Transport interphase

A dense-bed center-fed column (Fig. 22-li) having provision for internal crystal formation and variable reflux was tested by Moyers et al. (op. cit.). In the theoretical development (ibid.) a nonadiabatic, plug-flow axial-dispersion model was employed to describe the performance of the entire column. Terms describing interphase transport of impurity between adhering and free liquid are not considered. 

In many smdies of interphase transport, results are obtained which show a dependence on the diffusion coefficient somewhere between tlrese two values, and tlrerefore reflect the differing states of motion of the interface between studies. 

The effect of physical processes on reactor performance is more complex than for two-phase systems because both gas-liquid and liquid-solid interphase transport effects may be coupled with the intrinsic rate. The most common types of three-phase reactors are the slurry and trickle-bed reactors. These have found wide applications in the petroleum industry. A slurry reactor is a multi-phase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles. The reactor may operate continuously as a steady flow system with respect to both gas and liquid phases. Alternatively, a fixed charge of liquid is initially added to the stirred vessel, and the gas is continuously added such that the reactor is batch with respect to the liquid phase. This method is used in some hydrogenation reactions such as hydrogenation of oils in a slurry of nickel catalyst particles. Figure 4-15 shows a slurry-type reactor used for polymerization of ethylene in a sluiTy of solid catalyst particles in a solvent of cyclohexane. 

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

A Ghanem, W Higuchi, A Simonelli. Interfacial barriers in interphase transport III Transport of cholesterol and other organic solutes into hexadecane-gelatin-water matrices. J Pharm Sci 59 659, 1970. 

AH Goldberg, WI Higuchi. Mechanisms of interphase transport II Theoretical considerations and experimental evaluation of interfacially controlled transport in solubilized systems. J Pharm Sci 58 1341-1352, 1969. 

AH Goldberg, WI Higuchi, NFH Ho, G Zografi. Mechanism of interphase transport I Theoretical considerations of diffusion and interfacial barriers in transport of solubilized systems. J Pharm Sci 56(11) 1432-1437, 1967. 

AB Bikhazi, WI Higuchi. Interfacial barrier limited interphase transport of cholesterol in the aqueous polysorbate 80-hexadecane system. J Pharm Sci 59 744-748, 1970. 

Interphase Diffusion. When interphase transport rates are characterized it can be shown that the diffusion rate between two compartments i and j can be expressed as (3)... 

Supercritical fluids (SCFs) offer several advantages as reaction media for catalytic reactions. These advantages include the ability to manipulate the reaction environment through simple changes in pressure to enhance solubility of reactants and products, to eliminate interphase transport limitations, and to integrate reaction and separation unit operations. Benefits derived from the SCF phase Fischer-Tropsch synthesis (SCF-FTS) involve the gas-like diffusivities and liquid-like solubilities, which together combine the desirable features of the gas- and liquid-phase FT synthesis routes. 

CuCl, PEG6000-(TEMPO)2, and oxygen are essential for the oxidation of benzyl alcohol into benzaldehyde. The presence of C02 improves the reaction, presumably being ascribed to high miscibility of 02 into compressed C02, thus eliminating interphase transport limitation, and expandable effect of PEG in compressed C02 [63, 64],... 

For simultaneous treatment of interphase and intraparticle transport resistances, the boundary conditions at the external pellet surface are now given by eqs 15 and 16, whereas eqs 11 and 12 still hold for the case of negligible interphase transport resistance. The bound-... 

In the most general case, i.e. when intraparticlc and interphase transport processes have to be included in the analysis, the effectiveness factor depends on five dimensionless numbers, namely the Thiele modulus the Biot numbers for heat and mass transport Bih and Bim, the Prater number / , and the Arrhenius number y. Once external transport effects can be neglected, the number of parameters reduces to three, because the Biot numbers then approach infinity and can thus be discarded. 

A similar situation occurs when interphase transport effects are considered. Table 3 gives a survey of experimental criteria for the estimation of interphase transport effects. The most general relationship here is criterion 4. However, again it may be suggested that the separate isothermicity criterion 5 be used first, and... 

Table 3. Experimental diagnostic criteria for the absence of interphase, and combined intraparticle and interphase transport effects in twipip irreversible reactions (power law kinetics only). ...

Table 4 summarizes a number of well-known theoretical diagnostic criteria for the estimation of intraparticle transport effects on the observable reaction rate. Tabic 5 gives a survey of the respective criteria for interphase transport effects. It is quite obvious that these are more difficult to use than the simple experimental criteria given in Tables 2 and 3. In general, the intrinsic rate expression has to be specified and, additionally, either the first derivative of the intrinsic rate with respect to concentration (and temperature) at surface... 

In this type of three-phase catalytic reactor, centrifugal force is employed to vary the hydrodynamics and transport characteristics of the conventional gas-liquid-solid reactor. Interphase transport of momentum and mass in such a reactor is governed by the centrifugal forces. Dudukovic and co-... 

The above discussion demonstrates the multifaceted nature of spillover. The interphase transport of an activated species onto a surface (and sometimes into the bulk) where it is unable to be formed without the activator can induce a variety of changes on, and reactions with, the surface. All the reactions of atomic hydrogen are found to be induced by spillover exchange, bronze formation, reduction, demethoxylation, and catalytic activation. An activated species is able to gain indirect access to the nonsorbing surface. 

It is worth emphasizing that Eqs. (13-61) to (13-68) hold regardless of the models used to calculate the interphase transport rates and EJ. With a mechanistic model of sufficient complexity it is possible, at least in principle, to account for mass transfer from bubbles in the froth on a tray as well as to entrained droplets in a spray, as well as transport between the phases flowing over and through the elements of packing in a packed column. However, a completely comprehensive model for estimating mass-transfer rates in all the possible flow regimes does not exist at present, and simpler approaches are used. 

In the K-L model, reaction occurs within the bed s phases, and material is continuously transferred between the phases. Two limiting situations thus arise. In one, the interphase transport is relatively fast and transport equilibrium is maintained, causing the system performance to be controlled by the rate of reaction. In the other, the reaction rate is relatively fast and the performance is controlled by interphase transport. It will be shown that the ammonia oxidation example used above is essentially a reaction-limited system. 

The overall effectiveness factor is actually comprised of the individual effectiveness factors for intraphase and interphase transport ... 

Development of Specific Sub-models Reaction sources. Physical properties Interphase transport. Boundary condition ... 

The sources of interphase transport, Sk and Sh, can be formulated by considering particle-level phenomena, which will be of interest to the reactor engineers such as ... 

With this approach, even the dispersed phase is treated as a continuum. All phases share the domain and may interpenetrate as they move within it. This approach is more suitable for modeling dispersed multiphase systems with a significant volume fraction of dispersed phase (> 10%). Such situations may occur in many types of reactor, for example, in fluidized bed reactors, bubble column reactors and multiphase stirred reactors. It is possible to represent coupling between different phases by developing suitable interphase transport models. It is, however, difficult to handle complex phenomena at particle level (such as change in size due to reactions/evaporation etc.) with the Eulerian-Eulerian approach. 

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