Calculation of Mass Transfer Parameters

For designing the large-scale reactor, it is required to establish the controlling step. As outlined in Chapter 1, for this solid-catalyzed gas-liquid reaction, there are three resistances in series (1) gas-liquid mass transfer, (2) solid-liquid mass transfer, and (3) reaction at the catalyst surface. The detailed calculation procedure and equations used are given in the following section. The catalyst loading to be used is 20wt.%. 

STEP i GAS HOLDUP, s, AT THE OPERATING CONDITIONS The Correlation proposed by Inga and Morsi (1999) is appropriate for the present case since it has been derived using conditions representative of F-T synthesis  

STEP 2 CALCULATION OF A receut correlation provided by Behkish et al. 

STEP 3 ESTIMATION OF The Correlation proposed by Jadhav and Pangarkar (1991) is used to calculate 

STEP 4 Estimation of Relative Rates of the Various Steps CO, which has a lower diffusivity than H, diffuses slower, and hence, it is the rate-limiting component in the diffusion process across the gas-liquid and solid-liquid films. The solubility of CO, [ l ]co the C28 hydrocarbon liquid is 55 gmol/m (Marano and Holder 1997). 

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The surface tension is important for the calculation of mass transfer coefficients and the specific contact area (see Section 9.4.4). Depending on the availability of necessary parameters, the surface tension for a molecular species can be determined either with the simplest method of Hakim-Steinberg-Stiel or with a more complex DIPPR-method (see Ref. [52]). The mixture surface tension can be obtained via a mixing rule. A further extension to cover electrolyte mixtures is realized by the method of Onsager and Samaras (see Ref. [44]). The latter uses an additive term which can be estimated using the dielectric constant of the mixture and molar volumes of electrolytes. 

Two dimensionless variables play key roles in the analysis of single transition systems (and some multiple transition systems). These are the throughput parameter [see Eq. (16-129)] and the number of transfer units (see Table 16-13). The former is time made dimensionless so that it is equal to unity at the stoichiometric center of a breakthrough cui ve. The latter is, as in packed tower calculations, a measure of mass-transfer resistance. 

The plot of the rate of disappearance of CO per volume of liquid in the serum bottles versus partial pressure of CO in the gas phase based on (3.14.4.14) could give the constant slope value of KLa/H. Henry s constant is independent of the acetate concentration but it is only dependent on temperature. The overall volumetric mass transfer coefficient can be calculated based on the above assumption. The data for various acetate concentrations and different parameters were plotted to calculate the mass transfer coefficient. 

Strangely, Reaction 25.2 proceeds backward in the early part of the calculation (Fig. 25.1), producing a small amount of potassium feldspar at the expense of muscovite and quartz. This result, quite difficult to explain from the perspective of mass transfer, is an activity coefficient effect. As seen in Figure 25.2, the activity coefficient for K+ increases rapidly as the fluid is diluted over the initial segment of the reaction path, whereas that for H+ remains nearly constant. (The activity coefficients differ because the a parameter in the Debyc-IIuckcl model is 3 A for K+ and 9 A for H+.) As a result, aK+ increases more quickly than aH+, temporarily driving Reaction 25.2 from right to left. 

Reactor Model. The design of an industrial packed-bed reactor requires a reactor model as well as the chemical and the heat and mass transfer parameters of the catalyst bed - gas stream system. Since these parameters are model-specific, it seemed advisable to employ a continuum model for the reactor calculation. This is the only model to date for which the literature contains consistent data for calculating heat and mass transfer parameters (5,6,7). This model in its... 

The kinetic parameters reported in Table 1 was applied to calculate the mean value of activity of the catalyst in two industrial reactors to simulate their performance. The mass-transfer parameters of the bubble columnns were calculated using semiempirical equations [5,6], The physical constant values are reported in previous works [1,2]. 

The value of the mass transfer parameter ki for fluids flowing through tubes in laminar flow may be calculated from the Leveque equation, neglecting the influence of the concentration changes along the HF [46]... 

The absorption rate I>(e) (in gm moles/sec or cm /sec of component A), is measured experimentally, and Q 6)l6 is calculated for different kinetic regimes from the Higbie theory. The contact time 6, calculated from Eq. (86), can be altered by altering and the geometric parameters of the equipment. Thus, by carrying out experiments with the same chemical systems and with the same kinetic regime used to determine mass-transfer parameters in the industrial gas-liquid reactor, I>(6) can be determined as a function of 6 in the laboratory equipment and the variations of Q(6) = 6 6)/Am for different values of 6 serve to determine the parameters. 

Then a and By were optimized to minimize the percent absolute average relative deviation (% AARD) between the calculated solubility and the experimental solubilty measured here, and the experimental solubilities at 35 C reported by Tsekhanskaya et al. (11) and by McHugh and Paulaitis (12), The equilibrium solubilities of naphthalene in CO2 used to calculate the mass transfer coefficients are given in Table IL The optimized values of ay, By, and %AARD are 0.0402, 6.5384 and 9.23 respectively. Prediction of the solubility with these two optimized parameters is given in Figure 2 with data of Tsekhanskaya et al. (Ij, McHugh and Paulaitis (12) and our experimental solubility data (below the critical pressure). 

Peak profiles can be calculated with a proper column model, the differential mass balance equation of the compound(s), the adsorption isotherm, the mass transfer kinetics of the compound(s) and the boundary and initial conditions [13], When a suitable column model has been chosen, the proper parameters (isotherm and mass transfer parameters and experimental conditions) are entered into the calculations. The results from these calculations can have great predictive value [13, 114], The most important of the column models are the ideal model , the equilibrium-dispersive (ED) model , the... 

The calculated values of the mass transfer parameters for both the flow models with the results of the situations 1 and 3 are shown. 

Several drawbacks are connected to the application of the surfactant concentration as the parameter controlling ELM stability. The first one originates from the increasing swelling of the ELM with increasing surfactant concentration, due to increasing affinity for water [76]. If the ELM is prepared from a Newtonian liquid, then the second major drawback is the decrease in the rates of mass transfer inside the ELM, due to an increase in the viscosity of the ELM [77]. If the LM is prepared from a non-Newtonian liquid, then the diffusion coefficient of the extracted solute is virtually independent ofthe membrane viscosity [78, 79], below the critical concentration [80]. This concentration can be calculated from Eq. (5), as derived by SkeUand and Meng [81]. 

The determination of the real surface area of the electrocatalysts is an important factor for the calculation of the important parameters in the electrochemical reactors. It has been noticed that the real surface area determined by the electrochemical methods depends on the method used and on the experimental conditions. The STM and similar techniques are quite expensive for this single purpose. It is possible to determine the real surface area by means of different electrochemical methods in the aqueous and non-aqueous solutions in the presence of a non-adsorbing electrolyte. The values of the roughness factor using the methods based on the Gouy-Chapman theory are dependent on the diffuse layer thickness via the electrolyte concentration or the solvent dielectric constant. In general, the methods for the determination of the real area are based on either the mass transfer processes under diffusion control, or the adsorption processes at the surface or the measurements of the differential capacitance in the double layer region [56],... 

The analysis of initial rate data is useful in understanding the dependency of the reaction rate on individual reaction parameters and also in the evaluation of mass transfer effects. Initial rates of hydrogenation were calculated from the experimentally observed H2 consumption in the reservoir vessel vs time data. The initial rate data observed are presented in Table 3. The effects of individual parameters on the initial rate are dicussed below. 

Reaction kinetics represented by the general form of Equation 1 have been employed in a number of quantitative chemical models of natural systems. Under ideal conditions, the four parameters, total mass transfer, kinetic rate constants, time, and the reactive surface area can be determined independently, permitting the unique definition of the model. In most cases, at least one of the variables, most often surface area, is treated as a dependent term. This nonuniqueness arises when the reactive surface area of a natural system cannot be estimated, or because such estimates made either from geometric or BET measurements do not produce reasonable fits to the other parameters. Most often the calculated total mass transfer significantly exceeds the observed transfer based on measured aqueous concentrations. 

Now while those equations seem to go on and on, they essentially represent the simple combinations of reaction and mass transfer parameters that will either be known for the system (various k ) or that can be calculated (mass-transfer coefficients). Overall there are 22 separate reaction and mass-transfer steps represented in this... 

Simple experimental methods are discussed in this chapter for determination of the key equilibrium and heat and mass transfer parameters need in engineering calculations for common dryers. The coverage is by no means all-inclusive. The reader is referred to the literature cited for details. 

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