Tubular reactor systems optimization

NAUM AN AND MALLIKARJUN Optimization in Tubular Reactor Systems 307... 

The effect of some of these parameters is obvious, however several deserve additional comment. Phase equilibria and solute solubility relationships are important, not only with respect to assuring that adequate solute (reactant) solubility occurs in the critical fluid media, but that an adequate throughput of converted product is feasible to make the synthetic process viable and economical. Other important interrelationships are the optimization of reaction conditions via proper selection and activation of the catalyst (if required) and the moisture content of the substrate. Flow rate in tubular reactor systems is also critical, not only with respect to the critical fluid, but for the introduction of reactants and their solubilization into the critical fluid media. Flow rate is also linked to product throughput and must be optimized to allow proper kinetic conversion of the reactants. 

Optimization of a distributed parameter system can be posed in various ways. An example is a packed, tubular reactor with radial diffusion. Assume a single reversible reaction takes place. To set up the problem as a nonlinear programming problem, write the appropriate balances (constraints) including initial and boundary conditions using the following notation ... 

Precolumn derivatization is often inadequate for dirty samples. In these cases, application of a postcolumn reaction detection system will often suffice. Deelder et al. (44) and van der Wal (45) have examined different configurations for postcolumn reactors and defined optimal selections on the basis of reaction time and type and effect on resolution and sensitivity. Both studies preferred the packed-bed reactor to the open tubular reactors when conventional column geometries were employed for separation, that is, 4.6 mm i.d. X 15 or 25 cm. 

Optimal operating conditions and catalysts Acetylation of phenyl ethers was generally carried out in the absence of solvents, which makes easier the recovery of the acetylated product from the reaction mixture. On the other hand, because of the high melting point of substrate and acetylated products, solvents were always used in the acetylation of 2-methoxynaphthalene. Flow reactors (e.g. fixed bed tubular reactors), in which the detrimental effect of competitive adsorption of substrate and products on the acetylation yield is lower than in the batch reactors, should be preferred. However although the set up of fixed bed reactors for liquid phase reactions is relatively simple, their substitution to the batch reactors, which are the only system used in academic organic chemistry, remains essentially limited to commercial units. 

The necessary conditions for optimization of a system governed by non-linear partial differential equations, such as the equation governing the unsteady state behaviour of tubular reactors, have been derived by Chang and Bankoff (1969). Also, they derived the optimal unsteady state control of a iacketed tubular reactor with and without heat... 

Ogunye and Ray (1971a,b) have formulated the optimal control problem for tubular reactors with catalyst decay via a weak maximum principle for this distributed system. Detailed numerical examples have been calculated for both adiabatic and isothermal reactors. For irreversible reactions, constant conversion policies are found to not always be optimal. A practical technique for on-line optimal control for fixed bed catalytic reactors, has been suggested by Brisk and Barton (1977). Lovland (1977) derived a simple maximum principle for the optimal flow control of plug flow processes. 

Mixed immobilized enzyme systems of glucoamylase-D-glucose isomerase and D-glucose isomerase-D-glucose oxidase-catalase have been prepared and operated. Experimental results verified theoretical predictions that optimal bifunctional catalyst configurations could be superior to those where the catalysts were mixed uniformly or arranged sequentially in a tubular reactor. 

A robust mathematical tool is needed to perform an optimisation. We have found that optimal control theory provides such a tool. The system is constrained by the requirement to balance energy, momentum and mass. These constraints must be specified for each particular case. In optimal control terminology there are two classes of variables. The first class are the state variables, for instance the temperature, T z,t), the pressure, p z,t), and the concentrations, Cj z,t), in a tubular reactor. The second class are the control variables, which are determined from the outside. An example is the temperature, T (z,t), on the outside along the tubular reactor. Optimal control theory in this case provides a general method to obtain T (z,t) such that the total entropy production is minimal, given certain constraints. 

To accomplish optimal operation of an existing LDPE tubular reactor or to design a new reactor system, it is necessary to know the sensitivity of system responses caused by deviations of system parameters from their nominal values. It is well known that pol3mie-rization reactors are very sensitive to changes in operating and kinetic parameters. Therefore, it is very important to know the underlying relationships between the system outputs and the model parameters. 

When one is deciding what column geometry is optimal for trace analysis with unlimited sample volume, two additional points should be evaluated. First, to what extent does the analysis require accurate and reproducible injections Strict performance specifications may eliminate microbore columns from consideration. The accuracy and reproducibility of injection systems that deliver 0.1-, 0.2-, and 0.5-/xL samples have not been adequately characterized. Second, if the analyte of interest requires postcolumn derivatization, construction of a postcolumn reaction system that is compatible with the exceedingly small band volumes characteristic of microbore columns may be extremely difficult, but not impossible. Apffel et al. (28) developed and evaluated both packed-bed and open tubular postcolumn reactors for use with 1-mm i.d. analytical columns. Catecholamines were postcolumn derivatized with o-phthal-aldehyde and detected spectrofluorometrically. The 5-/zm particle... 

It is practically important to develop optimization techniques for dynamic processes in distributed systems. In Ref 31, Ozgiilsen and inar discussed an approach for numerical simulation of tubular wall-cooled reactor with periodical forcing of reactant concentration and flow rate. They simulated CO oxidation with single steady-state rate equation that did not include any dynamic processes on the catalyst surface. CO conversion exceeding the steady-state value was obtained, but even for this simple kinetic model computation time demand is too high to implement numerical optimization algorithms. 

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