Reactor design equation Species-based

Appendix B provides the derivation of the design equation from the species continuity equation. In Section 4.1, we carry out macroscopic species balances to derive the species-based design equation of any chemical reactor. In Section 4.2,... 

Equation 4.1.3 is the integral form of the general species-based design equation of chemical reactors, written for species j. 

The differential form of the general species-based design equation can be derived either by a formal differentiation of Eq. 4.1.3 or by conducting a balance for species j over a differential reactor shown schematically in Figure A. b. For a differential reactor, the balance over species j is... 

Equation 4.1.4 is the differential form of the general, species-based design equation for all chemical reactors. 

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

To obtain useful expressions from the general species-based design equation, we should know the formation rate of species j, (rj), at any point in the reactor. To express (vj), the local concentrations of aU species as well as the local temperatures should be provided. To obtain these quantities, we should solve the overall continuity equation, the individual species continuity equations, and the energy balance equation. This is a formidable task, and, in most situations, we cannot reduce those... 

SPECIES-BASED DESIGN EQUATIONS OF IDEAL REACTORS... 

Equation 4.2.2 is the integral form of the species-based design equation for an ideal batch reactor, written for species j. It provides a relation between the operating time, t, the amount of the species in the reactor, Nj(t) and Nj(0), the species formation rate, (rj), and the reactor volume, V. Note that when the reaetor volume does not change during the operation, Eq. 4.2.2 reduces to... 

A CSTR is a reactor model based on two assumptions (i) steady-state operation and (ii) the same conditions exist everywhere inside the reactor (due to good mixing). For steady operations, the accumulation term in the design equation vanishes. Since the same conditions exist everywhere, the rate (rj) is the same throughout the reactor and is equal to the rate at the reactor effluent, (r )out-Hence, the general, species-based design equation Eq. (4.1.3) reduces to... 

Equation 4.2.10 is the species-based differential design equations for a PFR, written for species j. To obtain the reactor volume of a PFR, we integrate Eq. 4.2.10,... 

Equation 4.2.13 is the species-based differential design equation of a plug-flow reactor, expressed in terms of the conversion of reactant A. To obtain the integral form of the design equation, we separate the variables and integrate Eq. 4.2.13 ... 

Equation 4.2.14 is the species-based integral design equation of a plug-flow reactor, expressed in terms of the conversion of reactant A. 

For an ideal batch reactor, the species-based design equation, written for species j, is given by Eq. 4.2.1,... 

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... 

We derived the species-based design equations for three ideal reactor models ideal batch reactor, plug-flow reactor, and CSTR. 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the component mass balances. This chapter focuses on explicit numerical calculations for the effective diffusion coefficient of species i within the internal pores of a catalytic pellet. This information is required before one can evaluate the intrapellet Damkohler number and calculate a numerical value for the effectiveness factor. Hence, 50, effective is called the effective intrapellet diffusion coefficient for species i. When 50, effective appears in the denominator of Ajj, the dimensionless scaling factor is called the intrapellet Damkohler number for species i in reaction j. When the reactor design focuses on the entire packed catalytic tubular reactor in Chapter 22, it will be necessary to calcnlate interpellet axial dispersion coefficients and interpellet Damkohler nnmbers. When there is only one chemical reaction that is characterized by nth-order irreversible kinetics and subscript j is not required, the rate constant in the nnmerator of equation (21-2) is written as instead of kj, which signifies that k has nnits of (volume/mole)"" per time for pseudo-volumetric kinetics. Recall from equation (19-6) on page 493 that second-order kinetic rate constants for a volnmetric rate law based on molar densities in the gas phase adjacent to the internal catalytic surface can be written as... 

Equations (19) and (22) are theoretically pleasing but their practical utility is limited. In a troubleshooting problem eq. (22) would allow us to recover E(s) of the system but we rarely deal with a homogeneous system of linear reactions I In a design problem we often do not know the actual RTD and are trying to design an ideal reactor. If the RTD can be predicted based on a nonideal reactor model, then species concentrations can also be calculated based on that model. Then eq. (22) represents at best only a mathematical short-cut I... 

Commonly, the design of a reactor requires the prediction of the rate of reaction. Two different approaches have been used to develop suitable kinetic models for the WGS reaction. The first is based on microkinetics by taking into account the elementary steps from the adsorption of the chemical species to the reaction and the product desorption the second is based on the macrokinetics that are empirical models in which the rate of reaction depends proportionally on the concentration of reactants and products and exponentially on temperature (typically expressed using the Arrhenius equation). The microkinetics approach is more complex, in particular from a mathematical and computational point of view, but it offers the possibility to better model the surface coverage and the enthalpy of the reaction (i.e., the temperature increase on the catalyst surface). Two different mechanisms for the WGS reaction are proposed in the scientific literamre the redox mechanism and the associative mechanism. 

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