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Local equivalence of reversible and general Markov kinetics
 Physica A 2013, 392
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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 ..."
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Cited by 3 (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...
Review of mixedinteger nonlinear and generalized disjunctive programming applications in Process Systems Engineering
, 2014
"... In this chapter we present some of the applications of MINLP and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixedinteger nonlinear optimization we refer the reader to the work by Belotti et al.[1]. Bonami et al.[2] review convex MI ..."
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In this chapter we present some of the applications of MINLP and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixedinteger nonlinear optimization we refer the reader to the work by Belotti et al.[1]. Bonami et al.[2] review convex MINLP algorithms and software in more detail. Tawarmalani and Sahinidis[3] describe global optimization theory,
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 more formal question: is there a continuous path between these states, along which the conservation laws hold, the concentrati ..."
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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 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 and have a convex Lyapunov function G. An admissible path is a continuous curve 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. The tree of G 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
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.
RESEARCH Attainable region analysis n
"... (corn, wheat, sorghum) is done using microorganisms such as S. cerevisiae or Z. mobilis in a fermentation proand operating and capital expenditures in the distillation operation [2,3]. However, microorganisms suffer from Scott et al. Biotechnology for Biofuels 2013, 6:171 http://www.biotechnologyfo ..."
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(corn, wheat, sorghum) is done using microorganisms such as S. cerevisiae or Z. mobilis in a fermentation proand operating and capital expenditures in the distillation operation [2,3]. However, microorganisms suffer from Scott et al. Biotechnology for Biofuels 2013, 6:171 http://www.biotechnologyforbiofuels.com/content/6/1/171the MoillerBoinot process (a fed batch process with cell2Bioenercel S.A. Barrio Universitario s/n, Ideaincuba building, Concepción, Chilecess [1]. Since, bioethanol has to be recovered from the mixture of water (as reaction media), residual sugars and nutrients, it is convenient to increase the concentration of inhibition at both high sugar and bioethanol concentration [4]. For alleviating ethanol inhibition, batch bioreactors and plug flow bioreactors (PFR) are the best options because they do not present backmixing, which effectively reduces their timeaveraged product inhibition [5]. Traditionally, batch fermentation has been used in the bioethanol industry especially for small scalefacilities, and
Synthesis of Optimal Chemical Reactor Networks
"... The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross flow reactor (CFR). The mathematical modeling leads to an optimal control formulation which is solved ..."
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The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross flow reactor (CFR). The mathematical modeling leads to an optimal control formulation which is solved using a control parameterization technique. The approach is applicable to general reaction mechanisms and is applied to a complex nonisothermal reaction problem. INTRODUCTION The goal of reactor network synthesis is to determine the types, sizes, and operating conditions of the reactor units as well as the interconnections among them which transform the given raw materials into the desired products. Previous approaches for addressing this problem can be classified as either superstructure based methods or targeting methods. The superstructure based methods employ a fixed reactor network which includes all the possible networks of interest. This approach was first introduced by Jackson (196...
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.