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Optimization Framework for the Synthesis of Chemical Reactor Networks
, 1998
"... The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks ..."
Abstract

Cited by 2 (1 self)
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The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...
Linear Programming Formulations for Attainable
"... We propose several linear programming (LP) models for attainable region (AR) analysis by considering a rate vector field in concentration space with an arbitrarily large number of points. One model provides a method to construct candidate ARs using a fully connected network of CSTRs of arbitrary ..."
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We propose several linear programming (LP) models for attainable region (AR) analysis by considering a rate vector field in concentration space with an arbitrarily large number of points. One model provides a method to construct candidate ARs using a fully connected network of CSTRs of arbitrary volume.
c ○ 2013 Society for Industrial and Applied Mathematics Thermodynamic Tree: The Space of Admissible Paths ∗
"... Abstract. Is a spontaneous transition from a state x to a state y allowed by thermodynamics? Such a question arises often in chemical thermodynamics and kinetics. We ask the following more formal question: Is there a continuous path between these states, along which the conservation laws hold, the c ..."
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Abstract. Is a spontaneous transition from a state x to a state y allowed by thermodynamics? Such a question arises often in chemical thermodynamics and kinetics. We ask the following more formal question: Is there a continuous path between these states, along which the conservation laws hold, the concentrations remain nonnegative, and the relevant thermodynamic potential G (Gibbs energy, for example) monotonically decreases? The obvious necessary condition, G(x) ≥ G(y), is not sufficient, and we construct the necessary and sufficient conditions. For example, it is impossible to overstep the equilibrium in 1dimensional (1D) systems (with n components and n−1 conservation laws). The system cannot come from a state x to a state y if they are on the opposite sides of the equilibrium even if G(x)>G(y). We find the general multidimensional analogue of this 1D rule and constructively solve the problem of the thermodynamically admissible transitions. We study dynamical systems, which are given in a positively invariant convex polyhedron D and have a convex Lyapunov function G. An admissible path is a continuous curve in D along which G does not increase. For x, y ∈ D, x � y (x precedes y) if there exists an admissible path from x to y and x ∼ y if x � y and y � x. ThetreeofG in D is a quotient space D / ∼. We provide an algorithm for the construction of this tree. In this algorithm, the restriction of G onto the 1skeleton of D (the union of edges) is used. The problem of existence of admissible paths between states is solved constructively. The regions attainable by the admissible paths are described.