Design equation ideal batch reactor

Design equation— ideal batch reactor— homogeneous reaction (moles)... 

The design equations for a chemical reactor contain several parameters that are functions of temperature. Equation (7.17) applies to a nonisothermal batch reactor and is exemplary of the physical property variations that can be important even for ideal reactors. Note that the word ideal has three uses in this chapter. In connection with reactors, ideal refers to the quality of mixing in the vessel. Ideal batch reactors and CSTRs have perfect internal mixing. Ideal PFRs are perfectly mixed in the radial direction and have no mixing in the axial direction. These ideal reactors may be nonisothermal and may have physical properties that vary with temperature, pressure, and composition. 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

Then, by the general design equation, our ideal batch reactor equation becomes... 

For an ideal batch reactor, the differential form of the design equation for... 

For each of the ideal reactor types, viz. ideal batch reactor, plug-flow reactor (PFR), and continuous-flow stirred-tank reactor (CSTR), continuity equations or design equations can be derived using mass (or rather molar) balance equations for each species involved. 

Comparison of Eqs. (4-2) and (4-5) shows that the form of the design equations for ideal batch and tubular-flow reactors are identical if the realtime variable in the batch reactor is considered as the residence time in the flow case. The important point is that the integral c/C/r is the same in both reactors. If this integral is evaluated for a given rate equation for an ideal batch reactor, the result is applicable for an ideal tubular-flow reactor this... 

Equation 4.2.1 is the species-based design equation of an ideal batch reactor, written for species j. To obtain the operating time, we separate the variables and integrate Eq. 4.2.1 ... 

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... 

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... 

To reduce the design equation of an ideal batch reactor, Eq. 4.3.8, to dimensionless form, we first select a reference state of the reactor (usually, the initial state) and use the dimensionless extent, Z , of the mth-independent reaction, defined by Eq. 2.7.1 ... 

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. ... 

For an ideal batch reactor, we write Eq. 4.4.4 for each of the three independent reactions. Noting that independent Reactions 5 and 6 do not actually take place 0, arid the design equations are... 

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. 

In this chapter, we anidyze the operation of ideal batch reactors. In Section 6.1, we review how the design equations are utilized and discuss the auxiliary relations that should be incorporated in order to solve the design equations. In the rest of the... 

The design equations and the species concentration relations contain another dependent variable, 6, the dimensionless temperature, whose variation during the reactor operation is expressed by the energy balance equation. For ideal batch reactors with negligible mechanical shaft work, the energy balance equation, derived in Section 5.2, is... 

For convenience. Tables A.3a and A.3b in Appendix A provide the design equation and the auxiliary relations for ideal batch reactors. Table A.4 provides the energy balance equation. 

Solution This example illustrates how to apply the design equation for ideal batch reactors with reactions whose rate expressions are not power functions of the species concentrations. 

The design formulation of nonisothermal batch reactors consists of + 1 nonlinear first-order differential equations whose initial values are specified. The solutions of these equations provide Z s and 6 as functions of t. The examples below illustrate the design of nonisothermal ideal batch reactors. 

This is the differential design equation for a distillation reactor, written for the mth-independent chemical reaction. Note that Eq. 9.3.2 is identical to the design equation of an ideal batch reactor. The difference between the two cases is in the variation of the reactor volume and species concentrations during the operation. 

---