Porous media adsorption

As mentioned in Sect. 5.5, in the classical diffusion theory for a porous medium, adsorption is described by a distribution coefficient Kd resulting from the transfer of the species from the fluid phase to the solid phase through the linearized equation of equilibrium adsorption isotherm (5.113). 

The adsorption plateaus on this solid, determined with each of the surfactants (Table II) and the individual CMC values, were used to calculate the adsorption constants input in the model. Figure 3 compares the total adsorption (sulfonate + NP 30 EO) of the pseudo-binary system investigated as a function of the initial sulfonate fraction of the mixtures under two types of conditions (1) on the powder solid, batch testing with a solid/liquid ratio, S/L = 0.25 g/cc (2) in the porous medium made from the same solid, for which this solid ratio is much higher (S/L = 4.0 g/cc). 

Such an idea was patented in 1981 (14). Besides research by Scamehom and Schechter (15) provided an experimental illustration of this by batch adsorption tests of kaolinite with some purified anionic/nonionic products. Our objective was to enlarge and test this technique under the dynamic flow conditions of industrial surfactant injection in an adsorbent porous medium. 

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. 

Experiment B is also a non-adsorption experiment in which flow through the capillary tube is used. The sample medium used is the surfactant solution prepared in the 1% acidified brine. Results will be combined with those from Experiment C to get the information on the permanent or irreversible adsorption on the porous medium by measuring peak areas. 

Contaminant adsorption includes retention on the porous medium solid phase, as a result of cation exchange processes, and surface retention of neutral molecules, due to van der Waals forces. 

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. 

Surface area is by no means the only physical property which determines the extent of adsorption and catalytic reaction. Equally important is the catalyst pore structure which, although contributing to the total surface area, is more conveniently regarded as a separate factor. This is because the distribution of pore sizes in a given catalyst preparation may be such that some of the internal surface area is completely inaccessible to large reactant molecules and may also restrict the rate of conversion to products by impeding the diffusion of both reactants and products throughout the porous medium. 

Barrer, R. M. and Grove, D. M. Trans. Faraday Soc. 47 (1951) 826, 837. Flow of gases and vapours in a porous medium and its bearing on adsorption problems I. Steady state of flow, II. Transient flow. 

Freezing soil is considered as porous medium of skeleton (s) of soil grains filled up with pore fluid (/) and ice (i). It is assumed that skeleton and ice are elastic solids and have equal displacements and velocities, pore fluid is an ideal solution of water (w) and dissolved salts (c) and governed by adsorption... 

Operations like pressure swing adsorption involve the condensation of the liquid in the porous medium. Several researchers developed predictive models of the configuration of liquid phase in the wet, unsaturated, porous media. The method developed by Silverstein and Fort (2000) is based on simulated annealing with random swapping of gas and liquid elements in the system to achieve a global energy minimum defined by... 

In the fractal porous medium, the diffusion is anomalous because the molecules are considerably hindered in their movements, cf. e.g., Andrade et al., 1997. For example, Knudsen diffusion depends on the size of the molecule and on the adsorption fractal dimension of the catalyst surface. One way to study the anomalous diffusion is the random walk approach (Coppens and Malek, 2003). The mean square displacement of the random walker (R2) is not proportional to the diffusion time t, but rather scales in an anomalous way ... 

The phenomenon of capillary condensation provides a method for measuring pore-size distribution. Nitrogen vapor at the temperature of liquid nitrogen for which cos(0) = 1 is universally used. To determine the pore size distribution, the variation in the amount of nitrogen inside the porous particle is measured when the pressure is slightly increased or decreased. This variation is divided into two parts one part is due to true adsorption and the other to capillary condensation. The variation due to adsorption is known from adsorption experiments with nonporous substances of known surface area, so the variation due to condensation can be calculated. The volume of this amount of nitrogen is equal to the volume of pores with the size as determined by the Kelvin equation. Once a certain model has been selected for the complicated pore geometry, the size of the pores can be calculated. Usually it is assumed that an array of cylindrical capillaries of uniform but different radii, and randomly oriented represents the porous medium. So the Kelvin equation in the form of Equation 3.9 is used. Since condensation is combined with adsorption, the thickness of the adsorption layer... 

One of the most intriguing aspects of surface diffusion is the strong dependence of the diffusivity on sorbate concentration. The dependence of surface diffusivities on pressure, temperature and composition is much more complicated than those of the molecular and Knudsen diffusivities, because of all the complexities of porous medium geometry, surface structure, adsorption equilibrium, mobility of adsorbed molecules, etc. 

The fluid-fluid tension and the wettability requirement in turn set limits on the tension between the porous medium and each of the fluids. These fluid-solid interfacial tensions are affected by the isotherm for surfactant adsorption. 

Surfactant adsorption can change the wettability of the porous medium from hydrophilic to hydrophobic and even back again. 

Phase Behavior and Surfactant Design. As described above, dispersion-based mobility control requires capillary snap-off to form the "correct" type of dispersion dispersion type depends on which fluid wets the porous medium and surfactant adsorption can change wettability. This section outlines some of the reasons why this chain of dependencies leads, in turn, to the need for detailed phase studies. The importance of phase diagrams for the development of surfactant-based mobility control is suggested by the complex phase behavior of systems that have been studied for high-capillary number EOR (78-82), and this importance is confirmed by high-pressure studies reported elsewhere in this book (Chapters 4 and 5). 

NaCl) was then injected into the porous medium until the rock adsorption was completed. 

To calculate the reduction in the concentration of surfactant in the fluid by adsorption it is necessary to have an estimation of the inner surface area of the reservoir. This parameter is related to the porosity of the medium and to its permeability. Attempts have been made to correlate these two quantities but the results have been unsuccessful, because there are parameters characteristic of each particular porous medium involved in the description of the problem (14). For our analysis we adopted the approach of Kozeny and Carman (15). These authors defined a parameter called the "equivalent hydraulic radius of the porous medium" which represents the surface area exposed to the fluid per unit volume of rock. They obtained the following relationship between the permeability, k, and the porosity, 0 ... 

From Equation 2 it is possible to calculate the inner s,urface area of the porous medium, S. Hence, from the adsorption data of Figure 4 it is possible to calculate the volume of rock necessary to adsorb all of the surfactant and the total volume of rock attained by the fluid. Assuming a radial penetration, these two volumes may be transformed into the radius of penetration of the fluid as a whole, ri, and the radius necessary to consume the surfactant, r2 The ratio will be higher than one if the surfactant is... 

The effect of geometry and axial orientation of spheroidal particles on the adsorption rate in a granular porous medium... 

There has always been some reluctance to assume that the pH in a porous medium is controlled solely by the carbonate buffer system in the pore waters. There are arguments that H ions on particle surfaces can affect pH measurements (Stumm and Morgan, 1981) and, even more importantly, comprehensive models of pore-water chemistry are beginning to demonstrate that H adsorption on mineral surfaces may play an important role in controlling the pH of pore waters. Conclusions of the pH measurements, however, have been confirmed by millimeter-scale measurements of both Pco and calcium concentration in the pore waters (Hales et al., 1997 Cai et al., 1995 Wenzhofer et ah, 2001.)... 

Filtration is the separation of suspended particles of solids from fluids (liquid or gas) by use of a porous medium (6). It is therefore a sieving process whereby sohds are separated from a solvent and does not involve solutes interacting with surfaces. In discussing oU processing, adsorption can be confused with filtration. For example, it could be argued as to whether soaps and phospholipids were separated by adsorption or filtration. Under low-solubihty conditions (low temperamre and high concentrations), soaps and phospholipids tend to be separated more by filtration than adsorption, and visa versa. Expressed simply, adsorption is described as the assimilation of oil-soluble impurities, whereas filtration is the removal of solid particulates and insoluble contaminants. 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

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. 

Equation 2.20 is the advection-dispersion (AD) equation. In the petroleum literature, the term convection-diffusion (CD) equation is used, or simply diffusion equation (Brigham, 1974). When a reaction term is included, the term advection-reaction-dispersion (ARD) equation is used elsewhere. When the adsorption term is expressed as a reaction term, the ARD equation is as discussed later in Section 2.4. Several solutions of Eq. 2.20 have been presented in the literature, depending on the boundary conditions imposed. In general, they are various combinations of the error function. When the porous medium is long compared with the length of the mixed zone, they all give virtually identical results. 

---