Mass transfer zone volume

There are data showing that at the same contact time, but different linear velocities, there is no difference in the performance of a carbon system. It is obvious then that the effect of linear velocity on the diffusion through the film around the particle and the ratio of the magnitude of the film diffusion to the pore diffusion are the factors that determine the effects, if any, that occur. Therefore, the linear velocity cannot be ignored completely when evaluating a system. Systems at the higher linear velocity (LV) treat more liquid per volume of carbon at low-concentration levels and the mass-transfer zone (MTZ) is shorter. 

In any evaluation of a remediation scheme utilizing surfactants, the effect of dose on HOC distribution coefficients must be quantified. Very often, only one coefficient value for HOC partitioning to sorbed surfactants has been reported in the literature, presumably because the experimental data covers only the sorption regions where the surfactant molecule interactions dominate at the surface (Nayyar et al., 1994 Park and Jaffe, 1993). However, all of the characteristic sorption regions will develop during an in-situ SEAR application as the surfactant front (i.e., mass transfer zone) advances through the porous medium. Therefore, the relative role ofregional HOC partition coefficients to sorbed surfactant should be considered in any remediation process. Finally, the porosity or solid volume fraction for the particular subsurface system must be taken into account when surfactant sorption is quantified. 

The use of an annular bed, however, has two disadvantages. The mass transfer zone concept, suggested by Michaels (2), indicates that due to a short flow path, breakthrough of the adsorbed species is expected to occur shortly after the start of the adsorption stage. In addition, the concentric tube structure containing the annular bed is more complex than that of a tubular bed and reduces the effective bed volume due to the existence of an empty core. 

V denotes the volume of the mass transfer zone in the extractor and a the interfacial area referred to the volume. The hold-up follows from (6.4-9). Avery complex task is the prediction of mean drop diameter as the correlatiorrs (6.4-5)-(6.4-8) presented before are not sufficiently reliable. Typically, the values of the volumetric interfacial area are in the range 200-500 m /m. ... 

Volume of Effluent Treated, V FIGURE 15 0 The breakthrough curve mass-transfer zone. 

Solution pH also affects the characteristics of carbon beds, as shown in Table 8.5. Thus, adsorption of ort/to-chlorophenol (OCR) is favored at acidic pH, as is further noted by their higher values of breakthrough volumes, Vb (cm ), and their lower values of the height of the mass transfer zone (MTZ), //mtz (cm), found at this pH (Section 4.5 - Breakthrough Curves). The lower adsorption at basic pH is due, as explained above, to the repulsion between the negatively charged carbon surface and the o/tho-chlorophenolate anions, Rivera-Utrilla et al. (1991). 

Determine the total bed height based on the volume of adsorbent calculated in step 4 and an estimated length of the mass transfer zone (MTZ). 

Even at 1,500 F, equilibrium eonstants for the first two reactions are high enough (about 10) to expect reaction to go essentially to completion except for kinetic-rate limitations. The reaction zone might be expected to be sized by volume of rabbled carbon bed, considering that the carbon gasification reactions that occur in it are governed by kinetics and are reaction-rate limited. Actually, it is sized by hearth area. The area exposed to the gases controls mass transfer of reactants from the gas phase to the carbon and heat transfer to support the endothermic reactions. 

The interfacial area in the contactor, which is directly related to the solids hold-up, strongly influences the mass transfer rate. To maximise the overall mass-transfer rate per unit volume of equipment, a high solids hold-up is necessary. On the other hand, the solids hold-up also influences the pressure drop over the contactor. The pressure drop has a hydrostatic and a dynamic component, both of which rise with increased solids hold-up. Since the adsorbent consists of extremely small particles, fluid friction between liquid and solids may lead to a relatively high dynamic pressure drop. The hydrostatic pressure drop is attributable to the density difference between the suspension in the contact zone and in the liquid. 

On the other hand, if bubble growth is diffusion controlled, then the mass transfer coefficient may be meaningful. However, in this case, the surface area for mass transfer is the surface area of the bubbles entrained in the solution and this depends on the volume of liquid in the extraction zone and not on the surface area of the extraction zone. Clearly, attempts to correlate experimental data for the extraction of a volatile component from a polymeric solution containing entrained bubbles using mass transfer coefficients can be misleading or totally erroneous. 

Of a more complete approach are the zone models [3], which consider two (or more) distinct horizontal layers filling the compartment, each of which is assumed to be spatially uniform in temperature, pressure, and species concentrations, as determined by simplified transient conservation equations for mass, species, and energy. The hot gases tend to form an upper layer and the ambient air stays in the lower layers. A fire in the enclosure is treated as a pump of mass and energy from the lower layer to the upper layer. As energy and mass are pumped into the upper layer, its volume increases, causing the interface between the layers to move toward the floor. Mass transfer between the compartments can also occur by means of vents such as doorways and windows. Heat transfer in the model occurs due to conduction to the various surfaces in the room. In addition, heat transfer can be included by radiative exchange between the upper and lower layers, and between the layers and the surfaces of the room. 

As shown in Fig. 3, the overall resistance to the reaction is considered to consist of three steps (i) gas phase mass transfer (ii) diffusion through the porous reacted zone (in reduction the solid products are generally smaller in volume than the reactants), and (iii) chemical reaction at the boundary. Additional assumptions usually made are... 

Shear zones can be loci of focused fluid flow and major element metasomatism and associated volume loss (e.g., O Hara, 1988 Selverstoneetaf., 1991 Dipple and Ferry, 1992a Ring, 1999). In their survey of ductile shear zones, Dipple and Ferry (1992a) concluded that time-integrated fluid fluxes of —2 X lO" m m attended down-T flow or up-T flow, leading to considerable alkali mass transfer and other major element metasomatism. 

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