Feed policies

Figure 1, Forcing functions for monomer (fu) and initiator (fi) feeds (a) sinusoidal (b) square-wave (c) reception vessel valve operating sequences which are synchronized with the feed policies (see Figure 2 for the location of the valves...

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. 

The control strategies for determining the feed policies were decided on the basis of a numerical solution of the terpolymerisations described by equations 1 - 3 using a microcomputer and a general purpose simulation package, BEEBSOC (10). Where necessary, these data were acquired in the course of this study, otherwise literature values were used. The apparent first order rate constants in terpolymerisations have been shown to be composition dependent. The variation in rate constants with... 

Level 7 Process-Control System. The key issues of process dynamics and control, namely fresh feed policy and stability in operation of the reaction/separation/ recycle system, are solved at Level 3. Consequently, the implementation of a process-control system may be realized without affecting the basic flowsheet structure, but taking into account fundamental process control principles, as proposed in the methodology developed by Luyben and Tyreus [20]. 

A number of alternatives can emerge, both as arrangement of internals and flowsheet configuration, such as for example, distribution of reaction and separation zones, feed policy, use of pre- or postreactors. The best alternative is selected taking into account economic and operational aspects, such as for example the minimization of byproducts and the preservation of catalyst activity over a longer period. 

Recently, many batch operations have been transformed into fed-batch (semicontinuous) operations by the gradual introduction of nutrient into the reactor. The rationale is to control the feed optimally to maximize a composite performance index. For the case of penicillin fermentation, for example, for which the specific growth rate and the specific penicillin formation rate are mutually disposed, the optimal feed policy is carried out in two phases. During the first phase, cell biomass is quickly built up to the allowable maximum level. During the second product formation phase, the feed is controlled such that... 

Fig. 3 Changed catalyst feeding policy the catalyst is fed sooner (second shot at 220 min, third shot at 380 min) and in smaller mass.

The first topic developed in this chapter is the interrelation between steady state design and controllability. Particular attention will receive the generic stmcture Reactor-Separator-Recycle. We consider that material balance has priority in establishing the plantwide control strategy. That is why we will examine in the first place the effects induced by the recycle of mass. Particular attention will receive the feed policy of the reactants, as well as the handling of impurities, both fundamental plantwide control issues. Then we will examine the effect of recycling energy, with emphasis on heat... 

The issue of reactant feed policy in recycle systems has been raised by Bill Luyben. Complete references and ampler presentation can be found in his recent book (1999). Here we will examine two typical situations involving a bimolecular reaction. In the first the reference reactant is completely converted, while the other one is recycled. The second case considers that both reactants are incompletely converted and recycled. 

Suppose that the reactant A is totally consumed. If the reaction rate is not infinite, the reactant B must be recycled at a convenient rate, in such a way that the resulting reaction rate leads to the total consumption of A. Therefore, we may speak about total conversion of the one-pass reactant, and partial conversion of the recycled reactant. Because the feed of fresh reactants must respect the stoichiometry, the feed policy of B must be adapted to fulfil the dynamic material balance. The above situation can be found often in industry, as for instance the synthesis of ethers from alchene-oxides and alcohols, the alkylation of benzene with ethylene or propylene to ethylbenzene or cumene, the addition of HCN to ketones, etc. 

Figure 13.10 Feed policy for a recycle system with incomplete bimolecular reaction. Alternative A both reactants on feed control...

Examine alternative feed policies for a fresh feed of 10 kmole/h of A and B. 

We start by examining the feasibility of alternative feeding policies by steady state simulation in Aspen Plus. Figure 13.12 depicts the flowsheet. The key units are the reactor and the distillation column. We chose a PFR model, with 100% per-pass conversion of A. The reactant B is converted exactly in the same proportion as the amount of fresh A, but the excess is recovered by distillation and recycled. Further, we consider a distillation column with 10 stages and feed in the middle. 

Summing up, the above example demonstrates that the feed policy is a plantwide control problem. When several reactants are involved, only one can be set on flow control. The make-up of the other reactants must be implemented in a way that prevents a permanent accumulation (positive or negative) in the dynamic material balance. Thus, fixing the recycle flow of the second partner in a bimolecular reaction has proved to be an efficient method to stabilise the variability of recycle streams. However, this is not the panacea for feeding the reactants. The next section will bring supplementary insights. 

Figure 13.14 Feed policy for a second order reaction with recycle of both reactants from a single distillation column...

The feed policy of reactants is a plantwide control problem. Setting all reactants on flow control leads typically to conflicts in the dynamic material balance. Control problems can be identified even for monomolecular reactions carried out in the simple flowsheet CSTR-... 

Two basic monomer feed policies employed in a semibatch copolymerization can be used to minimize composition drift [163]. Many highly effective commercial processes are based on one or a combination of these policies. Additional promising derivations of these policies have also been presented [167-173]. Henceforth, we refer to the two basic feed policies as Policy I and Policy II, as described in following sections. 

The practical implementation of the above policies is not necessarily as straightforward as solving the above equations. As can be deduced from Equations 6.70-6.76, Pjjjj is a function of the propagation rate coefficients, the monomer concentrations, and most importantly, the total radical concentration. Hence, to precalculate the optimal monomer feed rates, the radical concentration must be specified in advance and kept constant via an initiator feed policy and/or a heat production policy. This is especially important considering that a constant radical concentration is not a typical polymer production reality. This raises the notion that one could increase the reactor temperature or the initiator concentration over time to manipulate the radical concentration rather than manipulate the monomer feed flowrates, that is, keep P j constant for simpler pump operation. Furthermore, these semibatch policies provide the open-loop or off-line optimal feed rates required to produce a constant composition product. The online or closed-loop implementation of these policies necessitates a consideration of online sensors for monomer... 

Another practical consideration relates to the use of the semibatch feed policies in emulsion copolymerization. One would need to account for the partitioning of monomers in the different phases as well as the presence of monomer droplets (desired or not) during the particle nucleation and growth stages. 

There are two basic monomer feed policies (and several modiflcations of the basic ones) that may be used in semibatch polymerization to minimize compositional drift (or optimize other properties). See Hamielec et al. [22] and Fujisawa and Penlidis [43] for more details. 

It often becomes necessary in biochemical reactions to continuously add one (or more) substrate(s), a nutrient, or any regulating compound to a batch reactor, from which there is no continuous removal of product. A reactor in which this is accomplished is conventionally termed the semibatch reactor (Chapter 4) but is referred to as a fed-batch reactor in biochemical language. The fed-batch mode of operation is very useful when an optimum concentration of the substrate (or one of the substrates in a multisubstrate system) or of a particular nutrient is desirable. This can be achieved by imposing an optimal feed policy. 

Clearly, the feed rate Q t) can be manipulated to give an optimal feed policy (with respect to time) to maximize performance. Usually, a constant or exponential addition policy is the most practical and the simplest. Yet, in realistic situations, the feed rate must be judiciously varied so that a robust optimization criterion can be met. Thus first a suitable objective function must be evolved. Many such objective functions are possible, for example, maximization of yield and minimization of production cost. 

Lu, Y.P., Dixon, A.G., Moser, W.R. and Ma, Y.H., 1997c. Analysis and Optimization of Cross-Flow Reactors with Staged Feed Policies - Isothermal Operation with Parallel Series, Irreversible Reaction Systems. Chemical Engineering Science, 52(8) 1349-1363. 

Figure 7.39 a (F(t)A (t)) policies required to achieve the desired objective function values, (a) Feeding policy for when Ci = 0.3 mol/L is the objective function. Structure 2 is required, (b) Feeding policy for when c =0.4 mol/L is the objective function. Structure 1 is required. 

There are two basic monomer feed policies which maybe used in semibatch copolymerization to minimize compositional drift. Effective commercial processes are usually based on one or a combination of these feed policies. 

Quaghano JC, AmariUa F, Fernandes EG, Mata D, Miyazaki SS. Effect of simple and complex carbon sources, low temperature culture and complex carbon feeding policies on poly-3-hydroxybutyric acid (PHB) content. World J Microbiol Biotechnol 2001 17 9-14. 

Currently, commercially pure batch processes play a major role for suspension and bulk polymerization but only a minor role for emulsion polymerizations. The most important procedure for effecting polymer dispersions by emulsion polymerization on a technical scale is semibatch or feed processes, which are very flexible regarding product properties. Depending on the required properties with respect to particle size distribution, molecular weight distribution, chemical composition in the case of copolymerization, and particle morphology, numerous feeding policies have been developed. Almost all kinds of consecutive... 

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