Spatial moment analysis of single-species transport in unidirectional laboratory tracer tests using rock cores

In the study of solute transport in porous media, it is common to rely on the Advection Dispersion Equation (ADE) model to interpret effluent breakthrough curves (BTCs) post unidirectional tracer laboratory tests. But this approach is not suitable for typical porous rocks, characterised by transport processes that occur over a wide range of length- and temporal scales. As a result, a workflow which integrates an updated experimental approach, and a novel means of data processing is necessitated.

Here, we use the Multi-Rate Mass Transfer (MRMT) model to match the BTC data of Kurotori et al. (2020) measured on Bentheimer Sandstone (BS), Ketton Limestone (KL), and Edwards Brown Carbonate (EB), at different flowrates. The analysis is extended to the evaluation of the first four spatial moments of the concentration distribution, representing the temporal evolution of total mass (0th), centre of mass (1st), variance (2nd), skewness (3rd) and kurtosis (4th). These were deduced for a 1D rendering of the dynamic core-flooding data acquired through Positron Emission Tomography (PET) imaging.

We show that for BS the spatial moments are insensitive to flow rate when plotted as a function of pore volumes injected (PVI). However, for the two carbonate rocks, they feature a flow rate dependency, due to the presence of microporosity and vugs, which introduce porous regions of virtually stagnant flow - where transport is largely dominated by diffusion. For the two carbonate samples, both 0th and 1st moment yield earlier breakthrough, and greater tailing of the solute mass with increasing flowrate. The 2nd moment takes much larger values for KL and EB than BS, indicating greater spreading of the tracer pulse and less mixing due to the larger contrasts in activity between the immobile and mobile zones. This is further exacerbated at higher flowrates. For BS, the 3rd and 4th moments prior to breakthrough take constant values at 0 and 3, respectively, indicating that the tracer plume is normally distributed. Yet, lower values are observed for the carbonates, reflecting an evolving skeweness of the tracer plume during transport.

Kurotori, T., Zahasky, C., Benson, S.M. and Pini, R., 2020. Description of chemical transport in laboratory rock cores using the continuous random walk formalism. Water Resources Research, 56(9), p.e2020WR027511.