(106a) A Generalized Framework for Reactor Network Synthesis: A Graph Theoretic Approach

In general, the design of the reactor network has arguably the greatest influence on the overall process flowsheet, determining the necessary features of subsequent separation units and utilities required to carry out the chemical process. However, most studies that focused on the synthesis of reactor networks either considered the reactor system in isolation from the synthesis of other systems, or addressed a narrow problem statement. A narrow problem statement can obstruct the full potential of simultaneous optimization strategies for process synthesis, such as superstructure-based approaches.

To address this limitation, we propose a generalized superstructure-based framework for reactor network synthesis that allows seamless coupling with approaches for separation network synthesis. We develop a method based on graph theory tools to systematically build the reactor network superstructure. The proposed framework addresses a generalized problem statement characterized by variable input data of the reactor system, both in terms of inlet streams (e.g., feed and recycle streams) and candidate reactions modeled through tasks assigned to reactors. A task is defined in terms of a subset of reactions, range of operating conditions, and catalyst required. A single task is assigned to each selected (active) reactor.

Our method consists of three steps. First, we use graph theoretic ideas to represent the reaction network and task information through multiple graphs. We define the component–reaction and component–task graphs as bipartite directed graphs. In the component–reaction graph, components and reactions constitute the set of nodes, and arcs identify the reactants and products of each reaction. Similarly, in the component–task graph, components and tasks constitute the set of nodes, and arcs indicate the components that are reactants or products of at least one reaction associated to a task. Furthermore, we identify competition among tasks. A group of competing tasks includes tasks that can play similar roles in the reactor network, and the simultaneous selection and assignment (to reactors) of these tasks is not beneficial. We represent the competition information through an undirected task competition graph, where tasks are represented as nodes, and the groups of competing tasks are represented as cliques of this graph.

Second, we identify and solve a graph cover problem based on the task competition graph to reduce the number of candidate reactors required in the superstructure. Each candidate reactor has a subset of tasks available to be assigned to that reactor. We solve the cover problem to select the minimum number of cliques, thus minimizing the number of candidate reactors. Additional constraints can be incorporated into the cover problem to simultaneously minimize the number of reactors as well as the reactor–reactor streams required to have an efficient and yet rich superstructure.

Finally, we formulate the optimization model for the integrated synthesis problem. The proposed framework is flexible in terms of task modeling. We can use multiple task types associated to different reactor models (e.g., detailed kinetic models, or simpler extent-based linear models). Additional constraints are proposed to eliminate symmetric solutions with respect to reactor activation and task-to-reactor assignments. The applicability and flexibility of the framework is illustrated through several examples.