.036C_s². At higher S_n, k_rn ≈ S_n⁴, independent of C_s. We present a pore-scale conceptual model that provides a phenomenological basis for the use of C_s as a predictor of k_rn at low S_n. We then present a number of simulated case studies that highlight the effect of these three-phase relative permeabilities on risk assessment or remediation design.