Thermodynamics porous media

Consider the combustion reaction between a solid reactant and a gas oxidizer present initially in the constant volume of a porous medium (see Section IV,D,1). In this case, thermodynamic calculations for the silicon-nitrogen system have been made for constant volumes (Skibska et al, 1993b). The calculations yield the adiabatic combustion temperature, as well as pressures and concentration, as functions of the silicon conversion. As shown in Fig. 34a, the reactant gas pressure (curve 3) increases even though conversion increases. This occurs because... 

Biot assumed that porosity (< i) was a fixed parameter recent work shows that for porous media, i i is a thermodynamic variable similar to pressure and temperature, and it must be treated as a dynamic variable (Spanos et al. 2003). For the temporal evolution a porous medium, the porosity change must be stipulated as follows ... 

The AECL team used an in-house MOTIF finite-element code (Guvanasen and Chan 2000), which is based on an extension of the classical poroelastic theory of Biot (1941). This code has undergone extensive verification and validation (Chan et al. 2003). The CTH team employed the commercially available, general-purpose finite-element code ABAQUS/Standard 6.3 (ABAQUS manuals). This code adopts a macroscopic thermodynamic approach. The porous medium is considered as a multiphase material, and an effective stress principle is used to describe its behaviour. ABAQUS allows the value of bulk modulus of the mineral grains as an input parameter. In order to select an appropriate value for this low-permeability, low-porosity rock, the CTH team compared the ABACjus solution with Biot s (1941) analytical solution for ID consolidation in the form presented by Chan et al. 2003). 

Other factors affecting the mechanism of oil extraction from the formation were also studied. Thermal expansion of oil also exerts an influence on the process of oil displacement from a porous medium. The volume of displaced oil essentially depends on the oil s properties and on the thermodynamic conditions of the formation. The changes in the displacement coefficients attributed to thermal expansion of oil were given in Table 8. At temperatures of 125, 150, and 2(X)°C, the percentage share of oil yield due to its volumetric expansion within the reservoir rocks is 5.4. 

Gas filtration through a porous medium is often described mathematically in the form of the Darcy equation u = KI, where is a filtration rate, / is a head gradient, and permeability coefficient K is the main characteristics of the medium. To model gas reservoirs, it is necessary to know permeability coefficients for both gas and liquid phases and to have a model to calculate reservoir liquid saturation [1,2]. The equilibrium liquid saturation depends only on the thermodynamic functions of the fluids and reservoir walls. 

It is assumed that the flow is steady, laminar, incompressible, and two-dimensional. The porous medium is considered to be homogeneous, isotropic, and in thermodynamic equilibrium with the saturated fluid the gas phase radiation is neglected. 

For polymer solutions, a decrease in the solvent thermodynamic quality tends to decrease the polymer-solvent interactions and to increase the relative effect of the polymer-polymer interactions. This results in intermolecular association and subsequent macrophase separation. The term colloidally stable particles refers to particles that do not aggregate at a significant rate in a thermodynamically unfavourable medium. It is usually employed to describe colloidal systems that do not phase separate on the macroscopic level during the time of an experiment. Typical polymeric colloidally stable particles range in size from 1 nm to 1 xm and adopt various shapes, such as fibres, thin films, spheres, porous solids, gels etc. 

A common difficulty in all the aforementioned cases is the irregular geometry of the porous medium. In addition, a precise analysis will have to consider that the diffusion in the pores is modified by surface diffusion and surface reactions. A completely phenomenological approach based on irreversible thermodynamics would give theoretically consistent transport expressions but would be too complicated for experimental determination of the transport coefficients and for the solution of the conservation equations. 

Two major groups of performance models have been proposed. The first group considers the membrane as a homogeneous mixture of ionomer and water. The second group involves approaches that consider the membrane as a porous medium. Water vapor equilibrates with this medium by means of capillary forces, osmotic forces resulting from solvated protons and fixed ions, hydration forces, and elastic forces. In this scenario, the thermodynamic state of water in the membrane should be specified by (at least) two independent thermodynamic variables, namely, chemical potential and pressure, subdued to independent conditions of chemical and mechanical equilibrium, respectively. The homogeneous mixture model is the basis of the so-called... 

The problem of capillary equilibrium in porous media is complicated from both experimental and theoretical points of view. The mechanisms of saturation and depletion of the porous medium are essentially nonequilibriiun. Further equilibration is due to slow processes like diffusion. The process of equilibration may be unfinished, since no significant changes of fluid distribution may occur during the time of an experiment. This especially relates to the so-called discontinuous condensate existing in the form of separate drops. As a result, thermodynamic states, which are not fully equilibrated, are interpreted from the practical point of view as equilibrium [28]. To the best of our knowledge, a consistent theory of such quasiequihbrium states has not yet been developed. In the following, we discuss the possible states of the two-phase mixtures in a porous medium, assuming complete thermodynamic equihbrium. This serves as a first approximation to a more complicated picture of the realistic fluid distribution in porous media. 

The Structure of a Reservoir Simulator A reservoir simulator is software for solving the porous medium flow equations with detailed models of the spatial distribution of rock properties, detailed models of the thermodynamics of phase behaviour, of the wells and how the wells coimect with each other through surface networks. Further, a reservoir simulator will have built-in support for optimisation software in that derivatives of specified flow diagnostics, such as well rates, or masses of chemical components in specified volumes, with respect to a variety of parameters can be computed. 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

Wendt et al. (1976) proposed a model for solute dispersion in heterogeneous porous media based on nonequilibrium thermodynamics. Their model, which allows for both variable pore shape and size distribution, is constructed from parallel arrays of interacting pores arranged in series. The relative error introduced by assuming the medium can be described by an equivalent uniform pore-size distribution was shown to be small. 

Equation (8.1) shows that spontaneous (without work applied to the boundary) solid surface wetting by the composition in aqueous medium is possible for equality of surface tension values in adhesive and liquid, i.e., for -Ycv = 0- The maximum attainable t c,w is advisable, however, as it is in direct proportion to thermod5mamic work of adhesion. Therefore, it is impossible to ensiu-e high-quahty impregnation of porous materials with organic compositions without application of work to the composition-solid boundary, even if the thermodynamic conditions for selective wetting of material pores by the composition... 

In this chapter, connections will be established between electrocatalytic surface phenomena and porous media concepts. The underlying logics appear simple, at least at first sight. Externally provided thermodynamic conditions, operating parameters, and transport processes in porous composite electrodes determine spatial distributions of reaction conditions in the medium, specifically, reactant and potential distributions. Local reaction conditions in turn determine the rates of surface processes at the catalyst. This results in an effective reactant conversion rate of the catalytic medium for a given electrode potential. 

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