Molar rate of mass transfer

The molar rate of mass transfer from the bulk fluid to the external surface is... 

This molar rate of mass transfer to the surface, is equal to the net (total) rate of reaction on and within the pellet ... 

On the basis of each of the theories discussed, the rate of mass transfer in the absence of bulk flow is directly proportional to the driving force, expressed as a molar concentration difference, and, therefore ... 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

Chemical equilibrium constant for dimerization Liquid-liquid distribution ratio Liquid flow rate Number of equilibrium stages Number of relationships Number of design variables Minimum number of equilibrium stages Number of phases Number of repetition variables Number of variables Rate of mass transfer Molar flux... 

Rates of mass transfer to the catalyst surface and pore diffusion can be calculated by the methods of Section 2.2.2 if the diffusion coefficients are known. However, the molecular theory of diffusion in liquids is relatively undeveloped and it is not yet possible to treat diffusion in liquids with the same rigour as diffusion in gases. The complicating factors are that the diffusion coefficient varies with concentration and that the mass density is usually more constant than the molar density of the solution. An empirical equation, due to Wilke and Chang, which applies in dilute solution, gives... 

The course of reactions is determined by events at the molecular scale, whether or not the reactive molecules are in the liquid, solid, or gas phase when they enter the reaction zone. As in the case of homogeneous reactions, the course of a complex reaction will be determined by local molar ratios and chemical kinetics. The degree of deviation from expected kinetic behavior is determined by the reaction rate relative to the rates of mass transfer and mixing. Possible mixing... 

Revise the analysis of Example 11.5.3 and show how a method based on the film models of Chapter 8 could be used to compute the rates of mass transfer. Then use the Krishna-Standart method (of Sections 8.3 and 8.8.3) and compute the molar fluxes. Binary pair mass transfer coefficients may be estimated using the Chilton-Colburn analogy. 

The overall molar balance we used will not be adequate because the equilibrium relation between the two phases cannot be used. In the present case of nonequilibrium stages, we must introduce the mass transfer rate between the two phases, as shown in Figure 6.18. In the figure, the term RMT is the rate of mass transfer of the component A from the vapor phase. It can be expressed as,... 

Packed-bed absorption towers are distributed systems and Figure 6.19 shows the molar flow rates across a small element A/ of one of these towers. We consider the absorption of component A from the gas (vapor) phase to the liquid phase. The rate of mass transfer from the vapor phase to the liquid phase is given by the relation... 

Profile of q, z) at the end of the other step must be employed as an initial condition for each step. In Eqs. (11-32) and (11-36) an LDF model with partial pressure difference as a driving force is used, uho and Ulo are molar flow rates of the inert component in the adsorption and desorption steps, where total pressures are P and Pt. N,h and N,x represent the rates of mass transfer of component i between particle and fluid at the adsorption step and at the desorption step expressed in terms of linear driving force (LDF) model by taking the partial pressure difference or difference in amount adsorbed as the driving force of mass transfer. 

Applying mass transfer theory to a component / in the liquid, assumint good mixing and neglecting atmospheric concentrations, the evaporation molar rate of a single component can be expressed as... 

In distillation, equimolecular counterdiffusion takes place if the molar latent heats of the components are equal and the molar rate of flow of the two phases then remains approximately constant throughout the whole height of the column. In gas absorption, however, the mass transfer rate is increased as a result of bulk flow and, at high concentrations of soluble gas, the molar rate of flow at the top of the column will be less than that at the bottom, At low concentrations, however, bulk flow will contribute very little to mass transfer and, in addition, flowrates will be approximately constant over the whole column. 

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. 

The balance is made with respect to a control volume which may be of finite (V) or of differential (dV) size, as illustrated in Figure 1.3(a) and (b). The control volume is bounded by a control surface. In Figure 1.3, m, F, and q are mass (kg), molar (mol), and volumetric (m3) rates of flow, respectively, across specified parts of the control surface,6 and Q is the rate of heat transfer to or from the control volume. In (a), the control volume could be the contents of a tank, and in (b), it could be a thin slice of a cylindrical tube. 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

In various studies on molar mass regulation by variation of the amount of cocatalyst different interpretations concerning the rate of chain transfer between Mg, A1 and Zn on one hand and Nd on the other hand are given. Detailed kinetic studies on the complex molar mass regulation processes between Nd centers and the cocatalyst are still lacking. What are the relative rates of chain transfer and chain propagation ... 

Point efficiency is usually discussed in terms of the two-film theory. The theory postulates resistances to mass transfer in both the vapor and liquid films near a vapor-liquid ihterface (Fig. 7.2a). The molar rate of diffusion, N (moles/s), is given by... 

Large quantities of liquefied natural gas (LNG) are shipped by ocean tanker. At the miloading port provision is made for vaporization of the LNG so that it may be delivered to pipelines as gas. The LNG arrives in tlie tanker at atmospheric pressure and 77i.7 K, and represents a possible heat sink for use as the cold reservoir of a heat engine. For unloading of LNG as a vapor at the rate of 9000 ni s . as measured at 298.15 (25°C) and 1.0133 bar, and assuming tlie availability of an adequate heat source at 303.15 K (30°C), what is tlie maximum possible power obtainable and what is the rate of heat transfer from the heat source Assume that LNG at 298.15 K (25°C) and 1.0133 bar is an ideal gas with the molar mass of 77. Also assume that the LNG vaporizes only, absorbing only its latent heat of 512 kJ kg at 113.7 K. 

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