Optimal operation of a tubular chemical reactor

Abstract

A theoretical and experimental study was conducted on the optimal steady state operation of a jacketed, tubular, liquid-phase reactor in which consecutive secand-order reactions occurred in turbulent flow. To verify the proposed mathematical model, diethyl adipate was saponified with sodium hydroxide in aqueous solution. The 150 ft. long reactor jacket was divided into 5, 30 ft. sections. Hot water flow rates in the jacket sections were chosen to maximize the concentration of monoethyl adipate ion at the reactor exit. The plug-flow model and a position-dependent heat transfer coefficient accurately described temperature and concentration profiles. The Pontryagin maximum principle was used to choose idealized reactor temperature and wall heat flux profiles which would maximize the exit concentration of monoester. The maximum principle was shown t o be an effective tool for this type of reactor optimization. A technique is given for optimizing more complex reaction systems.A natural application of high speed computation in chemical engineering has been the optimal design and operation of processing equipment. I n recent years application of variational and numerical search methods has shown that the performance of many chemical reactors may be improved by operating in a nonisothermal fashion (1, 2, 4, 6 to 8, 11 ) . These studies have for the most part been confined to mathematical models and computer simulation. This work conceins the optimal operation of a jacketed, unpacked, tubular reactor in which consecutive second-order liquid-phase reactions occur in turbulent flow (9). The reaction considered is the saponification of diethyl adipate with sodium hydroxide.The first objective of this research was to model effectively the tubular reactor by comparing experimental concentrations and temperature profiles with predictions of various models. Numerical search techniques were then employed to maximize yields of monoethyl adipate at the reactor exit. Optimal operation was also verified experimentally.The second objective of this research was to obtain optimal constrained temperature and wall heat flux profiles for consecutive first-and second-order reactions occurring in a fixed length reactor, and for which El > E2. The Pontryagin maximum principle was employed to determine optimal profiles for several objective functions. Comparison of yields from the idealized reactor (amenable to study with the maximum principle) with yields from the experimental system indicated that the maximum principle is useful in obtaining an upper bound on yields in real reactors. DESCRIPTION OF EXPERIMENTAL SYSTEMThe reactor system, shown in Figure 1, consisted of a jacketed tubular reactor, storage drums for diethyl adipate and sodium hydroxide solutions, feed and hot water flowmeters and

Optimal design of dispersive tubular reactors at steady-state using optimal control theory

“…Consequently, the obtained results allow to infer case-independent insights, which can easily be transferred to various situations. Although analytical results have been reported for plug flow reactors [5][6][7][8][9], results for dispersive reactors are scarce [10] due to the increased complexity arising from the second-order terms and the split Danckwerts boundary conditions. Moreover, although conceptually intuitive, the extension of previous plug flow results [8,9] to include dispersion is analytically and numerically non-trivial.…”

Kinetics of the saponification of diethyl adipate

“…Separate control could be exercised over the heating rate in each of the shell sections. Details of construction, as well as feed system design and instrumentation, are available from Newberger (1967).…”

“…The equations governing the operation of the experimental reactor are derived in Newberger ( 1967). In these balances, the following assumptions were made:…”

“…In addition to the rate constant determination discussed above, measurements and calculations were carried out to determine the heat transfer characteristics of the reactor, the heats of reaction, the axial dispersion coefficient, and the effect of radial gradients. The reader may obtain details of heat transfer and mixing from Newberger ( 1967).…”

Experimental studies of a consecutive—competitive reaction in steady state and forced periodic CSTRs

“…04 06 0810 12 14 16 18 20 22 DIMENSIONLESS TIME (=FI/V) Simulated trajectories of reactants for feed concentration cycling (Dimensionless concentration definitions: XI = C,,/cAo, x2 = Ce/Fn,, XQ = C P l / C A J of the ionic strength, while k? increases with increasing salt on cent ration"^"^'.…”