Isothermal batch reactor example

Figure 12.2 Profiles for coil temperature (Tc) and heat transfer rate (Q) for an isothermal batch reactor (Example 12-4)...

Worked Example 6.1 Substitution Reaction in the Isothermal Batch Reactor... 

Following are examples for finding the time of an isothermal batch reactor for a given conversion of the reactant and other pertinent variables, and for gas phase reaction. 

Determine the conversion for an isothermal batch reactor using the stoichiometry of Example 5-1 and the same values of initial concentrations of A, B, C, and D in a reactor volume of 1 liter operating for 4 minutes. The rate constant is k = 105[(liter)2/(gmol2 min)]. 

In this section, we still restrict ourselves to the consideration of systems where only the overall behavior is of interest, but we extend the analysis to actual chemical reactors. Indeed, the discussion in the previous section was limited to the overall kinetics of multicomponent mixtures seen from the viewpoint of chemical reaction engineering, the discussion was in essence limited to the behavior in isothermal batch reactors, or, equivalently, in isothermal plug flow reactors. In this section, we present a discussion of reactors other than these two equivalent basic ones. The fundamental problem in this area is concisely discussed next for a very simple example. 

Three examples are given here to demonstrate various capabilities of DDAPLUS. In the first example, DDAPLUS is used to solve a system of ordinary differential equations for the concentrations in an isothermal batch reactor.In the second example, the same state equations are to be integrated to a given time limit, or until one of the state variables reaches a given limit. The last example demonstrates the use of DDAPLUS to solve a differential-algebraic reactor problem with constraints of electroneutrality and ionization equilibria. 

In Example 2.1, Maple was used to solve two simultaneous first order ODEs. The same methodology can be used to solve more than two simultaneous ODEs. Eor example, the material balance equations for the time dependent concentration of each species (A, B, and C) in an isothermal batch reactor with reversible series... 

The reactions represent a common type of substitution reaction for example, the successive chlorination of benzene considered in Example 2-8 is of this form. In that example yields of primary and secondary products were obtained for an isothermal batch reactor. As pointed out in Sec. 4-4, the results for batch reactors may be .used for tubular-flow reactors if the time is rgplacied by the "residence time. Actually, in Exainpie 2-8 the yield equations were expressed in terms of fraction of benzene unreacted rather than time... Therefore identical results apply for the tubular-flow reactor. Hence the yield of X is given by Eq. (F) of Example 2-8, with [ ]/[A]o replacing [,B ]J[B q that is,... 

Example 2.12 The gas-phase catalytic oxidation of ammonia is investigated in an isothermal batch reactor. The following reactions take place in the reactor ... 

ILLUSTRATIVE EXAMPLE 8.16 It is desired to produce 12,000 kg/day of ethyl acetate in an isothermal batch reactor by the following elementary reversible liquid reaction ... 

ILLUSTRATIVE EXAMPLE 13.19 The following liquid-phase reaction takes place in a constant volume, isothermal batch reactor ... 

Example 9.1 For the homogeneous polymerization of pure styrene with azobisisobutyr-onitrile at 60 °C in an isothermal, batch reactor,... 

It is obvious from Equation 9.13 that the rate of polymerization is an instantaneous quantity it depends on the particular values of [A/], [/], and T (through the temperature dependence of the rate constants) that exist as a particular instant (and location, for that matter) in a reactor. In a uniform, isothermal batch reaction (Example 9.1), the rate of polymerization decreases monotonically because of the decreases in both [M and [/] with time. In a similar fashion, according to Equation 9.35 is a function of [Af], [/], T. and [R H], all of which may vary with time (and/or location) in a reactor. But is the concept of an instantaneous valid How much do these quantities change during the lifetimes of individual chains This important point is clarified in the following example. 

Example 2.11 Suppose initially pure A dimerizes, 2A —> B, isothermally in the gas phase at a constant pressure of 1 atm. Find a solution to the batch design equation and compare the results with a hypothetical batch reactor in which the reaction is 2A B - - C so that there is no volume change upon reaction. 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

Example 7.5 Suppose the consecutive reactions 2A B C are elementary. Determine the rate constants from the following experimental data obtained with an isothermal, constant-volume batch reactor ... 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

Although semi-analytical solutions are available in some cases [5], these are cumbersome and it is more usual to employ a numerical method. A simple example is presented below which illustrates the solution of the design equation for a batch reactor operated isothermally the adiabatic operation of the same system is then examined. 

Example 5-1 Consider the reaction A B, r = kCA, 300 = min, AHr = -20 kcal/mole in a 10 liter reactor with C o = 2 moles/liter and To =300 K- At what rate must heat be removed to maintain the reactor isothermal at 300 K for (a) a batch reactor at 90% conversion ... 

If the reactor is to be operated isothermally, the rate of reaction diA can be expressed as a function of concentrations only, and the integration in equation 1.24 or 1.25 carried out. The integrated forms of equation 1.25 for a variety of the simple rate equations are shown in Table 1.1 and Fig. 1.8. We now consider an example with a rather more complicated rate equation involving a reversible reaction, and show also how the volume of the batch reactor required to meet a particular production requirement is calculated. 

Theories are not used directly, as in the discussion presented in Sect. 3.1, but allow building a mathematical model that describes an experiment in the unambiguous language of mathematics, in terms of variables, constants, and parameters. As an example, when considering the identification of kinetic parameters of chemical reactions from isothermal experiments performed in batch reactors, the relevant equations of mass conservation (presented in Sect. 2.3.1) give a set of ordinary differential equations in the general form... 

The design of chemical reactors encompasses at least three fields of chemical engineering thermodynamics, kinetics, and heat transfer. For example, if a reaction is run in a typical batch reactor, a simple mixing vessel, what is the maximum conversion expected This is a thermodynamic question answered with knowledge of chemical equilibrium. Also, we might like to know how long the reaction should proceed to achieve a desired conversion. This is a kinetic question. We must know not only the stoichiometry of the reaction but also the rates of the forward and the reverse reactions. We might also wish to know how much heat must be transferred to or from the reactor to maintain isothermal conditions. This is a heat transfer problem in combination with a thermodynamic problem. We must know whether the reaction is endothermic or exothermic. 

The design parameters for a batch reactor can be as simple as concentration and time for isothermal systems. The number of parameters increases with each additional complication in the reactor. For example, an additional reactant requires measurement of a second concentration, a second phase adds parameters, and variation of the reaction rate with temperature requires additional descriptors a frequency factor and an activation energy. These values can be related to the reactor volume by the equations in Section III. 

The mathematical techniques most commonly used in chemical kinetics since their formulation by Bodenstein in the 1920s have been the quasi-stationary state approximation (QSSA) and related approximations, such as the long chain approximation. Formally, the QSSA consists of considering that the algebraic rate of formation of any very reactive intermediate, such as a free radical, is equal to zero. For example, the characteristic equations of an isothermal, constant volume, batch reactor are written (see Sect. 3.2) as... 

Emulsion polymerization is usually carried out isothermally in batch or continuous stirred-tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small ( 0.5 fim) polymer particles, which are the locus of the reaction, are suspended in a continuous aqueous medium. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. In industrial practice, such a reactor often shows sustained oscillations. Solid-catalyzed olefin polymerization in a slurry batch reactor is a classic example of a slurry reactor where the solid particles change size and characteristics with time during the reaction process. 

This is the conversion that will be achieved in a batch reactor for a first-order reaction when the catalyst decay law is second-order. The purpose of this example was to demonstrate the algorithm for isothermal catalytic reactor design for a decaying catalyst. 

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. 

For non-isothermal or non-linear chemical reactions, the RTD no longer suffices to predict the reactor outlet concentrations. From a Lagrangian perspective, local interactions between fluid elements become important, and thus fluid elements cannot be treated as individual batch reactors. However, an accurate description of fluid-element interactions is strongly dependent on the underlying fluid flow field. For certain types of reactors, one approach for overcoming the lack of a detailed model for the flow field is to input empirical flow correlations into so-called zone models. In these models, the reactor volume is decomposed into a finite collection of well mixed (i.e., CSTR) zones connected at their boundaries by molar fluxes.4 (An example of a zone model for a stirred-tank reactor is shown in Fig. 1.5.) Within each zone, all fluid elements are assumed to be identical (i.e., have the same species concentrations). Physically, this assumption corresponds to assuming that the chemical reactions are slower than the local micromixing time.5... 

Here, a is a dummy variable of integration that will be replaced by the upper and lower limits after the integral is evaluated. The results are equivalent to those obtained earlier, for example. Equations 1.26 and 1.29 depending on the reaction order, and all the restrictive assumptions still apply a single reaction in a constant-volume, isothermal, perfectly mixed batch reactor. Note that Equation 1.33 becomes useless for the multiple reactions treated in Chapter 2. 

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