Ferenc Friedler

Decision-mapping: A tool for consistent and complete decisions in process synthesis

Decisions involved in process synthesis are often more complex than those involved in other disciplines. This arises from the fact that such decisions are concerned with specification or identification of highly interconnected systems, e.g. process structures, which may contain a multitude of recycling loops. It appears that no rigorous technique is available, which is capable of representing exactly and organizing efficiently the system of decisions for a process synthesis problem. A novel mathematical notion, decision-mapping, has been introduced in this work to render the complex decisions in process design and synthesis consistent and complete. The basic terminologies of decision-mapping, including extension, equivalence, completeness, complementariness, and active domain, have been defined based on rigorous set-theoretic formalism, and the most important properties of decision-mappings have been identified and proved. Decision-mapping, as a rigorously established technique, is directly applicable in developing efficient and exact process synthesis methods or improving existing methods. The applicability and meritorious features of this new technique are illustrated by synthesizing a large scale process.

Combinatorial algorithms for process synthesis

Abstract Analysis of the combinatorial properties of process synthesis has been carried out in the present work. Such analysis has given rise to some efficient combinatorial algorithms. Algorithm MSG generates the maximal structure (super-structure) of a process synthesis problem; it can also be the basic algorithm in generating a mathematical programming model for this problem. Algorithm MSG is effective in synthesizing a large industrial process since its complexity grows merely polynomially with the size of the synthesized process. Another algorithm, algorithm SSG, generates the set of feasible process structures from the maximal structure; it leads to additional combinatorial algorithms of process synthesis including those for decomposition and for accelerating branch and bound search. These algorithms have also proved themselves to be efficient in solving large industrial synthesis problems.

Downstream process synthesis for biochemical production of butanol, ethanol, and acetone from grains: generation of optimal and near-optimal flowsheets with conventional operating units.

Manufacturing butanol, ethanol, and acetone through grain fermentation has been attracting increasing research interest. In the production of these chemicals from fermentation, the cost of product recovery constitutes the major portion of the total production cost. Developing cost‐effective flowsheets for the downstream processing is, therefore, crucial to enhancing the economic viability of this manufacturing method. The present work is concerned with the synthesis of such a process that minimizes the cost of the downstream processing. At the outset, a wide variety of processing equipment and unit operations, i.e., operating units, is selected for possible inclusion in the process. Subsequently, the exactly defined superstructure with minimal complexity, termed maximal structure, is constructed from these operating units with the rigorous and highly efficient graph‐theoretic method for process synthesis based on process graphs (P‐graphs). Finally, the optimal and near‐optimal flowsheets in terms of cost are identified.

Combinatorially Accelerated Branch-and-Bound Method for Solving the MIP Model of Process Network Synthesis

Process network synthesis (PNS) has enormous practical impact; however, its mixed integer programming (MIP) model is tedious to solve because it usually involves a large number of binary variables. The present work elucidates the recently proposed accelerated branch-and- bound algorithm that exploits the unique feature of the MIP model of PNS. Implementation of the algorithm is based on the so-called decision-mapping that consistently organizes the system of complex decisions. The accelerated branch-and-bound algorithm of PNS reduces both the number and size of the partial problems. The efficacy of the algorithm is demonstrated with a realistic example.

A graph-theoretic method to identify candidate mechanisms for deriving the rate law of a catalytic reaction

Stoichiometrically, exact candidate pathways or mechanisms for deriving the rate law of a catalytic or complex reaction can be determined through the synthesis of networks of plausible elementary reactions constituting such pathways. A rigorous algorithmic method is proposed for executing this synthesis, which is exceedingly convoluted due to its combinatorial complexity. Such a method for synthesizing networks of reaction pathways follows the general framework of a highly exacting combinatorial method established by us for process-network synthesis. It is based on the unique graph-representation in terms of P-graphs, a set of axioms, and a group of combinatorial algorithms. In the method, the inclusion or exclusion of a step of each elementary reaction in the mechanism of concern hinges on the general combinatorial properties of feasible reaction networks. The decisions are facilitated by solving linear programming problems comprising a set of mass-balance constraints to determine the existence or absence of any feasible solution. The search is accelerated further by exploiting the inferences of preceding decisions, thereby eliminating redundancy. As a result, all feasible independent reaction networks, i.e. pathways, are generated only once; the pathways violating any first principle of either stoichiometry or thermodynamics are eliminated. The method is also capable of generating those combinations of independent pathways directly, which are not microscopically reversible. The efficiency and efficacy of the method are demonstrated with the identification of the feasible mechanisms of ammonia synthesis involving as many as 14 known elementary reactions.

Process network synthesis: Problem definition

Analyses of network problems have yielded mathematically and practically significant results. Naturally, it should be of substantial interest to extend such results to a general class of network problems where the structure of any system can be represented by a directed bipartite graph containing two types of vertices; the model for one of them is nonlinear. This class of problems is frequently encountered in the design of process systems for carrying out transformation of chemical or material species through physical, chemical, or biological means. General-purpose mathematical programming methods have failed so far to solve large-scale network problems involved in the design of such systems. This paper is intended to define this class of network problems, i.e., the problems of process network synthesis, and to elucidate the unique features of these problems.

Graph-theoretical identification of pathways for biochemical reactions

A rigorous method for identifying biochemical reaction or metabolic pathways through its systematic synthesis has been established. The current method for synthesizing networks of metabolic pathways follows the general framework of a highly exacting combinatorial method. The method is capable of generating not only all combinatorially independent, feasible reaction networks only once, but also those combinations of independent pathways. A case study involving the conversion of glucose to pyruvate with 14 elementary reactions illustrates the efficiency and efficacy of the method. All the results have been obtained with a PC (Pentium-III 550 MHz, 256 MB RAM) within 1 s.

Combinatorial technique for short term scheduling of multipurpose batch plants based on schedule-graph representation

Abstract This paper deals with the production scheduling of multipurpose batch plants. A novel graph representation is proposed that takes into consideration the specific characteristics of chemical processes in scheduling. In this graphs, the nodes represent the production tasks and the arcs the precedence relationships among them. The representation is flexible enough to consider a great variety of production structures (recipes with branches, alternative units, …). Both NIS and UIS transfer policies can be considered simply by choosing the appropriate precedence relationships. This representation provides the opportunity of incorporating highly efficient graph algorithms together with an appropriate branch-and-bound (B&B) algorithm for solving multipurpose scheduling problems effectively. The B&B algorithm takes care of the combinatorial optimization problem involved in each scheduling problem, while the graph algorithms allow to obtain the lower bounds that control the branching strategy. The efficiency of the proposed method is established by comparing it with the application of a generic B&B solving an equivalent MILP scheduling model.

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

Abstract 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.

A combinatorial approach for generating candidate molecules with desired properties based on group contribution

Abstract The problem of designing molecules or compounds with desired properties is complex primarily because it is combinatorial. A novel approach is proposed here by resorting to a combinatorial analysis of the problem. It is supposed that the set of functional groups is available and that the intervals of values of the desired properties of the molecule or compound to be designed are known. The desired properties constitute constraints on the integer variables assigned to the functional groups. The feasible region defined by such constraints is determined by an algorithm involving a branching strategy. This algorithm generates those collections of the functional groups that can constitute structurally feasible molecules or compounds satisfying the constraints on the given properties. The efficacy of the approach has been demonstrated with several examples.