Mass transfer concentrated systems

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

This boundary-layer theory applies to mass-transfer controlled systems where the membrane permeation rate is independent of pressure, for there is no pressure term in the model. In such cases it has been proposed that, as the concentration at the membrane increases, the solute eventually precipitates on the membrane surface. This layer of precipitated solute is known as the gel-layer, and the theory has thus become known as the gel-polarisation model proposed by Micii i i.si 0). Under such conditions C, in equation 8.15 becomes replaced by a constant Cq the concentration of solute in the gel-layer, and ... 

For the determination of the controlling mechanism, in the case of mass transfer-controlled systems, the following method can be used (Inglezakis, 2002b). This approximate method requires only the experimental bed data, and specifically, the set of exit concentrations and... 

Concentration polarization for Hquid film mass transfer can be coupled with the model for membrane transport (for example the solution-diffusion model Eq. (3)) [32, 38, 43, 44], to describe membrane transport in a mass transfer limited system. 

In mass-transfer-controlled systems in which extensive complexing or association takes place in the bulk phases, a proper mass transfer model must account for transport of all species. Otherwise, the transport model will not be consistent with a chemical model of phase equilibrium. For example. Fig. 8.4-4 indicates schematically the species concentration profiles established during the extraction of copper from ammonia-ammonium sulfate solution by a chelating agent such as LIX. In most such cases the reversible homogeneous reactions, like copper complexation by ammonia, will be fast and locally equilibrated. The method of Olandei can be applied in this case to compute individual species profiles and concentrations at the interfiice for use in an equilibrium or rate equation. This has been done in the rate analyses of several of the chloride and ammonia systems cited above. ... 

Electrochemistry is dominated by the study of species dissolved in solution. The use of a solvent as the reaction medium helps electrochemists to control important reaction conditions such as pH, rate of mass transfer, concentration of reactant, solubility, solvation, etc. Water and organic solvents are the most popular media. However, by using appropriate ionic liquids, reactants and products that are unstable in those media remain stable, and redox reactions that are impossible in water and organic solvents become possible. The reaction environments are markedly wider in some ionic liquids than in other solvent systems. In spite of this, some fundamental electrochemical concepts generally used in conventional solvent systems are not always valid in ionic liquids. 

Eor a linear system f (c) = if, so the wave velocity becomes independent of concentration and, in the absence of dispersive effects such as mass transfer resistance or axial mixing, a concentration perturbation propagates without changing its shape. The propagation velocity is inversely dependent on the adsorption equiUbrium constant. 

In principle, the catalytic converter is a fixed-bed reactor operating at 500—620°C to which is fed 200—3500 Hters per minute of auto engine exhaust containing relatively low concentrations of hydrocarbons, carbon monoxide, and nitrogen oxides that must be reduced significantly. Because the auto emission catalyst must operate in an environment with profound diffusion or mass-transfer limitations (51), it is apparent that only a small fraction of the catalyst s surface area can be used and that a system with the highest possible surface area is required. 

Ko Overall gas-pbase mass-transfer coefficient for concentrated systems kmoP(s-m ) lbmol/(h-fF)... 

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

For systems in which the solute concentrations in the gas and hquid phases are dilute, the rate of transfer may be expressed by equations which predic t that the rate of mass transfer is proportional to the difference between the bulk concentration and the concentration at the gas-liquid interface. Thus... 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

Mass-Transfer Principles Concentrated Systems When sohrte concentrations in the gas and/or liqrrid phases are large, the eqrrations derived above for dihrte systems no longer are applicable. The correct eqrrations to rrse for concentrated systems are as Follows ... 

The overall gas-phase and hquid-phase mass-transfer coefficients for concentrated systems are computed according to the following equations ... 

Kl Xbm /cl x bm kc y yt When the equilibrium cui ve is a straight line, the terms in parentheses can be replaced by the slope m as before. In this case the overall mass-transfer coefficients for concentrated systems are related to each other by the equation... 

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