Porous media characterization

Apparently the parameters of stochastic models are quite different from those of classic (deterministic) models where the permeability, the porosity, the pore radius, the tortuosity coefficient, the specific surface, and the coefficient of the effective diffusion of species represent the most used parameters for porous media characterization. Here, we will present the correspondence between the stochastic and deterministic parameters of a specified process, which has been modelled with a stochastic and deterministic model in some specific situations. 

The following sections summarize the reported experimental techniques for porous media characterization. The limitations inherent to the use of the original Young-Laplace equation to PTL materials will become apparent in light of the preceding discussion. 

In this formulation, the presence of inertia and viscous forces is neglected and the region is assumed as homogeneous porous media characterized by the permeability. 

Lavi, B., A. Marmm, and J. Bachmann. 2008. Porous media characterization by the two-liquid method Effect of dynamic contact angle and inertia. Langmuir 24 1918-1923. 

Structural models emerge from the notion of membrane as a heterogenous porous medium characterized by a radius distribution of water-filled pores. This structural concept of a water-filled network embedded in the polymer host has already formed the basis for the discussion of proton conductivity mechanisms in previous sections. Its foundations have been discussed in Sect. 8.2.2.1. Clearly, this concept promotes hydraulic permeation (D Arcy flow [80]) as a vital mechanism of water transport, in addition to diffusion. Since larger water contents result in an increased number of pores used for water transport and in larger mean radii of these pores, corresponding D Arcy coefficients are expected to exhibit strong dependencies on w. 

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. 

When a dilute solution of a polymer (c << c ) is equilibrated with a porous medium, some polymer chains are partitioned to the pore channels. The partition coefficient K, defined as the ratio of the polymer concentration in the pore to the one in the exterior solution, decreases with increasing MW of the polymer (7). This size exclusion principle has been used successfully in SEC to characterize the MW distribution of polymer samples (8). 

The objective of this work is to study the possible influence of the crude oil composition on the amount of coke deposit and on its ability to undergo in-situ combustion. Thus, the results would provide valuable information not only for numerical simulation of in-situ combustion but also to define better its field of application. With this aim, five crude oils with different compositions were used in specific laboratory tests that were carried out to characterize the evolution of the crude oil composition. During tests carried out in a porous medium representative of a reservoir rock, air injection was stopped to interrupt the reactions. A preliminary investigation has been described previously (8). 

Consider the flow of an incompressible fluid through a two-dimensional porous medium, as illustrated in Fig. 13-2. Assuming that the kinetic energy change is negligible and that the flow is laminar as characterized by Darcy s law, the Bernoulli equation becomes... 

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. 

Particle deposition from aqueous suspensions onto stationary surfaces is a dynamic phenomenon characterized by a transient or time-dependent rate of deposition. The deposition of contaminated suspended particles is affected by the nature of the surrounding porous medium. A declining deposition rate is observed when particle-particle interactions are repulsive, so that the potential deposition zone becomes progressively occluded as particles accumulate this leads to a blocking phenomenon. 

Generalized local Darcy s model of Teorell s oscillations (PDEs) [12]. In this section we formulate and study a local analogue of Teorell s model discussed previously. The main difference between the model to be discussed and the original one is the replacement of the ad hoc resistance relaxation equation (6.1.5) or (6.2.5) by a set of one-dimensional Nernst-Planck equations for locally electro-neutral convective electro-diffusion of ions across the filter (membrane). This filter is viewed as a homogenized aqueous porous medium, lacking any fixed charge and characterized... 

Here, the length L in (7.38) has been replaced by porous layer thickness d and the surface area Aeff. The effective diffusion coefficient D0,eff characterizes the transport through porous medium and includes both regular diffusion and the Knudsen diffusion coefficient >o,Kn, which has a different temperature dependence from diffusion in bulk. 

The flow through porous media of emulsions, foams, and suspensions can be important in a number of applications ranging from fixed-bed catalytic reactors in the chemical process industries, to flows through soil environments, to flow in underground reservoirs. To understand the flow of dispersions in porous media one needs a knowledge not only of the properties of the dispersion, but also of the porous medium. Pore characterization itself has been reviewed elsewhere [30,416]. 

Advection is the transport of dissolved contaminant mass due to the bulk flow of groundwater, and is by far the most dominant mass transport process [2]. Thus, if one understands the groundwater flow system, one can predict how advection will transport dissolved contaminant mass. The speed and direction of groundwater flow may be characterized by the average linear velocity vector (v). The average linear velocity of a fluid flowing in a porous medium is determined using Darcy s Law [2] ... 

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). 

In the scientific literature, we can find a large quantity of experimental results where the flow characterization inside a porous medium has shown that the value of the dispersion coefficient is not constant. Indeed, for the majority of porous structures the diffusion is frequently a function of the time or of the concentration of the diffusing species. As far as simple stochastic models cannot cover these situations, more complex models have been built to characterize these dependences. One of the first models that gives a response to this problem is recognized as the modd of motion with states having multiple vdodties. 

Here is the molecular diffusion coefficient of the pair C-T and K. 3 (2/3)V(8RgT/7tMT) is the Knudsen constant for the tracer T, Rg is the gas constant, T temperature, and Mt the tracer molecular weight. v t and vi/ are parameters characterizing the porous medium (transport parameters). stands for the integral mean radius of pores through which the... 

In this section we will define some of the terms used to characterize a porous medium and briefiy discuss those properties of porous materials that may have relevance to the flow of emulsions. 

Soo and Radke 12) found that emulsion flow in a porous medium is characterized by three parameters a filter coefficient, an interpore flow redistribution factor, and a local flow restriction factor. The filter coefficient... 

The electrochemical behavior of the powdered active carbon electrode depends on the surface chemistry, and cyclic voltammetry can be used as a simple method of characterizing active carbon materials. A new heterogeneous copper catalyst was developed using highly porous active carbon as the catalyst support [282]. The advantages of a porous-medium supported catalyst are that the active phase could be kept in a dispersed but stable state, and that, as an example, the oxidized organic pollutant is adsorbed onto carbon, thereby enhancing its surface concen-... 

In the near future, the development of the molecular simulation methods and the availability of results of comparison studies for a wide range of microporous sorbents should make the situation clearer However, these methods are always based on the same kind of experimental data a N2 adsorption isotherm at 77 K. These experimental conditions are very often far from those prevailing in the industrial applications. The use of a single adsorption isotherm within standard conditions could be considered as an advantage as it simplifies the experimental part of the characterization procedure. On the other hand, the possibility of using adsorption data in a wider temperature and pressure domain of conditions and for a large range of adsorbates should be helpful to prove or to invalidate the efficiency of the theoretical treatments. Besides, it would allow to adapt the complete characterization procedures and thus the choice of the experimental conditions in order to fit the final application in which the porous medium will be involved. 

He used three length scales derived from mercurj -injection data to characterize a porous medium. He defined thresholds pressure as the pressure at which mercury forms a connected pathway across the sample and indicated that the measured threshold pressure corresponded graphically to the inflection point on a mercury injection plot. This protocole is often insufficient to characterize the porous space and to describe completly the phenomena in mercury injection. Experiments often show that between two successive experiments points the decrease of capillary pressure can be important and during this time the volume of injected mercury can be 50% of the total volume. Indeed, it observed sudden falls of pressure eorresponding to the spontaneous redistribution of mercury in porous network. For similar porosity of samples we have unexplained different mercury saturation time of pore network. 

For flow through porous media studies, the sandpacks used as porous media were flushed vertically with carbon dioxide for an hour to replace interstitial air. Distilled water was pumped and the pore volume (PV) of the porous medium was determined. By this procedure, the trapped gas bubbles in the porous media can be easily eliminated because carbon dioxide is soluble in water. For determining the absolute permeability of the porous medium, the water was pumped at various flow rates and the pressure drop across the sandpack as a function of flow rate was recorded. After the porous medium was characterized, the mixed surfactant solutions of known surface properties were injected. This was followed by air injection to determine the effect of chain length compatibility on fluid displacement efficiency, breakthrough time and air mobility in porous media. 

The first-order mass transfer model can be readily interpreted in terms of the various diffusion-based models and several researchers have done so Isee Brusseau and Rao (1989a) and references cited therein]. A straightforward means of equating the two models is to define the mass transfer constant in terms of the aqueous diffusion coefficient, shape factor, and diffusion path length characterizing the porous medium. Ball (1989) reported the following equation, equating k2 from the first-order bicontinuum model to the RIPD model... 

---