Modeling Quasi-Steady NAPL Dissolution in Fractured Permeable Media

Abstract

This work explores the rate-limited dissolution of entrapped nonaqueous phase liquids (NAPLs) in a fractured “permeable” formation through the use of mathematical models, developed on the basis of a simple conceptual framework. The feasibility of pump-and-treat operations in such formations is assessed through characterization of dimensionless system parameters governing NAPL dissolution and solute transport. These dimensionless parameters include the ratio of permeable block to fracture flow (mobility number), the system dimensionless mass transfer coefficient, and the number of contaminated fracture sections. A closed form analytical solution is developed for the simple case of a single contaminated fracture section. For domains with a large number of contaminated fracture sections, a numerical approach is presented that combines a finite difference scheme for simulation of solute transport in the fracture network together with an analytical solution for solute transport in the permeable block flow. The most favorable conditions for pump-and-treat systems are shown to be systems with large mobility numbers and large mass transfer coefficients. In systems with intermediate and small values of these parameters, effluent solute concentrations may be significantly below equilibrium values, reducing the effectiveness of pump-and-treat remediation. It is also shown that an equivalent continuum approach can be used to model rate-limited NAPL dissolution and transport in the simplified fractured permeable formation. The effective mass transfer coefficient for the representative continuum, however, is nonlinearly related to the local mass transfer coefficient.