(79b) A Superstructure-Based Process Synthesis Framework
AIChE Annual Meeting
2010 Annual Meeting
Computing and Systems Technology Division
Advances In Process Design
Monday, November 8, 2010 - 12:55pm to 1:20pm
Introduction: Current chemical processes synthesis methodologies can be classified in two different categories: the more traditional sequential-conceptual methods and the more systematic superstructure optimization-based methods. The sequential methods are based on the existence of a natural hierarchy among the engineering decisions, leading to a procedure in which the main subsystems of the plant are designed one at a time. In superstructure optimization-based methods, an initial process structure is proposed, including all potentially useful unit operations and all relevant interconnections between them. Here, the optimal set of units, interconnections and operational conditions are found simultaneously by solving an optimization problem that incorporates unit mathematical models, interconnection equations, and thermodynamic property calculation equations. In theory, the second kind of methods are more powerful since they pursue a simultaneous determination of the optimum structure and operational conditions, thus accounting for all the complex interactions between design decisions. However, the superstructure approach presents its own challenges, namely the creation of a superstructure that is rich enough to include optimal process structure without including a plethora of unreasonable ones; as well as the mathematical formulation of a solvable superstructure optimization problem. In this work, several new ideas are discussed regarding the generation of superstructures for the synthesis of a general reaction-separation system and the modeling of such superstructures at two different levels: the process level and the unit operation level.
Superstructure generation: The creation of an adequate superstructure comes with the selection of a proper set of unit operations and its connectivity. Over the years, several techniques have been proposed for the generation of such superstructures in the context of a general process synthesis problem. One of the earliest approaches involves the creation of a set of promising but simple process structures, followed by the formulation of a superstructure containing all of them; that is, a complex structure which can be reduced to any of the original ones by deleting some of its units and interconnections. More systematic techniques make use of graph theory to identify what has been called a maximal structure - i.e. union of all feasible process structures - by using a set of axioms which characterize the combinatorial properties of any feasible structures within the context of a process synthesis problem. In this work, we propose a stage-based methodology that lies in between the mentioned approaches. In the first stage, the formulation of a reduced number of promising process diagrams supports the selection of a set of unit operations (to include in the superstructure) and the definition of the "processing functions" each one of such units is expected to carry out. In the second stage, the selected set of operations is used to generate the superstructure by considering full connectivity between all unit inlet and outlet ports (i.e. the points where a unit meets their inlet and outlet streams). In the final stage, the connectivity is refined by eliminating unreasonable and inconvenient connections, using engineering judgment and logic rules based on the minimal and maximal sets of components expected in every unit port. The objective is to generate a rich connectivity based on engineering judgment, obtaining a superstructure that selectively includes as many feasible process alternatives as possible.
Superstructure modeling: A superstructure model involves two different levels: the process level and the unit operation level. At the process level, a mathematical architecture is established to account for the way the units are connected while allowing the activation/deactivation of the constraints (equations and inequalities) associated with each process unit in the superstructure. This is what makes possible the exploration of the structure alternatives embedded in the superstructure. Depending on the kind of modeling used (e.g. Generalized Disjunctive Programming (GDP), Mixed Integer Non Linear Programming (MINLP), etc.) , particular challenges appear (e.g. in a MINLP equivalent of a GDP superstructure model where both extensive and intensive stream variables are considered, the deactivation of units sometimes lead to the unintended deactivation of neighboring unit streams). At the unit operation level, when realistic unit operation models are used, much mathematical complexity concentrates around the equations describing the behavior of the such units (e.g. reaction kinetic expressions, thermodynamic property calculation equations, etc.) resulting in nearly unsolvable optimization problems. In order to face those challenges, this work introduces some modeling elements at the process level and the replacement of complex unit operation models with surrogate models at the unit operation level. Particularly, such surrogates are general-purpose multivariable mappings used to fit detailed unit operation data generated via commercial process simulators.
Unit surrogate model design and reformulation: A reduction in the mathematical complexity of a superstructure MINLP via replacement of unit models with surrogates can only come from a reduction in the total number of variables, equations, and the non-linearities in them. In this work, we introduce a systematic methodology for the proper selection of surrogate independent and dependent variables. This method is based on the degrees of freedom analysis of the original detailed models and the form of the superstructure optimization problem. We also show how this methodology results in highly accurate and yet dimensionally reduced surrogate models which contribute to the reduction of the superstructure model mathematical complexity. In addition, we discuss the way such surrogates are reformulated to allow their activation/deactivation using the superstructure model binary variables. In particular, this reformulation is fully presented for Multi Layer Perceptrons (MLP), where its simplicity and the implicit replacement of multiple types of non-linearities in the original unit models with only one type of non-linearity (i.e. the MLP tanh function) significantly facilitate the numerical solution process that follows.