Reactor Network Synthesis Research Articles

Integration of reactor network synthesis: A literature review and opportunities for future research

AbstractThe reactor network synthesis (RNS) is one of the subtopics of the chemical process synthesis, the purpose of which is to find an optimal reactor network for the specific objective function of the studied reaction system. This review discusses the principles, advantages, and disadvantages of various methods of RNS, together with the state of the research in each field. These methods could be divided into four categories: the process‐based approach (such as the attainable region, the targeting approach, and the method based on the elementary process functions), superstructure‐based approach, stochastic optimization, and parametric method. Finally, the paper discusses the existing problems of RNS in academic researches and practical applications, as well as its research directions in the future. This paper is helpful to the readers who have interests in the design and optimization of the reactor networks.

Nonisothermal reactor networks optimization using metaheuristics in a bi-level approach

In the present article, an optimization approach for the synthesis of reactor networks is proposed. A stage-wise superstructure containing a continuous stirred tank reactor (CSTR) and a plug flow reactor (PFR) is used to formulate the mathematical model without the use of differential equations and with a mixed-integer nonlinear programming (MINLP) formulation. To solve the optimization problem a bi-level meta-heuristic approach combining simulated annealing (SA) and particle swarm optimization (PSO) is used. Two case studies involving complex nonisothermal homogeneous reaction systems were used to test the applicability of this technique, and a methodology based on temperature profiles was developed to guide the search for operating temperatures during the optimization. The results achieved improvements in the objective function when compared to the majority of results reported in the literature, which demonstrates that the developed methodology is suitable to perform the reactor network synthesis in homogeneous systems.

A Generalized Framework for Reactor Network Synthesis: A Graph Theoretic Approach

We propose a generalized superstructure-based framework for reactor network synthesis that allows seamless coupling with approaches for separation network synthesis. The proposed framework addresses a generalized problem statement that considers additional degrees of freedom in terms of inlet streams and candidate reactions modeled through tasks assigned to reactors. We develop a graph theoretic approach to systematically build the reactor network superstructure. First, we represent the reactions and tasks through multiple graphs and identify competition among tasks. A group of competing tasks includes tasks that can play similar roles and are represented as subsets of vertices that are fully connected in a task competition graph. Second, we solve optimization problems, based on the task competition graph, to minimize the number of reactors required in the superstructure. Finally, we formulate and solve the optimization model for the integrated synthesis problem. The applicability and flexibility of the framework is illustrated through several examples.

MIPSYN-Global: Process Synthesis Enabled by Graphical Modelling

We introduce MIPSYN-Global - a unique computer-based process synthesizer. It is built on the foundations of its predecessor MIPSYN, using the knowledge and experience gained from decades of research in the field of PSE. One of its main features is the newly developed Graphical User Interface - MIPSYN- Global Modeler (MGM), which is specifically designed for fast modeling of process superstructures and representation of results. In addition, the modeler generates an Aspen Plus process simulator input file and runs the Aspen Plus simulation in which more rigorous thermodynamic and process unit models can be used. MGM is evidently the most notable new feature in the development of MIPSYN-Global. However, it is important to note that MIPSYN-Global inherits and builds upon the capabilities of its predecessor, making it a versatile and robust platform for solving process synthesis problems from engineering fields beyond chemical engineering. Nevertheless, since graphical modeling capability is a rather rare approach in equation-oriented synthesis, we present MGM's capabilities with an illustrative example of simple reactor network synthesis.

A generalized distillation network synthesis model

We propose a generalized superstructure-based distillation network synthesis model with improved modeling capabilities resulting in an extended solution space. The model can assign multiple mixtures to be separated (e.g., reactor network effluents) to different columns of the network while considering the interactions among different separation steps. In terms of outlets, products with general specifications, including pure components and multi-component mixtures, as well as streams without strict specifications (e.g., reactor recycle streams) can be readily handled. Furthermore, stream bypass is considered to avoid unnecessary separations, and thermal coupling is considered to yield novel solutions. The proposed model enables seamless integration with reactor network synthesis models thereby leading to solutions that are superior to the ones obtained by conventional sequential approaches.

A Unified Reactor Network Synthesis Framework for Simultaneous Consideration of Batch and Continuous-Flow Reactor Alternatives

Determining the optimal operating mode (batch or continuous-flow) for chemical manufacturing remains a pressing open problem. Focusing on reactors, an accurate determination must account for fundam...

Isothermal and non-isothermal reactor network synthesis by combination of mathematical method and imperialist competitive algorithm

The Reactor network (RN) synthesis of optimization problems leads to mixed-integer non-linear programming (MINLP) models that are very difficult to solve, especially for non-isothermal cases. In this research, a new and simple robust approach is presented for RN synthesis. To reduce the complexity of the model, instead of solving discrete and continuous variables simultaneously, a combination of a stochastic algorithm (i.e. imperialist competition algorithm (ICA)) and mathematical methods (i.e. modified Quasi Linear Programming (QLP)) has been used. The ICA is used to produce structural configuration, whereas continuous variables are handled using a modified QLP formulation. Each structure of the RN generated by ICA includes continuous stirred tank reactor (CSTR), plug flow reactor (PFR), PFR with recycle stream, and differential side- stream reactor (DSR) which are addressed by generating numerical codes in a vector. The RNs structures are then sent to the modified QLP to compute the amount of overall objective function (OOF). In the modified QLP model, first, the continuous variables are divided into two groups I and II, and the optimal values of these variables are obtained at internal and external levels respectively, taking into account the OOF. With this method, the complex MINLP model of RN synthesis is converted to an IAC + modified QLP which is much easier to solve. The cases studied showed that this method can reach better solutions compared to the literature.

Synthesis of performance-optimal heat exchanger networks using attainable regions

The attainable region (AR) is a region in a performance space in which all physically realizable reactor network designs must exist. ARs have been used since the 1960s for solving reactor network synthesis problems. The benefits of these methods are that the feasibility of a performance target can be assessed prior to running a synthesis routine, the solutions they give are guaranteed to be physically realizable, and they are amenable to convex optimization. In this article, the theory of attainable regions is extended to bring these benefits to the heat exchanger network (HEN) synthesis problem, with constant thermophysical properties and no stream splits. The HENS problems of the optimal outlet stream temperature and the minimum utility usage problems are linear optimization problems, solvable by simplex search with n−1 state variables for an n-stream problem. The quality of solutions regarding number and size of heat exchangers is discussed, with examples.

Conceptual design of a treatment process for centrifugal mother liquor wastewater in the PVC industry

The centrifugal mother liquor (CML) discharged by polymer enterprises is a typical refractory organic wastewater with a variety of pollutants. This paper proposes a novel homogeneous and heterogeneous mixed Fenton oxidation strategy for the degradation of phenol and other organic compounds in CML. First, two promising CML treatment schemes are selected from six alternatives. Second, with the minimal equipment investment cost as object, a better CML treatment scheme is selected from these two alternatives using reactor network synthesis method. This optimal scheme is further modeled and simulated by Aspen Plus, and the effect of Fe2+ and H2O2 flowrate on organic compound removal rate is studied by sensitivity analysis. The removal rate of organic compound is found increasing from 71 % to 82.6 % under the optimal flowrate of Fe2+ and H2O2. Finally, the importance of each variable in CML treatment process is evaluated based on mutual information. Three variables including the temperature of homogeneous reactor, the liquid level of homogeneous reactor, and the temperature of heterogeneous reactor are selected as key variables in the stability control study by Aspen Dynamics. The dynamic simulation results prove that the CML treatment process has high stability in the face of disturbances.

Geometry, kinetics and reactor network synthesis: Attainable limits for minimizing residence time in biomethane digesters

This paper presents a theoretical framework to model anaerobic digester structures and define performance targets using regions of attainability constructed using kinetic models and fundamental processes: mixing and biodegradation. Two digestion cases, diary manure (case 1) and diary manure + lagoon inoculum (case 2) were considered and the following main findings were obtained. Case 1 presents a linear acidogenic and exponential methanogenic uncoupling, an optimized performance target of 216.45% with optimal digester structure consisting of CSTR (continuous stirred reactor) + PFR (plug flow reactor) run in parallel with a CSTR (6 days retention time, RT) or a CSTR with bypass from feed (2 days RT). Case 2 presents a linear methanogenic response, an optimized target of 142.47% with optimal digester structure consisting of a CSTR + PFR with bypass (2 & 6 days RT). The framework presented in this study can be used for simultaneous optimization of performance targets and digester networks.

A New Robust Approach for Reactor Network Synthesis by Combination of Mathematical Method and NSGAII

Abstract In this research, a simple procedure for synthesis of reactor network (RN) is presented. This method could find the best possible optimum solutions with high grantees for the synthesis of RN, which generally is kind of mixed integer nonlinear programming (MINLP) models. In this work, instead of solving the discrete and continuous variables simultaneously, (like MINLP problems), a combination of stochastic algorithm and mathematical methods (i. e. Non-dominated Sorting Genetic Algorithm II (NSGA II) + quasi LP (QLP)) has been used. The reason for using NSGA II is because of the possibility of considering several objective functions instead of a single function in obtaining RN synthesis solutions. This algorithm could provide several optimal structure of RNs as set of final optimal solutions by use of its operators. The isothermal RNs produced by NSGA II are sent to QLP model to compute the amount of objective functions. In the QLP model, whilst all continues variables of RN calculated with just using a linear and a non-linear equations set with outer search loop, their general objective functions are also calculated. Comparison the results with the references shows that the presented method is capable of producing better solutions, which, in some cases improvement of about one percent in concentration of the main material in the product and a decrease of 77 % of the residence time of the materials in the reactor system is observed.

A generalized superstructure-based framework for process synthesis

We propose a general framework for the formulation of superstructure-based optimization models for holistic process synthesis. First, we redefine the fundamental problems of reactor, separation, and heat exchanger network synthesis, by presenting generalized problem statements, to make them amenable to seamless integration with each other. Second, we describe the general forms of models that can be developed to address these generalized problems and identify some key characteristics. Notably, for each system, we identify internal variables used only within the system, cost variables used in the objective function, and, importantly, coupling variables for the coupling between systems. Third, we outline some literature models that can be used to address the generalized problems and present new models to couple the three systems. Finally, we show how the individual components (systems and coupling models) can be integrated to formulate a single simultaneous reactor, separation, and heat exchanger network synthesis.

Optimization-Based Approach to Process Synthesis for Process Intensification: Synthesis of Reaction-Separation Processes

Process synthesis and intensification are powerful tools for the development of cost- and energy-efficient chemical processes. However, even though their combination maximizes the potential for improvements, they are mostly applied separately. The current article presents the extension of a phenomena-based process synthesis method by an aditional building block for reactor network synthesis and reactive separations. The method facilitates the automatic generation of thermodynamically feasible phenomena-based flowsheet variants by means of superstructure optimization, which are subsequently translated into equipment-based flowsheets taking into account classical as well as intensified equipment. By composing a flowsheet from mass and energy transfer phenomena instead of predefined unit operations, counterintuitive solutions and significant improvements can be achieved. In the current contribution, the capabilities of the method are demonstrated using the transesterification of propylene carbonate with meth...

Fast synthesis of optimal chemical reactor networks based on a universal system representation

We propose a new approach for the synthesis of optimal chemical reactor networks based on the concept of elementary process functions [1] and dynamic optimization. This approach is capable of incorporating process intensification options at an early design stage. Only one single differential equation is required to describe the mass balance of the whole reactor system along the reaction route. This equation contains terms describing mass fluxes from outside the reactor system and mass fluxes which flow between different positions of the reaction route. We demonstrate that different reactor types and different reactor connections can be represented by such a formulation. After solving an optimization problem using such a model, optimal profiles of state variables and fluxes are obtained. Based on these profiles, the optimal reactor system is determined. After the presentation of the theoretical background and the derivation of the new approach, it is illustrated in case studies and validated by comparison with literature results. The advantages of this new approach presented in our contribution are its simplicity in description and implementation, universality in representing different reactor types and networks, and the potential to consider different intensification and integration options at an early design stage.

Reactor-network synthesis via flux profile analysis

Within the framework of elementary process functions (Freund and Sundmacher, 2008) an approach is developed to derive reactor-network candidates from the solution of a dynamic optimization of a batch process scheme by analyzing its optimal mass and energy control fluxes. Thereby, any characteristics of the reaction progress can be identified, e.g. benefits from mixing, back-mixing, recycling, heating, cooling, etc. The approach is used to (i) determine the attainable region for the modified, isothermal van-de-Vusse reaction, which matches literature results; and (ii) synthesize reactor-network candidates for the standard, non-isothermal van-de-Vusse reaction, which gives new insights compared to previous results from literature using superstructure optimization approaches. The results indicate how this approach can be used to determine the attainable region of a process and to rationally select candidates for detailed reactor design with, e.g. superstructure optimization. It further closes the gap between dynamic batch optimization and continuous reactor-network synthesis.

Closed-loop reactor network synthesis with guaranteed robustness

This paper presents a systematic methodology to design closed-loop reactor networks with guaranteed robustness. The methodology is based on the superstructure approach for reactor network synthesis and extends our previous work (Zhao and Marquardt, 2016) to simultaneously design the process and the control system structure. The spectral abscissa of the Jacobian matrix of the closed-loop reactor network is chosen to measure the response speed of the designed process. A mixed-integer nonlinear program (MINLP) with complementarity constraints and a robust eigenvalue constraint is formulated and solved sequentially by a two-step solution strategy. Structural alternatives of the process and the control system as well as parametric uncertainties are considered in an integrated framework. A case study involving continuous stirred-tank (CSTR) and plug flow (PFR) reactors is presented to illustrate the novel approach and compared with an established two-step design approach.

English

This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a genetic algorithm (GA) coupled with the quasi-linear programming (LP) method. The GA is used to produce structural configuration, whereas continuous variables are handled using a quasi-LP formulation for finding the best objective function. Quasi-LP consists of LP together with a search loop to find the best reactor conversions (x i ), as well as split and recycle ratios (y i ). Quasi-LP replaces the nonlinear programming (NLP) problem, and is easier to solve. To prevent complexity and ensure an optimum solution, two types of ideal reactors, namely plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), were considered in the network. Since PFRs require the introduction of differential equations into the problem formulation, a CSTR cascade was used instead in order to eliminate differential equations. To demonstrate the effectiveness of the proposed method, three reactor-network synthesis case studies are presented.

Semantically enabled process synthesis and optimisation

This paper introduces a new framework to support synthesis of complex engineering problems using a paradigm that combines optimisation with ontological knowledge modelling. The framework registers and analyzes new solutions by introducing a mechanism of digital certificates to translate structural information and solution features through semantics of an ontology. The solutions are respectively clustered by design features. Tested against complex synthesis of reactor networks, the framework offers a potential to visualize optimization in the course of its development and demonstrates noticeable advantages over conventional methods of a similar basis in convergence and performance.

Reactor network synthesis with guaranteed robust stability

This paper proposes a systematic approach to design reactor networks with guaranteed robust stability. The approach is based on the superstructure approach for reactor network synthesis. A structured dynamic model for reactor network modeling is formulated and embedded in a MINLP with robust eigenvalue constraints. Design parameters, structural alternatives and parametric uncertainty are considered simultaneously as design degrees of freedom. Structural alternatives result from decisions on the existence of reactors and flow connections in the superstructure. Parametric uncertainty may either result from model uncertainties such as reaction kinetic constants or heat transfer coefficients, or from process uncertainties including slow disturbances in load or quality of raw materials. A tailored two-step solution strategy is proposed to tackle the robust mixed-integer optimization problem. A case study with five continuous stirred-tank reactors (CSTR) and five plug flow reactors (PFR) is presented for illustration.

Optimal flowsheet configuration of a polymerization process with embedded molecular weight distributions

We consider the optimal reactor network synthesis of a polymerization process with detailed molecular weight distributions (MWDs). Based on an industrial high‐density polyethylene (HDPE) slurry process model including an embedded MWD, a fully connected process superstructure of continuous stirred tank reactors (CSTRs) is established through the introduction of splitters. Using this generalized superstructure as a basis, two nonlinear programming (NLP) problem formulations, which simultaneously maximize the monomer conversion and minimize the deviation between the calculated and target MWDs, are developed by applying multiobjective optimization (MO) methods. Different optimal flowsheet configurations are generated by systematically manipulating a set of continuous decision variables. Several case studies that consider different specifications on MWD are conducted to illustrate the effectiveness and efficiency of the proposed synthesis approach. Numerical results show that the optimal flowsheet configurations overcome the limitations of conventional reactor network structures and help to increase reactor productivity at the desired product quality. © 2015 American Institute of Chemical Engineers AIChE J, 62: 131–145, 2016