A similarity solution for light oil spreading on groundwater

Abstract

Spreading of a LNAPL lens (oil) in the vicinity of the groundwater table in a 2-D planar or axisymmetric homogeneous domain is described using a multiphase flow model including capillary forces and oil entrapment by water. Assuming vertical flow equilibrium the equations are vertically integrated. Hence, the free oil volume per unit lateral area and the vertically averaged relative permeability are explicitly related to the vertical position of the interface between zones with either two or three phases. The trapped oil volume is approximated by a linear hysteretic relation that is based on the maximum in time of the free oil volume. The resulting nonlinear diffusion equation admits a similarity solution for the free oil volume per unit lateral area as a function of time and the lateral space coordinate. Additionally, expressions for the extension and amount of trapped oil are obtained. The applicability of the analytical solution is demonstrated by comparison to a simulation, which is based on the nonreduced flow model. Special attention is paid to criteria to determine the remaining volume parameter and the time scale of the similarity solution. After determination of these parameters the analytical solution is a good approximation of the spreading at all larger times.