Description of chemical transport in laboratory rock cores using the continuous random walk formalism

Abstract

We investigate chemical transport in laboratory rock cores using unidirectional pulse tracer experiments. Breakthrough curves (BTCs) measured at various flow rates in one sandstone and two carbonate samples are interpreted using the one-dimensional Continuous Time Random Walk (CTRW) formulation with a truncated power law (TPL) model. Within the same framework, we evaluate additional memory functions to consider the Advection-Dispersion Equation (ADE) and its extension to describe mass exchange between mobile and immobile solute phases (Single-Rate Mass Transfer model, SRMT). To provide physical constraints to the models, parameters are identified that do not depend on the flow rate. While the ADE fails systematically at describing the effluent profiles for the carbonates, the SRMT and TPL formulations provide excellent fits to the measurements. They both yield a linear correlation between the dispersion coefficient and the Péclet number (DL Pe for 10 < (Pe) < 100), and the longitudinal dispersivity is found to be significantly larger than the equivalent grain diameter, De. The BTCs of the carbonate rocks show clear signs of nonequilibrium effects. While the SRMT model explicitly accounts for the presence of microporous regions (up to 30% of the total pore space), in the TPL formulation the time scales of both advective and diffusive processes (t1 (Pe) and t2) are associated with two characteristic heterogeneity length scales (d and l, respectively). We observed that l  2.5 × De and that anomalous transport arises when ld (1). In this context, the SRMT and TPL formulations provide consistent, yet complementary, insight into the nature of anomalous transport in laboratory rock cores.