Equilibrium chemical reaction, effect mass transfer

The solutions of each situation involve the simultaneous formulation of convenient chemical reaction and mass transfer models. For the case of phase equilibrium the widely spread equilibrium-based model (Seader, 1985) should be considered. In the case of rate limited mass transfer non-equilibrium models (Taylor and Krishna, 2000, 1993 Wesselingh, 1997) are to be used. The effect of Damkohler number on the unit performance should be taken into account if the chemical reaction is rate-limited. A detailed overview of the aforementioned situations is given in section 2.5. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

A useful empirical approach to the design of heterogeneous chemical reactors often consists of selecting a suitable equation, such as one in Table 3.3 which, with numerical values substituted for the kinetic and equilibrium constants, represents the chemical reaction in the absence of mass transfer effects. Graphical methods are often employed to aid the selection of an appropriate equation140 and the constants determined by a least squares approach<40). It is important to stress, however, that while the equation selected may well represent the experimental data, it does not... 

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 plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

Additionally, the rate of heat transfer may also become important. Nonuniform temperature distributions within the solid particles result in differing local rates of reaction, as the reaction rates are strongly depending on the temperature according to the Arrhenius law. Heat- and mass-transfer effects become increasingly important with increasing rates of reaction [1]. Whereas the macroscopic kinetics describe the rate of a chemical reaction, thermodynamics determines the maximum extent to which reactions can occur. Provided that the rate of reaction is sufficiently fast, the thermodynamical equilibrium can be reached. 

Most reactions on surfaces are complicated by variations in mass transfer and adsorption equilibrium [70], It is precisely these complexities, however, that afford an additional means of control in electrochemical or photoelectrochemical transformations. Not only does the surface assemble a nonstatistical distribution of reagents compared with the solution composition, but it also generally influences both the rates and course of chemical reactions [71-73]. These effects are particularly evident with photoactivated surfaces the intrinsic lifetimes of both excited states and photogenerated transients and the rates of bimolecular diffusion are particularly sensitive to the special environment afforded by a solid surface. Consequently, the understanding of surface effects is very important for applications that depend on chemical selectivity in photoelectrochemical transformation. 

Many commercial absorption processes involve a chemical reaction between the solute and the solvent. The occurrence of a reaction affects not only gas-liquid equilibrium relationships but also the rate of mass tmasfer. Sioce the reaction occurs in the solvent, only the liquid mass transfer rate is affected. Normally, the effect is an iocrease in the liquid mass tmaster coefficianl kL. The development of correlations for predicting the degree of enhancement for various types of chemical reaction and system configuration has been the subject of numerous studies. Comprehensive discussions of the theory of mass transfer with ckemical reaction are presented in recent books by Aslarita,27 Danckwarts,2 and Aslarita et al.J... 

A typical LLPTC cycle involves a nucleophilic substitution reaction, as shown in Eq. (8). A difficult problem in the kinetics of PT-catalyzed reactions is to sort out the rate effects due to equilibrium anion-transfer mechanism for transfer of anions from the aqueous to the organic phase. The reactivity of the reaction by PTC is controlled by the rate of reaction in the organic phase, the rate of reaction in the aqueous phase, and the mass transfer steps between the organic and aqueous phases [27-29]. In general, one assumes that the resistances of mass transfer and of chemical reaction in the aqueous phase can be neglected for a slow reaction in the organic phase by LLPTC. 

Process models for RD have to take into account both the chemical and the physical side of the process. Two basic types of model are used stage models, which are based on the idea of the equilibrium stage with phase equilibrium between the outlet streams, and rate-based models, which explicitly take into account heat and mass transfer. Similarly to the physical side of RD, the chemical reaction is either modeled using the assumption of chemical equilibrium or reaction kinetics are taken into account. Note that a kinetic model, either for physical transport processes or for chemical reactions, always includes an equilibrium model. The equilibrium model is the stationary solution of the kinetic model, for which all derivatives with respect to time become zero. Hence, whatever model type is used, it has to be based on a sound knowledge of the chemical and phase equilibrium, which is supplied by thermodynamic methods. Starting from there, kinetic effects can be included. 

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