Soil hydraulic properties derived from pore-scale simulations: Digital assessment of Ksat through model intercomparison and verification with experimental data

The saturated soil hydraulic conductivity, $K_{sat}$, controls infiltration, storage, and redistribution of water in soils and often serves as an “anchor” at water saturation for the description of unsaturated soil hydraulic properties. However, experimental determination of soil hydraulic properties poses numerous problems that have potential to be effectively solved by using pore-scale simulations. This modeling technology requires further developments to serve as a robust substitute for or complement to conventional measurements in routine soil property surveys. The three major limitations preventing pore-scale modeling from becoming widely used include: (1) imaging resolution limitations for obtaining multi-scale images of soil structure with the necessary spatial resolution that capture the inherently hierarchical nature of soil structure; (2) highly uncertain segmentation procedures of pore-scale models prohibit the accurate processing of soil structure images to obtain the spatial distribution of soil constituents; and (3) the high computational demands of pore-scale modeling to numerically simulate flow processes for obtaining homogenized soil physical properties. We are at a technical development point where most if not all these limitations can be efficiently solved and a significant step forward in soil property evaluations can be made. In this work, we aim to demonstrate recent advances in pore-scale modeling by simulating saturated hydraulic conductivity ($K_{sat}$) of samples taken from three horizons (A, Ah, and B) from a Haplic Greyzem soil, based on X-ray computed tomography (XCT) images. We apply a new segmentation technique accounting for organic matter classification uncertainty which either merges the organic phase with the pores (named high porosity images) or the solids (named low porosity images). Three pore-scale modeling techniques are compared: finite difference solution of the Stokes equation, lattice Boltzmann method, and pore-network models. Verifying simulated $K_{sat}$ values against field measurements illustrated a significant overestimation of the field data by all three modeling techniques (based on two subsamples and across different method simulations; only simulation results with best agreement are shown): (1) for the A horizon experimental $K_{sat}$ was 53 ± 50.71 cm/day compared to simulated values from 103 to 521 cm/day (based on high porosity images), (2) for the Ah horizon experimental $K_{sat}$ was 432 ± 135.15 cm/day compared to simulated values from 1410 to 3171 cm/day (based on low porosity images), and (3) for the B horizon experimental $K_{sat}$ was 180 ± 160.67 cm/day compared to 786 to 1862 cm/day (based on low porosity images). By comparing simulated and field-measured $K_{sat}$ values we illustrated how the earlier mentioned limitations can be at least partly resolved: (1) based on a XCT image resolution on the order of 15.85 $\mu$m micrometer, saturated hydraulic conductivity can be derived from pore-scale simulations, albeit significantly overestimating field data; (2) segmentation based on a gray-scale histogram results in inadequate $K_{sat}$ values and the border between pores and solids should be closer to the void peak; (3) use of pore-network models and modern multi-grid solvers on GPU units results in computationally efficient solutions. Finally, we report directional hydraulic conductivities generated from pore-scale simulations to illustrate that pore-scale simulations can provide additional soil information, such as tensorial properties, not captured by conventional lab or field measurements.