Mass transfer reaction rates

In Figure 7.2 is a simple representation of gradients for several cases of relative mass transfer/reaction rates. Since these gradients are established when transport rates become finite, the net effect is to reduce the overall rate of reaction due to the lower incident concentration of reactant within the catalyst as compared to external surface (or bulk) concentration. The net activity of the catalyst is diminished, and it is common to define this quantitatively in terms of the catalytic effectiveness factor, given by... 

The lUPAC defines a membrane reactor as a device for simultaneously carrying out a reaction and membrane based separation in the same physical enclosure. In fact, designing a cost-effective membrane reactor requires that heat transfer, mass transfer, reaction rate, and membrane permeance are well matched in the reactor design. 

Mass transfer limits rate of reaction Treatment of spent water... 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

Consider an extreme case in which there is no resistance to reaction and all of the resistance is due to mass transfer. The rate of mass transfer is proportional to the interfacial area and the concentration of the driving force. An expression can be written for the rate of transfer of Component i from gas to liquid through the gas film per unit volume of reaction mixture ... 

The cases considered thus far have all been based upon the premise that one process, ash-layer diffusion, surface reaction, or gas-film mass transfer, is rate controlling. However, in some cases, more than one process affects the overall kinetics for the conversion of the solid. This has two implications ... 

The mass-transfer-lLmited growth time is much shorter than the reaction-limited growth time, and the reaction should therefore be nearly reaction controlled with a reaction time of 2.77 min. If we heated the reactor to increase k , then the limiting time if k —> oo may be the mass-transfer-limited rate of < 1 sec. 

A commonly used mass transfer reaction model is presented in Figure 8.1a, where the reaction occurs in the bulk aqueous phase [35, 47]. It is assumed that the substrate dissolved in the organic phase diffuses into the aqueous phase, reaching equilibrium. In the absence of reaction, once equilibrium is achieved, apparent mass transfer ceases. Given the presence of active enzyme, depletion of substrate in the aqueous phase occurs, and the system moves into a new equilibrium. Thus, the overall reaction rate depends both on reaction and mass transfer. 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

The resultant ions (both primary and produced) are mass-selected using a quadruple mass analyzer and measured as count rates by an electron multiplier detector. Count rates of the MH+ species are subsequently converted to ionic densities and then to mixing ratios of constituent M after consideration of instrumental transmission coefficients, temperature, and DT pressure. Instrumental accuracy, which is largely determined by the uncertainties associated with the reported proton transfer reaction rate coefficients (k), is estimated to be better than 30% (Hayward et al, 2002 Lindinger, Hansel and Jordan, 1998). 

A stand-alone mixer requires the mass transfer/reaction to be completed within the mixer. If the gas flow rate matches the stoichiometry of the liquid phase, all the gas should be dissolved and reacted at the end of the mixer. This generally involves very high volumetric ratios between gas and liquid. If there is excess gas, there will be some gas at the mixer outlet, which needs to be separated. 

The heart of the pilot plant study normally involves varying the speed over two or three steps with a given impeller diameter. The analysis is done on a chart, shown in Fig. 36. The process result is plotted on a log-log curve as a function of the power applied by the impeller. This, of course, implies that a quantitative process result is available, such as a process yield, a mass transfer absorption rate, or some other type of quantitative measure. The slope of the line reveals much information about likely controlling factors. A relatively high slope (0.5-0.8) is most likely caused by a controlling gas-liquid mass transfer step. A slope of 0, is usually caused by a chemical reaction, and a further increase of power is not reflected in the process improvement. Point A indicates where blend time has been satisfied, and further reductions of blend time do not improve the process performance. Intermediate slopes on the order of 0.1-0.4, do not indicate exactly which mechanism is the major one. Possibilities are shear rate factors, blend time requirements, or other types of possibilities. 

Despite the clear importance of reactive absorption, its behavior is still not properly understood. This can be attributed to a very complex combination of process thermodynamics and kinetics, with intricate reaction schemes including ionic species, reaction rates varying over a wide range, and complex mass transfer-reaction coupling. As compared to distillation, reactive absorption is a fully rate-controlled process and it occurs definitely far from the equilibrium state. Therefore, both practitioners and theoreticians are highly interested to establish a proper understanding and description of this process. 

For the system (2.36), in the limit e —> 0, the term (l/sjkfx) becomes indeterminate. For rate-based chemical and physical process models, this allows a physical interpretation in the limit when the large parameters in the rate expressions approach infinity, the fast heat and mass transfer, reactions, etc., approach the quasi-steady-state conditions of phase and/or reaction equilibrium (specified by k(x) = 0). In this case, the rates of the fast phenomena, as given by the explicit rate expressions, become indeterminate (but, generally, remain different from zero i.e., the fast reactions and heat and mass transfer do still occur). 

Thus it is seen that the validity of a chemical kinetic model does extend as far as providing a linear plot from which a mass transfer related rate constant may be obtained. Further literal chemical kinetic interpretation breaks down for diffusion controlled ion exchange reactions as evident from observing that ... 

Surface reactions options for rate controlling steps/UD Multiphase reactive flows mass transfer/reactions in all phases ... 

Reported [41-44] values of , for the thermal decomposition of NaHCOj were in the range 42 to 65 kJ mol. The initial reaction results [42] in the formation and growth of NajCOj and subsequently the effects of heat and mass transfer become rate limiting. 

In the first case, the reactions of interest are those which are intrinsically fast and exothermic, but which are currently limited by the poor heat and mass transfer for rates achievable in a stirred pot. Existing technology routinely entails substantial hazardous process inventories, possible reactor runaway and indifferent product selectivity. Fast response reactors open up the possibility of switching to more severe process conditions which would be prohibited in conventional reactors in view of the tendency to degrade the product. It may therefore be possible to exploit a virtuous circle - short residence time -higher temperature - faster kinetics - smaller reactor - shorter residence time. 

This reaction is of simple stoichiometry and often occurs with great ease and in high yield. Nevertheless, its mechanism is complex and difficult to unravel. It involves radical intermediates " and occurs with a mass-transfer-limited rate ... 

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. 

When the internal mass transfer/reaction step is rate limiting, an effectiveness factor, I , is usually introduced related to dimensionless parameters characteristic of the reacting system as a Thiele modulus.109 It is worthwhile noting that most of the available correlations are based upon theoretical models assuming diffusion as the only mass transfer pattern. Hence, effects related to external mass transfer resistances are neglected. 

The results obtained in equations (8-136) to (8-142) assume constant B, i.e., the reaction is pseudo-first-order in A. Another limiting case that yields to analytical solution is that in which the rate of reaction is very rapid and the reaction occurs wholly within the film. Here we consider the reaction A -I- P to occur very rapidly compared to mass-transfer/diffusion rates. The profiles look as in Figure 7.17b, and the overall flux and enhancement factor are given by... 

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