B Semi-Batch Reactor

A semi-batch reactor is used to convert reactant, A, to product, B, by the reaction A - 2 B. The reaction is carried out adiabatically. The reaction kinetics are as before 

The balances for the two components A and B, with flow of A, into the reactor 

With initial conditions for the initial molar quantities of A and B (VCA, VCB), the initial temperature, T, and the initial volume of the contents, V, specified, the resulting system of equations can be solved to obtain the time-varying quantities, V(t), VCA(t), VCB(t), T(t) and hence also concentrations CA and CB as functions of time. Examples of semi-batch operations are given in the simulation examples HMT, SEMIPAR, SEMISEQ, RUN, SULFONATION and SEMIEX. 

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Figure 7.1 Modes of reactor operation (a) batch reactor, (b) semi-batch reactor, (c) continuous stirred-tank reactor, and (d) continuous plug flow reactor.

Optimization sequence (experimental data, arbitrary units) Runs 1 and 2 are initial experiments. From run 3 to run 6 the amounts of A, B, G, and feed rate of G are fixed. These constraints are relaxed for runs 7 and 8. (Reprinted from Marchal-Brassely et al. (1992), Optimal operation of a semi-batch reactor by self-adaptive models for temperature and feed profiles . Copyright (1992), with permission from Elsevier Science). 

A complex reaction is run in a semi-batch reactor with the purpose of improving the selectivity for the desired product, P. The kinetics are sequential with respect to components A, P and Q but parallel with respect to B. The relative orders of the reactions for the reactions determine the feeding policy. 

For a simple A + B C reaction the semi-batch reactor balance is... 

Figure 5.137. Program SEMISEG Varying THETAMIX (0.03, 0.1, 0.3 and 0.6, curves D, C, A, B) gave these results for the semi-batch reactor. Note that when THETA > 1 the reactor becomes continuous.

The triangular region in Fig. 5.12 can also be used to analyze the effect of micromixing in semi-batch reactors wherein the stream containing B is slowly added to a reactor initially containing only A. In this reactor, the mean mixture fraction is an increasing function of time ... 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

Generally the oxidation of compounds with ozone is considered to be second order, which means first order with respect to the oxidant (03 or OH°) and to the pollutant M (Hoigne and Bader, 1983 a, b). A requirement for the experimental determination of the reaction order with respect to the pollutant is that the ozone concentration in the bulk liquid remains constant. A further requirement for determining kinetic parameters in general, is that the reaction rate should be independent of the mass transfer rate. These are easy to achieve for (very) slow reactions by using a continuously sparged semi-batch reactor. Such a reaction... 

Figu re 7.1 Semi-batch reactor compound A is initially charged and B is fed during the reaction, providing additional control of the reaction course. 

Equations 7.4 and 7.5 form a system of differential equations for which no analytical solution is known. Thus, the description of the behavior of the semi-batch reactor with time requires the use of numerical methods for the integration of the differential equations. Usually, it is convenient to use parameters which are more process-related to describe the material balance. One is the stoichiometric ratio between the two reactants A and B ... 

Figure 7.3 Concentrations in molkg as a function of time in a semi-batch reactor with the fast addition reaction. Compound B is fed at constant rate within 4 hours in a stoichiometric excess of 25%. B is fed in stoichiometric amounts.

Figure 7.6 Concentration profiles in a semi-batch reactor showing the accumulation (bold line). The total feed time is 4 hours and B is fed in 25% stoichiometric excess. Hence the accumulation is at its maximum at the stoichiometric point reached after 3.2 hours.

It is clear that a low concentration of B will maximize the formation of the desired product P and minimize the formation of the secondary product S. This goal can be achieved with a semi-batch reactor where B is added progressively to the reaction mass. 

C. Filippi, J.L. Greffe, J. Bordet, J. Villermaux, J.L. Barnay, B. Ponte, and C. Georgakis. Tendency modeling of semi-batch reactors for optimization and control. Chemical Engineering Science, 41 913-920, 1986. 

O. Ubricha, B. Srinivasanb, P. Lerenac, D. Bonvin, and B. Stoessel. The use of calorimetry for on-line optimisation of isothermal semi-batch reactors. Chemical Engineering Science, 56 5147-5156,2001. 

Fig. 7.1 Nonideal batch reactors liquid-phase batch reactor (a), liquid-phase batch reactor with release of gaseous bubbles (b), semi-batch gas-liquid bubble column (c), and slurry batch reactor (d)...

The model predicts the yield of S Xg = 2S/ (2 S + R) at the end of the reaction (when all B is consumed). It was developed for batch and semi-batch reactors (119, 120), and later extended to continuous stirred reactors via a somewhat complicated procedure (121-112). Some criticism may be adressed, to the MIRE-model, in spite of its great interest arbitrary choice of spherical shape, assimilation of R to half the Kolmogorov microscale (which is not obvious as we have seen above) and above all, assumption that the initial reactant in the particle cannot diffuse outside, which creates an unwanted dissymmetry between A and B when V = Vg. 

Figure 3.10 Fractions of paraffins, olefins, naphthene and aromatic products from the catalytic degradation of plastics over spent FCC catalyst in a semi-batch reactor (400°C, P/C= 10, A/= 200 rpm) (a) HDPE (b) LDPE [70]. (Reproduced with permission from Elsevier)...

This reaction is conducted in an isothermal semi-batch reactor. The desired product in this system is C. The objective is to convert as much as possible of reactant A by the controlled addition of reactant B, in a specified time //= 120 min. It is not appropriate to add all B initially because the second reaction will take place, increasing the concentration of the undesired by-product D. Therefore, to keep a low concentration of product D and at the same time increase the concentration of product C, the reactant B has to be fed in a stream with concentration = 0.2. A mechanistic model for this process can be found in [11]. 

Styrene-acrylonitrile copolymerization in a semi-batch reactor Two cases (a) maximization of monomer conversion and minimization of polydispersity index at the end of reaction, and (b) maximization of monomer conversion at the end of reaction while minimizing polydispersity index at the end of reaction and molar ratio of unreacted monomer in the reactor at any time. NSGA-11 The decision variables for optimization were trajectories of addition rate of a monomer-solvent-initiator mixture and reactor temperature. Nayak and Gupta (2004)... 

UDP4-Sb The liquid-phase reaction 2A + B esC -I- D is carried out in a semi-batch reactor. Plot the conversion, volume, and species concentrations as a function of time. Reactive distillation is also considered in part (e). [2nd Ed. P4-27]... 

Semi-batch reactor addition of component B to starting... 

Figure 10 UV-VIS spectra of LaHY zeolite used in a semi-batch reactor, isobutane alkylation with C4 olefins, (I) Influence of reaction temperature at LHSV=4.07 h , (A)80 °C, (B) 100°C (II) influence ofLHSVat 80 °C, (A) 2.27 h (B) 3.86 h , (C) 4.07 h (from Ref 55)...

Brooks, B.W., 1988. Semi-batch reactors and their use for autocat-alytic reactions. Chem. Eng. Sci. 43, 1287-1290. 

In this case, we maximize Sp by maintaining a low [A]. Maintaining a high [B] ensures a high P formation rate. Thus, we would choose a semi-batch reactor for this process we would charge the reactor with B and feed A at a rate appropriate to obtain a high p. If a < 7 and P<6, then... 

If C enters the process with A and D enters the process with B, then we would use a semi-batch reactor. Which reactant is completely charged to the reactor and which reactant is fed to the reactor during the process is a matter of our convenience. If C and D enter the process with either A or B, then we would, again, use a semi-batch reactor however, we would charge the reactor with the C- and D-free reactant and feed the other reactant to it. 

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