Synthesis Of Separation Networks Research Articles

Accounting for costs in attainable‐region‐based reactor–separation network synthesis: Models, tradeoffs, and insights

AbstractIn reaction engineering, the attainable region defines the set of all possible states attainable in the outlet stream of any steady‐state reactor network, given specified feed and reaction kinetics. Costs in approaches that aim to determine the attainable region are often neglected, resulting in targets that require expensive processes. In this work, we propose modeling methods that allow us to account for costs in reactor–separation synthesis while accurately identifying the attainable region. Our goal is to holistically analyze cost trade‐offs within the attainable region as well as provide a method to obtain practical targets to be used as benchmarks. We generate the attainable region using the continuous stirred tank reactor (CSTR) equivalence principle and introduce separation models accounting for costs to perform the required separation tasks. Through several case studies, we show how some subregions, typically close to the attainable region boundary, are expensive to achieve.

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.

Systematic Design and Evaluation of Energy-Efficient Alternatives of Heterogeneous Azeotropic Distillation: Furfural Case Study

Separation of azeotropic mixtures receives special attention for their impact on various significant industrial processes. Because of the non-ideal behaviour of these mixtures, it is impossible to separate them by conventional distillation. Instead of a single distillation unit, a system of multiple operations is to be employed. Heterogeneous azeotropic distillation (HAD) is an example of this kind of systems, where entrainers are applied to modify the behaviour of the mixture. The selection of the best separation system is a key objective during the synthesis of the process network. However, synthesis of HAD is especially difficult because of the complex interaction between its continuous and discrete features. Therefore, traditional separation network synthesis tools are incapable of solving this problem. In this work, the properties of the ternary vapor-liquid-liquid equilibrium diagram are exploited for systematically identifying plausible operating units that perform the separation of the azeotrope. Subsequently, energy consumption of the entire network is estimated through rigorous simulation. The P-graph framework is employed to represent the system’s structure. Additionally, its combinatorial algorithms generate a rigorous superstructure for the synthesis problem, and the set of n-best designs that minimize energy consumption. The method is illustrated by synthesizing the dehydration of furfural through HAD. The results demonstrate that it constitutes a valuable tool for the designer by being effective in the systematic identification and assessment of HAD alternatives.

Optimization Framework for Energy-induced Separation Network: Application to the Chilling Train System in Ethylene Plants

The mass-exchange equilibrium relation depends on the temperature and pressure. Therefore, there are strong interactions between heat-exchange network and mass-exchange network. A modular framework methodology that combines the commercial sequential process simulator and optimization tools is proposed to perform the energy-induced separation network synthesis. As a case, the synthesis of the chilling train process in ethylene plants is used to illustrate the applicability of the proposed approach.

Solving a separation-network synthesis problem by interval global optimization technique

A novel method is presented here for solving certain classes of separation-network synthesis (SNS) problems, which are inherently non-linear, using branch-and-bound framework and linear programming. The proposed method determines effectively the structure and flowrates of the optimal separation network.The examined problem contains simple and sharp separators, mixers, and dividers; its aim is to produce three pure product streams from two three-component feed streams with minimal cost. The cost of the network is the sum of the costs of the separators and the cost of a separator is a concave function of its mass load. The mathematical programming model generated from the rigorous super-structure is non-linear.The goal of our work is to determine the optimum of the aforementioned model effectively. The splitting ratios of the dividers are handled as intervals. A B&B method operates on them. The cost functions of the separators are approximated with lower estimating functions.

Solving a Separation-network Synthesis Problem by Interval Global Optimization Technique

A new solution technique is proposed here for a specific kind of separation-network synthesis (SNS) problem, using Branch-and-Bound (B&B) framework and linear programming (LP). The suggested method determines effectively the structure and flowrates of the optimal separation network. The method is illustrated by the solution of an SNS problem introduced in (Kovacs et al., 1995). The aim is to produce three pure product streams from two three-component feed streams with minimal cost. The rigorous super-structure of the problem is given by (Kovacs et al., 1995). The term itself was defined by Kovacs et al. (1999). The main idea is that it can be proved that the rigorous super-structure contains at least one optimal structure. The mathematical programming model generated from this rigorous super-structure is non-linear. The goal of the present work is to determine the optimum of the aforementioned model effectively. The proposed method handles the splitting ratios of the dividers as intervals. A B&B method operates on these intervals. A branching step split one of the intervals. The bounding function approximates the concave cost functions of the separators. This function can be determined by solving LPs. The solution of the non-linear problem can be determined with arbitrary precision.

Energy Induced Separation Network Synthesis of an Olefin Compression Section: A Case Study

When latent heat is transferred in a heat exchanger network, the formation of the second phase creates an opportunity for separation. This network is known as a Heat Induced Separation Network (HISEN). HISENs have been extended to include pressure adjusting devices for improving the thermodynamic feasibility of the network. This extended network is termed an Energy Induced Separation Network (EISEN). Most examples of EISENs in the literature are environmental pollution treatment case studies which do not require liquid phase mass integration or shaft power integration. They assume a predetermined extent of separation and mostly are based on conceptual methods of design. This paper explains how the optimization framework must be developed in order to systematically address the general characteristics of EISENs. The framework is illustrated using a case study of the synthesis problem of an olefin compression section.

Solution of separation-network synthesis problems by the P-graph methodology

The current work demonstrates that separation-network synthesis (SNS) problems can be transformed into process-network synthesis (PNS) problems: the SNS problems constitute a particular class of PNS problems. Thus, the transformed SNS problems are solvable by resorting to the P-graph methodology originally introduced for the PNS problems. The methodology has been unequivocally proven to be inordinately effective.

Algorithmic synthesis of an optimal separation network comprising separators of different classes

A novel class of separation-network synthesis (SNS) problems is examined, where the separators in the separation network can be affected by various separation methods subject to different constraints imposed on the product specifications. Such a class of SNS problems has been rapidly gaining importance for chemical processing in general and biochemical processing in particular. The available methods for SNS are not intended to address these problems; therefore, an efficient method is proposed here to amend this situation. The method composes algorithmically the necessary mathematical model of the super-structure on which the determination of an optimal separation network is based. The resultant mathematical model is linear, thus the proposed method renders it possible to generate the optimal solution without fail. The solution might serve as the lower bound for a separation network with a non-linear cost function. The uniqueness and efficacy of the proposed method are amply demonstrated by two examples of different complexities.

IDEAS approach to the synthesis of globally optimal separation networks: application to chromium recovery from wastewater

In this work, we present an optimal separation network synthesis methodology within the novel Infinite DimEnsionAl State-space (IDEAS) framework. The resulting network synthesis problem is formulated as an infinite dimensional convex (linear) optimization, where the objective function is a weighted combination of the cost of utilities associated with the network operation and the capital cost of the separation units employed. The IDEAS methodology is illustrated on a chromium recycling case study. The globally optimal cost is identified and compared with that of a conventional (tree) design. The IDEAS design is less than half as expensive as the conventional tree design, exhibits no need for waste disposal, and employs a smaller number of units.

Separation-network synthesis: global optimum through rigorous super-structure

The available algorithmic methods often fail to yield with certainty the global optima in solving even a relatively simple class of separation-network synthesis problem for which the cost functions are considered to be linear. This is attributable to two complications; firstly the super-structures on which the solutions are based are incomplete; and the secondly, the mathematical programming models derived for the problems are unnecessarily cumbersome. To circumvent these complications, a novel method is proposed here to generate the complete super-structure and the corresponding mathematical programming model necessary for the separation-network synthesis problem with linear cost function. The efficacy of the proposed method is demonstrated by re-examining four published problems for which the optima obtained are claimed to be global. For all the problems re-examined, the costs of the solutions resulting from the present method are the same or as much as 30% lower than those of the published solutions.

Exact super-structure for the synthesis of separation-networks with multiple feed-streams and sharp separators

Recent insights into the nature of optimal separation-networks indicate a need to develop a rigorous technique capable of generating the optimal solution of a separation-network synthesis (SNS) problem. In principle, an SNS problem can be solved if an exact super-structure is available. Hitherto, no method has been established for generating such a super-structure when multiple feed-streams are involved. Even when a super-structure is complete, the corresponding mathemaucal-programming problem may not be solvable if it is unnecessarily complex. Thus, the exact super-structure should be as simple as possible. The present paper proposes an algorithm for generating an exact super-structure for the following class of SNS problems: multiple feed-streams and multicomponent product-streams where the cost function of each separator is linear with a fixed charge. It has been proved that the super-structure generated always includes the optimal separation-network of this class of problems and that the super-structure does not include unnecessary operating units. The proposed method have been demonstrated by successfully solving several problems.

Parametric study of separation network synthesis: extreme properties of optimal structures

Parametric study of separation network synthesis: extreme properties of optimal structures

Parametric study of separation network synthesis: Extreme properties of optimal structures

Optimal separation sequencing or network synthesis (SNS) has been carried out either by a heuristic or mathematical programming method. The former gives rise only to those networks that can be deduced from its heuristic rules, and the latter, only to those networks whose structures are the substructures of the super-structure. If the set of heuristic rules or super-structure is incomplete, a substantial fraction of structures that can be optimal may very likely be excluded from consideration. Our study of various SNS problems involving sharp separators, dividers, and mixers encompasses a wide variety of problems yielding pure or multicomponent product streams from single or multiple feed streams. The counter examples generated indicate that basic structural components, such as recycling or redundancy in separators, may not necessarily render the separation network structures non-optimal. The available methods, however, tend to exclude these basic structural components a priori.The present work parametrically examines hypothetical and real SNS problems to determine under which circumstances recycling or redundancy may be involved in optimal separation structures, and under what situations bypasses should not be maximized in such structures. These results are useful in improving the available synthesis techniques.