Computers and Chemical Engineering 34 (2010) 821–824 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng Graph-theoretic approach to the catalytic-pathway identification of methanol decomposition Yu-Chuan Lin a , L.T. Fan b,∗ , Shahram Shafie b , Botond Bertók c , Ferenc Friedler c a Department of Chemical Engineering and Materials Science, Yuan Ze University, 135 Yuan-Tung Rd., Chungli, Taoyuan 32003, Taiwan b Department of Chemical Engineering, Kansas State University, 1005 Durland Hall, Manhattan, KS 66506-5102, USA c Department of Computer Science and Systems Technology, University of Pannonia, Veszprem, Egyetem u. 10, H-8200, Hungary article info Article history: Received 7 July 2009 Received in revised form 6 December 2009 Accepted 10 December 2009 Available online 21 December 2009 Keywords: Methanol decomposition Graph theory Reaction pathways Independent pathways Acyclic combined pathways abstract Catalytic decomposition of methanol (MD) plays a vital role in hydrogen production, which is the desir- able fuel for both proton exchange membrane and direct methanol fuel cell systems. Thus, the catalytic mechanisms, or pathways, of MD have lately been the focus of research interest. Recently, the feasible independent pathways (IP i s) have been reported on the basis of a set of highly plausible elementary reac- tions. Nevertheless, no feasible acyclic combined pathways (AP i s) comprising IP i s have been reported. Such AP i s cannot be ignored in identifying dominant pathways. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction The graph-theoretic approach resorting to various formal graphs is increasingly being deployed in identifying and repre- senting catalytic or metabolic pathways because of its distinctive efficacy (Djega-Mariadassou & Boudart, 2003; Fan, Bertók, & Friedler, 2002; Fan, Bertók, Friedler, & Shafie, 2001; Lee et al., 2005; Lin, Fan, Shafie, Bertok, & Friedler, 2009; Lin et al., 2008; Murzin, 2007; Murzin, Smeds, & Salmi, 1997). The current contribution rep- resents the latest effort towards such a trend. The graph-theoretic method based on P-graphs (process graph) (Brendel, Friedler, & Fan, 2000; Fan et al., 2002; Fan et al., 2001; Fan et al., 2005; Friedler, Tarjan, Huang, & Fan, 1992; Friedler, Tarjan, Huang, & Fan, 1993; Friedler, Varga, & Fan, 1995) has been exten- sively adopted in exploring the mechanisms of catalytic (Fan, Lin et al., 2008; Lin et al., 2009; Lin et al., 2008) as well as metabolic reac- tions (Lee et al., 2005; Seo et al., 2001). Redundancy can be largely circumvented prior to the follow-up investigation, e.g., the deriva- tion of mechanistic rate equations (Lin et al., 2008), by determining only the feasible networks of elementary reactions algorithmi- cally and rigorously. It is worth noting that the efficacy of the graph-theoretic method based on P-graphs has been increasing rec- ognized through its wide-ranging applications (Fan, Lin et al., 2007; ∗ Corresponding author. Tel.: +1 785 532 4326; fax: +1 785 532 7372. E-mail address: fan@k-state.edu (L.T. Fan). Fan, Zhang et al., 2007; Fan, Zhang et al., 2008; Halim & Srinivasan, 2002a; Halim & Srinivasan, 2002b; Liu, Fan, Seib, Friedler, & Bertók, 2006; Xu & Diwekar, 2005). Besides graph-theoretic methods, other methods have been deployed in the identification of catalytic pathways. They are the linear algebraic methods and the method of stoichiometric network analysis. The linear algebraic-determination of the stoichiometric number for each elementary reaction in a catalytic pathway (mech- anism) frequently yields an over-determined system of algebraic equations with the number of constraints exceeding the number of unknowns. This has given rise to the two conventional algorith- mic methods for exhaustively identifying the independent feasible catalytic pathways, which can be constituted from a set of plausi- ble elementary reactions. One of the two algorithmic methods is based on combinatorics (Seller, 1971, 1972; Temkin, 1971, 1973). The other algorithmic method is based on mixed integer linear pro- gramming (MILP), often via the construction of a super-structure (see, e.g., Hatzimanikatis, Floudas, & Bailey, 1996a; Hatzimanikatis, Floudas, & Bailey, 1996b). Stoichiometric network analysis (SNA) (Clarke, 1980; Clarke, 1983; Clarke, 1988) is based on qualitative analysis of the nonlinear dynamics reaction pathways. Unlike the linear algebraic methods, SNA refines a pathway of interest in light of constrains (dynamic behavior of chemical reactions, e.g., reactant concentrations). Hence, it can substantially reduce the size of the super-structure of reaction pathways. It is also capable of estimating the potential 0098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2009.12.004