Search

The objective of this article is to make use of the phenomenological approach to construct models for the transport of extensive quantities, such as mass of a fluid phase, mass of a component of a fluid phase, momentum of a phase and energy, in porous medium domains. Special attention is devoted to express the fluxes of these extensive quantities, especially the non-advective ones, as functions of their relevant driving forces, obeying the principle of minimum entropy production. It is shown that for each extensive quantity, we have a linear diffusive flux term, a non-linear diffusive term, and a dispersive flux term. The latter is shown to be proportional to the velocity squared. In each case, the number of moduli that describe fluid and porous matrix properties is determined. The momentum balance equation for a porous medium domain, which is the 'motion equation,' is analyzed and simplified for special cases, leading to Darcy's law and to Brinkman's equation. [ABSTRACT FROM AUTHOR]

The capillary pressure-saturation relationship, P( S), is an essential element in modeling two-phase flow in porous media (PM). In most practical cases of interest, this relationship, for a given PM, is obtained experimentally, due to the irregular shape of the void space. We present the P( S) curve obtained by basic considerations, albeit for a particular class of regular PM. We analyze the characteristics of the various segments of the capillary pressure curve. The main features are the behavior of the P( S) curve as the wetting-fluid saturation approaches zero, and as this saturation is increased beyond a certain critical value. We show that under certain conditions (contact angle, distance between spheres, and saturation), the value of the capillary pressure may change sign. [ABSTRACT FROM AUTHOR]

Comment by Xu-Sheng Wang; Comment by Shlomo P. Neuman; Comment by Otto D. L. Strack; Comment by Arnold Verruijt, Mirmosadegh Jamali, Brian Seymour; Comment by Jacob Bear, Alexander H.-D. Cheng; Authors' reply by Chongxi Chen, Xingxing Kuang and Jiu Jimmy Jiao [ABSTRACT FROM AUTHOR]

The coefficient of dispersion, D, and the dispersivity, a, appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain. [ABSTRACT FROM AUTHOR]

The article discusses derivative methods for the differential equation of the free surface boundary. It explains that the mentioned surface is an unconfined aquifer which has atmospheric pressure. It says that although the differential equation for free surface boundaries is considered to be one of the most basic, collected literature reveals the use of the wrong equation in most cases. It also mentions an experiment that shows that the differential equation is complete in a physical aspect.

Nitrogen dynamics in the soil under the condition of environmentally friendly fertilization practices (EFFPs) is described by a comprehensive N dynamics model. The model (first paper of this series, Transport in Porous Media 31(3) (1998), 249–274) is different from other models in its capability of simulating the special phenomena related to the application of EFFPs. In this paper, a finite difference method is used to solve the mathematical model. The numerical model is verified by simulating several water flow and conservative solute transport problems with existing numerical or analytic solutions. The good agreements between our simulation results and the solutions given by others show that our model is reliable in simulating flow and transport problems in the soil. Preliminary model validation is conducted by applying the model to simulate two field experiments. The acceptable agreements between our numerical simulation results and experimental data demonstrate that the model can reasonably model N dynamics in the soil under field conditions. [ABSTRACT FROM AUTHOR]

Abstract. In order to increase the efficiency of nitrogen (N) use, and to reduce the potential for environmemtal contamination, certain Environmentally Friendly Fertilization Practices (EFFPs) have been proposed and used in agriculture. Based on existing knowledge, a comprehensive N-dynamics model has been developed to describe N-behavior in the soil under EFFPs conditions. While including most of the relevant transport and transformation processes that are related to the N-cycle, the model emphasizes the description of some special phenomena that occur due to the application of EFFPs. Such phenomena include multi-dimensional N transport, N-release from controlled release nitrogen (CRN) granules, and nitrification inhibition caused by locally high ammonium concentrations. The model considers two-phase flow by water and air, multicomponent solute transport of ammoniacal nitrogen, carbon, oxygen, urea, nitrate, heat transfer, and pH changes in the soil. Chemical equilibria of ammoniacal N-species and carbonate species are also included. [ABSTRACT FROM AUTHOR]

Evaporation of groundwater in a region with a shallow water table and small natural replenishment causes accumulation of salts near the ground surface. Water in the upper soil layer becomes denser than in the depth. This is a potentially unstable situation which may result in convective currents. When free convection takes place, estimates of the salinity profile, salt precipitation rate, etc., obtained within the framework of a 1-D (vertical) model fail. Very simplified model of the process is proposed, in which the unsaturated zone is represented by a horizontal soil layer at a constant water saturation, and temperature changes are neglected. The purpose of the model is to obtain a rough estimate of the role of natural convection in the salinization process. A linear stability analysis of a uniform vertical flow is given, and the stability limit is determined numerically as a function of evaporation rate, salt concentration in groundwater, and porous medium dispersivity. The loss of stability corresponds to quite realistic Rayleigh numbers. The stability limit depends in nonmonotonic way on the evaporation rate. The developed convective regime was simulated numerically for a 2-D vertical domain, using finite volume element discretization and FAS multigrid solver. The dependence of the average salt concentration in the upper layer on the Rayleigh number was obtained. [ABSTRACT FROM AUTHOR]

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating. Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil. Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts. A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed. The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid. [ABSTRACT FROM AUTHOR]

A methodology for eliminating nondominant effects in models that describe transport phenomena in porous media is presented. The methodology is based on the introduction of dimensionless numbers and on a proper evaluation of the order of magnitude of terms. These dimensionless numbers are redefined as characteristics of transport and transformation phenomena in porous media. It is shown that different time scales and different length scales may have to be employed for different variables. A method for evaluating the order of magnitude of the error of prediction when terms are deleted, is presented. [ABSTRACT FROM AUTHOR]

We present a model of heat and mass transfer in an unsaturated zone of sand and silty clay soils, taking into account the effects of temperature gradients on the advective flux, and of the enhancement of thermal conduction by the process of latent heat transfer through vapor flow. The motivation for this study is to supply information for the planned storage of thermal energy in unsaturated soils and for hot waste storage. Information is required on the possibility of significant drying at a hot boundary, as this would reduce the thermal conductivity of a layer adjacent to the boundary and, thus, prevent effective heat transfer to the soil. This study indicates the possibility that the considered system may be unstable, with respect to the drying conditions, with the occurrence of drying depending on the initial and the boundary conditions. An analysis performed for certain boundary conditions of heat transfer and for given soil properties, disregarding the advective flux of energy, indicated that there are initial conditions of water content for which heating will not cause significant drying. Under these conditions, fine soils may be better suited for heat transfer at the hot boundary, due to their higher field capacity, although their heat conduction coefficients at saturation are lower than those of sandy soils. At present, these conclusions are limited to the range of 50-80°C. Potential effects of solute concentration at the hot boundary are indicated. [ABSTRACT FROM AUTHOR]

A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates. [ABSTRACT FROM AUTHOR]

We consider the case in which more than one fluid phase occupies the void space of a porous medium. The advective flux law is formulated for a fluid phase, under nonisothermal conditions and with the presence of solutes in the fluid phases. The derivation of the flux laws is based on an approximated version of the averaged balance equation for linear momentum. Taking into account momentum transfer through the interface between the fluid phases, leads to coupling between the flow in adjacent phases. Fluxes are also shown to depend on the surface tension at the interface between the adjacent fluid phases. Since the latter depends on temperature and solute concentration in the two phases, the advective flux is shown to depend on both temperature and solute concentration gradients in the two phases. A preliminary order of magnitude analysis gives conditions under which the coupling phenomena are not negligible. The approach is applied to the unsaturated zone, as a typical example of a multiphase porous medium. The main conclusion is that the well known Darcy law for single phase flow, may have to be modified for a multi fluid phase system, especially when temperature and solute concentration are not uniform. [ABSTRACT FROM AUTHOR]

A model composed of a three-dimensional orthogonal network of capillary tubes was used to simulate the flow behavior in an unsaturated anisotropic soil. The anisotropy in the network's permeability was introduced by randomly selecting the radii in the three mutually orthogonal directions of the network tubes from three different lognormal probability distributions, one for each direction. These three directions were assumed to be the principal directions of anisotropy. The sample was gradually drained, with only tubes smaller than a certain diameter remaining full at each degree of saturation. Computer experiments were conducted to determine the network's effective permeability as a function of saturation. The main conclusion was that the relationship between saturation and effective permeability depends on direction. Consequently the concept of relative permeability used in unsaturated flow should be limited to isotropic media and not extended to anisotropic ones. [ABSTRACT FROM AUTHOR]

In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain. It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media. [ABSTRACT FROM AUTHOR]

This is the first of two papers presenting a systematic development of a continuum model of a porous medium and of transport processes occurring in it. The concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified. A universal criterion for selecting the size of an REV as a function of measurable characteristics of a porous medium and selected tolerance levels of estimation errors, is developed. The rules of spatial averaging are extended by including the effects of both the configuration of the solid matrix and of interphase transfer phenomena within an REV. [ABSTRACT FROM AUTHOR]

The concept of 'capillary,' or 'matric,' potentials is commonly used in soil physics to describe water movement in unsaturated soils. The rigorous definition of these and other potentials is presented from fundamental thermodynamic principles at the microscopic level and extended to the macroscopic level by averaging over a representative elementary volume. Of special interest is the treatment of adsorptive surface forces and their associated potentials. Porous medium potentials are extended to a domain containing multiple fluid phases and multiple components. A macroscopic motion equation for a fluid phase (Darcy's law) is derived, incorporating the effect of potentials and surface forces. It relates advective fluxes to gradients of macroscopic chemical potentials and temperature. It reduces to the usual form of Darcy's law only when the aqueous phase is sufficiently dilute and temperatures are uniform. Kelvin's law, which relates relative humidity to matric potential, is extended to the case of multiple multicomponent fluid phases in a porous medium domain. The concept of 'irreducible' (or 'residual') wetting fluid saturation and its relationship to capillary pressure, surface forces, and the Gibbs chemical potential, are discussed. Common methods for determining the matric potential are reexamined in light of this work. [ABSTRACT FROM AUTHOR]

This work examines some conditions under which contaminant transport in fractured porous rocks can be described by an equivalent porous medium (single continuum) model. For this purpose, a two-dimensional mathematical and numerical model for flow and contaminant transport was developed. The model allows for contaminant transport by advection, diffusion, and dispersion in both fractures and porous blocks. Concentration distributions were calculated for different flow conditions and medium properties. The resulting S-shaped breakthrough curves, characteristic of ordinary porous media, indicated the possibility of regarding the fractured porous medium as a single (equivalent) continuum. The results were compared to an existing analytical solution for contaminant movement in ordinary porous media. Analysis showed that within the range of considered parameter values, and except for the region close to the source, a single continuum model is sufficient for modelling the movement of contaminants. In such cases, application of the equivalent porous medium model is an actual field situation requires knowledge of the 'equivalent' porosity and the equivalent coefficient of dispersion appearing in the governing transport equation. In practice, these coefficients must be determined by analysis of breakthrough curves obtained from field tests. [ABSTRACT FROM AUTHOR]

The author reflects on the establishment of the journal "Transport in Porous Media" (TIPM). He notes that TIPM is a result of making the discipline of transport in porous media into its own journal that was formed in 1986. He states that TIPM attracted many researchers and practitioners working on porous medium domains with which the journal has presented. Moreover, he cites his gratitude to the people who are part of TIPM such as the new editor in chief Martin Blunt and the associate editors.

The author reflects on the efforts of their committee to improve the quality of "Transport in Porous Media" (TIPM). He states that TIPM assist the scientific as well as the professional community particularly those that deals with the phenomena of transport in porous medium domains. An overview of the efforts of the associate editors with regards to the implementation of the review process is offered. Moreover, the author mentions the seven associates editors who were appointed on January 1, 2011.

Discusses the importance of proper management of a coastal aquifer. Impact of heavily populated coastal aquifers; Factors that affect the management of the coastal aquifer; Sources of water that should be considered when planning water resource allocation in coastal zones.