Mass transfer coefficients estimation

This part of Sec. 5 provides a concise guide to solving problems in situations commonly encountered by chemical engineers. It deals with diffusivity and mass-transfer coefficient estimation and common flux equations, although material balances are also presented in typical coordinate systems to permit a wide range of problems to be formulated and solved. 

The binary mass transfer coefficients estimated from these correlations and analogies are the low flux coefficients and, therefore, need to be corrected for the effects of finite transfer rates before use in design calculations. 

Although the method of Bravo and Fair makes use of Onda s equations for k and k, it should be noted that the liquid-phase mass transfer coefficients estimated from the two procedures will be different since Eq. 12.3.29 for k depends on the interfacial area density (through the liquid-phase Reynolds number). 

Figure 11 shows the effect of the volumetric mass transfer coefficient estimated by the simulation in SBCR without liquid circulation. Methanol production increases 6.5 mol/kgcat-hr for the volumetric mass transfer coefficient of 0.75 and then the methanol production is no longer limited by volumetric mass transfer coefficient. This trend matched with that given in the Viking (10) report. The estimated volumetric mass transfer coefficient has a good agreement with experimental values shown in literatures (10, 43, and 44). 

The kinetic theory model was extended to include the effect of the mass transfer coefficient between the liquid and the gas and the water gas shift reaction in the slurry bubble column reactor. The computed granular temperature was around 30 cm /sec and the computed catalyst viscosity was closed to 1.0 cp. The volumetric mass transfer coefficient estimated by the simulation has a good agreement with experimental values shown in the literature. The optimum particle size was determined for maximum methanol production in a SBCR. The size was about 60 - 70 microns, found for maximum granular temperature. This particle size is similar to FCC particle used in petroleum refining. 

Similar discrepancies were noted by Blatt et al32 for colloidal suspensions such as skimmed milk, casein, polymer latexes, and clay suspensions. Actual ultrafiltration fluxes are far higher than would be predicted by the mass transfer coefficients estimated by conventional equations, with the assumption that the proper diffusion coefficients are the Stokes-Einstein diffusivities for the primary particles. Blatt concluded that either (a) the "back diffusion flux" is substantially augmented over that expected to occur by Brownian motion or (b) the transmembrane flux is not limited by the hydraulic resistance of the polarized layer. He favored the latter possibility, arguing that closely packed cakes of colloidal particles have quite high permeabilities. However, this is not a plausible hypothesis for the following reasons ... 

Using Dextran for mass transfer coefficient estimation probably results in an overestimate of concentration polarisation, due to the larger size of Dextran compared to humic substances and calcium. However the diffusion characteristics of humic acid, calcium-humate complexes, and even calcium in the highly viscous boundary layer are not known, and Dextran is probably a conservative assumption. Corrections for calcium and HA (molecular weight 1 and 10 kDa) were performed using... 

The reason for this is the higher concentration of large molecular weight compounds in the boundarjf layer, which is evident from mass transfer coefficient estimations. The ks increases significantly with a decreasing size of the solute, and, therefore, the concentration polarisation in the boundary layer is significantly lower for smaller compounds. 

Volumetric mass transfer coefficient estimated with the empirical equation (Equation 7.14) [26] ... 

Table 2.6 Relationships between structure features and mass transfer coefficient estimated for commercial polymeric membranes...

Gas mixing in laboratory internal recycle reactors used for gas-solid catalytic studies may be assessed from pressure drop (Berty, 1974 Berty, 1979), temperature drop measurements across the bed (Mahoney, 1984), or from mass transfer coefficient estimations (Caldwell, 1983). For a given impeller speed, the first method involves comparing the bed pressure drop of the recycle reactor v/iih pressure drop of a calibrated fixed catalyst bed conducted in a separate unit. Then knowing the fluid velocity versus pressure drop for the calibrated bed, the impeller speed versus fluid velocity can be drawn. The recycle rate can also be determined from thermodynamics based on the ratio of the adiabatic temperature change and the measured temperature difference. This method requires the measurements of temperatures across the bed and the mass flow rate. 

Microreactors proved to be much more eflicient for the phase transfer reactions (23). The two-phase reactions proceed on the phase boundary. As a result of mass transfer coefficient estimation, it can be ascertained that the application of microtechnology for the two-phase liquid reactions promotes instantaneous mixing and intensifies the interfusion of reagents, which is not to be assumed in standard reactors. By slow reactions due to increase in interfacial area, the reaction can be shifted from diffusion to kinetic control. Thus, Dan C 1, which means that there is no mass transfer limitation and the plug flow reactor model can be used to describe such a reaction (see Section 12.2). 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ji is an apparent value because it is determined on the basis of an uncorrected. A tme volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

To estimate the slumping motion of the kiln bed which periodically exposes a fresh, vapor saturated surface at the bed—freeboard interface must be considered. Based on Pick s second law in a bed of porosity, S, and for an effective diffusion coefficient, the mass-transfer coefficient on the bed side is... 

For consistency, clearance here is expressed in cm /s although the more common clinical units, and those used later in this chapter, are ml,/min. Combination and rearrangement of equations 6—8 allows clearance to be estimated from mass-transfer coefficient and vice versa the conditions of countercurrent flow with no dialysate recycling are shown below. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Estimation of for Irreversible Reactions Figure 14-14 illustrates the influence of either first- or second-order irreversible chemical reactions on the mass-transfer coefficient /cl as developed by Van Krevelen and Hoftyzer [Rec. Trav. Chim., 67, 563 (1948)] and as later refined by Periy and Pigford and by Brian et al. [Am. Inst. Chem. Eng. /., 7, 226(1961)]. 

External mass-transfer coefficients for particles suspended in agitated contactors can be estimated from equations in Levins and Glastonbury [Trans. Instn. Chem. E/ig., 50, 132 (1972)] and Armenante and Kirwan [Chem. Eng. ScL, 44, 2871 (1989)]. 

Dl = diffusivity of transferring solute in liquid, m /sec If the diffusivity, Dl, needed for use in the above equations is not known, it can be estimated from data or methods given in the Perry s Chemical Engineers, Handbook (Section 14 in 4th Edition or Section 3 in 5th Edition). Note that the calculation of the mass transfer coefficients for a given regime involves only physical properties and is independent of agitation conditions. 

Correlations for estimating overall mass-transfer coefficients can be found in McCabe et al. (1993), Perry and Green (1984), Geankoplis (1983), Henley and Seader (1981), King (1980) and Treybal (1980). 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

The cooling duty can be provided by either making the draught tube an internal heat exchanger or with a heat exchanger in an external circulation loop. The mass transfer coefficient for external loop airlift Fermenter is estimated as 8... 

Because the mechanisms governing mass transfer are similar to those involved in both heat transfer by conduction and convection and in momentum transfer (fluid flow), quantitative relations exist between the three processes, and these are discussed in Chapter 12. There is generally more published information available on heat transfer than on mass transfer, and these relationships often therefore provide a useful means of estimating mass transfer coefficients. 

There have been comparatively few experimental studies in this area and the results of different workers do not always show a high degree of consistency. Frequently, estimates of mass transfer coefficients have been made by applying the analogy between heat transfer and mass transfer, and thereby utilising the larger body of information which is available on heaL transfer. 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

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