Isothermal operation, batch reactor

An ideal batch reactor is a perfectly stirred tank of constant volume with no mass transfer from or to the outside. There is a single residence time, which is simply the duration of the reaction. Generally, a batch reactor is operated isothermally and therefore the reaction temperature may be considered as an independent variable. 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

Most kinetic experiments are run in batch reactors for the simple reason that they are the easiest reactor to operate on a small, laboratory scale. Piston flow reactors are essentially equivalent and are implicitly included in the present treatment. This treatment is confined to constant-density, isothermal reactions, with nonisothermal and other more complicated cases being treated in Section 7.1.4. The batch equation for component A is... 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

ILLUSTRATION 10.1 DETERMINATION OF REQUIRED REACTOR VOLUMES FOR ISOTHERMAL AND ADIABATIC OPERATION IN A BATCH REACTOR... 

Pure phosphine is to be admitted to a constant volume batch reactor and allowed to undergo decomposition according to the above reaction. If pure phosphine enters at 672 °C and the initial pressure is 1 atm, determine the times necessary to decompose 20% of the original phosphine for both isothermal and adiabatic operation. 

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. 

Determine the time required for 80% conversion of 7.5 mol A in a 15-L constant-volume batch reactor operating isothermally at 300 K. The reaction is first-order with respect to A, with kA = 0.05 min-1 at 300 K. 

The Diels-Alder liquid-phase reaction between 1,4-benzoquinone (A, C6H4O2) and cy-clopentadiene (B, C5H6) to form the adduct CnHm02 is second-order with a rate constant kx = 9.92 X 10 6 m3 mol 1 s 1 at 25°C (Wassermann, 1936). Calculate the size (m3) of a batch reactor required to produce adduct at the rate of 125 mol h 1, if cAo = cBo = 100 mol m 3, the reactants are 90% converted at the end of each batch (cycle), the reactor operates isothermally at 25°C, and the reactor down-time (for discharging, cleaning, charging)... 

A liquid-phase reaction, A products, was studied in a constant-volume isothermal batch reactor. The reaction rate expression is (-rA) = kAcA, and k = 0.030 min 1. The reaction time, t, may be varied, but the down-time, td, is fixed at 30 min for each cycle. If the reactor operates 24 hours per day, what is the ratio of reaction time to down-time that maximizes production for a given reactor volume and initial concentration of A What is the fractional conversion of A at the optimum ... 

A performance comparison between a BR and a CSTR may be made in terms of the size of vessel required in each case to achieve the same rate of production for the same fractional conversion, with the BR operating isothermally at the same temperature as that in the CSTR. Since both batch reactors and CSTRs are most commonly used for constant-density systems, we restrict attention to this case, and to a reaction represented by... 

The batch reactor operates isothermally at the same temperature as the CSTR. The CSTR operates at steady-state. 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

Operate the batch reactor of Exercise 1 with a constant cooling water flowrate (Parameter batch = 1 und isothermal = 0) Flowrates FC = 0, 0.02, 0.025 and 0.03. For each value of FC observe the profiles of Tl, TC, XA. Zoom in to make observations on the initial phase of the reaction. 

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 experimental batch reactor is usually operated isothermally and at constant volume because it is easy to interpret the results of such runs. This reactor is a relatively simple device adaptable to small-scale laboratory set-ups, and it needs but little auxiliary equipment or instrumentation. Thus, it is used whenever possible for obtaining homogeneous kinetic data. This chapter deals with the batch reactor. 

When we can predict the response of the reacting system to changes in operating conditions (how rates and equilibrium conversion change with temperature and pressure), when we are able to compare yields for alternative designs (adiabatic versus isothermal operations, single versus multiple reactor units, flow versus batch system), and when we can estimate the economics of these various alternatives, then and only then will we feel sure that we can arrive at the design well fitted for the purpose at hand. Unfortunately, real situations are rarely simple. 

In this chapter we consider the fundamentals of reaction in continuous isothermal reactors. Most industrial reactors are operated in a continuous mode instead of batch because continuous reactors produce more product with smaller equipment, require less labor and maintenance, and frequently produce better quahty control. Continuous processes are more difficult to start and stop than batch reactors, but they make product without stopping to change batches and they require rninimum labor. 

All reactors, batch or flow, may be operated in three main ways in regard to temperature. These are isothermal, adiabatic and temperature-programmed. For the last, in a batch reactor the variation of temperature with time may be programmed, or in a fixed bed reactor the variation of temperature along the length of the bed may be controlled. 

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. 

A more quantitative analysis of the batch reactor is obtained by means of mathematical modeling. The mathematical model of the ideal batch reactor consists of mass and energy balances, which provide a set of ordinary differential equations that, in most cases, have to be solved numerically. Analytical integration is, however, still possible in isothermal systems and with reference to simple reaction schemes and rate expressions, so that some general assessments of the reactor behavior can be formulated when basic kinetic schemes are considered. This is the case of the discussion in the coming Sect. 2.3.1, whereas nonisothermal operations and energy balances are addressed in Sect. 2.3.2. 

First, the detailed model is used to simulate the behavior of the real system, and a set of simulated isothermal experimental data is generated including the total heat released by reaction. Then, these data are used to estimate the kinetic parameters of the reduced models and the heats of reaction of the lumped reactions. Finally, the reduced kinetic models are tested in a validation procedure which simulates the operation of a batch reactor and allows one to identify the best reduced model. 

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)]. 

Consider a non-isothermal batch reactor that is operated adiabatically. The reactor contains a liquid reaction mixture in which the reaction A —> Products occurs, where (-rA) = kCA and k = k0e E/RT,... 

External mass transfer limitations, which cause a decrease in both the reaction rate and selectivity, have to be avoided. As in the batch reactor, there is a simple experimental test in order to verify the absence of these transport limitations in isothermal operations. The mass transfer coefficient increases with the fluid velocity in the catalyst bed. Therefore, when the flow rate and amount of catalyst are simultaneously changed while keeping their ratio constant (which is proportional to the contact time), identical conversion values should be found for flow rate high enough to avoid external mass transfer limitations.[15]... 

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