Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour

A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-trivial geometry corresponding to a porous medium

Impact of pressure dissipation on fluid injection into layered aquifers

Carbon dioxide (CO2) capture and subsurface storage is one method for reducing anthropogenic CO2 emissions to mitigate climate change. It is well known that large-scale fluid injection into the subsurface leads to a buildup in pressure that gradually spreads and dissipates through lateral and vertical migration of water. This dissipation can have an important feedback on the shape of the CO2 plume during injection, and the impact of vertical pressure dissipation, in particular, remains poorly understood. Here, we investigate the impact of lateral and vertical pressure dissipation on the injection of CO2 into a layered aquifer system. We develop a compressible, two-phase model that couples pressure dissipation to the propagation of a CO2 gravity current. We show that our vertically integrated, sharp-interface model is capable of efficiently and accurately capturing water migration in a layered aquifer system with an arbitrary number of aquifers. We identify two limiting cases --- `no leakage' and `strong leakage' --- in which we derive analytical expressions for the water pressure field for the corresponding single-phase injection problem. We demonstrate that pressure dissipation acts to suppress the formation of an advancing CO2 tongue during injection, resulting in a plume with a reduced lateral extent. The properties of the seals and the number of aquifers determine the strength of pressure dissipation and subsequent coupling with the CO2 plume. The impact of pressure dissipation on the shape of the CO2 plume is likely to be important for storage efficiency and security

Global existence of weak solution to the heat and moisture transport system in fibrous porous media

This paper is concerned with theoretical analysis of a heat and moisture transfer model arising from textile industries, which is described by a degenerate and strongly coupled parabolic system. We prove the global (in time) existence of weak solution by constructing an approximate solution with some standard smoothing. The proof is based on the physcial nature of gas convection, in which the heat (energy) flux in convection is determined by the mass (vapor) flux in convection.Comment: 19 page

Imbibition in Disordered Media

The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.Comment: Review article, to appear in Advances in Physics, 53 pages LaTe

Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid approximation) measured in suitable norms are derived, showing optimal orders of convergence

Measurement and Modeling of Reduced-Gravity Fluid Distribution and Transport in Unsaturated Porous Plant-Growth Media

The effect of reduced gravity on the balanced management of liquid, gaseous and ionic fluxes in unsaturated porous media remains a central challenge for plant-based bio-regenerative life support systems needed for long-duration space missions. This research investigated how shifting capillary and gravitational forces alter the sample-scale transport and distribution of fluids in mm-sized porous ceramic aggregates. Measurements in variably saturated media conducted on the International Space Station in microgravity ($sim1cdot10^{-3} g_{earth}$) and measurements during parabolic flight in variable gravity encompassing microgravity, terrestrial gravity and hypergravity ($sim1.8 g_{earth}$) were supported by numerical modeling based on fundamental, earth-derived soil-physical relationships. Measurements of water fluxes in rigid saturated media suggested Darcian flow unaffected by gravity. Observations of hydraulic potential and sample water content were used to estimate the primary draining and wetting water-retention characteristic (WRC). Terrestrial parameterizations of the WRC were largely unaffected by reduced gravity. However, because the WRC is hysteretic, heterogenous water-content distributions resulted within the confines of the primary draining and wetting characteristics. Ensuing distributions were fundamentally different from terrestrial observations and were stable in the absence of a significant gravity gradient. We showed that these distributions, though unexpected, could be predicted using the Richards equation. One consequence of altered water distribution could be the reduction in, and increased tortuosity of, continuous gas-filled pathways for diffusive transport compared to terrestrial estimates. Measurements of oxygen diffusion in microgravity suggested reduced diffusivities during draining. These observations, particularly for the smaller particle-sized media, were suggestive of the delayed formation of critical air-filled pathways at lower water contents. This dissertation further uses a case history of a stratified root-zone developed based on water-retention characteristics of different particle-sized media. The root-zone design provided a more uniform water-content distribution at terrestrial gravity suggested to provide more optimal conditions for root growth. Additionally, the design and testing of a novel integrated sensor for measurements of water content based on the dissipation of heat and estimation of nutrient status based on electrical resistivity are discussed. These results should provide insights into microgravity fluid distribution and transport contributing to the design and implementation of controllable plant-growth systems for use in microgravity and future planetary habitats