From spheres to ellipsoids: Speeding up considerably the morphological modeling of pore space and water retention in soils

In recent years, technological advances have stimulated researchers to try to unravel the extremely complex microscale processes that control the activity of microorganisms in soils. In particular, significant work has been carried out on the development of models able to accurately predict the microscale distribution of water, and the location of air water interfaces in pores. A comparison, by Pot et al. (2015), of two different modeling approaches with actual synchrotron-based tomography data, shows that a two-phase lattice Boltzmann model (LBM) is able to predict remarkably well the location of air water interfaces but is extremely slow, whereas a morphological model (MOSAIC), representing the pore space as a collection of spherical balls, provides a reasonable approximation of the observed air water interfaces when each ball is allowed to drain independently, but does so blazingly fast. Interfaces predicted by MOSAIC, however, tend to have nonphysical shapes. In that general context, the key objective of the research described in the present article, based on the same tomography data as Pot et al. (2015), was to find out to what extent the use of ellipsoids instead of spherical balls in MOSAIC could not appreciably speed up computations, or at least, at equal computational time, provide a quantitatively better approximation of water-air interfaces. As far as we know, this is the first time an ellipsoids-based approximation of the soil pore space is proposed. A secondary objective was to assess whether ellipsoids might yield smoother, more physical, interfaces. Simulation results indicate that the use of ellipsoids provides a sizeable increase in accuracy in the prediction of air-water interfaces, an approximately 6-fold drop in computation time, and much more realistic-looking interfaces, compared to what is obtained with spherical balls. These observations are encouraging for the use of models based on geometric primitives to describe a range of microscale processes, and to address the still daunting issue of upscaling to the macroscopic scale.