Diffusion multiphase reactors

J. J. Linderman, P. A. Mahama, K. E. Forsten, and D. A. Lauffenburger, Diffusion and Probability in Receptor Binding and Signaling Rakesh K. Jain, Transport Phenomena in Tumors R. Krishna, A Systems Approach to Multiphase Reactor Selection... 

Another classification of chemical reactors is according to the phases being present, either single phase or multiphase reactors. Examples of multiphase reactors are gas liquid, liquid-liquid, gas solid or liquid solid catalytic reactors. In the last category, all reactants and products are in the same phase, but the reaction is catalysed by a solid catalyst. Another group is gas liquid solid reactors, where one reactant is in the gas phase, another in the liquid phase and the reaction is catalysed by a solid catalyst. In multiphase reactors, in order for the reaction to occur, components have to diffuse from one phase to another. These mass transfer processes influence and determine, in combination with the chemical kinetics, the overall reaction rate, i.e. how fast the chemical reaction takes place. This interaction between mass transfer and chemical kinetics is very important in chemical reaction engineering. Since chemical reactions either produce or consume heat, heat removal is also very important. Heat transfer processes determine the reaction temperature and, hence, influence the reaction rate. 

Multiphase reactors include, for instance, gas-liquid-solid and gas-liq-uid-liquid reactions. In many important cases, reactions between gases and liquids occur in the presence of a porous solid catalyst. The reaction typically occurs at a catalytic site on the solid surface. The kinetics and transport steps include dissolution of gas into the liquid, transport of dissolved gas to the catalyst particle surface, and diffusion and reaction in the catalyst particle. Say the concentration of dissolved gas A in equilibrium with the gas-phase concentration of A is CaLt. Neglecting the gas-phase resistance, the series of rates involved are from the liquid side of the gas-liquid interface to the bulk liquid where the concentration is CaL, and from the bulk liquid to the surface of catalyst where the concentration is C0 and where the reaction rate is r wkC",. At steady state,... 

The linear interpolation approach cannot accurately treat the abrupt changes of diffusivity that may occur in some locations in multiphase reactors where the phase fractions change rapidly (e.g., across the transition zone from the dense bed to the freeboard section in a bubbling fluidized bed). To improve the interpolation procedure, one seeks an approximation of the diffusivity that gives an accurate approximation of the diffusive flux for cases with large changes in the material properties. 

As in the situation for tank-type reactors, we need first to define the characteristic time quantities associated with the reactor design. The characteristic diffusion time, tj), is given in equation (8-207), and the extent-of-reaction time, is given in equation (8-208). The third time here is tp, the length of time an element of fluid remains in the reactor. This is reminiscent of the exit-age distribution function developed for homogeneous tubular-flow reactors, but the development of the theory for multiphase reactors has been different. " ... 

Optimal reactor design is critical for the effectiveness and economic viability of AOPs. The WAO process poses significant challenges to chemical reactor engineering and design, due to the (i) multiphase nature of WAO reactions (ii) temperatures and pressures of the reaction and (iii) radical reaction mechanism. In multiphase reactors, complex relationships are present between parameters such as chemical kinetics, thermodynamics, interphase/intraphase intraparticle mass transport, flow patterns, and hydrodynamics influencing reactant mass transfer. Complex models of WAO are necessary to take into account the influence of catalyst wetting, the interface mass-transfer coefficients, the intraparticle effective diffusion coefficient, and the axial dispersion coefficient. " ... 

Physical deactivation Demanding reaction, 20 Design of reactor. See Fixed-bed Fluidized-bed design Multiphase reactors Differential reactor, 72 Diffusion... 

The presence of a liquid phase and a liquid-solid interface in multiphase reactors results in added transport resistances. For instance, the effective diffusivity in liquid-filled pores (of the order of 10 to 10 cmVsec) is much smaller than that in gas-filled pores (of the order of 10 cmVsec). The solubility of the gaseous reactant is an important factor since the gaseous reactant has to be dissolved into the liquid reactant for the reaction to take place on the catalyst surface. As emphasized in Chapter 4, the Biot number for heat is much larger than the Biot number for mass for liquid-solid systems the opposite is true for gas-solid systems. Therefore, the major external resistance lies in the mass transport, and the pellet is not necessarily isothermal. In many cases, however, the equilibrium gas concentration in the liquid is quite low and, thus, the heat evolved is small in spite of high heats of reaction. The pellet can be considered isothermal in such a case,... 

Direct measurement of particle velocity and velocity fluctuations in fluidized beds or riser reactors is necessary for validating multiphase models. Dudukovic [14] and Roy and Dudukovic [28] have used computer-automated radioactive particle tracking (CARPT) to foUow particles in a riser reactor. From their measurements, it was possible to calculate axial and radial solids diffusion as well as the granular temperature from a multiphase KTGF model. Figure 15.10 shows one such measurement... 

Example 9.11 Modeling of a nonisothermal plug flow reactor Tubular reactors are not homogeneous, and may involve multiphase flows. These systems are called diffusion convection reaction systems. Consider the chemical reaction A -> bB described by a first-order kinetics with respect to the reactant A. For a nonisothermal plug flow reactor, modeling equations are derived from mass and energy balances... 

A qualified question is then whether or not the multicomponent models are really worthwhile in reactor simulations, considering the accuracy reflected by the flow, kinetics and equilibrium model parts involved. For the present multiphase flow simulations, the accuracy reflected by the flow part of the model is still limited so an extended binary approach like the Wilke model sufEce in many practical cases. This is most likely the case for most single phase simulations as well. However, for diffusion dominated problems multicomponent diffusion of concentrated ideal gases, i.e., for the cases where we cannot confidently designate one of the species as a solvent, the accuracy of the diffusive fluxes may be significantly improved using the Maxwell-Stefan approach compared to the approximate binary Fickian fluxes. The Wilke model might still be an option and is frequently used for catalyst pellet analysis. 

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