Virus transport in porous media is affected by the water flow regime. During transient, variably saturated flow, fluctuating flow regimes can enhance virus detachment from both solid–water interfaces (SWIs) and air–water interfaces (AWIs). The objective of this study was to simulate the influence of drainage and imbibition events on the remobilization of attached viruses. Three different modeling approaches were examined. In the first approach, all attachment and detachment coefficients were assumed to be constant, but the values of the detachment coefficients were increased drastically for the duration of transient, unsaturated flow. The second and third modeling approaches involved extensions of the model of Cheng and Saiers, who assumed enhanced detachment of viruses to be proportional to the time rate of change in the water content. Their model was extended to include separate terms for virus attachment–detachment on SWIs and AWIs. In our second approach, we assumed kinetic sorption onto the AWI, with the desorption rate being described as a function of temporal changes in the air content. This approach did not explicitly account for the specific air–water interfacial area. Thus, in our third approach we explicitly included the presence and variation of air–water interfaces and assumed AWI attachment–detachment to be an equilibrium sorption process. The available air–water interfacial area was assumed to be a function of fluid saturation. The models were used to simulate a series of saturated–unsaturated virus transport experiments reported in the literature for conditions of both drainage and imbibition. The most promising results were obtained with the third approach, which explicitly accounts for adsorption to air–water interfaces and assumes equilibrium sorption on the available air–water interfacial area.
We present a new numerical model for macroscale two‐phase flow in porous media which is based on a physically consistent theory of multi‐phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy's law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid‐fluid interfaces. The alternative is to use an extended model, which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We present results of a numerical modeling study based on this extended model. We show that the extended model can capture additional physical processes compared to the standard model, such as hysteresis.
Abstract A series of experiments and related numerical simulations were carried out to study one‐dimensional water redistribution processes in an unsaturated soil. A long horizontal Plexiglas box was packed as homogenously as possible with sand. The sandbox was divided into two sections using a very thin metal plate, with one section initially fully saturated and the other section only partially saturated. Initial saturation in the dry section was set to 0.2, 0.4, or 0.6 in three different experiments. Redistribution between the wet and dry sections started as soon as the metal plate was removed. Changes in water saturation at various locations along the sandbox were measured as a function of time using a dual‐energy gamma system. Also, air and water pressures were measured using two different kinds of tensiometers at various locations as a function of time. The saturation discontinuity was found to persist during the entire experiments, while observed water pressures were found to become continuous immediately after the experiments started. Two models, the standard Richards equation and an interfacial area model, were used to simulate the experiments. Both models showed some deviations between the simulated water pressures and the measured data at early times during redistribution. The standard model could only simulate the observed saturation distributions reasonably well for the experiment with the lowest initial water saturation in the dry section. The interfacial area model could reproduce observed saturation distributions of all three experiments, albeit by fitting one of the parameters in the surface area production term.
Correct specification of conditions at macroscopic surfaces of discontinuity and along the boundary is essential to the complete mathematical description of flow and transport in porous media. This work provides the framework for systematic derivation of appropriate conditions. It thereby allows for generalization of the conditions commonly in use and exposes the assumptions which underlie them. General balance equations for a zone separating two regions are simplified to the case where the regions are in good thermodynamic contact. By application, interface conditions for balance of mass, chemical species, momentum, and energy are obtained for (1) adjacent porous media containing the same fluid, (2) water flooding of an oil reservoir, (3) a salt water/freshwater interface, and (4) the boundary between a surface water body and the porous medium.
Abstract The engineering of microbially induced calcium carbonate precipitation (MICP) has attracted much attention in a number of applications, such as sealing of CO 2 leakage pathways, soil stabilization, and subsurface remediation of radionuclides and toxic metals. The goal of this work is to gain insight into pore‐scale processes of MICP and scale dependence of biogeochemical reaction rates. This will help us develop efficient field‐scale MICP models. In this work, we have developed a comprehensive pore‐network model for MICP, with geochemical speciation calculated by the open‐source PHREEQC module. A numerical pseudo‐3‐D micromodel as the computational domain was generated by a novel pore‐network generation method. We modeled a three‐stage process in the engineering of MICP including the growth of biofilm, the injection of calcium‐rich medium, and the precipitation of calcium carbonate. A number of test cases were conducted to illustrate how calcite precipitation was influenced by different operating conditions. In addition, we studied the possibility of reducing the computational effort by simplifying geochemical calculations. Finally, the effect of mass transfer limitation of possible carbonate ions in a pore element on calcite precipitation was explored.
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