CN4246E: CHEMICAL AND BIOCATALYSISTerm Paper: Water-Gas Shift Reaction (Carboxyl Mechanism)

TEAM 1

1Wai Ming HuiA0066050R

2Chong Xue Li CherieA0066081J

Derivation for water-gas shift reaction carboxyl mechanismThe water-gas shift reaction (CO+H2O CO2 + H2) is a slightly exothermic equilibrium-controlled reaction. The elementary steps for the carboxyl mechanism is proposed by Mhadeshwar and Vlachos (2005). The original 46 reactions has been narrowed to these few elementary steps through principal component analysis. Although there appears to be 18 elementary steps, reaction pairings between R1-R2, R7-R8, R13-R14, R19-R20, R21-R22, R25-R26, R29-R30, R31-R32, R33-R34 actually produces 9 reversible elementary steps. The reduced elementary steps are mentioned by the authors to be thermodynamically consistent by keeping the equilibrium constant fixed with changing the pre-exponential factors.

Here steady-state approximation assumption is applicable for species coverage which provides the complete steady state balance for species coverage.

Overall site coverage equation:

To simplify the expressions above, CO* and H* are found to be the most abundant reactive intermediate (MARI). Furthermore, reversibility of reaction pairs are analyzed which results in simplified steady state balance for species coverage.

MARI assumption is applicable for and .The following site coverage terms can be obtained:

Substitute (13) into (8) to obtain the following expression for .

Since as is rate-determining step. can be further simplified.

Substitute the (15), (16) and (19) into (9) and obtain following expression for .

Substitute (15), (17) and (19) into (18) and obtain following expression for .

as is rate-determining step to simplify the expression into:

Substitute (16) and (19) into simplified site coverage equation (14)

Derivation for forward reactionThe net rate of is used to determine overall reaction rate. Through the stoichiometry of the global reaction (CO+H2O CO2 + H2), the net rate for other species can be determined in terms of net rate of . is chosen as the rate-determining step for the forward reaction.

Derivation for reverse reaction and simplified net rate equation is chosen as the rate-determining step for the reverse reaction since this reaction is not found to be in equilibrium for the reverse reaction. The global water-gas shift reaction is equilibrium-controlled which implies that the terms that were derived for the forward reaction is equivalent to reverse reaction. Hence, the site coverage expressions for the intermediates and adsorbed species (15), (16), (17), (19), (20) and (21) can be used.

The net rate equation for global water-gas shift reaction is shown below:

This form of equation (26) will be used for model fitting against Grabow (2009) experimental data.Derivation for full net rate equationWhen MARI is not assumed in the site coverage equation (7), the net rate equation (25) will be very detailed since the behavior of all coverage species is captured in the site coverage equation (7) as shown below:

Substitute (27) into (25)

Model fitting using MATLABA universal water gas shift reaction mechanism is still not well-understood and agreed upon. But kinetic studies on platinum (Pt) is especially limited. Current research on water-gas shift reaction uses a lot of first-principle analysis and transition state theory ([2], [4], [5] and [6]) to elucidate the reaction mechanism. However, such analysis is computationally intensive. Another method to analyze and elucidate reaction mechanism efficiently is to conduct model fitting and discrimination against available experimental data to determine possible reaction mechanisms. The simplified carboxyl rate equation (26) will be used in model fitting against experimental data from Grabow (2008) [2].

The experiment on water-gas shift reaction was done on Pt/Al2O3 catalyst by introducing different components (CO, H2, H2O and CO2) at different temperature. The total pressure was kept constant at 1 atm with inert He introduced as balance gas. The turnover frequency (TOF) is expressed as moles of product species produced per moles of active catalytic sites per unit time (min-1). The experimental data from [2] is selected and compiled in Appendix 8A.For model fitting and analysis, nlinfit command is first used to determine the equilibrium constants in (26) at 548K. However in order to determine if the results obtained from nlinfit is statistically significant, the nlparci function can be used to determine the upper bound and lower bound of a coefficient at a certain percentage interval. For this analysis, 90% confidence interval is used.For nlinfit command to work, initial estimates are required and such estimates are obtained through trial and error method to obtain positive coefficient. Several attempts to make initial estimates has to be used. This is because negative equilibrium constant or rate constant does not have physical meaning. Hence, the initial estimates that gives positive coefficient are given in Table 1. The results for the 7 coefficients are tabulated in Table 3a, 3b and 3c.

Table 2: Initial estimates for constants for nlinfit function in MATLABk33K19K13k34K21K1K31

Initial estimatesfor equilibrium constants101000.15000.9201

Table 3a: Results of non-linear model fitting at 90% confidence intervalk33K19K13

T (K)MSEL.LmeanU.LL.LmeanU.LL.LmeanU.L

5481.13151.1315118.7447118.7459118.7474.8879.730114.57151.07441.1875

Table 3b: Results of non-linear model fitting at 90% confidence intervalk34K21K1

T (K)MSEL.LmeanU.LL.LmeanU.LL.LmeanU.L

5481.131559.69159.702459.7138-6.20410.10756.41911.253217.236233.2193

Table 3c: Results of non-linear model fitting at 90% confidence intervalK31

Temperature(K)MSEL.LmeanU.L

5481.13154.71894.85884.9986

DiscussionA) Equilibrium constants and statistical significanceThe rate constants and equilibrium obtained from non-linear fitting display positive values However if statistical significance is to be properly accounted for, the model may not describe the reaction mechanism accurately because K21 which is the equilibrium constant for CO2 adsorption and desorption from active sites is -6.2041 at the lower limit and 6.4191 at the upper limit. However, more attempts on initial estimates need to be done to confirm that K21 is truly statistically insignificant.B) Uncertainty in determining rate-determining step (RDS)One possible reason for the statistical insignificance of [26] is the uncertainty in predicting the rate-determining step in the carboxyl mechanism. R7-R8, R25-R26, R29-R30 are also potential RDS identified because these reactions are found to be far from equilibrium at various temperature [1]. L.C Grabow et al [2] conducted Campbells rate control analysis and found that water activation (R7-R8) is the next possible rate-determining step after (COOH*+* CO2*+H*). Possible attempts to better elucidate the reaction mechanism could include deriving the rate equation based on possible rate-determining steps (R7-R8, R25-R26 and R29-R30) and conduct non-linear fitting to determining the most likely reaction mechanism.ConclusionThe net rate equation for water gas shift reaction catalyzed on Pt/Al2O3 has been derived based on CO* and H* as the most abundant reactive intermediate (MARI) and R33-R34 as the rate-determining step. Non-linear model fitting nearly yielded positive values for the rate constants and equilibrium constants in the model at 90% confidence interval. However, only K21 is found to be statistically insignificant which affects the validity of the model. There is also uncertainty in determining the rate-determining step as R7-R8, R25-R26 and R29-R30 are also potential RDS [2]. Future work involves deriving rate equation based on possible rate-determining steps and fitting against experimental data to determine the most likely reaction mechanism.

Reference[1] A.B Mhadeshwar, D.G Vlachos. Is the water-gas shift reaction on Pt simple? Computer-aided microkinetic model reduction, lumped rate expression, and rate-determining step. Catalysis Today (2005), 105, 162-172.[2] L.C Grabow, A.A Gokhale, S.T Evans, J.A Dumesic, M Mavrikakis. Mechanism of the Water Gas Shift Reaction on Pt: First Principles, Experiments and Microkinetic Modeling. Journal of Physical Chemistry C (2008), 112, 4608-4617.[3] W.F Podolski, Y.G Kim. Modeling the Water-Gas Shift Reaction. Ind. Eng. Chem. Process Des. Dev (1974), 13 (4), 415-421.[4] A.A Gokhale, J.A Dumesic, M Mavirikakis. On the mechanism of low temperature water gas shift reaction on copper. J. Am. Chem. Soc (2008), 130(4), 1402-1414.[5] H.N Chiang, J.C Jiang. Density Functional Theory Study of Water-Gas-Shift Reaction on 3Cu/-Al2O3(0001) Surface. J. Phys. Chem. C(2013), 117 (23), 1204512053.[6] A.B Vidal, P Liu. Density functional study of water-gas shift reaction on M3O3x/Cu(111). Phys. Chem. Chem. Phys (2012),14, 16626-16632.

Appendix

A) Selected experimental kinetics data on Pt/Al2O3 catalyst taken from [2] No of runsT (K)PCO(atm)PH2O(atm)PCO2(atm)PH2(atm)measured TOF(min^-1)

15230.1540.208003.68

25480.0550.208008.56

35480.1050.208008.06

45480.1370.062003.63

55480.1440.104004.81

65480.1480.145005.56

75480.1450.208007.27

85480.1060.2080.06806.05

95480.1040.2080.10905.59

105480.140.2080.15106.12

115480.1020.2080.19206.03

125480.1340.20800.0374.13

135480.1560.20800.0972.77

145480.130.20800.1232.67

155480.1340.2080.1770.1232.67

165480.1320.20800.1732.55

175480.1460.20800.1912.28

185480.1590.20800.2082.29

195480.1980.208007.29

205480.2230.208007.09

215730.150.2080015.44

B) MATLAB Code for nlinfit and nlparci functionFunction file

function yhat=wgs_carboxylmechanismvlachos(beta,x)yhat=(x(:,1).*x(:,2).*beta(1)*beta(2)*beta(3)-x(:,3).*x(:,4).*beta(4)*beta(5)*beta(6)*(beta(7)^-1))./(1+((x(:,4).*beta(6)).^0.5)+x(:,1).*beta(2)).^2;

Domain file

% Mhadeshwar&Vlachos 2005 model is fitted with Grabow 2008 experimental% data.p=partial pressure of components (atm),v=measured TOF(min^-1)% x(:,1) is the partial pressures of CO,x(:,2) is the partial pressures of H2O,x(:,3) is the partial pressures of CO2,x(:,4) is the partial pressures of H2,% previous intial values are [1000 1 1 1500 1 1 2] and eventually [375.8356 9.7301 0.3752 105.4530 0.0703 17.2363 5.6143],[10 100 0.1 500 0.9 20 1] .The latter one produces the best results thus far.p=[0.055 0.105 0.137 0.144 0.148 0.145 0.106 0.104 0.14 0.102 0.134 0.156 0.13 0.134 0.132 0.146 0.159 0.198 0.223;0.208 0.208 0.062 0.104 0.145 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208;0 0 0 0 0 0 0.068 0.109 0.151 0.192 0 0 0 0.177 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0.037 0.097 0.123 0.123 0.173 0.191 0.208 0 0]';v=[8.56 8.06 3.63 4.81 5.56 7.27 6.05 5.59 6.12 6.03 4.13 2.77 2.67 2.67 2.55 2.28 2.29 7.29 7.09]';[beta,r,J,sigma,mse]=nlinfit(p,v,@wgs_carboxylmechanismvlachos,[10 100 0.1 500 0.9 20 1])ci=nlparci(beta,r,'covar',sigma,'alpha',0.1)