Transfer in series

Component Transport Transport through membranes can be considered as mass transfer in series (1) transport through a polarization layer above the membrane that may include static or dynamic cake layers, (2) partitioning between the upstream polarization layer and membrane phases at the membrane surface, (3) transport through the membrane, and (4) partitioning between the membrane and downstream fluid. 

Transfer in series. There is a gas-to-water mass transfer into the liquid and no direct gas-to-organic phase contact is possible. 

For beading oils, the most probable pathway is mass transfer in series. Assuming a shuttle effect of the oil phase, investigators consider that the solute absorbed in the oil droplets near the gas-aqueous phase interface is given up to the water phase outside the boundary layer. 

This integration by quadratures works well for a number of transfer problems in burning or dissolution, for example, the burning of a sphere where the burnt ash builds up an insulating layer on the outside. With the various resistances to heat and mass transfer in series and the assumption that the... 

Finite transferability is a weaker form where the recipient in a transfer is not in the same position as the original recipient The certainty about the fact that one can win disputes about this message may decrease with each transfer, so that only a finite number A of successive transfers is guaranteed. (This happens in the extension to [ChRo91] described in [PfWa92], whereas [ChRo91] has no transferability see Section 6.3.4. ) This restriction only refers to transfers in series, whereas the number of transfers by the same recipient is not restricted. The parameter A can be a specification parameter or an input parameter in initialization (as a component of the general parameter par omitted for brevity, see the end of Initialization in Section 5.2.4). 

Many mass transfer models exist, but most of them depend on three assumptions and are simplified versions of actual mass transfer mechanisms, many of which occur simultaneously. The first assumption is that the different phases and the phase interface offer resistance to mass transfer in series, in a similar manner to heat transfer resistances. The second assumption maintains that mass transfer is controlled by the phase equilibrium near the interface, which changes more quickly than the bulk phase equilibrium (Azbel, 1981). In other words, mass transfer occurs at the microscale level (van Elk et ak, 2007). Finally, gases are assumed to be single component. Multiple component problems are more complicated because each individual gas component making up the mixture has to be considered for the limiting gas-liquid mass transfer step. The complexity grows further once the relationships between each gas component and, for example, the bacteria in a bioreactor are considered. 

A comprehensive analysis dealing with the various asymptotic cases of gas-liquid mass transfer in series with various particle conversion mechanisms in the bulk has been presented recently by Doraiswamy and Sharma [l] Such a model has been successfully applied to oxydesulfurization of coal [l5l]. As far as we know, no analysis has been presented as yet for the case where the particles are small with respect to the gas-liquid film for mass transfer, and consequently may enhance the gas-liquid mass transfer process. According to our experience it plays a role in a new process that we recently developed for the concentration of hydrogen from lean gas mixtures with a slurry containing finely hydridable metal part-Icles [16,139,152-154], (Fig. 23). 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Hgura 7.10 A large overall temperature cross requires shells in series to reduce the cross in individual exchangers. (From Ahmad, Linnhoff, and Smith, Trans. ASME, J. Heat Transfer, 110 304, 1988 reproduced by permission of the American Society of Mechanical Engineers.)... 

Figure C3.2.7. A series of electron transfer model compounds with the donor and acceptor moieties linked by (from top to bottom) (a) a hydrogen bond bridge (b) all sigma-bond bridge (c) partially unsaturated bridge. Studies with these compounds showed that hydrogen bonds can provide efficient donor-acceptor interactions. From Piotrowiak P 1999 Photoinduced electron transfer in molecular systems recent developments Chem. Soc. Rev. 28 143-50.

Expressions similar to equations 6 and 7 may be derived in terms of an overall Hquid-phase driving force. Equation 7 represents an addition of the resistances to mass transfer in the gas and Hquid films. The analogy of this process to the flow of electrical current through two resistances in series has been analyzed (25). 

In the slurry process, the hydrolysis is accompHshed using two stirred-tank reactors in series (266). Solutions of poly(vinyl acetate) and catalyst are continuously added to the first reactor, where 90% of the conversion occur, and then transferred to the second reactor to reach hiU conversion. Alkyl acetate and alcohols are continuously distilled off in order to drive the equiUbrium of the reaction. The resulting poly(vinyl alcohol) particles tend to be very fine, resulting in a dusty product. The process has been modified to yield a less dusty product through process changes (267,268) and the use of additives (269). Partially hydroly2ed products having a narrow hydrolysis distribution cannot be prepared by this method. 

Electrodialysis. Electro dialysis processes transfer ions of dissolved salts across membranes, leaving purified water behind. Ion movement is induced by direct current electrical fields. A negative electrode (cathode) attracts cations, and a positive electrode (anode) attracts anions. Systems are compartmentalized in stacks by alternating cation and anion transfer membranes. Alternating compartments carry concentrated brine and purified permeate. Typically, 40—60% of dissolved ions are removed or rejected. Further improvement in water quaUty is obtained by staging (operation of stacks in series). ED processes do not remove particulate contaminants or weakly ionized contaminants, such as siUca. 

Electrodialysis. In reverse osmosis pressure achieves the mass transfer. In electro dialysis (qv), dc is appHed to a series of alternating cationic and anionic membranes. Anions pass through the anion-permeable membranes but are prevented from migrating by the cationic permeable membranes. Only ionic species are separated by this method, whereas reverse osmosis can deal with nonionic species. The advantages and disadvantages of reverse osmosis are shared by electro dialysis. 

The feed to a multiple-effecl evaporator is usually transferred from one effect to another in series so that the ultimate product concentration is reached only in one effect of the evaporator. In backward-feed... 

The terms on the right are the transfer functions. With the two units in series. 

The reaction mixture and contents of the cold trap are then transferred (Note 7) to a 500-ml. distilling flask attached through a short fractionating column to a water-cooled condenser which is connected in series to a receiver, a trap cooled in a dry ice-acetone bath, and a hydrogen chloride absorption trap which may later be attached to a water pump. The mixture is then distilled until the pot temperature reaches 100° and practically all of the acetyl chloride has been driven over. 

In the above example, 1 lb of initial steam should evaporate approximately 1 lb of water in each of the effects A, B and C. In practice however, the evaporation per pound of initial steam, even for a fixed number of effects operated in series, varies widely with conditions, and is best predicted by means of a heat balance.This brings us to the term heat economy. The heat economy of such a system must not be confused with the evaporative capacity of one of the effects. If operated with steam at 220 "F in the heating space and 26 in. vacuum in its vapor space, effect A will evaporate as much water (nearly) as all three effects costing nearly three times its much but it will require approximately three times as much steam and cooling water. The capacity of one or more effects in series is directly proportional to the difference between the condensing temperature of the steam supplied, and the temperature of the boiling solution in the last effect, but also to the overall coefficient of heat transfer from steam to solution. If these factors remain constant, the capacity of one effect is the same as a combination of three effects. 

Loss of Heat in Series Fractionation System - In series fractionation, i.e., where the bottoms from the first column feeds into the second column and the bottoms from the second feeds into the third, it is possible for the loss of heat input to a column to overpressure the following column. Loss of heat results in some of the light ends remaining with the bottoms and being transferred to the next column as feed. Under this circumstance, the overhead load of the second column may consist of its normal vapor load, plus the light ends from the first column. If the second column does not have the condensing capacity for the additional vapor load, excessive pressure could occur. 

A continuous flow stirred tank reactor (CFSTR) differs from the batch reactor in that the feed mixture continuously enters and the outlet mixture is continuously withdrawn. There is intense mixing in the reactor to destroy any concentration and temperature differences. Heat transfer must be extremely efficient to keep the temperature of the reaction mixture equal to the temperature of the heat transfer medium. The CFSTR can either be used alone or as part of a series of battery CFSTRs as shown in Figure 4-5. If several vessels are used in series, the net effect is partial backmixing. 

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