Direct methods to calculate the mass exchange between solutes inside and outside aggregates in macroscopic model for solute transport in aggregated soil

Macroscopic modeling of solute transport in aggregated soil is often based on the dual-domain approach assuming that water flow occurs mainly in the inter-aggregates pores while the water inside the aggregates is stagnant; the solutes in the two waters can exchange driven by molecular diffusion. Since such a mass exchange is not measurable, practical modeling often uses pre-defined empirical memory functions to describe it with the parameters in the functions calculated by calibration against experimental measurement. It is hence difficult to verify that the calibrated memory functions correctly describe the mass exchange process or just to bridge the model and the measurements in that a shift from the experimental conditions could invalidate the model. Furthermore, most researches on such mass exchanges are for inert tracers, while most solutes in soil are reactive. How to link the mass exchange rates for inter tracer and reactive solutes is poorly studied. The purpose of this paper is to present direct methods to calculate the mass exchange rates for inert tracer and reactive solute using x-ray tomography and pore-scale simulations. Sample of an aggregated soil is scanned using x-ray micro-tomography by assuming, judged by visual observation in imaging the soil, that the sizes of the inter-aggregate pores are larger than 40 μm and using 40 μm as the resolution can separate the inter-aggregate pores from the aggregates. The aggregates are assumed to be permeable and their ability to conduct solute is described by an effective diffusion coefficient. We then numerically simulate the movement of both inert tracer and reactive solute from the inter-aggregate pores into the aggregates using pore-scale modeling. The simulated solute concentration in all voxels is sampled and then volumetrically averaged to calculate the average mass exchange rates between solute inside and outside the aggregates in the soil image. For reactive solute, we take nitrate as an example and analytically link its mass exchange rate to that for the inert tracer assuming that the nitrate reduction is a first-order kinetics. We also analytically establish the relationship between the mass exchange rates of solutes with different molecular diffusion coefficients, and verify this relationship against the results directly calculated from the pore-scale simulations. We additionally examine the accuracy of the commonly used empirical memory functions against those directly calculated from pore-scale simulations, finding that none of these functions can accurately describe the mass exchange process. To verify these directly- calculated mass exchange rates, we apply them to model the leaching of the inert tracer and the reactive nitrate in an aggregated soil column.