Porous medium properties

The porous medium properties for the different tests are presented in Table II. The tests are carried out in a porous medium constituted of silica sand, kaolinite (4%), mixed with heavy crude oil and water. 

Much of the recent research in combustion in porous media has focused on developing a porous burner as a radiant heater [7-13]. This is an attractive application because the porous solid is an efficient radiator while still permitting the use of a clean fuel such as methane. One design that has shown promise is a burner consisting of two sections of porous medium with different characteristics [2, 9, 10]. This design is based on the idea that the effective flame speed within the matrix is determined by the porous medium properties such as solid conductivity, porosity, and pore diameter. The interface between the two sections of porous media acts as a flame holder preventing flashback. 

Hsu et al. [9] studied the two-section burner through experiments and computations. As the upstream extinction coefficient increased, the amount of preheating was reduced, resulting in lower peak flame temperatures. Their computational results predicted a smaller range of stable burning velocities than observed in the laboratory, and the sensitivity to various other porous medium properties was not investigated. 

It should be noted that Ward (17) attempted to cast equation 6 into a more usable form by relating a and Q to the known porous medium properties for isotropic porous media. In a one-dimensional situation, Ward s model gave... 

Equation 20 shows that a porous medium is permeative, that is, a shear factor exists to account for the microscopic momentum loss. Our preliminary study recently reveals that, however, a porous medium is not only permeative but dispersive as well. The dispersivity of a porous medium has been traditionally characterized through heat transfer (in a single- or multifluid flow) and mass transfer (in a multifluid flow) studies. For an isothermal single-fluid flow, the dispersivity of a porous medium is characterized by a flow strength and a porous medium property-de-pendent apparent viscosity. For simplicity, we discuss the single-fluid flow behavior in this chapter without considering the dispersivity of the porous medium. 

Normally, the permeability of a porous medium can be related to other porous medium properties through a model of the porous medium structure. Pragmatically, the complexity of the flow rules out any rigorous analytical attempts to resolve the problem. Ideally, one would like to use heuristic arguments to derive an expression for k or F in terms of universal constants and easily measurable properties of the porous material and the flowing fluid. Such attempts have been made by many researchers in the past. A large collection of these studies has been... 

In this chapter, some of the basic ideas on polymer adsorption at a solid-liquid interface are briefly discussed. The different types of polymer retention mechanism within a porous medium as referred to above are then reviewed, together with discussion of how these may be measured in the laboratory both static and dynamic adsorption are discussed in this context. Retention of HPAM and xanthan are then considered and the levels observed and their sensitivities to polymer, solution and porous medium properties are discussed. The effect of polymer retention in reducing core permeability is also considered. Finally, some work on the effect of polymer adsorption on two-phase relative permeability, which is of some relevance in the polymer treatment of producer wells in order to control water production, is reviewed. 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

The simplest physical property that can be exploited in a separation is size. The separation is accomplished using a porous medium through which only the analyte or interferent can pass. Filtration, in which gravity, suction, or pressure is used to pass a sample through a porous filter is the most commonly encountered separation technique based on size. 

Most authors who have studied the consohdation process of soflds in compression use the basic model of a porous medium having point contacts which yield a general equation of the mass-and-momentum balances. This must be supplemented by a model describing filtration and deformation properties. Probably the best model to date (ca 1996) uses two parameters to define characteristic behavior of suspensions (9). This model can be potentially appHed to sedimentation, thickening, cake filtration, and expression. 

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. 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Static leak-off experiments with borate-crosslinked and zirconate-cross-Unked hydroxypropylguar fluids showed practically the same leak-off coefficients [1883]. An investigation of the stress-sensitive properties showed that zirconate filter-cakes have viscoelastic properties, but borate filter-cakes are merely elastic. Noncrosslinked fluids show no filter-cake-type behavior for a large range of core permeabilities, but rather a viscous flow dependent on porous medium characteristics. 

The theory of regular solutions applied to mixtures of aromatic sulfonate and polydispersed ethoxylated alkylphenols provides an understanding of how the adsorption and micellization properties of such systems in equilibrium in a porous medium, evolve as a function of their composition. Improvement of the adjustment with the experimental results presented would make necessary to take also in account the molar interactions of surfactants adsorbed simultaneously onto the solid surface. 

This equation defines the permeability (K) and is known as Darcy s law. The most common unit for the permeability is the darcy, which is defined as the flow rate in cm3/s that results when a pressure drop of 1 atm is applied to a porous medium that is 1 cm2 in cross-sectional area and 1 cm long, for a fluid with viscosity of 1 cP. It should be evident that the dimensions of the darcy are L2, and the conversion factors are (approximately) 10 x cm2/darcy C5 10-11 ft2/darcy. The flow properties of tight, crude oil bearing, rock formations are often described in permeability units of millidarcies. 

Tortuosity is a long-range property of a porous medium, which qualitatively describes the average pore conductivity of the solid. It is usual to define x by electrical conductivity measurements. With knowledge of the specific resistance of the electrolyte and from a measurement of the sample membrane resistance, thickness, area, and porosity, the membrane tortuosity can be calculated from eq 3. 

The solid phase of the subsurface is a porous medium composed of a mixture of inorganic and organic natural materials in various stages of development. The surface area and the surface (chemical) properties of the solid phase are major factors that control the behavior of chemicals. 

Within the subsurface zone, two hquid phase regions can be defined. One region, containing water near the solid surfaces, is considered the most important surface reaction zone. This near solid phase water, which is affected by the sohd phase properties, controls the diffusion of the mobile fraction of the solute adsorbed on the solid phase. The second region constimtes the free water zone, which governs liquid and chemical flow in the porous medium. 

The extent of trapping is determined primarily by the physical properties of the vadose zone. If the organic liquids are characterized by a low vapor pressure and a low solubility in water, they remain trapped in the partially saturated zone. In this particular case, the porous medium behaves like an inert material and the behavior of the organic liquids depends only on their own properties, with no interaction between the liquid and the solid phases. 

Speciation is a dynamic process that depends not only on the ligand-metal concentration but on the properties of the aqueous solution in chemical equilibrium with the surrounding solid phase. As a consequence, the estimation of aqueous speciation of contaminant metals should take into account the ion association, pH, redox status, formation-dissolution of the solid phase, adsorption, and ion-exchange reactions. From the environmental point of view, a complexed metal in the subsurface behaves differently than the original compound, in terms of its solubility, retention, persistence, and transport. In general, a complexed metal is more soluble in a water solution, less retained on the solid phase, and more easily transported through the porous medium. 

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