Batch reactors isothermal design

As with the batch reactor, the design equations in differential form for the PFR must be integrated to solve engineering problems. The same three possibilities that woe discussed for the batch reactor also exist here, except that the variable of time for the batch reactor is replaced by position in the direction of flow for the ideal PFR. For Case 3, where ttie reactor is either isothermal or adiabatic, Eqns. (3-26) and (3-27) can be integrated symbolically to give... 

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. 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

In general, when designing a batch reactor, it will be necessary to solve simultaneously one form of the material balance equation and one form of the energy balance equation (equations 10.2.1 and 10.2.5 or equations derived therefrom). Since the reaction rate depends both on temperature and extent of reaction, closed form solutions can be obtained only when the system is isothermal. One must normally employ numerical methods of solution when dealing with nonisothermal systems. 

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. 

Numerical integration of design equation for a batch reactor operated non-isothermally... 

The approach to the design of non-isothermal tubular reactors with plug flow parallels that already outlined for batch reactors (see Sect. 2.4.)... 

Batch reactor Vessel used for chemical reaction that has no feed or effluent streams. The reactor is well stirred and usually run either isothermally or adiabatically. The main design variable is how much time the reactants are allowed to remain in the reactor to achieve the desired level of conversion. 

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. 

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

If this reaction is performed in a well-mixed isothermal batch reactor, determine the time necessary to achieve 95 percent conversion of the limiting reactant (from C. Hill, An Introduction to Chemical Engineering Kinetics and Reactor Design, Wiley, 1977, p. 259). 

This chapter focuses attention on reactors that are operated isothermally. We begin by studying a liquid-phase batch reactor to determine the specific reaction rate constant needed for the design of a CSTR. After illustrating the design of a CSTR from batch reaction rate data, we cany out the design of a tubular reactor for a gas-phase pyrolysis reaction. This is followed by a discussion of pressure drop in packed-bed reactors, equilibrium conversion, and finally, the principles of unsteady operation and semibatch reactors. 

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. 

Design Stmcture for Isothermal Reactors 125 Scale-up of Liquid-Phase Batch Reactor Data to the Design of a CSTR 129... 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

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. 

The main difficulty in determining the reaction rate r is that the extent is not a measurable quantity. Therefore, we have to derive a relationship between the reaction rate and the appropriate measurable quantity. We do so by using the design equation and stoichiometric relations. Also, since the characteristic reaction time is not known a priori, we write the design equation in terms of operating time rather than dimensionless time. Assume that we measure the concentration of species j, Cj(t), as a function of time in an isothermal, constant-volume batch reactor. To derive a relation between the reaction rate, r, and Cj(t), we divide both sides of Eq. 6.2.4, by obtain... 

Below, we describe tbe design formulation of isothermal batch reactors with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically by applying a numerical technique such as the Runge-Kutta method, but, in some simple cases, analytical solutions are obtained. Note that, for isothermal operations, we do not have to consider the effect of temperature variation, and we use the energy balance equation to determine tbe dimensionless heat-transfer number, HTN, required to maintain the reactor isothermal. 

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