Porous materials thermodynamic models

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)—(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, comers in steps found on flat surfaces). In the second paper, they presented an improved solution for multilayer adsorption they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested... 

Abstract Dynamic and thermodynamic balance principles for porous materials consisting of three components are deduced by using, as a logical tool, only three fundamental principles proposed by Truesdell for classical mixtures the principles are adapted to the context of soils mechanics where the mixture is considered immiscible and the porous solid matrix is modeled as a continuum with ellipsoidal microstmcture. 

Fischer et al, [122] proposed a model to predict the adsorption isotherm of krypton in porous material at supercritical temperature. In their study, a model pore of infinite length is formed by concentric cylindrical surfaces on which the centers of solid atoms are located. The interaction between an adsorbate and an individual center on the pore wall is described by the LJ 12-6 theory, and the overall potential is the integral of this interaction over the entire pore surface. With thermodynamic relations, Fischer et al. obtained the functional dependence of the saturation adsorption excess and the Henry s law constant on the pore structure. The isotherm was then produced by the interpolation between Henry s law range and saturation range. They tested their theory with the adsorption of krypton on activated carbon. It was shown that, with information on the surface area of the adsorbent and thermodynamic properties of the adso bate, their model gives more than quantitative agreement with experimental data. If a few experimental data such as the Henry s law constant at one temperature are available, the isotherms for all temperatures and pressures can be predicted with good quality. 

In part II of the present report the nature and molecular characteristics of asphaltene and wax deposits from petroleum crudes are discussed. The field experiences with asphaltene and wax deposition and their related problems are discussed in part III. In order to predict the phenomena of asphaltene deposition one has to consider the use of the molecular thermodynamics of fluid phase equilibria and the theory of colloidal suspensions. In part IV of this report predictive approaches of the behavior of reservoir fluids and asphaltene depositions are reviewed from a fundamental point of view. This includes correlation and prediction of the effects of temperature, pressure, composition and flow characteristics of the miscible gas and crude on (i) Onset of asphaltene deposition (ii) Mechanism of asphaltene flocculation. The in situ precipitation and flocculation of asphaltene is expected to be quite different from the controlled laboratory experiments. This is primarily due to the multiphase flow through the reservoir porous media, streaming potential effects in pipes and conduits, and the interactions of the precipitates and the other in situ material presnet. In part V of the present report the conclusions are stated and the requirements for the development of successful predictive models for the asphaltene deposition and flocculation are discussed. 

The Theory of Porous Media (TPM) is a concept based on the fundamentals of classical continuum mechanics and thermodynamics. It is used in numerous fields of research to model the behavior of saturated porous solid materials. The fluid-stracture interaction within the material is incorporated by a statistical homogenization of a representative elementary volume. Hence, no knowledge of the geometry and the stracture of the interfering components is required the investigated domain has to be rather large and it has to comprise a sufficiently homogenous substmcture. 

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