Reactors, batch

Batch reactors (Fig. 9.3a) are simple closed systems, which may be suitable for systems with a low rate of gas production. Any size of the reactor can be used, but smaller reactors enable higher concentration of gaseous products due to their 

A batch reactor represents a closed system, i.e., no material crosses its boundaries, and the design equation is obtained by a mass balance on one of the species involved in the reaction, which is presumed to be the limiting 

The rate of accumulation is expressed from equation 2.3 as follows, where Na is the number of moles of A present at zero fractional conversion (fA = 0)  

The rate of disappearance due to reaction in the reactor volume, Vr, actually occupied by the reacting fluid is (— rA)Vr, where rA is the rate per unit volume. 

In constant-volume batch reactors, equation 4.6 can also be written as 

Note that the rate term (—rA) will be a positive value because the stoichiometric coefficient va in the rate expression is negative (see chapter 2.1). Obviously in such reactors, sufficient mixing must be provided to assure a homogeneous system exists with no heat or mass transfer limitations. 

The classical batch reactor is a perfectly mixed vessel in which reactants are converted to products during the course of a batch cycle. All variables change dynamically with time. The reactants are charged into the vessel. Heat and/or catalyst is added to initiate reaction. Reactant concentrations decrease and product concentrations increase with time. Temperature or pressure is controlled according to some desired time trajectory. Batch time is also a design and operating variable, which has a strong impact on productivity. 

Temperature profiles are established so that conversion and yield objectives are achieved while not exceeding heat transfer capacity limitations. These optimum temperature profiles depend on the chemistry. For example, if the reaction is reversible and exothermic, the temperature profile may ramp up to a high temperature to get the reactions going and then drop off with time to avoid the decrease in the chemical equilibrium constant at high temperature. If the reaction is reversible and endothermic, the temperature profile would rise to the highest possible temperature as quickly as possible because the chemical equilibrium constant increases with temperature. 

Several special features of a batch reactor impact control  

Rigorous nonlinear models must be used in analyzing batch reactors because of the changing process parameters. Continuous reactors operate around some steady-state level, so linear models are sometime adequate for establishing controller tuning constants. 

Selecting the best time-temperature trajectory is a challenging dynamic optimization problem with constraints. There are rigorous nonlinear programming approaches to this problem, but there are also some more simple and practical methods that can be employed, as discussed in Chapter 4. 

The left-hand side of Eqn. 7.1 corresponds to the accumulation of A in the reactor. The right-hand side corresponds to the production of A. 

For a single reaction and known kinetics the balance for A, either Eqn. 7.1 or 7.3, can be integrated at a given temperature to yield a relation between the batch time and the degree of conversion  

In special cases an analytical expression can be derived for Eqn. 7.4. The assumption of constant density allows us to write  

Batch reactor relations between conversion, Xa, or concentration Ca, and batch time (constant density) 

If more than one reaction occurs, it is convenient to define the selectivity for a product Q  

Recall that F. corresponds to the flow rate of the reactant or product. We also assume that the contents of the reactor are well mixed. This simplifies the calculation of the rate  

Substituting these assumptions into the material balance provides 

We can rearrange this equation, and rewrite the number of moles in terms of the concentration and reactor volume, N.= CV. Then, for a constant volume reactor, we find 

We can put this equation in terms of the conversion by noting that 

In most cases, we are interested in either the time needed to achieve a particular conversion, or the conversion that will be obtained after a specific reaction time. Highlight 6.8 provides an application example related to the production of ethanol. 

For a BR where just one reaction takes place, an approximate transient energy balance can be written in the form as 

In Equation 6.65, it is assumed that the molar heat capacities at constant pressure and temperature have approximately the same values (CpL Cvl CpG Cvg)- The catalyst mass meat and the energy flux can be expressed by Equations 6.7 and 6.58, respectively. By inserting these definitions, the energy balance for a BR becomes 

For several simultaneous chemical reactions, the energy balance is generalized to 

The initial conditions for the energy balance equations. Equations 6.70 and 6.71, are 

The energy balance. Equation 6.70 or 6.71, is coupled to the mass balance of the BR, for example. Equations 6.39 and 6.41 or Equations 6.44 and 6.45, via the reaction rates. The mathematical similarity of the batch and plug flow models is apparent. The same numerical methods that are used to solve the plug flow model can thus be used to solve the BR model. 

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For batch reactors, account has to be taken of the time required to achieve a given conversion. Batch cycle time is addressed later. 

Using a batch reactor, a constant concentration of sulfuric acid can be maintained by adding concentrated sulfuric acid as the reaction progresses, i.e., semi-batch operation. Good temperature control of such systems can be maintained, as we shall discuss later. 

Fixing the rate of heat transfer in a batch reactor is often not the best way to control the reaction. The heating or cooling characteristics can be varied with time to suit the characteristics of the reaction. Because of the complexity of hatch operation and the fact that operation is usually small scale, it is rare for any attempt to be made... 

Figure 13.2 The heat transfer characteristics of batch reactors.

Ma.nufa.cture. In general, manufacture is carried out in batch reactors at close to atmospheric pressure. A moderate excess of finely divided potassium hydroxide is suspended in a solvent such as 1,2-dimethoxyethane. The carbonyl compound is added, followed by acetylene. The reaction is rapid and exothermic. At temperatures below 5°C the product is almost exclusively the alcohol. At 25—30°C the glycol predominates. Such synthesis also... 

The mbber latex is usually produced in batch reactors. The mbber can be polybutadiene [9003-17-2] or a copolymer of 1,3-butadiene [106-99-0] and either acrylonitrile [107-13-1] or styrene [100-42-5]. The latex normally has a polymer content of approximately 30 to 50% most of the remainder is water. 

Eigure 2 shows that even materials which are rather resistant to oxidation ( 2/ 1 0.1) are consumed to a noticeable degree at high conversions. Also the use of plug-flow or batch reactors can offer a measurable improvement in efficiencies in comparison with back-mixed reactors. Intermediates that cooxidize about as readily as the feed hydrocarbon (eg, ketones with similar stmcture) can be produced in perhaps reasonable efficiencies but, except at very low conversions, are subject to considerable loss through oxidation. They may be suitable coproducts if they are also precursors to more oxidation-resistant desirable materials. Intermediates which oxidize relatively rapidly (/ 2 / i — 3-50 eg, alcohols and aldehydes) are difficult to produce in appreciable amounts, even in batch or plug-flow reactors. Indeed, for = 50, to isolate 90% or more of the intermediate made, the conversion must... 

Eig. 3. Plot of maximum yield as a % of maximum (zero conversion) efficiency to a primary intermediate x axis is ratio of oxidation rate constants ( 2 / i) for primary intermediate vs feed ( ) plug-flow or batch reactor (B) back-mixed reactor (A) plug-flow advantage, %. 

The typical SEA process uses a manganese catalyst with a potassium promoter (for solubilization) in a batch reactor. A manganese catalyst increases the relative rate of attack on carbonyl intermediates. Low conversions are followed by recovery and recycle of complex intermediate streams. Acid recovery and purification involve extraction with caustic and heat treatment to further decrease small amounts of impurities (particularly carbonyls). The fatty acids are recovered by freeing with sulfuric acid and, hence, sodium sulfate is a by-product. 

Soap-starved recipes have been developed that yield 60 wt % soHds low viscosity polymer emulsions without concentrating. It is possible to make latices for appHcation as membranes and similar products via emulsion polymerization at even higher soHds (79). SoHds levels of 70—80 wt % are possible. The paste-like material is made in batch reactors and extmded as product. 

The reaction is exothermic reaction rates decrease with increased carbon number of the oxide (ethylene oxide > propylene oxide > butylene oxide). The ammonia—oxide ratio determines the product spht among the mono-, di-, and trialkanolamines. A high ammonia to oxide ratio favors monoproduction a low ammonia to oxide ratio favors trialkanolamine production. Mono- and dialkanolamines can also be recycled to the reactor to increase di-or trialkanolamine production. Mono- and dialkanolamines can also be converted to trialkanolamines by reaction of the mono- and di- with oxide in batch reactors. In all cases, the reaction is mn with excess ammonia to prevent unreacted oxide from leaving the reactor. 

The relatively low capital cost of the simple batch reactor is its most enticing feature. The inabiUty to operate under pressure typically limits the simple batch reactor to use with the higher alkenes ie, octenes, nonenes, and dodecenes. For mainly economic reasons, these reactors are usually mn at phenol to alkene mole ratios of between 0.9 and 1.1 to 1. 

The complex batch reactor is a specialized pressure vessel with excellent heat transfer and gas Hquid contacting capabiUty. These reactors are becoming more common in aLkylphenol production, mainly due to their high efficiency and flexibiUty of operation. Figure 2 shows one arrangement for a complex batch reactor. Complex batch reactors produce the more difficult to make alkylphenols they also produce some conventional alkylphenols through improved processes. 

The same four operating steps are used with the complex batch reactor as with the simple batch reactor. The powerhil capabiUties of the complex batch reactor offset their relatively high capital cost. These reactors can operate at phenol to alkene mole ratios from 0.3 to 1 and up. This abiUty is achieved by designing for positive pressure operation, typically 200 to 2000 kPa (30 to 300 psig), and for the use of highly selective catalysts. Because these reactors can operate at low phenol to alkene mole ratios, they are ideal for production of di- and trialkylphenols. 

Unrefined alkylphenols are generally produced in the simple batch reactors described eadier. An alkene with between 8 and 12 carbon atoms reacts with phenol to produce a mixture of reactants, mono alkylphenols, and dialkylphenols. These mixtures usually do not free2e above 25 °C and so are Hquid at production and storage conditions. The product is generally used in the same factory or complex in which it is produced so shipment typically consists of pumping the material from the reactor to a storage tank. 

Dialkylphenols are also produced in specialized plants. These plants combine complex batch reactors with vacuum distillation trains or other recovery systems. Alkenes with carbon numbers between 4 and 9 react with phenol to make an unrefined alkylphenol mixture, which is fed into the recovery section where very high purity product is isolated. The product is stored, handled, and shipped just as are the monoalkylphenols. 

Batch vs Continuous Reactors. Usually, continuous reactors yield much lower energy use because of increased opportunities for heat interchange. Sometimes the savings are even greater in downstream separation units than in the reaction step itself Especially for batch reactors, any use of refrigeration to remove heat should be critically reviewed. Batch processes often evolve Httle from the laboratory-scale glassware setups where refrigeration is a convenience. 

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

Batch reactors often are used to develop continuous processes because of their suitabiUty and convenient use in laboratory experimentation. Industrial practice generally favors processing continuously rather than in single batches, because overall investment and operating costs usually are less. Data obtained in batch reactors, except for very rapid reactions, can be well defined and used to predict performance of larger scale, continuous-flow reactors. Almost all batch reactors are well stirred thus, ideally, compositions are uniform throughout and residence times of all contained reactants are constant. 

The manufacture of siHcone polymers via anionic polymerization is widely used in the siHcone industry. The anionic polymerization of cycHc siloxanes can be conducted in a single-batch reactor or in a continuously stirred reactor (94,95). The viscosity of the polymer and type of end groups are easily controUed by the amount of added water or triorganosUyl chain-terminating groups. 

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