Reactive solute transport in a single fracture

The transport of reactive and nonreactive solutes under the action of fully developed laminar flow in a parallel plate fracture has been analyzed. Three types of surface reactions are examined: (1) irreversible first-order kinetic, (2) instantaneous reversible, and (3) reversible first-order kinetic. Approximate analytical models for the dispersion of nonreactive and reactive solutes with an irreversible first-order reaction are developed, and numerical ''exact'' solutions for the three surface reaction types are obtained. The conditions under which the approximate solutions hold are determined by comparison with the numerical solutions. The solute migration patterns and the extent of retardation due to surface reactions are then analyzed and compared with the nonreactive case. Dimensionless reaction coefficients incorporated into the solutions are estimated from data available in the literature. It is found that the approximate solutions are consistent with the numerical solutions; that the criterion for applicability of a local equilibrium assumption is based on the values of dimensionless time and a dimensionless number representing the ratio of the rate at which the surface reaction reaches equilibrium to the rate of the molecular diffusion in the transverse direction; and that the effect of surface reaction can be described by a retardation factor R(f) = 1 + K-d* for the case in which the reaction can be assumed at equilibrium, with small Peclet number, small dimensionless distribution coefficient K-d*, and large dimensionless time. Conditions are also found under which reactive solute transport can be well approximated by nonreactive solute transport and reversible reactions can be treated as irreversible. These results and the dimensionless analysis method employed herein may serve as a basis for development of more complex models of reactive solute transport in saturated fractured media.