Porous media flows description

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Compared with the use of arbitrary grid interfaces in combination with reduced-order flow models, the porous medium approach allows one to deal with an even larger multitude of micro channels. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a coarse-grained description it does not reach the level of accuracy as reduced-order models. Compared with the macromodel approach as propagated by Commenge et al, the porous medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

Ideally, cross-flow microfiltration would be the pressure-driven removal of the process liquid through a porous medium without the deposition of particulate material. The flux decrease occurring during cross-flow microfiltration shows that this is not the case. If the decrease is due to particle deposition resulting from incomplete removal by the cross-flow liquid, then a description analogous to that of generalised cake filtration theory, discussed in Chapter 7, should apply. Equation 8.2 may then be written as ... 

To calculate the effective diffusivity in the region of molecular flow, the estimated value of D must be multiplied by the geometric factor e/x which is descriptive of the heterogeneous nature of the porous medium through which diffusion occurs. 

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

Another attractive feature of two-dimensional network models is the fact that they can be carefully tested with laboratory experiments on well-defined porous media that closely replicate the media in the model. Thus, at this level the ambiguities that arise from the necessarily simplified description of a natural porous medium can be avoided. Experimental work on flow in two-dimensional etched media is represented by Chapter 12 by Shirley. Chapter 13, by Elsik... 

A critical review of emulsion flow in porous media has been presented. An attempt has been made to identify the various factors that affect the flow of OAV and W/O emulsions in the reservoir. The present methods of investigation are only the beginning of an effort to try to develop an understanding of the transport behavior of emulsions in porous media. The work toward this end has been difficult because of the complex nature of emulsions themselves and their flow in a complex medium. Presently there are only qualitative descriptions and hypotheses available as to the mechanisms involved. A comprehensive model that would describe the transport phenomenon of emulsions in porous media should take into account emulsion and porous medium characteristics, hydrodynamics, as well as the complex fluid-rock interactions. To implement such a study will require a number of experi-... 

Darcy s law (Darcy, 1856) is a phenomenological law that is valid for the viscous flow of a single-phase fluid (e.g. groundwater flow) through porous media in any direction. This basic law of fluid flow is a macroscopic law providing averaged descriptions of the actual microscopic flow behaviour of the fluids over some representative elementary volume of the porous medium. For isothermal and isochemical subsurface conditions, the law can be written as (Hubbert, 1953)... 

A porous medium is simply a solid containing void spaces. Several properties of porous media that affect the flow of suspensions in these media are as follows porosity, permeability, and pore size distribution of the rock. In the following sections, a brief description of these properties is given. 

This review is organized as follows. The general electrokinetic equations that govern the flow of an electrolyte are presented in Sec. II along with a description of the infinite spatially periodic porous medium. 

A layered medium is one of the simplest examples in which the mathematical description of physical or chemical processes depends on the spatial scales chosen. Let us take diffusion as the underlying process in order to make this clear. We may think of diffusion of a chemical species in a substrate, of electric currents in a nonhomogeneous material, of heat fiow in a layered insulator, or of fluid flow in a porous medium. In all these examples we have a law of the form... 

Abstract. This article describes a hydrodynamic model of collaborative flnids (oil, water) flow in porons media for enhanced oil recovery, which takes into account the influence of temperature, polymer and surfactant concentration changes on water and oil viscosity. For the mathematical description of oil displacement process by polymer and surfactant injection in a porous medium, we used the balance equations for the oil and water phase, the transport equation of the polymer/surfactant/salt and heat transfer equation. Also, consider the change of permeabihty for an aqueous phase, depending on the polymer adsorption and residual resistance factor. Results of the numerical investigation on three-dimensional domain are presented in this article and distributions of pressure, saturation, concentrations of poly mer/surfactant/salt and temperature are determined. The results of polymer/surfactant flooding are verified by comparing with the results obtained from ECLIPSE 100 (Black Oil). The aim of this work is to study the mathematical model of non-isothermal oil displacement by polymer/surfactant flooding, and to show the efficiency of the combined method for oil-recovery. 

It appears, then, that the mechanical degradation process is intimately connected with the molecular structure of the macromolecule and the resulting fluid rheology that arises from this structure. For a flexible coil macromolecule, such as HPAM or polyethylene oxide, the polymer solutions are known to display viscoelastic behaviour (see Chapter 3) and thus a liquid relaxation time, may be defined as the time for the fluid to respond to the changing flow field in the porous medium. It may be computed from several possible models (Rouse, 1953 Warner, 1972 Durst et al, 1982 Haas and Durst, 1982 Bird et al. 1987). The finite extendible non-linear elastic (FENE) (Warner, 1972 Bird et al, 1987a Haas and Durst, 1982 Durst et al, 1982) dumbbell model of the polymer molecule may be used to find the relaxation time, tg, as it is known that this model provides a good description of HPAM flow in porous media (Durst et al, 1982 Haas and Durst, 1982) the expression for fe is ... 

The rheological description of foam flow in porous media has been treated in different ways. one approach has been to use the single-phase fluid viscosities to calculate relative permeabilities to each fluid on the basis of experimental measurements of flow rates and pressure drop in foam flow through a porous medium. 

The description of the behavior of fluids in porous media is based on knowledge gained in studying these fluids in pure form. Flow and transport phenomena are described analogous to the movement of pure fluids without the presence of a porous medium. The presence of a permeable solid influences these phenomena significantly. The individual description... 

The flow velocity, pressure and dynamic viscosity are denoted u, p and fj and the symbol (...) represents an average over the fluid phase. Kim et al. used an extended Darcy equation to model the flow distribution in a micro channel cooling device [118]. In general, the permeability K has to be regarded as a tensor quantity accounting for the anisotropy of the medium. Furthermore, the description can be generalized to include heat transfer effects in porous media. More details on transport processes in porous media will be presented in Section 2.9. 

Abstract The theoretical background for the mechanistic description of flow phenomena in open channels and porous media is elucidated. Relevant works are described and the equations governing flow are explained. Fundamental concepts of dispersion, convection and diffusion are clarified and models that describe these processes are evaluated. The role of bulk and dispersive flow in dye transfer within a packed bed medium and the effect of including flow parameters on modelling dye dispersion and diffusion are then evaluated, and various models incorporating flow properties are examined. 

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