Fed-batch reactors

The quantities VCX and VCS represent the mass of biomass and substrate respectively in the reactor. Dividing these masses by the volume V gives the concentrations Cx and Cs as a function of time, which are required in the kinetic relationships to determine rx and rs. 

A quasi-steady state process is a fed-batch fermenter where dCx/dt = 0 and p = u/V. Because V increases, p therefore decreases, and thus the reactor moves through a series of changing steady states for which p = D, during which Cs and p decrease and Cx remains constant. 

For batch reactors in which two reactants are involved, the problems encountered with a pure batch reactor can sometimes be reduced if only one of the reactants is initially charged to the vessel and the other reactant is fed gradually at a rate such that the heat removal capacity is not exceeded. We will study this mode of operation in the next section. 

Two reactor temperature controllers are now used. The first manipulates the hot and cold streams used to heat or cool the reactor. The second controller manipulates the feed flowrate. More details about this control structure are presented in Section 4.2. 

One important issue of the fed-batch operation is the variable volume of material in the reactor and its effect on heat transfer area. If jacket cooling is used, the heat transfer area covered by the liquid in the reactor will be proportional to the volume of the liquid at any point in time. However, if the reaction liquid is circulated through an external heat exchanger, the full heat transfer area is available throughout the batch cycle. 

The response is fairly oscillatory during the first 2 h when a controller gain of Kc = 0.2 and a 40 min integral time are used. Note also the droop or offset in the reactor temperature, that is, the temperature does not come up to the setpoint of 340 K. This is caused by the constantly changing load on the system. The feed flowrate is ramping up as the reactor fills and more heat transfer area permits more feed. The cooling water is wide open until the feed is cut off. 

The initial oscillatory response is reduced somewhat, and the droop toward the end of the batch is greatly reduced. The batch time decreases to 440 min. 

An important faetor in seale-up is to maintain eonstant tip speed (i.e., the speed at the end of the impeller is equal to the veloeity in both the model and full-seale plant). If the speed is too high, it ean lyse (i.e., kill) off the baeteria, and if the speed is too slow, the reaetor eontents will not be well mixed. 

Fig ure 11-23. Piping and instrumentation diagram of a fermenter. (Source Bartow [13], Supersizing the aerobic fermenter, Chem ca Engineering, pp. 70-75, July 1999. Courtesy of Chemical Engineering.) 

Choose a fermenter volume required based on tlie desued capacity. 

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Biocatalysts in nature tend to be optimized to perform best in aqueous environments, at neutral pH, temperatures below 40 °C, and at low osmotic pressure. These conditions are sometimes in conflict with the need of the chemist or process engineer to optimize a reaction with respect to space-time yield or high product concentration in order to facilitate downstream processing. Furthermore, enzymes and whole cells are often inhibited by products or substrates. This might be overcome by the use of continuously operated stirred tank reactors, fed-batch reactors, or reactors with in situ product removal [14, 15]. The addition of organic solvents to increase the solubility of substrates and/or products is a common practice [16]. 

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

Tubular reactors sometimes have side entrance points for downstream injection. Like the case of fed-batch reactors, this raises the question of how quickly the new ingredients are mixed. Mixing in the radial direction is the dominant concern. If radial mixing is fast, the assumption of piston flow may be reasonable and the addition of new ingredients merely reinitializes the problem. The equivalent phenomenon was discussed in Section 2.6.2 for fed-batch reactors. 

Reactions in fine chemicals can be divided into three categories based on their tendency to accumulate heat in a batch or fed-batch reactor [54]. This is a useful basis for assessing suitability and requirements for conversion to a continuous reactor [45], Table 14.2, and formulate a short list of suitable reactors. Figure 14.3 [55]... 

Reaction class Batch or fed-batch reactor characteristics Representative reaction time Continuous reactor requirements/benefits... 

Kapdan IK, Oztekin R (2003) Decolorization of textile dyestuff Reactive Orange 16 in fed-batch reactor under anaerobic condition. Enzyme Microb Technol 33 231-235... 

Some typical results from their simulations are presented in Fig. 16 in which the yield XQ of the product Q from the slow reaction of a set of two competitive reactions in a fed batch reactor has been plotted vs. impeller speed for two micromixing models, viz. their own CSV model and Bourne s EDD model their simulation results are compared with experimental data from Bourne and Yu (1991). For the cases shown, the CSV model may perform better than Bourne s EDD model, in particular when A is fed near to the impeller where mixing is most intense. 

Fig. 16. The yield Xg of the product Q of the slower reaction of a set of two competitive parallel reactions in a fed batch reactor plotted vs. impeller speed (in /s). The experimental data are due to Bourne and Yu (1991) the crosses refer to feeding reactant A at the top of the vessel, while the diamonds refer to feeding more closely to the impeller. The various types of lines refer to simulations as specified in the legend. Reproduced with permission from R. A. Bakker (1996).

The above simulations as to the occurrence of hot spots once more illustrate the power and promises of LES over RANS-type simulations. The hot spots can never be found by means of a RANS-type of simulation. The same technique was used by Van Vliet et al. (2006) to study the influence of the injector geometry and inlet temperature on product quality and process efficiency in the LDPE reactor. On the contrary, the RANS-based simulations due to R. A. Bakker and Van den Akker (1994, 1996) were pretty much suited to arrive at yield predictions for a fed batch reactor as a whole. 

Goronszy, M.C., Rigel, D. Simplified biological phosphorus removal in a fed-batch reactor without anoxic mixing sequences. J. W P C F 63 (3), 1991, 248-258. 

To develop analytical models that describe the performance of a cyclic enzyme system (herein termed the basic system) and a cyclic enzyme system with an external inhibitor (termed the extended basic system) when operated in different modes as a fed-batch reactor or a continuous reactor. These models enable us to design systems and select operational conditions according to needs. 

Extensive numerical simulations were performed for the basic system when operated as a fed-batch reactor. The sets of basic values used for the parameters... 

Figure 4.5 Effect of Vm,i and Vm,2 (when V. i = on the concentration of Si in the basic system when operated as a fed-batch reactor. The values of V( ,i and V 2 are indicated above. The values used for all other parameters are given in Table 4.1, set I.

In Section 4.1.4.1 results of numerical simulations were presented for the case when the basic system is operated as a fed-batch reactor. In this section, results of the numerical simulations are presented for the case when the basic system is operated in continuous reactors. The results were obtained for several reactor types. In terms of compartmental analysis (see Section 4.1.3.2) these types are determined by the number of compartments (n) considered to make up the reactor (see Figure 4.3). Three cases are presented here n = ... 

Network A is huilt of n basic systems, and all the reactions take place in a fed-batch reactor. As such, the analytical model developed for network A is an extension of the model developed for the basic system (see Section 4.1.3.1). Based on the principles detailed in Section 4.1.3.1, the operational rules of network A are described by... 

The analytical model developed for network C assumes that the reactions take place in a fed-batch reactor and is a variation of the model developed for network B (see Section 4.2.2.2). Equations (57) to (59), written for networkB, are valid here as well. In addition, the mass balances of the cofactors A and B are given by... 

The experimental system was selected based on the conclusions obtained from numerical simulations. Thus, in Section 4.1.4.1a it was found that to obtain an on/off output signal in a fed-batch reactor, the values of Vm,i and... 

To avoid massive dilution of the reaction mixture in the fed-batch reactor, the initial reactor volume was rather large relative to the flow rate of the feed streams. However, the initial volume of the reactor affects the amounts of enzymes that are required. As shown in Section 4.1.4.1, large amounts of enzymes are needed for each volume unit in the reactor, and in order to work with reasonable amounts of enzymes, this volume was limited to 50 mL. 

The initial volume of 50 mL chosen for the fed-batch reactor imposes relatively low flow rates for the feed stream, as indicated above. However, variations in the concentrations of the substrates in the feed stream are based on variations in the flow rates, and these should be accurate. These considerations lead to a need for accurate changes in a limited range of flow rates. The flow rate of 7 mL/h is in the lowest range of the rates defined by the producer for the peristaltic pumps used, so in the settings defined by the producer, accurate variations could not be obtained. Thus, the peristaltic pumps were operated with tubings of very small diameter. These tubings, of 0.5 mm inner... 

Figure 4.58 Experimental configuration employed for operation of the basic system in a fed-batch reactor. (.) control lines (----) ...

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