The Isothermal Batch Reactor

Batch and semibatch reactors are most often used for low production capacities, where the cost of labor and dead time are only a small fraction of the unit cost of the product. They are generally encountered in the area of specialty chemicals and polymers and in pharmaceuticals, in particular, in plants with a wide variety of products. Large batch reactors are used in fermentations for antibiotic production, an example of which is given in Fig. 8-1. 

Because of the uniformity of concentration, the continuity equation for the key reactant A may be written for the entire reactor volume  

These mass balances, for example (8.1-1), are often written in terms of conversions  

Note that the batch residence time 6 can be interpreted as the area from Xao to X.4/under the curve of Nao / VrA xa) versus Xa- 

The above equations were already encountered in Section 1.1.2 of Chapter 1. The equations defining reaction rates were written there for a point , a volume in which the composition is uniform. This is also assumed here for the ideal, well stirred batch reactor, whatever its volume. 

These mass balances are often written in terms of conversions  

For constant (T, p,), this reduces to the special case defined by Levenspiel [1]. Next, the concentrations, for substitution into the rate formula, can be expressed as 

---

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

Some authors [120—122] have collected simple kinetic systems and attempted to solve the corresponding characteristic equations explicitly in the case of an isothermal, constant volume batch reactor. In view of the fact that most reaction mechanisms are not simple ones or are not considered in these collections or are not amenable to an explicit solution and that types of reactors other than the isothermal batch reactor are used in kinetics, this approach (involving, furthermore, standard mathematics) will not be discussed further here. 

Equations will be derived for three representative cases the tubular reactor of annular cross-section the isothermal, well-mixed batch reactor and the isothermal batch reactor inside a recirculating system. The chosen exemplifications will deal with these types of reactors that are, without doubt, the most widely used. 

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. 

The following reactions are occurring in a constant-volume, isothermal batch reactor ... 

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

Miller et al. (1981) studied the kinetics of the reaction of phenol and acetone to bisphenol A in the presence of hydrogen chloride (see Fig. 5.4-31) in an isothermal batch reactor. 

The experimental method used for this kinetie study is reaetion ealorimetry. In the ealorimeter, the energy enthalpy balance is continuously monitored the heat signal can then be easily converted in the reaction rate (in the case of an isothermal batch reactor, the rate is proportional to the heat generated or consnmed by the reaction). The reaction orders and catalyst stabihty were determined with the methodology of reaction progress kinetic analysis (see refs. (8,9) for reviews). 

Volume changes on reaction may be neglected. At 25 °C the reaction rate constant is equal to 9.92 x 10 3 m3/kmole sec. If one employs a well-stirred isothermal batch reactor to carry out this reaction, determine the holding time necessary to achieve 95% conversion of the limiting reagent using initial concentrations of 0.1 and 0.08 kmole/m3 for cyclopentadiene and benzoquinone, respectively. 

A liquid-phase reaction A + B - products is conducted in an isothermal batch reactor. The... 

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 ... 

Investigate an isothermal, batch reactor (Set batch=l und isothermal=l) with an irreversible first-order (k1 k2). For this purpose set REST to a very high value, say le20. Determine the necessary reaction time to achieve a fraction conversion, XA, of 90, 95 und 99%. Determine also the cycle time and the productivity. For this assume the down-time between batches is 30 min (1800 s). Perform this for two different temperatures between 300K and 320K. 

The maximum conversion of reactants which can be achieved in an isothermal batch reactor is determined by the position of thermodynamic equilibrium. If this conversion is regarded as unsatisfactory, the use of a simple batch reactor may be abandoned in favour of a reactor which permits removal of products from the reaction mixture. Alternatively, the reactor temperature may be changed to obtain a more favourable equilibrium however, this may result in an unacceptable reduction in the net reaction rate. Such conflicts are often resolved by the use of optimisation procedures (see Sect. 8). 

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. 

Reactant A decomposes in an isothermal batch reactor (Cao = 100 ) to produce wanted R and unwanted S, and the following progressive concentration readings are recorded ... 

One measures Cj (t, T) for given Cjo and then finds a suitable method of analyzing these data to find a suitable rate expression that will fit them. For liquid solutions the typical method is to obtain isothermal batch-reactor data with different Cjo and continues to gather these data as a function of temperature to find a complete rate expression. For a simple irreversible reaction we expect that the rate should be describable as... 

Assuming that we have an irreversible reaction with a single reactant and power-law kinetics, r = kC, the concentration in a constant-volume isothermal batch reactor is given by integrating the expression... 

For a first-order irreversible reaction in an isothermal batch reactor X(t) = 1 — e (Chapter 2) so the average value of X is... 

Ethyl acetate is to be manufactured by the esterification of acetic acid with ethanol in an isothermal batch reactor. A production rate of 10 tonne/day of ethyl acetate is required. 

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. 

The gas-phase decomposition of sulfuryl chloride, S02C12 — S02 + Cl2, is thought to follow a first order rate law. The reaction is performed in a constant volume, isothermal batch reactor, and the concentration of S02C12 is measured at several reaction times, with the following results. 

Assuming that the reaction is first order in an isothermal batch reactor of constant volume, then the rate equation for the reaction... 

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. 

Consider an isothermal batch reactor for a given conversion of the reactant... 

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,... 

Insert the rate expression into batch-reactor material balance. A transient material balance for the NaOH on an isothermal batch reactor becomes (NaOH in) — (NaOH out) + (net NaOH generation) = NaOH accumulation. For this system,... 

---