Stochastic analysis of sorption macrokinetics in heterogeneous aquifers

A stochastic analysis of the transient characteristics of sorption at field scales shows that sorption macrokinetics arise as a result of aquifer physical and chemical heterogeneities. Analytical expressions for the time evolution of the held scale retardation factor and longitudinal macrodispersivity for a reactive solute are obtained and compared with previous theoretical findings. Sorption macrokinetics are characterized by a timescale related to the average solute velocity, mean retardation factor, and variability correlation scale. A comparison of this timescale with the intragrain diffusion characteristic timescale provides a quantitative criterion to determine the relative importance of intragrain processes and aquifer physical and chemical heterogeneities on the characteristic field scale features of reactive solute plumes: retardation and dispersion. Calculations performed for the Borden field site in Ontario, Canada, show that the macrokinetics timescale is potentially much larger than the intragrain diffusion characteristic time, rendering natural heterogeneities as the controlling mechanism in the transient development of reactive plumes in the field. Analytically derived expressions for spatial moments of a reactive plume are evaluated to obtain results for the mass in solution, center of mass displacement, and longitudinal second moment. These results compare favorably with numerical simulations, but a comparison with field measurements is limited at this time owing to a lack of reliable data.