Reactor, batch single reaction

For constant-volume batch reactors with single reactions, and selecting the initial state as the reference state, the design equation, Eq. 6.2.1, reduces to... 

We continue the analysis of ideal, isothermal, constant-volume batch reactors with single reactions and consider now chemical reactions involving more than one reactant. Consider the general reaction form... 

From diese various estimates, die total batch cycle time t(, is used in batch reactor design to determine die productivity of die reactor. Batch reactors are used in operations dial are small and when multiproducts are required. Pilot plant trials for sales samples in a new market development are carried out in batch reactors. Use of batch reactors can be seen in pharmaceutical, fine chemicals, biochemical, and dye industries. This is because multi-product, changeable demand often requues a single unit to be used in various production campaigns. However, batch reactors are seldom employed on an industrial scale for gas phase reactions. This is due to die limited quantity produced, aldiough batch reactors can be readily employed for kinetic studies of gas phase reactions. Figure 5-4 illustrates die performance equations for batch reactors. 

The general stoichiometric relationships for a single reaction in a batch reactor are... 

Generally, the temperature changes with time or, equivalently, with distance from the reactor inlet (for flow reactors). This change is usually controlled well in reaction calorimeters but can become uncontrolled in other conventional laboratory flow or (semi)batch reactors. The balance equations of a batch reactor for a single reaction of a-th order kinetics are given by ... 

The next two steps after the development of a mathematical process model and before its implementation to "real life" applications, are to handle the numerical solution of the model s ode s and to estimate some unknown parameters. The computer program which handles the numerical solution of the present model has been written in a very general way. After inputing concentrations, flowrate data and reaction operating conditions, the user has the options to select from a variety of different modes of reactor operation (batch, semi-batch, single continuous, continuous train, CSTR-tube) or reactor startup conditions (seeded, unseeded, full or half-full of water or emulsion recipe and empty). Then, IMSL subroutine DCEAR handles the numerical integration of the ode s. Parameter estimation of the only two unknown parameters e and Dw has been described and is further discussed in (32). 

Single Reactions—For all reactions of orders above zero, tire CSTR gives a lower production rate than the batch, semi-batch, or kinetically equivalent plug-flow reactor. 

Dynamics of an Equalisation Basin 560 Dimensionless Kinetics in a Batch Reactor 235 Batch Reactor with Complex Reaction Sequence 240 Single Solute Batch Extraction 442 Mixing and Segregation 394... 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

For a single reaction in a nonisothermal batch reactor we can write the species and energy-balance equations... 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

COMPARISON OF BATCH, TUBULAR AND STIRRED-TANK REACTORS FOR A SINGLE REACTION. REACTOR OUTPUT... 

We shall now proceed to compare the three basic types of reactor—batch, tubular and stirred tank—in terms of their performance in carrying out a single first order irreversible reaction ... 

Figu re 6.3 Batch reactor For a single reaction of the type A + B -> P, both reactants A and B are charged initially into the vessel. Therefore, temperature control is practically the only way to influence the reaction course. 

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

The fed-batch reactors considered in Sections 4.1, 4.2, and 4.6 all involved single reactions. The control problem was to prevent reaction temperature mnaways. In fed-batch... 

In batch reactors, for thermally simple types of reactions, that is, ones that can be attributed to a single reaction step, generally applicable to the propagation step of polymerization reactions, we can write the following thermal energy balance (6)... 

A general method is presented for the development of chemical reaction rate equations from integral reactor and single-sample batch reactor data such as are obtained in process development studies. Following the scope of the method, three earlier foundation stones upon which the method rests, the method itself, and a simple illustration are presented. 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

The following example concerning the rate of esterification of butanol and acetic acid in the liquid phase illustrates the design problem of predicting the time-conversion relationship for an isothermal, single-reaction, batch reactor. 

Figure 6.8 shows the reaction operating curve for different values of 2/ 1 Note that the design equation for batch reactors with single reversible reactions has two parameters ( 1 and 2). whereas the design equation for reactors with an irreversible reaction has only one parameter. Also note that for an irreversible reaction, 2 = 0, and, from Eq. 6.3.3, Zi q = aCO). 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

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