Flow rates mass transfer correlations

The mass-transfer zone width and shape depends on the adsorption isotherm, flow rate, mass-transfer rate to the particles, and diffusion in the pores. A number of theoretical methods have been published which predict the mass-transfer zone and concentration profiles in the bed. The predicted results may be inaccurate because of many uncertainties due to flow patterns and correlations to predict diffusion and mass transfer. Hence, experiments in laboratory scale are needed in order to scale up the results. 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

The measurement of liquid side gas - liquid mass transfer coefficient kia, showed that the value of kia increase with increasing rotation speed (V) and gas flow rate (Qg). hi the present research, the effect of impeller rotation on mass transfer coefficient was more significant than the effect of gas flow rate. The following correlation was obtained kia =1.7 x 10 ... 

This article presents a brief account of theory and practical aspects of rotating hemispherical electrodes. The fluid flow around the RHSE, mass transfer correlations, potential profile, and electrochemical application to the investigations of diffusivity, reaction rate constants, intermediate reaction products, passivity, and AC techniques are reviewed in the following sections. 

Since dissolved gas concentrations in the liquid phase are more difficult to measure experimentally than the liquid reactant concentration, Equation 8 evaluated at the reactor exit 5=1 represents the key equation for practical applications involving this model. Nevertheless, the resulting expression still contains a significant number of parameters, most of which cannot be calculated from first principles. This gives the model a complex form and makes it difficult to use with certainty for predictive purposes. Reaction rate parameters can be determined in a slurry and basket-type reactor with completely wetted catalyst particles of the same kind that are used in trickle flow operation so that DaQ, r 9 and A2 can be calculated for trickle-bed operation. This leaves four parameters (riCE> St gj, Biw, Bid) to be determined from the available contacting efficiency and mass transfer correlations. It was shown that the model in this form does not have good predictive ability (29,34). 

Closure. After completing this chapter, the reader should be able to define and describe molecular diffusion and how it varies with temperature and pressure, the molar flux, bulk flow, the mass transfer coefficient, the Sherwood and Schmidt numbers, and the correlations for the mass transfer coefficient. The reader should be able to choose the appropriate correlation and calculate the mass transfer coefficient, the molar flux, and the rate of reaction. The reader should be able to describe the regimes and conditions under which mass transfer-limited reactions occur and when reaction rate limited reactions occur and to make calculations of the rates of reaction and mass transfer for each case. One of die most imponant areas for the reader apply the knowledge of this (and other chapters) is in their ability to ask and answer "What if. , questions. Finally, the reader should be able to describe the shrinking core model and apply it to catalyst regeneration and pharmacokinetics. 

SCALE-UP. The width of the mass-transfer zone depends on the mass-transfer rate, the flow rate, and the shape of the equilibrium curve. Methods of predicting the concentration profiles and zone width have been published, but lengthy computations are often required, and the results may be inaccurate because of uncertainties in the mass-transfer correlations. Usually adsorbers are scaled up from laboratory tests in a small-diameter bed, and the large unit is designed for the same particle size and superficial velocity. The bed length need not be the same, as shown in the next section. 

A few measurement and assumption issues are built into the existing correlations. Gas-liquid mass transfer correlations, which are calculated at high gas flow rates, may be 15% lower than the system experiences because an incorrect assumption of ideal phase mixing is often made (Blazej et al., 2004b). A further problem is that a normal bubble size distribution is often assumed in the analysis, but the truth of this or any other assumption has not been thoroughly verified (Fadavi et al., 2008). 

Although pressure drop correlations follow the Ergun equation, the high porosity gives much lower pressure drop than equivalent beds of particles. Mass transfer follows standard correlations but turbulent flow is seen at much lower flow rates. Heat transfer is enhanced by the superior conductivi of the web structure. These feature combine to make ceramic foams attractive possibilities for many applications. The only disadvantage is the relatively low strength, a feature which may be controlled in some cases. 

Mass transfer correlations from liquid to solids are based on total interfacial area of the solids. Hence, the correlations include partial wetting effects. As expected, the mass transfer coefficient increases with Increasing liquid flow rate. It is somewhat insensitive to the gas flow rate. The sensitivity to the gas rate increases in the pulse and dispersed bubble regime. 

One of the most accepted mass transfer correlations gives values of 0.0165, 0.86, and 0.33 for respectively, a, p, and / for fully developed turbulent flow in smooth pipes [27 28]. The Sherwood number represents the ratio of total mass transport to diffusion mass transport (D). Sh can therefore be directly related to corrosion rates ([29]) and it can be expressed in terms of the mass transfer coefficient with Eq. (6.5) ... 

All of these flooding data were based purely on hydraulic flow data with no mass transfer of solute occurring. The extrapolation of Figure 11-7, or its use outside the range of applicable physical properties, should be done with considerable caution. If the continuous phase velocity (Vq) is less than 40 ft/h, efficiency of mass transfer can be reduced. Likewise, as the dispersed phase velocity (Vq) is increased, the holdup of dispersed phase increases until coalescence occurs with loss of interfacial area. Regardless of the allowable flow rate from the correlation, the dispersed phase velocity should be limited to 200 ft/h. 

Convection mass transfer coefficients are often used as convective boundary conditions for gas diffusion in a stationary media. However, while applying mass transfer correlations to describe mass species transport from the electrode-gas diffusion layer to gas flow stream in the channel, it is assumed that species mass transport rate at the wall is small and does not alter the hydrod5mamic, thermal, and concentration boundary layers like in boundary layers with wall suction or blowing. 

Solution The variation of reaction rate with flow indicates that the process is controlled by diffusion outside of particle. By inference, the resistance of any ash formed is apparently negligible. At the same time, the variation of particle radius with time is in the range suggested by case B in Table 16.4-1 checking this point further requires using a mass transfer correlation in fluid beds parallel to Eq. 16.4-6. Although no dependence on temperature is mentioned, we would expect this dependence to be small. 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Flow Reactors Fast reactions and those in the gas phase are generally done in tubular flow reaclors, just as they are often done on the commercial scale. Some heterogeneous reactors are shown in Fig. 23-29 the item in Fig. 23-29g is suited to liquid/liquid as well as gas/liquid. Stirred tanks, bubble and packed towers, and other commercial types are also used. The operadon of such units can sometimes be predicted from independent data of chemical and mass transfer rates, correlations of interfacial areas, droplet sizes, and other data. 

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. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

Some performance data of plants with DEA are shown in Table 23-11. Both the absorbers and strippers have trays or packing. Vessel diameters and allowable gas and liquid flow rates are estabhshed by the same correlations as for physical absorptions. The calciilation of tower heights utilizes data of equilibria and enhanced mass-transfer coeffi-... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

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