Chemical engineering meets graph theory

Chemical engineering first emerged in the early 20th Century as the branch of engineering dedicated to the large-scale production of commodity chemicals. As its name suggests, it is linked to the basic science of chemistry, since at the core of the discipline is the fundamental task of synthesizing a desired molecule from available raw materials via a sequence of reactions. However, the discipline also has unique features due to the problem context of commercial-scale production. Thus, chemical engineers need to understand how to isolate the target molecule from other components, up to the level of purity required by a given market (consider, for example, the difference in alcohol content of beer, at roughly 5 percent, as compared to the purity level of fuel-grade bioethanol, which is about 95 percent). Due consideration must also be given to complicating aspects, such as the need to physically transfer materials from one container to another on a massive scale, or the need to regulate temperatures to prevent reactors from overheating or cooling off. In addition, chemical engineers need to consider all of these points while also taking into account various economic, environmental and legal/regulatory constraints. 

One of the most basic aspects of chemical engineering practice is the design of processes and plants. Since the 1950s, the emergence of the modern computer has naturally led to the emergence of a sub-discipline within chemical engineering that deals specifically with computational tools for increasingly complex industrial problems – process systems engineering (PSE). PSE, which is also sometimes referred to as computer-aided process engineering (CAPE), focuses on the development and use of mathematical models and algorithms for the effective design and operation of process plants. Various strategies ranging from mathematical programming to pinch analysis have been developed for specific problems faced by process engineers. Many such techniques have gained widespread acceptance among professionals, and are embedded in commercial process engineering software. However, PSE researchers throughout the world continue to explore new techniques to further expand the chemical engineer’s “professional toolbox.”

One interesting approach based on graph theory was developed in the early 1990s in a series of papers by Ferenc Friedler and coworkers. In these papers, graph theory was used to develop streamlined, efficient algorithms for network synthesis problems. Early applications dealt specifically with hard-core chemical engineering problems: determination of optimal chemical reaction pathways (since in the chemical industries, the target molecule can often only be formed through a sequence of chemical reaction steps), and process network synthesis (PNS). In the latter application, individual process equipment (e.g., chemical reactors, mixers, etc.) are specified as “building blocks,” while P-graph methodology automatically determines a “best design” by piecing together the components into a process network like a jigsaw puzzle, using three algorithms known as MSG (maximal structure generation), SSG (solution structure generation) and ABB (accelerated branch-and-bound). These steps ensure efficient search so that software code does not bog down when dealing with large problems. The methodology has since come to be known as P-graph (the “P” stands for “process”), and has matured sufficiently to be integrated in a standard chemical engineering textbook (Peters et al. 2003. “Plant Design and Economics for Chemical Engineers.” McGraw-Hill). There is also a website (www.p-graph.com) from which various resources, including free software called PNS Studio and PNS Draw, may be obtained. Numerous applications have appeared in chemical engineering literature in the past two decades, many of which are described in a review by Honloong Lam in Current Opinion in Chemical Engineering. In addition, other P-graph application domains have been reported, such as optimal planning of vehicle fleet maintenance and emergency building evacuation.

I myself first learned about P-graphs in 2008 while attending a major international PSE conference in the Czech Republic. It was only in late 2012 (after listening to a talk by the aforementioned Dr. H. Lam) that I came to understand the methodology well enough to begin integrating it in my lectures at De La Salle University. At present, P-graph methodology is taught as part of the Plant Design course in the final semester of our undergraduate chemical engineering program; it is also integrated in similar postgraduate courses at both masters and Ph.D. level. In addition, our nascent PSE research group at DLSU is exploring novel applications of P-graphs, based on exploration of analogous problem structures. At the moment we have looked at such problems as the design or operation of low-carbon polygeneration plants, planning of biomass supply chains (in collaboration with colleagues from Universiti Teknologi Malaysia), and the allocation of scarce resources in the immediate aftermath of a disaster (in collaboration with a colleague from George Washington University in the US). It is likely that the coming years will see more research in surprising new P-graph applications. Meanwhile, the current body of P-graph literature from the past two decades amply demonstrates how the intersection of two seemingly unrelated disciplines – one as abstract as graph theory, and the other as industry-rooted as chemical engineering – can lead to elegant solutions to practical problems.

Further Reading

The interested reader can visit the website dedicated to P-graphs (www.p-graph.com), where tutorials, free software as well as links to relevant literature can be found. Additional case studies can be found in the 2003 edition of the classic textbook by Peters et al., “Plant Design and Economics for Chemical Engineers” (McGraw-Hill). Also, an account of many chemical engineering applications of P-graphs was recently published (Lam, H. 2013. Current Opinion in Chem. Eng. 2: 475 – 486). Finally, a more in-depth discussion of the mathematical foundations (including rigorous proofs) of P-graphs can be found in the early series of seminal papers by Friedler and coworkers (Friedler et al. 1992. Chem. Eng. Sc., 47: 1973-1988; Friedler et al. 1992. Comp. & Chem. Eng., 16: 313 – 320.; Friedler et al. 1993. Comp. & Chem. Eng. 17: 929-942).

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Raymond R. Tan is a full professor of chemical engineering, university fellow and current Vice-Chancellor for Research and Innovation at De La Salle University, Manila, Philippines. His main areas of research are process systems engineering and process integration. Prof. Tan received his BS and MS in chemical engineering and PhD in mechanical engineering from De La Salle University, and is the author of more than 100 published and forthcoming articles in ISI-indexed journals in the fields of chemical, environmental and energy engineering. He currently has over 130 publications listed in Scopus with an h-index of 26, is member of the editorial board of the journal Clean Technologies and Environmental Policy (Springer) and is editor of the book Recent Advances in Sustainable Process Design and Optimization (World Scientific). He is also the recipient of multiple awards from the Philippine Commission on Higher Education (CHED), the National Academy of Science and Technology (NAST) and the National Research Council of the Philippines (NRCP), as well as commendations for highly cited papers in Computers & Chemical Engineering and Institution of Chemical Engineers (IChemE) journals. E-mail: [email protected].