Rate factors mass transfer

Rate Equations with Concentration-Independent Mass Transfer Coefficients. Except for equimolar counterdiffusion, the mass transfer coefficients appHcable to the various situations apparently depend on concentration through thej/g and factors. Instead of the classical rate equations 4 and 5, containing variable mass transfer coefficients, the rate of mass transfer can be expressed in terms of the constant coefficients for equimolar counterdiffusion using the relationships... 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

It has been observed that under reaction conditions mass transfer is often significantly faster than would be expected based on the film model. This is modelled by introducing an enhancement factor, E. In case the concentration in the bulk liquid, ca, is zero, the rate of mass transfer of A now becomes ... 

The derivation and experimental verification of the MMHS model represented a significant accomplishment and a natural plateau for film models. To be sure, there are general criticisms of film models and more specific criticisms of the MMHS model [6], However, overall the MMHS model should be recognized as a robust but simply applicable model which serves to demonstrate how factors such as intrinsic solubility of the acid drug, ionization and pA of the drug, and concentration of the reactive base all contribute to increasing the dissolution rate and mass transfer. 

At steady state the rate of mass transfer must equal the reaction rate and, if one neglects the change in the number of moles on reaction, the drift factor may be taken as unity. Thus... 

Work on the rate of dissolution of regular shaped solids in liquids has been carried out by Linton and Sherwood(1), to which reference is made in Volume 1. Benzoic acid, cinnamic acid, and /3-naphthol were used as solutes, and water as the solvent. For streamline flow, the results were satisfactorily correlated on the assumption that transfer took place as a result of molecular diffusion alone. For turbulent flow through small tubes cast from each of the materials, the rate of mass transfer could be predicted from the pressure drop by using the 1 j-factor for mass transfer. In experiments with benzoic acid, unduly high rates of transfer were obtained because the area of the solids was increased as a result of pitting. 

The rate of mass transfer of a snbstance across a water-gas bonndary is controlled by the diffnsion film model as well. Gas transfer from a water sonrce is faster than from a solid sonrce, and the chemical does not nndergo a chemical reaction during the transfer process. Under these conditions, the interface concentration may be interpreted in terms of the Henry constant (K ), which indicates whether the controlling resistance is in the liqnid or the gas film. When 5, a water film is the controlling factor, while a gas film controls the behavior when K >500. 

It is possible that the pores of wetted catalyst particles eire filled with liquid. Hence, by virtue of the low values of liquid diffusivities (ca. 10 cm s" ), the effectiveness factor will almost certainly be less than unity. A criterion for assessing the importance of mass transfer in the trickling liquid film has been suggested by Satterfield [40] who argued that if liquid film mass transport were important, the rate of reaction could be equated to the rate of mass transfer across the liquid film. For a spherical catalyst particle with diameter dp, the volume of the enveloping liquid fim is 7rdp /6 and the corresponding interfacial area for mass transfer is TTdn. Hence... 

The conclusions we may draw from these results are that, in general, interfacial turbulence will occur, and that it will increase the rate of mass transfer in these otherwise unstirred systems. Monolayers will prevent this turbulence, and theory and experiment are then in good agreement, in spite of spontaneously formed emulsion. There are no interfacial barriers greater than 1000 sec. cm. due to the presence of a mono-layer, though polymolecular films can set up quite considerable barriers. Usually there are no appreciable barriers due to re-solvation however, in the passage of Hg from the liquid metal into water, the change between the metallic state and the Hg2++ (aq) ion reduces the transfer rate by a factor of the order 1000. 

There are two useful measures of the effect of bounding walls on the heat- or mass-transfer rate. A mass transfer factor can be defined based on the same relative velocity between the particle and the fluid ... 

Although HETP is a useful concept, it is an empirical factor. Since plate theory does not explain the mechanism that determines these factors, we must use a more sophisticated approach, the rate theory, to explain chromatographic behavior. Rate theory is based on such parameters as rate of mass transfer between stationary and mobile phases, diffusion rate of solute along the column, carrier gas flowrate, and the hydrodynamics of the mobile phase. 

The rate of mass transfer from fluid to solid in a bed of porous granular adsorbent is made up of several factors in series ... 

The mass transfer factor has also been correlated as a function of the Reynolds number only and thus taking account only of hydrodynamic conditions. If e is the voidage of the packed bed and the total volume occupied by all of the catalyst pellets is Vp, then the total reactor volume is Vp/(l - e). Hence the rate of mass transfer of component A per unit volume of reactor is NASx(l - e)/Vp. If we now consider a case in which only external mass transfer controls the overall reaction rate we have ... 

Alternatively, equation 3.66 may be written in terms of the /-factor. The unknown interface concentration Cm can now be eliminated in the usual way, by equating the rate of mass transfer to the rate of chemical reaction. 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

Complexity in multiphase processes arises predominantly from the coupling of chemical reaction rates to mass transfer rates. Only in special circumstances does the overall reaction rate bear a simple relationship to the limiting chemical reaction rate. Thus, for studies of the chemical reaction mechanism, for which true chemical rates are required allied to known reactant concentrations at the reaction site, the study technique must properly differentiate the mass transfer and chemical reaction components of the overall rate. The coupling can be influenced by several physical factors, and may differently affect the desired process and undesired competing processes. Process selectivities, which are determined by relative chemical reaction rates (see Chapter 2), can thenbe modulated by the physical characteristics of the reaction system. These physical characteristics can be equilibrium related, in particular to reactant and product solubilities or distribution coefficients, or maybe related to the mass transfer properties imposed on the reaction by the flow properties of the system. 

Factors that influence growth of sucrose crystals have been listed by Smythe (1971). They include supersaturation of the solution, temperature, relative velocity of crystal and solution, nature and concentration of impurities, and nature of the crystal surface. Crystal growth of sucrose consists of two steps (1) the mass transfer of sucrose molecules to the surface of the crystal, which is a first-order process and (2) the incorporation of the molecules in the crystal surface, a second-order process. Under usual conditions, overall growth rate is a function of the rate of both processes, with neither being rate-controlling. The effect of impurities can be of two kinds. Viscosity can increase, thus reducing the rate of mass transfer, or impurities can involve adsorption on specific surfaces of the crystal, thereby reducing the rate of surface incorporation. 

During metal-RNa exchange (Fig. 17) the selectivity of the resin for the metals Cu, Ni is always high so that the rate of mass transfer depends only on the concentration factor. The rate versus concentration dependencies is close to linear for these cases (Fig. 17). The small difference in rates for Ni/Na and Cu/Na exchange is due to the difference in difiiisivity of Cu and Ni ions. 

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