Mass transfer scale

This transfer coefficient, which varies inversely with the resistance to mass transfer, scales as the one-half power of the quotient of a, mix and time. Since the... 

Closed models (chemical relaxation) time of mass transport At = 0, scales t and events Models of total equilibrium scales are absent Models of mass transfer scales of t and physicochemical events... 

The G/L mass transfer scales only with and increasing or decreasing... 

Rambhatla, S., Pikal, M. J., 2003. Heat and mass transfer scale up issues during freeze drying, I A typical radiation and the edge vial effect. AAPS Pharm. Sci. Tech. 4-2(14) 1-10. 

In general, the desorptive behavior of contaminated soils and soHds is so variable that the requited thermal treatment conditions are difficult to specify without experimental measurements. Experiments are most easily performed in bench- and pilot-scale faciUties. Full-scale behavior can then be predicted using mathematical models of heat transfer, mass transfer, and chemical kinetics. 

Suspended Particle Techniques. In these methods of size enlargement, granular soHds are produced direcdy from a Hquid or semiliquid phase by dispersion in a gas to allow solidification through heat and/or mass transfer. The feed Hquid, which may be a solution, gel, paste, emulsion, slurry, or melt, must be pumpable and dispersible. Equipment used includes spray dryers, prilling towers, spouted and fluidized beds, and pneumatic conveying dryers, all of which are amenable to continuous, automated, large-scale operation. Because attrition and fines carryover are common problems with this technique, provision must be made for recovery and recycling. 

One goal of catalyst designers is to constmct bench-scale reactors that allow determination of performance data truly indicative of performance in a full-scale commercial reactor. This has been accompHshed in a number of areas, but in general, larger pilot-scale reactors are preferred because they can be more fully instmmented and can provide better engineering data for ultimate scale-up. In reactor selection thought must be given to parameters such as space velocity, linear velocity, and the number of catalyst bodies per reactor diameter in order to properly model heat- and mass-transfer effects. 

Research and development efforts have been directed toward improved ceU designs, theoretical electrochemical studies of magnesium ceUs, and improved cathode conditions. A stacked-type bipolar electrode ceU has been operated on a lab scale (112). Electrochemical studies of the mechanism of magnesium ion reduction have determined that it is a two-electron reversible process that is mass-transfer controUed (113). A review of magnesium production is found ia Reference 114. 

Tank Cells. A direct extension of laboratory beaker cells is represented in the use of plate electrodes immersed into a lined, rectangular tank, which may be fitted with a cover for gas collection or vapor control. The tank cell, which is usually undivided, is used in batch or semibatch operations. The tank cell has the attraction of being both simple to design and usually inexpensive. However, it is not the most suitable for large-scale operation or where forced convection is needed. Rotating cylinders or rotating disks have been used to overcome mass-transfer problems in tank cells. An example for electroorganic synthesis is available (46). 

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. 

A number of factors limit the accuracy with which parameters for the design of commercial equipment can be determined. The parameters may depend on transport properties for heat and mass transfer that have been determined under nonreacting conditions. Inevitably, subtle differences exist between large and small scale. Experimental uncertainty is also a factor, so that under good conditions with modern equipment kinetic parameters can never be determined more precisely than 5 to 10 percent (Hofmann, in de Lasa, Chemical Reactor Design and Technology, Martinus Nijhoff, 1986, p. 72). 

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. 

Selection of Equipment Packed columns usually are chosen for very corrosive materials, for liquids that foam badly, for either small-or large-diameter towers involving veiy low allowable pressure drops, and for small-scale operations requiring diameters of less than 0.6 m (2 ft). The type of packing is selected on the basis of resistance to corrosion, mechanical strength, capacity for handling the required flows, mass-transfer efficiency, and cost. Economic factors are discussed later in this sec tion. 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

Asymptotic Solution Rate equations for the various mass-transfer mechanisms are written in dimensionless form in Table 16-13 in terms of a number of transfer units, N = L/HTU, for particle-scale mass-transfer resistances, a number of reaction units for the reaction kinetics mechanism, and a number of dispersion units, Np, for axial dispersion. For pore and sohd diffusion, q = / // p is a dimensionless radial coordinate, where / p is the radius of the particle, if a particle is bidisperse, then / p can be replaced by the radius of a suoparticle. For prehminary calculations. Fig. 16-13 can be used to estimate N for use with the LDF approximation when more than one resistance is important. 

For other mechanisms, the particle-scale equation must be integrated. Equation (16-140) is used to advantage. For example, for external mass transfer acting alone, the dimensionless rate equation in Table 16-13 would be transformed into the ( — Ti, Ti) coordinate system and derivatives with respect to Ti discarded. Equation (16-138) is then used to replace cfwith /ifin the transformed equation. Furthermore, for this case there are assumed to be no gradients within the particles, so we have nf=nf. After making this substitution, the transformed equation can be rearranged to... 

Ga.s-Lic(uid Ma.s.s Tran.sfer Gas-liqiiid mass transfer norrnallv is correlated bv means of the mass-transfer coefficient K a ersiis powder le el at arioiis superficial gas elocities. The superficial gas clocitv is the ohirne of gas at the a erage temperature and pressure at the midpoint in the tank di ided bv the area of the essel. In order to obtain the partial-pressure dri ing force, an assumption must be made of the partial pressure in equilibrium wdth the concentration of gas in the liquid, Manv times this must be assumed, but if Fig, 18-26 is obtained in the pilot plant and the same assumption principle is used in e ahiating the mixer in the full-scale tank, the error from the assumption is limited. 

Although methanol from synthesis gas has been a large-scale industrial chemical for 70 years, the scientific basis of the manufacture apparently can stand some improvement, which was undertaken by Beenackers, Graaf, and Stamhiiis (in Gheremisinoff, ed., Handbook of Heat and Mass Transfer, vol. 3, Gulf, 1989, pp. 671—699). The process occurs at 50 to 100 atm with catalyst of oxides of Gii-Zn-Al and a feed stream of H2, GO, and GO2. Three reactions were taken for the process ... 

Three criteria for scale-up are that the laboratory and industrial units have the same mass-transfer coefficients /cg and E/cl and the same ratio of the specific interfacial surface and liquid holdup Tables 23-9 and 23-10 give order-of-magnitude values of some parameters that may be expected in common types of liquid/gas contactors. 

Many reactions of solids are industrially feasible only at elevated temperatures which are often obtained by contact with combustion gases, particularly when the reaction is done on a large scale. A product of reaction also is often a gas that must diffuse away from a remaining solid, sometimes through a solid product. Thus, thermal and mass-transfer resistances are major factors in the performance of solid reactions. 

The ROTOBERTY internal recycle laboratory reactor was designed to produce experimental results that can be used for developing reaction kinetics and to test catalysts. These results are valid at the conditions of large-scale plant operations. Since internal flow rates contacting the catalyst are known, heat and mass transfer rates can be calculated between the catalyst and the recycling fluid. With these known, their influence on catalyst performance can be evaluated in the experiments as well as in production units. Operating conditions, some construction features, and performance characteristics are given next. 

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