Detecting the pore size distribution or the layered structure based on the radial seepage flow of shear-thinning fluids

An improved characterization of pore structure would provide a valuable input for flow and transport models both in the vadose zone or groundwater applications. The idea that the flow of non-Newtonian fluids (such as the aqueous xanthan gum solutions) in the saturated porous media can be utilized to reveal the effective pore size distribution has led to the development of affordable and efficient methods for both laboratory measurement or field infiltration experiments. In both the yield stress method (YSM, e.g. [1]) or, more recently, ANA method (e.g., [2]), the experimental setup ensures that the flow is one-directional, with both the volumetric flux and the hydraulic gradient being independent of the space variable.

We address the possibility to extend this methodology to the radial flow, such as for example the flow generated in a confined aquifer around an injection well, or in a similar laboratory experiment. Analogously to the capillary bundle framework with a set of effective pore radii equi-present in every representative elementary volume, one can deal with the presence of horizontal layers of different thickness, assuming that each layer is well represented by one characteristic pore size. The extension would then aim to reveal the structure of such layers based on the injection of shear-thinning fluids.

In contrast to the one-directional flow, both the flux and the hydraulic gradient vary with the radial coordinate. The very principle of both the YSM and ANA methods stems from the fact that the relation between the flux and the gradient for non-Newtonian fluid depends on the effective pore size. The obvious difficulty with the radial flow is that, given the injection rate, different pore sizes lead to different progression of the hydraulic head with the radial coordinate. Two distinct cases may be discussed. First, that the hydraulic head is shared by all present pore sizes. That would be the case of a homogeneous porous material with  multiple pore sizes, or the case of thin alternating layers where the gradient across the layers cannot develop. With the shear-thinning fluid, the distribution of the total volumetric flux across the pore sizes or layers would then vary with the radial variable. In the second case, the layers would be hydraulically separated, leading to a uniform distribution of the flux but a significant hydraulic gradient across the pore sizes or layers (such as in [3]).

This research is supported by Czech Science Foundation under grant 21-27291S.

[1] Rodríguez de Castro, A., Agnaou, M., Ahmadi-Sénichault, A., Omari, A., 2020. Numerical porosimetry: Evaluation and comparison of yield stress fluids method, mercury intrusion porosimetry and pore network modelling approaches. Computers and Chemical Engineering 133. https://doi.org/10.1016/j.compchemeng.2019.106662

[2] Hauswirth, S.C., Abou Najm, M.R., Miller, C.T., 2019. Characterization of the Pore Structure of Porous Media Using non-Newtonian Fluids. Water Resources Research 55, 7182–7195. https://doi.org/10.1029/2019WR025044

[3] Chiapponi, L., Petrolo, D., Lenci, A., Di Federico, V., Longo, S., 2020. Dispersion induced by non-Newtonian gravity flow in a layered fracture or formation. Journal of Fluid Mechanics. https://doi.org/10.1017/jfm.2020.624