Reactor design equation Reaction-based

The viability of one particular use of a membrane reactor for partial oxidation reactions has been studied through mathematical modeling. The partial oxidation of methane has been used as a model selective oxidation reaction, where the intermediate product is much more reactive than the reactant. Kinetic data for V205/Si02 catalysts for methane partial oxidation are available in the literature and have been used in the modeling. Values have been selected for the other key parameters which appear in the dimensionless form of the reactor design equations based upon the physical properties of commercially available membrane materials. This parametric study has identified which parameters are most important, and what the values of these parameters must be to realize a performance enhancement over a plug-flow reactor. 

In this project, we make use of platinum-type catalyst on silica gel. Although this is less selective than more modem palladium-based catalysts, kinetic data are available in the literature as an LHHW model [2], better suited for flexible reactor design. The reaction rate equations are ... 

The performance of a biochemical reactor is designed and evaluated based the reaction rate equation. The rate of biomass generation is based on the Monod rate model ... 

A wide variety of new approaches to the problem of product separation in homogeneous catalysis has been discussed in the preceding chapters. Few of the new approaches has so far been commercialised, with the exceptions of a the use of aqueous biphasic systems for propene hydroformylation (Chapter 5) and the use of a phosphonium based ionic liquid for the Lewis acid catalysed isomerisation of butadiene monoxide to dihydrofuran (see Equation 9.1). This process has been operated by Eastman for the last 8 years without any loss or replenishment of ionic liquid [1], It has the advantage that the product is sufficiently volatile to be distilled from the reactor at the reaction temperature so the process can be run continuously with built in product catalyst separation. Production of lower volatility products by such a process would be more problematic. A side reaction leads to the conversion of butadiene oxide to high molecular weight oligomers. The ionic liquid has been designed to facilitate their separation from the catalyst (see Section 9.7)... 

By comparison, the catalyzed transesterification reaction between ethylene carbonate and methanol (Equation 7.3) offers an alternative for greening DMC production. In this Asahi Kasei process [27], the preferred catalyst is based on an anion-exchange resin operating under catalytic distillation conditions between 333-353 K. This reactor design shifts the thermodynamic equilibrium towards complete conversion of ethylene carbonate, such that both the yield and selectivity for DMC and monoethylene glycol are 99.5%. The process is capable of supplying monoethylene glycol to the market, and DMC for captive use to produce DPC. 

Equations (59) and (60) are in a form often used for tubular, idealized, plug-flow reactors when the reaction rate is based on the volume of the reactor. When the reaction is heterogeneous, such as one occurring on the surface of a catalyst, it is common practice to base the reaction rate on the mass of the catalyst rather than on the volume of the reactor and substitute ric for r,. The resulting design equation equivalent to Eq. (60) is... 

Independently of the work on the chemical composition of sulphuric acid catalysts, attempts to develop kinetic equations to describe the rate of reaction both for mechanistic analysis and reactor design purposes have been numerous. There is much evidence to suggest that in common with its catalytically oxidative behaviour in other environments, valency states of vanadium of V " and V " are involved. Mars and Maessen in 1964 developed a rate expression based on a simple two-step redox mechanism ... 

This method of writing the mass balance, like Eq. (3-10) for batch operation of a tank reactor, separates the extensive variables F and F and relates them to an integral dependent on the intensive conditions in the reaction mixture. It is worthwhile to note the similarity between Eq. (3-13) and the more familiar design equation for heat-transfer equipment based on an energy balance. This may be written... 

For reactors with single chemical reactions, it has been customary to write the species-based design equation for the limiting reactant A. Hence,... 

To analyze and design chemical reactors more effectively and to obtain insight into the operation, we adopt reaction-based design formulation. In this section, we derive the reaction-based design equations for the three ideal reactor models. Reaction-based design equations of other reactor configurations are derived in Chapter 9. 

Equation 4.3.8 is the reaction-based, differential design equation of an ideal batch reactor, written for the mth-independent reaction. As will be discussed below, to describe the operation of a reactor with multiple chemical reactions, we have to write Eq. 4.3.8 for each of the independent reactions. Note that the reaction-based design equation is invariant of the specific species used in the derivation. For an ideal batch reactor with a single chemical reaction, Eq. 4.3.8 reduces to... 

Equation 4.3.22 is the reaction-based design equation for CSTRs, written for the mth-independent reaction. To describe the operation of the reactor with multiple reactions, we have to write Eq. 4.3.22 for each independent reaction. 

The reaction-based design equations derived in the previous section are expressed in terms of extensive quantities such as reaction extents, reactor volume, molar flow rates, and the like. To describe flie generic behavior of chemical reactors, we would like to express the design equations in terms of intensive, dimensionless variables. This is done in two steps ... 

Equation 4.4.4 is die dimensionless, reaction-based design equation of an ideal batch reactor, written for die mth-independent reaction. The factor ( / Co) is a scaling factor that converts die design equation to dimensionless form. Its physical significance is discussed below (Eqs. 4.4.13-4.4.15). 

To reduce the reaction-based design equation of a plug-flow reactor to dimensionless form, we differentiate Eqs. 4.4.5 and 4.4.8,... 

Adams et al. (/. Catalysis 3, 379, 1964) investigated these reactions and expressed the rate of each as second order (first order with respect to each reactant). Formulate the dimensionless, reaction-based design equations for an ideal batch reactor, plug-flow reactor, and a CSTR. 

Formulate the dimensionless, reaction-based design equations for ideal batch reactor, plug-flow reactor, and CSTR using the heuristic rule. ... 

We derived the reaction-based design equations for three ideal reactors. 

Equation 5.2.18 is the dimensionless, differential energy balance equation of ideal batch reactors, relating the reactor dimensionless temperature, 0(t), to the dimensionless extents of the independent reactions, Z (t), at dimensionless operating time T. Note that individual dZ /dfr s are expressed by the reaction-based design equations derived in Chapter 4. 

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