Determination of rate parameters of complex reactions by polymath

Abstract

Generally, consecutive and/or parallel reactions pose a great deal of difficulty in determining meaningful reaction rate parameters. One way to determine such parameters is to separate the whole reaction network into different regions and to study each region independently through initial rates. This method is not only tedious, but also a waste of money and time. The other method is to use the fact that, if the reaction rates are known at any “t” time then an optimization technique in MATLAB, MATHCAD, LINDO or POLYMATH ready package programs can be used to determine rate parameters. In this study, the POLYMATH program is chosen for a highly complex rate expression for the reaction of CO + 2H 2 catalyst CH 3OH with Langmuir-Hinshelwood kinetic expression rA = kKCOKH 2PH 2PCO (1+ KCO .PCO + KH2 .PH2 + KCH3OH .PCH3OH ) 2 Rate parameters k, KCO, KH2 and KCH3OH were determined. INTRODUCTION In chemical reaction engineering and in purely chemical kinetics, due to the nature of the reaction one may face very complex reaction networks. Among the complex models, the most suitable one must be determined. In this determination, well-established regression techniques are used. These regression techniques are [1] a) Linear regression (such as y = ax + b) b) Multiple regression (such as y = a1x1 + a2x2 + ....+ anxn ) c) Polynomial regression (such as y = anx n + an 1x n 1 + ...+ a1x + a0 ) d) Non-linear regression, (such as y = f (x1, x2 , ..., xn ,a1,a2 , ...,an ) where n = # of experiments, m = # of parameters to be determined providing n > m+1.) This is very common and can be used almost under any condition. In using these techniques, one has to watch for the following criteria [2] 1. Variance must be minimum 2. Correlation coefficient (R) must be as close to unity as possible *Address correspondence to this author at the Do u University, Acıbadem, Kadıköy 34722, Istanbul, Turkey; E-mail: burcuozdemir@dogus.edu.tr 3. Determined rate parameters must be physically meaningful 4. 95 % confidence interval determination is also essential in order to eliminate (ignore) certain parameters Reactions networks such as A B C D [3] E or A B F [4] C D E are not uncommon in reaction engineering. REACTION RATE EXPRESSION Reaction rate expression of rA = KAKBk 'PAPB (1+ KAPA + KBPB + KCPC ) 2 can be observed on a heterogeneous catalytic reaction of such as CO + 2H 2 catalyst CH 3OH Then for the above reaction, we can write dual-site Langmuir-Hinshelwood model as follows: 22 The Open Catalysis Journal, 2009, Volume 2 Özdemir and Gültekin rA = kKCOKH 2PH 2PCO (1+ KCO .PCO + KH2 .PH2 + KCH3OH .PCH3OH ) 2 (dual site assumption is made) In this study, the data given in Table 1 for the above reaction were considered for the determination of rate parameters through POLYMATH [1, 5]. Table 1. Initial Rate of Reaction at Various Partial Pressures of Reactants and Product Experiment No PCO * PH2 PCH3OH Rate** 1 0.5 0.5 0.5 0.0457 2 1.0 0.5 0.5 0.0457 3 2.0 0.5 0.5 0.0384 4 4.0 0.5 0.5 0.0241 5 8.0 0.5 0.5 0.0141 6 1.0 1.0 0.5 0.0640 7 1.0 2.0 0.5 0.0727 8 1.0 4.0 0.5 0.0653 9 1.0 8.0 0.5 0.0474 10 1.0 1.0 1.0 0.0527 11 1.0 1.0 2.0 0.0375 12 1.0 1.0 4.0 0.0218 13 1.0 1.0 8.0 0.0100 14 0.5 1.0 0.5 0.0561 15 0.5 0.5 1.0 0.0332 * Pi = [atm], ** rate = [mole/kg cat-s].