Regression and dimensional analysis for modeling two-phase flow

Numerical models describing multiphase flow phenomena are typically used to predict the displacement of water during the infiltration of non-aqueous phase liquids (NAPLs) into a groundwater system. In this paper, the applicability of regression and dimensional analysis to develop simple tools to by-pass these time consuming numerical simulations is assessed. In particular, the infiltration of NAPL through a vertical, homogeneous soil column initially saturated with water is quantified. Two output variables defining the extent of infiltration were considered - the elevation of the NAPL front and the volume of NAPL which had entered the system. Dimensional analysis was initially performed to identify dimensionless terms associated with the underlying relations between these two output variables and the input variables (independent variables and system parameters). Artificial neural network techniques were then employed to develop regression equations for approximating the input-output relationships over a given domain. Application of these equations illustrated the interrelationships among capillary, buoyancy, and viscous forces driving the NAPL infiltration process.