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- W2786811740 abstract "In this chapter the method of Pontryagin's maximum principle is applied to optimize some chemical lumped parameter and distributed parameter systems with the catalyst decay described by a simple model of the first-order, temperature-independent deactivation. Continuous and discrete algorithms with either ordinary or partial differential equations along with appropriate boundary conditions are employed to calculate optimal temperature profiles in reactors with deactivating catalyst. The state equations contain two state variables: reaction extent, x (or concentration c ), catalyst activity, a , and temperature, T , as a single control. The distributed system theory serves to obtain an analytical solution for extremum temperature control in a fixed bed reactor with a first-order reaction and the first-order catalyst deactivation. Application of the distributed algorithm shows that an optimal profile for the effective reaction constant, k eff ( t ), is formed as the result of prescribed activity distributions, initial w p ( τ ) and final w k ( τ ). When the chronological time t k increases, the effective reaction rate constant corresponds to higher reaction temperatures. A decrease in the operation time causes time-dependent temperature profiles T ( τ , t ). This function may appear because of too high temperatures at the final moments of the process, which may cause excessive corrosion of the reactor material. Therefore, a generalized optimization problem with constrained temperature control is formulated and solved for short-duration processes. The solution is supplemented by an analysis of a cycle composed of an infinite number of deactivation and regeneration steps working sequentially in a steady cyclic operation." @default.
- W2786811740 created "2018-02-23" @default.
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- W2786811740 date "2018-01-01" @default.
- W2786811740 modified "2023-10-17" @default.
- W2786811740 title "Reactors With Catalyst Decay and Regeneration" @default.
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- W2786811740 doi "https://doi.org/10.1016/b978-0-12-813582-2.00008-2" @default.
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