Batch Reactor with Consecutive Reactions

If consecutive reactions are conducted in a batch reactor, the optimization of the process includes finding the optimum time to stop the batch and determining the optimum temperature. To illustrate the issues, we take the simple reactions 

We assume the desired product to be B. If the reaction is allowed to run for too long, the amount of undesirable C produced may be too high and the yield of B may be lower than if the batch were stopped earlier. If the activation energy of the second reaction is larger than the first, increasing reactor temperature lowers the yield of B but reduces the batch time. Therefore both the reactor temperature and the batch time must be optimized. 

For an illustrative numerical example, the preexponenhal factor and activation energy given in Table 2.1 are used for the first specific reaction rate k (k,n = 20.75 x 106 s-1 and Ei = 69.71 x 106 J/krnol). The activation energy of the second reaction is assumed to be twice that of the first. The preexponential factor for the second reaction is calculated to give a ratio of k to ky of 10 when the temperature is 340 K ( 02 = 10.642 x 1016 s-1). 

Determining the optimum time and optimum temperature involves an economic balance between shorter batch times and less concentrated reaction liquid at the end of the batch, which implies higher capital and energy costs to purify the product and recover byproducts. 

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Figure 4.44 Fed-batch reactor with consecutive reactions F ramped from 2 to 1 L/min.

Consider the consecutive reactions, A -A B -A C, with rate constants of kj = 1015exp(— 10,000/r) and kn = 10s exp(—5000/T). Find the temperature that maximizes bout for a CSTR with 1=2 and for a batch reactor with a reaction time of 2 h. Assume constant density with = cin = 0. 

For the situation in which each of the series reactions is irreversible and obeys a first-order rate law, eqnations (5.3.4), (5.3.6), (5.3.9), and (5.3.10) describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For consecutive reactions in which all of the reactions do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time at which the concentration of a particular intermediate passes through a maximum. If interested in designing a continuous-flow process for producing this species, the chemical engineer must make appropriate allowance for the flow conditions that will prevail within the reactor. That disparities in reactor configurations can bring about wide variations in desired product yields for series reactions is evident from the examples considered in Illustrations 9.2 and 9.3. 

Suppose the consecutive first-order reactions described on page 77 occur at constant density in a batch reactor, with an initial mixture containing only AdXz. concentration [ ]o- Show on a triangular diagram the reaction paths for three cases k jk — 0.5, 1.0, and 2.0. 

Figure 1.10 Batch reactor with two consecutive reactions.

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

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 ... 

The first-order consecutive exothermic reaction sequence, A —> B —> C, is carried out in a thick-walled, jacketed batch reactor, provided with both jacketed heating and cooling, as shown below. 

The catalyst/substrate ratio is 1.5 mol% for the supported ionic liquid phase (SILP) catalyst, 3 mol% for the impregnated catalyst and 2 mol% for the homogeneous reaction aRuns 1 -4 are consecutive experiments with the same catalyst in a stirred batch reactor. bDimeric Cr (salen) catalyst impregnated on silica cHomogeneous reaction at 0-2 OC optimized for product selectivity dHomogeneous reaction at room temperature optimized for product selectivity... 

With consecutive—parallel systems in which the reaction steps are not first order, analytical expressions for species concentrations as functions of time (which would apply to batch reactors) are sometimes unobtainable. Numerical procedures can be used. However, analytical procedures can still be used to obtain some indication of relative yields of reaction... 

The major advantage of the use of CuHY as a catalyst for this reaction is the ease with which it can be recovered from the reaction mixture by simple filtration if used in. a batch reactor (alternatively it can be used in a continuous flow fixed bed reactor). We have carried out the heterogeneous asymmetric aziridination of styrene until completion, filtered and washed the zeolite then added fresh styrene, PhI=NTs and solvent, without further addition of chiral bis(oxazoline), for several consecutive experiments. The yield and the enantioselectivity decline slightly on reuse we have found that adsorbed water can build up within the pores of the zeolite on continued use and we believe that this is the cause of loss of activity and enantioselection. However, full enantioselectivity and yield can be recovered if the catalyst is simply dried in air prior to reuse, or alternatively the catalyst can be recalcined and fresh oxazoline ligand added. 

Despite the experience with batch reactors it may be worthwhile to operate continuous reactors also for fine chemicals. Continuously operated reactors only demand for one start-up and one shut-down during the production series for one product. This increases the operating time efficiency and prevents the deactivation of dry catalysts this implies that the reactor volume can be much smaller than for batch reactors. As to the reactor type for three phase systems an agitated slurry tank reactor [5,6] is not advisable, because of the good mixing characteristics. Specially for consecutive reaction systems the yields to desired products and selectivities will be considerably lower than in plug flow type reactor. The cocurrent down flow trickle flow reactor... 

A Fortran IV computer program developed by Redifer and Wilson (10) was used to predict thermodynamic equilibrium compositions for 400-700°K and 1 atm total pressure. The calculations are based on a procedure presented by Meissner, Kusik, and Dalzell (11) in which the set of simultaneous reactions is simplified to a set of series-consecutive reactions. Each reaction is carried out in turn on the reactant mixture as though a set of ideal batch equilibrium reactors were aligned in series in which the products from one equilibrium stage become reactants for the next reactor. After all the reactions have been completed, products from the last reactor are recycled to the first reactor, and the reaction sequence is repeated. Equilibrium of all components is complete when the product compositions at the end of two consecutive cycles are identical. The method compares favorably with the free energy minimization technique and is useful for changing conditions or input parameters. 

Viewed from the perspective of ethylene oxide, these reactions are competitive by contrast, from the perspective of the amines, they are consecutive. Consider a research scale batch reactor operating at 60°C and 20 bar to maintain all species in the liquid phase. Actual production of these commodity products on a large scale would be conducted in flow reactors, as described in Illustration 9.5. The rate laws are of the mixed second-order form (first-order in each reactant), with hypothetical rate constants ki, k2, and equal to 1,0.4, and 0.1 L-moCV min, respectively. MEA and DEA are both high-volume chemicals, while TEA is less in demand. The distribution of alkanolamine products obtained under the specified conditions can be influenced by controlling the initial mole ratio of EO to A and the time of reaction. 

The fluorous biphase catalyst recovery concept was tested by performing nine consecutive reactions in a batch reactor. A total loss of 4.2% of rhodium was detected, and the decreasing 1 b ratio suggested some ligand leaching. The total turnover number reached with the system was 35,000 mole of aldehyde/mole rhodium, with a rhodium loss of 1.18 ppm per mole of aldehyde. Further optimization of this system, i.e. the use ofheavier fluorous solvents and longer pony tails, should decrease the amoimt of catalyst and fluorous solvent leaching. 

Consecutive reactions. Evolution of conversions with holding- or space time in batch or plug flow and perfectly mixed reactors. 

For consecutive reactions batch and plug flow reactors will always give a higher selectvity than well mixed continuous reactors. For competitive-consecutive reactions the best selectivity can be found in semi-batch reactors. However, this type of reactions can in some cases be carried out with an acceptable selectivity in a continuous well mixed reactor, when sufficient excess of the "other reactant (that does not cause undesired reactions) is applied. 

Staged reactions, where only part of the initial reactants are added, either to consecutive reactors or with a time lag to the same reactor, maybe used to reduce dipentaerythritol content. This technique increases the effective formaldehyde-to-acetaldehyde mole ratio, maintaining the original stoichiometric one. It also permits easier thermal control of the reaction (66,67). Both batch and continuous reaction systems are used. The former have greater flexibiHty whereas the product of the latter has improved consistency (55,68). 

Dilution, separation, and neutralization can take place in the same reactor or several batch units may be used for the consecutive steps (see also Sec. XX.X). Sulfuric acid sulfonation in a continuous loop reactor system is feasible when an H2S04/AB ratio of at least 1.80 is applied. In this case, as well as when 20% oleum is used, reasonably short reaction times are sufficient to complete the reaction. With increasing H2S04/AB ratio, the amount of dark 80% sulfuric acid (spent acid) will increase proportionally. 

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