The dispersion of a nonuniform slug flowing in a porous medium

Abstract

Analytical solutions to the convection-dispersion equation are provided for the time-dependent dispersion of a nonuniform slug, flowing axially in a porous medium. Both longitudinal and transverse dispersion in a porous medium of finite radius and infinite or semi-infinite length are considered in this unit mobility ratio displacement process. Inasmuch as these solutions, which are also given in rectangular coordinates, are the only ones which incorporate the transient and steady-state solutions, transverse and longitudinal dispersion, and boundary effects for a nonuniform slug of solvent, they provide an excellent means of evaluating the accuracy of numerical simulators. Previous solutions to the convection-dispersion equation for the longitudinal dispersion of uniform slugs can be obtained from these expressions by imposing the appropriate constraints.