A methodology for the quantification of entropy generation and energy consumption in isothermal, isobaric reactor networks is presented. The proposed methodology employs the Infinite Dimensional State-space (IDEAS) conceptual framework, which is shown to be applicable to the problem under consideration. The IDEAS framework considers all possible reactor units, and all possible mixing and splitting interconnections among them. It will be shown mathematically that, under certain conditions, entropy generation and energy consumption are functions of only the inlet and outlet stream compositions and flow rates and are not dependent on the reactor network structure, as long as there exists a network able to deliver the considered outlets from the known inlets. This theoretical result provides the foundation for a graphical method that can quantify entropy generation and energy consumption, by first identifying the reactor network’s Attainable Region (AR) and then depicting the behavior of the entropy generation and energy consumption functions within the AR. The proposed methodology is demonstrated on a case study featuring reversible reactions both in series and in parallel. Finally, conclusions are drawn.
It was shown in an earlier work by us that entropy generation and energy (hot utility or cold utility) consumption of isothermal, isobaric reactor networks depend only on the network's inlet and outlet stream compositions and flow rates and are not dependent on the reactor network structure, as long as the universe of realizable reactor units and network outlet mixing units are either all endothermic interacting with a single hot reservoir, or all exothermic interacting with a single cold reservoir, respectively. It is shown that when the universe of realizable reactor/mixer units, of isothermal, isobaric, continuous stirred tank reactor networks, consists of both endothermic units interacting with a single hot reservoir and exothermic units interacting with a single cold reservoir, the network's net (hot minus cold) utility consumption depends only on the network's inlet and outlet stream compositions and flow rates (and does not depend on the network's structure). In contrast, the network's entropy generation depends on the network's inlet and outlet stream compositions and flow rates, and the network's hot utility (or cold utility) consumption. The latter, in general, depends on the network structure, thus making entropy generation also, in general, depend on network structure. Thus, the synthesis of isothermal, isobaric reactor networks, with fixed inlet and outlet stream specifications, is equivalent to the synthesis of minimum hot (or cold) utility consuming such networks. The Infinite DimEnsionAl State-space conceptual framework is used for the problem's mathematical formulation, which is then used to rigorously establish the above equivalence. A case study involving Trambouze kinetics demonstrates the findings. sible reactor units include units of both the exothermic and endothermic type. The IDEAS framework decomposes a reactor network into an operator, OP network, where the reactor unit operations occur, and a distribution, DN network, where the flow operations (mixing, splitting, recycling, and bypass) occur. IDEAS has been successfully applied to numerous globally optimal process network synthesis problems, such as mass exchange network synthesis, 8 complex distillation network synthesis, 9-11 power cycle synthesis, 12 reactor network synthesis, 13,14 reactive distillation network synthesis, 15 separation network synthesis, 16 attainable region construction, 17-20 and batch attainable region construction. 21 The rest of the article is structured as follows: CSTR models using a mass basis and a molar basis are presented, the applicability of IDEAS to the entropy generation and energy consumption quantification problem is demonstrated, and the resulting IDEAS mathematical formulation is presented. Next, properties of the entropy generation and net energy consumption functions are rigorously established in a theorem, which establishes the net energy consumption function's dependence on only network inlet and outlet information, and the entropy generation function's dependence on both network inlet and ou...
In this article, a methodology for the globally optimal synthesis of a network of vapor−liquid equilibrium flash separators that can operate at multiple pressures and separate an azeotropic mixture is presented. The objective function minimized is the total flow entering the network flashes. The proposed synthesis methodology employs the infinite-dimensional state-space (IDEAS) conceptual framework, which is shown to be applicable to the problem under consideration. The resulting infinite linear programming (ILP) IDEAS formulation is shown to have several properties that allow its simplification. The approximate solution of this IDEAS ILP is pursued through the solution of a number of finitedimensional linear programs (FLPs) of ever increasing size, whose optimum values form a sequence that converges to the ILP's infimum. The proposed optimal design methodology is general in nature and can be used to separate any number of pressure-sensitive azeotropic mixtures, with or without use of an entrainer. The method is demonstrated on a first case study involving the dual-pressure separation of a methyl acetate/methanol binary mixture, which exhibits a minimumboiling azeotrope, without using an entrainer, and a second case study involving the dual-pressure separation of a ternary mixture of water, methanol, and acetone that also exhibits a minimum-boiling azeotrope for the methanol/acetone binary mixture, again without using an entrainer. The IDEAS-generated globally optimal design is shown to be 31.54% better than an optimized, dual-pressure, traditional, two-column design for the binary mixture (case 1) and 15.15% better for the ternary mixture (case 2).
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