In this paper, an optimal control strategy is applied to the problem of finding the flux profiles for the conversion of methane to ethylene and acetylene in a plug flow reactor. A chlorinecatalyzed oxidative pyrolysis mechanism is used in the calculations, in which two mechanistic pathways to the C 2 products were examined. One involves CH 3 Cl and/or CH 2 Cl, and the other involves C 2 H 6 and/or C 2 H 5 as reaction intermediates. Optimal control designs were performed with respect to the final mass fractions of ethylene and acetylene in a plug flow reactor using heat, oxygen, and chlorine fluxes as controls. The simulation results show that for the temperatures (1200 K < T < 1900 K) and pressure (P ) 1 atm) considered, C 2 H 4 is formed initially, which is subsequently converted to C 2 H 2 . Because of the abundant supply of H 2 formed during the reaction, it is possible to reform C 2 H 4 from C 2 H 2 by controlled extraction of energy. The heat flux plays the most important role in determining the final concentration of the desired C 2 products by controlling the temperature and the rate of H-atom radical generation, and thus, the interconversion between C 2 H 2 and C 2 H 4 through the C 2 H 3 radical. The solutions obtained, although not proven to be globally optimal, are of very high quality. More than 40% yield of the desired C 2 products, either ethylene or acetylene, can be obtained in all cases.
Optimal control problems appear frequently in chemical reactor design. We study the application of a strategy belonging to the class known as gradient methods in function space to solve such problems by discretization of the function space and an iterative conjugate gradient algorithm. The algorithm is applied to a plug flow reactor model with various levels of reaction mechanism complexities. The examples, in which the properties of the algorithm are examined in detail, range from the control of the first-order reaction model of a hexane isomerization mechanism to the control of oscillation patterns and mechanistic re-routing in the oscillatory Belouzov-Zhabotinski reaction. The algorithm is successful in treating these highly nonlinear systems and hence provides a prospect of solving other complicated nonlinear optimal reactor control problems.
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