Porous media bulk property

We may begin by describing any porous medium as a solid matter containing many holes or pores, which collectively constitute an array of tortuous passages. Refer to Figure 1 for an example. The number of holes or pores is sufficiently great that a volume average is needed to estimate pertinent properties. Pores that occupy a definite fraction of the bulk volume constitute a complex network of voids. The maimer in which holes or pores are embedded, the extent of their interconnection, and their location, size and shape characterize the porous medium. 

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. 

The constitutive equations of transport in porous media comprise both physical properties of components and pairs of components and simplifying assumptions about the geometrical characteristics of the porous medium. Two advanced effective-scale (i.e., space-averaged) models are commonly applied for description of combined bulk diffusion, Knudsen diffusion and permeation transport of multicomponent gas mixtures—Mean Transport-Pore Model (MTPM)—and Dusty Gas Model (DGM) cf. Mason and Malinauskas (1983), Schneider and Gelbin (1984), and Krishna and Wesseling (1997). The molar flux intensity of the z th component A) is the sum of the diffusion Nc- and permeation N contributions,... 

Homogeneous Models. The basic assumption in these models is that the emulsion is a continuum, single-phase liquid that is, its microscopic features are unimportant in describing the physical properties or bulk flow characteristics. It ignores interactions between the droplets in the emulsions and the rock surface. The emulsion is considered to be a single-phase homogeneous fluid, and its flow in a porous medium is modeled by using well-documented concepts of Newtonian and non-Newtonian fluid flow in porous media (26, 38). 

Characterization of porous media based on the pore (microscopic) level is carried out for the purpose of understanding, modeling, and sometimes controling the macroscopic behavior and properties of the medium. The macroscopic (bulk) properties needed to relate to the pore description are porosity, permeability, tortuosity, and connectivity. When one examines a sample of a porous medium, for example, sandstone, it is obvious that the number of pore sizes, shapes, orientations, and interconnections is enormous. Furthermore, even the identification of a pore is not unique. Because of this complexity, pore structure is often characterized based on an idealized model. A true description is not realistic for a natural porous medium. 

Porosity and Permeability Distributions. The porosity and permeability are bulk properties of a porous medium. They are normally expected to be constant for a given porous medium. However, because... 

Areal Porosity and Tortuosity. Areal porosity or areosity, Ap, is defined as the effective areal ratio of the open pore cross-section to the bulk space. A more strict definition of areosity was introduced by Ruth and Suman (56). However, the areosity as defined by them is not a property of the porous medium only but a property of both the porous medium and the transport strength of the fluid such as the flow strength and electric current strength. The areal porosity is undoubtedly a very useful quantity for a bundled or ensemble passage model because it represents the ratio of the total passage cross-sectional area to the total cross-sectional area of the porous medium at a given planar section. 

A macroscopic description is based on average or bulk properties at sizes much larger than a single pore. In characterizing a porous medium macroscopically, one must deal with the scale of description. The scale used depends on the manner and size in which we wish to model the porous medium. A simplified, but sometimes accurate, approach is to assume the medium to be ideal meaning homogaieous, uniform and isotropic. 

Depending on the resolution of the mathematical model, different forms of the species conservation equations may be considered in the porous electrodes. For instance, in the multi-scale modehng of Khaleel et al. [18], a mesoscale lattice Boltzmarm model of the electrodes resolves the species transport in the gas, on the surface of the electrode, and through the bulk solid of the electrode. In this model, Eq. (26.1) is solved in three separate domains with corresponding transport properties and source terms. In contrast, in the macroscale distributed electrochemistry model of Ryan et al. [19], the porous medium of the SOFC electrodes is not explicitly resolved but is included in the model via effective properties. In the effective properties model, the diffusion coefficient of Eq. (26.1) is replaced with an effective diffusion coefficient, which is discussed in Section 26.3.3. 

Data describing the flow of polymers in porous media can be obtained by conducting steady-state flow tests in core plugs or sand-packs over the range of frontal-advance rates anticipated in the bulk of the reservoir and in the vicinity of the wellbore. In these tests, polymer of a specific concentration is injected at a constant rate. Pressure drops are measured across the entire length of the porous medium and between measuring ports spaced along the porous medium, as depicted in Fig. 5.30. A constant rate is maintained until the pressure drop reaches a steady state. A series of measurements of flow rate vs. pressure drop is taken to determine the flow properties of the polymer in the porous material. 

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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