Mass-transfer process

The first assumption in all such physical mass transfer processes is that equiHbrium exists at the interface between the two phases. This assumption implies that, at the interface, the concentration of the gas in the Hquid, is equal to its solubiHty at its partial pressure in the gas phase,Since, for sparingly soluble gases such as oxygen, there is a direct proportionaHty between the two,... 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Equipment Absorption, stripping, and distiUation operations are usually carried out in vertical, cylindrical columns or towers in which devices such as plates or packing elements are placed. The gas and liquid normally flow countercurrently, and the devices serve to provide the contacting and development of interfacial surface through which mass transfer takes place. Background material on this mass transfer process is given in Sec.. 5. 

The main objective for calculating the number of theoretical stages (or mass-transfer units) in the design of a hquid-liquid extraction process is to evaluate the compromise between the size of the equipment, or number of contactors required, and the ratio of extraction solvent to feed flow rates required to achieve the desired transfer of mass from one phase to the other. In any mass-transfer process there can be an infinite number of combinations of flow rates, number of stages, and degrees of solute transfer. The optimum is governed by economic considerations. 

Emission from an open liquid face (e.g., open tanks, liquid spills on the floor surface) can be evaluated using equations based on criteria relations and empirical data. Assuming that the heat and mass transfer processes can be described using similar differential equations, the criteria equation describing the evaporation process will be similar to one describing the heat transfer ... 

KjMdman, L., and R. Huhtanen. 1986. Numerical simulation of vapour cloud and dust explosions. Numerical Simulation of Eluid Elow and Heat/Mass Transfer Processes. Vol. 18, Lecture Notes in Engineering, 148-158. 

Distillation is probably Ihe most widely used separation (mass transfer) process in the chemical and allied industries. Its applications range from the rectification of alcohol, which has been practiced since antiquity, lo the fractionation of crude oil. The separation of liquid mixtures by distillation is based on differences in volatility between the components. The greater the... 

Water-cooling in towers operates on the evaporative principles, which are a combination of several heat/mass transfer processes. The most important of these is the transfer of liquid into a vapor/air mixture, as, for example, the surface area of a droplet of water. Convective transfer occurs as a result of the difference in temperature between the water and the surrounding air. Both these processes take place at the interface of the water surface and the air. Thus it is considered to behave as a film of saturated air at the same temperature as the bulk of the water droplet. 

Foaming of the bioreactor is a nuisance, reflects on the mass transfer process and must be prevented, for many reasons. The problems related to foaming are obvious if they are due to gas sparging. The problems are the loss of broth, clogging of the exhaust gas system... 

Fig. 13.2. Liquid gas mass transfer process in biological filter, attached growth system.

A form of cooling, and the one of prime interest, concerns ablative cooling. It is essentially a heat and mass transfer process in which mass is expended to achieve thermal dissipation, absorption, and blocking. The process is passive in nature, serves to control the surface temperature, and greatly restricts the flow of heat into the material substrate. As a result of these desirable attributes, ablative cooling (includes use of plastic compositions) has been widely used for thermal protection of solid propellant motors and less extensively in liquid propellant motors. 

In the theoretical treatment, the heat- and mass-transfer processes shown in Fig. 6 were considered. Simultaneous solution of the equations describing the behavior of the unsteady-state reaction system permits the temperature history of the propellant surface to be calculated from the instant of oxidizer propellant contact to the runaway reaction stage. 

More recently, Zucrow et al. (Zl) have run experiments which show that in the region of low flow rates the burning rates of certain propellants actually decrease with increasing gas flow. As the gas flow rate increases, the burning rate is observed to go through a minimum and then increase with further increases in gas flow rate. The decrease in burning rate was attributed to undefined mass-transfer processes. Eventually, the convective heat-transfer processes overcome this effect to give results similar to those obtained by others. 

The term mass transfer is used to denote the transference of a component in a mixture from a region where its concentration is high to a region where the concentration is lower. Mass transfer process can take place in a gas or vapour or in a liquid, and it can result from the random velocities of the molecules (molecular diffusion) or from the circulating or eddy currents present in a turbulent fluid (eddy diffusion). 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

In several important processes, one component in a gaseous mixture will be transported relative to a fixed plane, such as a liquid interface, for example, and the other will undergo no net movement. In gas absorption a soluble gas A is transferred to the liquid surface where it dissolves, whereas the insoluble gas B undergoes no net movement with respect to the interface. Similarly, in evaporation from a free surface, the vapour moves away from the surface but the air has no net movement. The mass transfer process therefore differs from that described in Section 10.2.2. 

In many practical mass transfer processes, unsteady state conditions prevail. Thus, in the example given in Section 10.1, a box is divided into two compartments each containing a different gas and the partition is removed. Molecular diffusion of the gases takes place and concentrations, and concentration gradients, change with time. If a bowl of liquid... 

The mass transfer process is again governed by equation 10.66, but the third boundary condition is applied at y = L, the film thickness, and not at y = oo. As before, the Laplace... 

Thus either the penetration theory or the film theory (equation 10.144 or 10.145) respectively can be used to describe the mass transfer process. The error will not exceed some 9 per cent provided that the appropriate equation is used, equation 10.144 for L2 jDt > n and equation 10.145 for L2/Dt < n. Equation 10.145 will frequently apply quite closely in a wetted-wall column or in a packed tower with large packings. Equation 10.144 will apply when one of the phases is dispersed in the form of droplets, as in a spray tower, or in a packed tower with small packing elements. 

Mass transfer processes involving two fluid streams are frequently carried out in a column countercurrent flow is usually employed although co-current flow may be advantageous in some circumstances. There are two principal ways in which the two streams may be brought into contact in a continuous process so as to permit mass transfer to take place between them, and these are termed stagewise processes and continuous differential contact processes. 

In a steady-state process, a gas is absorbed in a liquid with which it undergoes an irreversible reaction. The mass transfer process is governed by Fick s law, and the liquid is sufficiently deep for it to be regarded as effectively infinite in depth. On increasing the temperature, the concentration of reactant at the liquid surface CAi falls to 0.8 times its original value. The diffusivity is unchanged, but the reaction constant increases by a factor of 1.35. It is found that the mass transfer rate at the liquid surface falls to 0.83 times its original value. What is the order of the chemical reaction ... 

Flat platelets in which the mass transfer process can be regarded as onedimensional, with mass transfer taking place perpendicular to the faces of the platelets. Furthermore, the platelets will be assumed to be sufficiently thin for deviations from unidirectional transfer due to end-effects to be negligible. 

In a thin flat platelet, the mass transfer process is symmetrical about the centre-plane, and it is necessary to consider only one half of the particle. Furthermore, again from considerations of symmetry, the concentration gradient, and mass transfer rate, at the centre-plane will be zero. The governing equation for the steady-state process involving a first-order reaction is obtained by substituting De for D in equation 10.172 ... 

In these experiments, it might be anticipated that, with high concentrations of vapour in the air, the rate of evaporation would no longer be linearly related to the partial pressure difference because of the contribution of bulk flow to the mass transfer process (Section 10.2.3), although there is no evidence of this even at mole fractions of vapour at the surface as high as 0.5. Possibly the experimental measurements were nol sufficiently sensitive to detect this effect. 

In the previous section, the molecular basis for the processes of momentum transfer, heat transfer and mass transfer has been discussed. It has been shown that, in a fluid in which there is a momentum gradient, a temperature gradient or a concentration gradient, the consequential momentum, heat and mass transfer processes arise as a result of the random motion of the molecules. For an ideal gas, the kinetic theory of gases is applicable and the physical properties p,/p, k/Cpp and D, which determine the transfer rates, are all seen to be proportional to the product of a molecular velocity and the mean free path of the molecules. 

A similar argument can be applied to the mass transfer process when a concentration gradient exists. Thus, if the molar concentration of A remote from the surface is Ca, and at the surface it is Caw, the moles of A transferred to the surface will be (M/pHC — Cam ), if the density (p) can be assumed to be constant over the range of concentrations encountered, Thus the moles of A transferred to the surface per unit area and unit time (-/V Ov-o is given by ... 

When the mass transfer process deviates significantly from equimolecular counterdiffusion, allowance must be made for the fact that there may be a very large difference in the molar rates of transfer of the two components. Thus, in a gas absorption process, there will be no transfer of the insoluble component B across the interface and only the soluble component A will be transferred. This problem will now be considered in relation to the Reynolds Analogy. However, it gives manageable results only if physical properties such as density are taken as constant and therefore results should be applied with care. 

It may be assumed that the penetration model may be used to represent the mass transfer process. The depth of penetration is small compared with the radius of the droplets and the effects of surface curvature may he neglected. From the penetration theory, the concentration C, at a depth y below the surface at time r is given by ... 

Stagewise mass transfer processes 622 Standard orifice meter 249... 

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