A SIMILARITY SOLUTION FOR OIL LENS REDISTRIBUTION INCLUDING CAPILLARYFORCES AND OIL ENTRAPMENT

Redistribution of a LNAPL lens (oil) at the phreatic surface is descri bed using a multiphase flow model, with emphasis on the effect of oil entrapment by water. The flow process is analyzed under the assumption that the vertical capillary and gravitational forces balance. Vertica l integration leads to explicit functions which approximate the relati ons between the free oil volume per unit lateral area and the vertical ly averaged oil relative permeability on the one hand and the vertical position of the interface between zones with either two or three phas es on the other hand. A linear relation between the trapped and free o il volume per unit lateral area approximates the vertically integrated nonlinear expression for the trapped oil saturation. The resulting di fferential equation admits a similarity solution describing the latera l spreading of free oil and the amount and location of trapped oil. Co mparison with illustrative numerical computations, which are based on the nonreduced flow model in a two-dimensional planar or axisymmetric domain, shows that the analytical solution provides a good approximati on of the free oil distribution at all later times.