Surface mass transfer resistance

Figure 3 shows that beyond 750 rev/min for the hydrolysis (curve A) and beyond S(X)rev/min for oxidation the speed (curve B) had no effect on conversion and hence on the rates of reaction, thereby indicating absence of liquid-to-membrane surface mass transfer resistance both inside and outside the capsules. The reaction could be taken as kinetically controlled and governed by eq.(5) beyond the said speeds in each case. This was further confirmed by studying the effect of temperature and the values of activation energies, which will be discussed later. Since the capsules were well dispersed in the agitated outer phase the bulk concentration of benzyl chloride within a capsule would be uniform. Further experiments were conducted beyond these speeds which were safe to maintain the fidelity of the capsules. 

Figure 13. Influence of the surface mass transfer resistance on the progress of carhonation under accelerated condition.

A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. 

As an example, it may be supposed that in phase 1 there is a constant finite resistance to mass transfer which can in effect be represented as a resistance in a laminar film, and in phase 2 the penetration model is applicable. Immediately after surface renewal has taken place, the mass transfer resistance in phase 2 will be negligible and therefore the whole of the concentration driving force will lie across the film in phase 1. The interface compositions will therefore correspond to the bulk value in phase 2 (the penetration phase). As the time of exposure increases, the resistance to mass transfer in phase 2 will progressively increase and an increasing proportion of the total driving force will lie across this phase. Thus the interface composition, initially determined by the bulk composition in phase 2 (the penetration phase) will progressively approach the bulk composition in phase 1 as the time of exposure increases. 

When the mass transfer resistance within the particle is significant, a concentration gradient of reactant is established within the particle, with the concentration, and hence the reaction rate, decreasing progressively with distance from the particle surface. The overall reaction rate is therefore less than that given by equation 10.195. 

When the resistance to mass transfer to the external surface of the pellet is significant compared with that within the particle, part of the concentration driving force is required to overcome this external resistance, and the concentration of reacting material at the surface of the pellet Cm is less than that in the bulk of the fluid phase Cao- In Sections 10.7.1-10.7.3, the effect of mass transfer resistance within a porous particle... 

When there is an external mass transfer resistance, the value of C i (the concentration at the surface of the particle) is less than that in the bulk of the fluid (Cao) and will not be known. However, if the value of the external mass transfer coefficient is known, the mass transfer rate from the bulk of the fluid to the particle may be expressed as ... 

If a concentration gradient exists within a fluid flowing over a surface, mass transfer will take place, and the whole of the resistance to transfer can be regarded as lying within a diffusion boundary layer in the vicinity of the surface. If the concentration gradients, and hence the mass transfer rates, are small, variations in physical properties may be neglected and it can be shown that the velocity and thermal boundary layers are unaffected 55. For low concentrations of the diffusing component, the effects of bulk flow will be small and the mass balance equation for component A is ... 

For the case where there is a mass transfer resistance in the fluid external to the particle (mass transfer coefficient hn), express the mass transfer rate in terms of the bulk concentration C , rather than the concentration Cts at the surface of the particle. 

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

It is possible to eliminate the mass transfer resistances in Steps 2, 3, 7, and 8 by grinding the catalyst to a fine powder and exposing it to a high-velocity gas stream. The concentrations of reactants immediately adjacent to the catalytic surface are then equal to the concentrations in the bulk gas phase. The resulting kinetics are known as intrinsic kinetics since they are intrinsic to the catalyst surface and not to the design of the pores, or the pellets, or the reactor. 

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

For future studies on MOF-based slurry systems, there is basic selection of criteria that needs to be satisfied by both MOF and the liquid solution. The selection of the MOF possessing the appropriate pore size for the preparation of the slurry system is very important to guarantee that the size of the liquid is large enough and does not occupy the pores which leaves no space for C02 to adsorb. Moreover, the structural stability of the MOF in the aqueous solution is essential so that it does not lose its porous framework nor its surface area. The selection of the liquid candidate is crucial, as it should not provide any extra mass transfer resistance for C02 molecules. Further, experimental and computational investigations are still required to understand the separation mechanism in slurry mixtures and to have insight into the different types of interactions between the gas, liquid, and solid materials. 

Practical Aspects There are a number of process-specific concerns that are accounted for in good design. In regenerate systems, sorbents age, losing capacity because of fouling by heavy contaminants, loss of surface area or crystallinity, oxidation, and the like. Mass-transfer resistances may increase over time. Because of particle shape, size distribution, or column packing method,... 

A kinetics or reaction model must take into account the various individual processes involved in the overall process. We picture the reaction itself taking place on solid B surface somewhere within the particle, but to arrive at the surface, reactant A must make its way from the bulk-gas phase to the interior of the particle. This suggests the possibility of gas-phase resistances similar to those in a catalyst particle (Figure 8.9) external mass-transfer resistance in the vicinity of the exterior surface of the particle, and interior diffusion resistance through pores of both product formed and unreacted reactant. The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius A at a particular instant of time, in terms of the general case and two extreme cases. These extreme cases form the bases for relatively simple models, with corresponding concentration profiles for A and B. 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

Heterogeneously catalyzed hydrogenation is a three-phase gas-liquid-solid reaction. Hydrogen from the gas phase dissolves in the liquid phase and reacts with the substrate on the external and internal surfaces of the solid catalyst Mass transfer can influence the observed reaction rate, depending on the rate of the surface reaction [15]. Three mass transfer resistances may be present in this system (Fig. 42.1) ... 

The mass transfer coefficient describes the effect of mass transfer resistance of the reactants flowing from the gas phase to the surface of the individual particles in the bed. The mass transfer coefficient can be obtained from a correlation for the Sherwood number (or dimensionless mass transfer coefficient) given by Eq. (7) ... 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

Simple sublimation is a batch-wise process in which the solid material is vaporised and then diffuses towards a condenser under the action of a driving force attributable to difference in partial pressures at the vaporising and condensing surfaces. The vapour path between the vaporiser and the condenser should be as short as possible in order to reduce mass-transfer resistance. Simple sublimation has been used for centuries, often in very crude equipment, for the commercial production of ammonium chloride, iodine, and flowers of sulphur. 

The signal generated by the complex is governed by several physical phenomena associated with the matrix thickness. As soon as the probe is placed in contact with the analyte, external mass transfer controls the movement of the analyte toward the surface of the optical probe.(S4) The osmotic pressure and Gibbs free energy dictate the permeation of the analyte into the matrix. Once the analyte has penetrated the matrix, internal mass transfer resistance controls the movement of the analyte in the matrix. Eventually, the probe reaches a steady state of equilibrium with molecules continuously moving in and out of the matrix. 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

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