Chemical Reactions and Kinetics of the Carbon Monoxide Coupling in the Presence of Hydrogen

Similar documents
Effect of Ni Loading and Reaction Conditions on Partial Oxidation of Methane to Syngas

Hydrogen addition to the Andrussow process for HCN synthesis

and mol of Cl 2 was heated in a vessel of fixed volume to a constant temperature, the following reaction reached equilibrium.

ALE 9. Equilibrium Problems: ICE Practice!

The table shows three possible reversible reactions that he could use. The enthalpy changes are also shown. O(g) CO 2. (g) + 4H 2.

Reactors. Reaction Classifications

2.0 Equilibrium Constant

The Equilibrium Law. Calculating Equilibrium Constants. then (at constant temperature) [C] c. [D] d = a constant, ( K c )

6. Which expression correctly describes the equilibrium constant for the following reaction? 4NH 3 (g) + 5O 2 (g) 4NO(g) + 6H 2 O(g)

The partial pressure of sulphur dioxide in the equilibrium mixture was 24 kpa and the total pressure in the flask was 104 kpa.

2. Which of the following liquids would have the highest viscosity at 25 C? A) CH 3 OCH 3 B) CH 2 Cl 2 C) C 2 H 5 OH D) CH 3 Br E) HOCH 2 CH 2 OH

Exam 4, Ch 14 and 15 December 7, Points

Microkinetics of H 2 S Removal by Zinc Oxide in the Presence of Moist Gas Atmosphere

WINTER-15 EXAMINATION Model Answer

Name AP CHEM / / Collected AP Exam Essay Answers for Chapter 16

Chemistry 123: Physical and Organic Chemistry Topic 4: Gaseous Equilibrium

Effects of Solvent Acidity on the Free-Radical-Initiated Synthesis of Methanesulfonic Acid from CH 4 and SO 3

CFD Simulation of Catalytic Combustion of Benzene

F325: Equilibria, Energetics and Elements How Far?

Effects of Different Processing Parameters on Divinylbenzene (DVB) Production Rate

Chapter 9. Chemical Equilibrium

Synthesis of jet fuel range cycloalkanes with diacetone alcohol. from lignocellulose

Studies on the Kinetics of Heavy Oil Catalytic Pyrolysis

AP CHEMISTRY NOTES 8-1 CHEMICAL EQUILIBRIUM: AN INTRODUCTION

Studies on Mo/HZSM-5 Complex catalyst for Methane Aromatization

Surface Chemistry & States of Matter

Direct Synthesis of H 2 O 2 on AgPt Octahedra: The Importance of Ag-Pt Coordination for High H 2 O 2 Selectivity

SUPeR Chemistry CH 222 Practice Exam

Thermodynamic and Stochiometric Principles in Materials Balance

BAE 820 Physical Principles of Environmental Systems

Be prepared to discuss the quantitative comparison method in the oral exam.

Chemical Equilibria. OCR Chemistry A H432

ERT 216 HEAT & MASS TRANSFER SEM2, 2013/2014

Catalyst Characterization Using Thermal Conductivity Detector *

CHEM J-8 June /01(a) With 3 C-O bonds and no lone pairs on the C atom, the geometry is trigonal planar.

Synthesis of isoalkanes over core (Fe-Zn-Zr)-shell (zeolite) catalyst

Class Results Simulator:

2/18/2013. Spontaneity, Entropy & Free Energy Chapter 16. The Dependence of Free Energy on Pressure Sample Exercises

A Brief Catalyst Study on Direct Methane Conversion Using a Dielectric Barrier Discharge

Modeling, Simulation and Control of a Tubular Fixed-bed Dimethyl Ether Reactor

Definitions and Concepts

Kinetic study of ethane oxydehydrogenation over AlPO-5

Chemical Equilibrium Basics

How sulphur really forms on the catalyst surface

The mechanism of ammonium bisulfate formation and

Chapter 15 Equilibrium

Chemical Equilibrium. Professor Bice Martincigh. Equilibrium

1. Why are chemical reactions important to energy, environmental and process engineering? Name as many reasons as you can think of.

CFD study of gas mixing efficiency and comparisons with experimental data

FUNDAMENTALS of Thermodynamics

Stoichiometric Reactor Module

EEC 503 Spring 2009 REVIEW 1

(02) WMP/Jun10/CHEM2

Oxygen Reduction Reaction

Problems Points (Max.) Points Received

ALE 1. Chemical Kinetics: Rates of Chemical Reactions

Review Unit #11. Review Unit # H 2 O (g) + CO (g) H 2(g) + CO 2(g) H>1

2SO 2(g) + O 2(g) Increasing the temperature. (Total 1 mark) Enthalpy data for the reacting species are given in the table below.

Chemistry 142 (Practice) MIDTERM EXAM II November. Fill in your name, section, and student number on Side 1 of the Answer Sheet.

Thermochemistry: Energy Flow and Chemical Reactions

AQA A2 CHEMISTRY TOPIC 4.2 EQUILIBRIA BOOKLET OF PAST EXAMINATION QUESTIONS

CHEM 101A EXAM 1 SOLUTIONS TO VERSION 1

AP CHEMISTRY 2009 SCORING GUIDELINES

LECTURE 9: Chemical Equilibrium

AE 205 Materials and Energy Balances Asst. Prof. Dr. Tippabust Eksangsri. Chapter 4 Stoichiometry and MB with Reactions

Sub-10-nm Au-Pt-Pd Alloy Trimetallic Nanoparticles with. High Oxidation-Resistant Property as Efficient and Durable

DETAILED MODELLING OF SHORT-CONTACT-TIME REACTORS

INTRODUCTION TO CHEMICAL PROCESS SIMULATORS

15/04/2018 EQUILIBRIUM- GENERAL CONCEPTS

Combined metallocene catalysts: an efficient technique to manipulate long-chain branching frequency of polyethylene

CSTR 1 CSTR 2 X A =?

Chemistry 1A, Spring 2007 Midterm Exam 3 April 9, 2007 (90 min, closed book)

Name AP CHEM / / Chapter 12 Outline Chemical Kinetics

High-Temperature HCl Removal with Sorbents in a Fixed-Bed Reactor

All reversible reactions reach an dynamic equilibrium state.

Unit 12: Chemical Kinetics

(04) WMP/Jan11/CHEM2

B 2 Fe(s) O 2(g) Fe 2 O 3 (s) H f = -824 kj mol 1 Iron reacts with oxygen to produce iron(iii) oxide as represented above. A 75.

CHEMICAL EQUILIBRIA. Section A Q1 The dissociation of dinitrogen tetraoxide into nitrogen dioxide is represented by the equation below.

have also been successfully tested in low temperature NH 3 Noble metals, especially platinum, have been reported to be active catalysts in NH 3

THE IRANIAN JAM PETROCHEMICAL S H 2 -PSA ENHANCEMENT USING A NEW STEPS SEQUENCE TABLE

Simultaneous Removal of COS and H 2 S at Low Temperatures over Nanoparticle α-feooh Based Catalysts

Name AP Chemistry / / Chapter 5 Collected AP Exam Free Response Questions Answers

Hydrogenation of CO Over a Cobalt/Cerium Oxide Catalyst for Production of Lower Olefins

Chemical reactions. C2- Topic 5

MODELING AND SIMULATION OF AN AUTOTHERMAL REFORMER

LECTURE 4 Variation of enthalpy with temperature

AS Paper 1 and 2 Kc and Equilibria

Chemistry in society. Homework

Consequences of Surface Oxophilicity of Ni, Ni-Co, and Co Clusters on Methane. Activation

LIMONENE HYDROGENATION IN HIGH PRESSURE CO 2 : EFFECT OF FLOW

Useful Information to be provided on the exam: 1 atm = 760 mm Hg = 760 torr = lb/in 2 = 101,325 Pa = kpa. q = m C T. w = -P V.

Strategic use of CuAlO 2 as a sustained release catalyst for production of hydrogen from methanol steam reforming

Q.1 Write out equations for the reactions between...

INTEGRATED PROCESS FOR γ-butyrolactone PRODUCTION

REACTION RATES AND REVERSIBLE REACTIONS

Le Châtelier's Principle. Chemical Equilibria & the Application of Le Châtelier s Principle to General Equilibria. Using Le Châtelier's Principle

Chemical Kinetics: NOx Mechanisms

1. The reaction between solid barium hydroxide and solid ammonium chloride can be represented by the equation below.

Fundamentals of Combustion

Transcription:

Journal of Natural Gas Chemistry 11(2002)145 150 Chemical Reactions and Kinetics of the Carbon Monoxide Coupling in the Presence of Hydrogen Fandong Meng 1,2, Genhui Xu 1, Zhenhua Li 1, Pa Du 1 1. State Key Laboratory of C1 Chemical Technology, Tianjin University, Tianjin 300072, China 2. Luoyang Petrochemical Engineering Corporation, Luoyang 471003, China [Manuscript received August 26, 2002; revised October 1, 2002] Abstract: The chemical reactions and kinetics of the catalytic coupling reaction of carbon monoxide to diethyl oxalate were studied in the presence of hydrogen over a supported palladium catalyst in the gaseous phase at the typical coupling reaction conditions. The experiments were performed in a continuous flow fixed-bed reactor. The results indicated that hydrogen only reacts with ethyl nitrite to form ethanol, and kinetic studies revealed that the rate-determining step is the surface reaction of adsorbed hydrogen and the ethoxy radical (EtO-). A kinetic model is proposed and a comparison of the observed and calculated conversions showed that the rate expressions are of rather high confidence. Key words: CO coupling, diethyl oxalate, hydrogen, chemistry, kinetics 1. Introduction A novel synthesis route for diethyl oxalate (DEO) from carbon monoxide and ethyl nitrite (EN) over supported palladium catalysts in the gaseous phase at atmospheric pressure has been studied by several groups [1 7]. The main reactions can be described by the following two equations: (1) Coupling reaction; (2) Regeneration reaction. 2CO + 2EtONO (COOEt) 2 + 2NO (1) 2NO + 2EtOH + 1/2O 2 2EtONO + H 2 O (2) The overall equation is: 2CO + 2EtOH + 1/2O 2 (COOEt) 2 + H 2 O (3) The fresh feeds in diethyl oxalate production are carbon monoxide, oxygen and ethanol. In industrial situations, carbon monoxide is mainly obtained from coal gas or syngas, and hydrogen is an inherent concomitant of coal gas and syngas. A scale-up test of diethyl oxalate production was recently completed [8], and the technology for commercial production has been established. Therefore, it is necessary to investigate the behavior of the process in the presence of hydrogen. In this experiment, the chemical reactions occurring after the introduction of hydrogen to the reaction system were verified experimentally. The reaction mechanism was then proposed and the rate expression was derived. 2. Experimental The generation of ethyl nitrite took place in a special vessel into which 50 ml of ethanol was added and reacted with nitrogen monoxide and oxygen at ca. 308 K. The coupling reaction experiments were performed in a flow-type apparatus with a glass-made, fixed-bed reactor at atmospheric pressure. The flow scheme is depicted in figure 1. The reactor tube, with a 2 cm internal diameter and a length of 60 cm, was electrically heated with a temperature control accuracy of ±0.5 K. In each experiment, the reaction zone was Corresponding author.

146 Fandong Meng et al./ Journal of Natural Gas Chemistry Vol. 11 No. 3 4 2002 filled with 2 ml of catalyst pellets with quartz of the same particle size filling the rest of the reactor. The gas mixtures before and after each reaction were analyzed by capillary gas chromatography using a thermal conductivity detector. Pd-Fe/α-Al 2 O 3 with 1wt% of palladium and 0.5wt% of iron was used as the catalyst. The catalyst was prepared by impregnating α-al 2 O 3 with a 20wt% aqueous solution of PdCl 2 and 5wt% FeCl 3 H 2 O and then was dried in air at ca. 393 K for 12 h. Lastly, the catalyst was pretreated in-situ with pure hydrogen for 4 h at 623 K. As mentioned above, there are four components (i.e. CO, EtONO, (CO 2 Et) 2, NO) in the coupling reaction system, so the reactions which may take place are: 2H 2 + 2CO CH 4 + CO 2 (4) H 2 + 2EtONO 2EtOH + 2NO (5) 4H 2 + (CO 2 Et) 2 (CH 2 OH) 2 + 2EtOH (6) 5H 2 + 2NO NH 3 + 2H 2 O (7) Table 1 lists the Gibbs free energy G 0 of the above reactions. The table illustrates that all the reactions are thermodynamically possible. The following description will experimentally verify which reactions take place and analyze the reasons on the basis of thermodynamic principles. Table 1. G 0 of reactions(4) (7) at 393 K Reaction G 0 ( kj mol 1 ) (4) -130.33 (5) -163.28 (6) -7.58 (7) -498.70 3.1.1. Reaction of hydrogen with ethyl nitrite Figure 1. Flowsheet of CO coupling reaction in the presence of H 2. (1) N 2, (2) H 2, (3) CO, (4) EtONO, (5) Mass floweter, (6) Mixer, (7) Temperature control system, (8) Reactor, (9) Thermocouple, (10) Cold trap, (11) Wet flowmeter. In the coupling reaction system, there are two reactants (CO, EtONO) and two products ((CO 2 Et) 2, NO). The reactions between hydrogen and every component mentioned above were tested, and the kinetics of the coupling reaction of carbon monoxide to diethyl oxalate was also investigated. The reaction conditions utilized were typical coupling reaction conditions obtained from previous work [8]. 3. Results and discussion 3.1. Chemical reactions in the presence of hydrogen At a reaction temperature of 393 K, residence time of 1.8 s and atmospheric pressure, hydrogen, ethyl nitrite and nitrogen were fed into the reactor at a flow rate of 7.4 ml/min, 16.67 ml/min and 43 ml/min, respectively. During the 10 h stable run time, the conversions of hydrogen and ethyl nitrite were 76.8% and 73.4%, respectively, which corresponds to an absolute consumed amount of 0.15 mol hydrogen and 0.33 mol ethyl nitrite. The analytic results revealed that the liquid collected in cold trap is pure ethanol, weighted 14.8 g, i.e. 0.32 mol. So, the ratio of stoichiometric coefficients of hydrogen, ethyl nitrite and ethanol is equal to 0.15 : 0.33 : 0.32 1 : 2 : 2 and the reaction can be described by equation (5). 3.1.2. Reaction of hydrogen with carbon monoxide, diethyl oxalate and nitrogen monoxide In the same conditions, hydrogen, carbon monoxide and nitrogen were introduced into the reactor at a flow rate of 7.4 ml/min, 13.3 ml/min and 45.3 ml/min, respectively. An analysis of inlet and outlet gases of the reactor revealed that the concentration of hydrogen and carbon monoxide remained unchanged during the 4 h run time, indicating that no chemical reactions occurred. Similarly, carbon monoxide was replaced by diethyl oxalate or nitrogen monoxide. Furthermore, there was no conversion of diethyl oxalate or nitrogen monoxide. For this reason, it is not possible for

Journal of Natural Gas Chemistry Vol. 11 No. 3 4 2002 147 reactions (4), (6) or (7) to take place under typical coupling reaction conditions. 3.1.3. Thermodynamic analysis An RO NO bond of alkyl nitrite is easily cleaved homolitically. The bond dissociation energy of ethyl nitrite into an ethoxy radical (EtO-) and NO is estimated to be about 176 (kj mol 1 ), which is extremely low when compared to the dissociation energy of the C=O or N=O bond (at least twice that value). The decomposition of ethyl nitrite is accelerated by the presence H 2 and creates a fair amount of ethanol. On the other hand, it is rather difficult for reactions (4), (6) and (7) to occur under typical coupling reaction conditions due to the high dissociation energy of the C=O or N=O bond. 3.2. Kinetics of the coupling reaction in the presence of hydrogen Starting from different plausible mechanisms, Hougen-Watson-type rate expressions were derived. The best fit for the experimental data was achieved using the following reaction mechanism (Z is a free active site and the adsorption of the inert gas, nitrogen, is negligible): CO + Z COZ (8) H 2 + Z 2HZ (9) EtONO + 2Z EtOZ + NOZ (10) COZ + EtOZ COOEtZ (11) HZ + EtOZ EtOH + 2Z (12) 2COOEtZ (COOEt) 2 + 2Z (13) NOZ NO + Z (14) In Equation (10), ethyl nitrite first dissociates into an adsorbed ethoxy radical and NO, whereupon the ethoxy radical reacts in Equation (11) with adsorbed carbon monoxide to form alkoxycarboxide (COOEt), which further associates to diethyl oxalate, as shown in Equation (13). In Equation (9), hydrogen is also dissociated and adsorbed, after which it reacts in equation (12) with the adsorbed ethoxy radical to form ethanol. Finally, in Equation (14), the gaseous phase NO forms from adsorbed nitrogen monoxide. For the derivation of the rate expression it was assumed that steps (8), (9), (10), (13) and (14) are in equilibrium and that step (11) and (12) are the ratedetermining steps. The resulting Hougen-Watsontype rate expressions are: r CO = r H2 = K 6 P CO P EtONO P 1 NO (1 + K 1 P CO + K 2 P EtONO P 1 NO + K 3P NO + K 4 P 1/2 (COOEt) 2 + K 5 P 1/2 H 2 ) 2 (15) K 7 P 1/2 H 2 P EtONO P 1 NO (1 + K 1 P CO + K 2 P EtONO P 1 NO + K (16) 3P NO + K 4 P 1/2 (COOEt) 2 + K 5 P 1/2 H 2 ) 2 The parameters K i (i=1, 2, 3, 4, 5, 6, 7) were determined using experimental data (see Table 2). Parameter estimation was based on minimization of the objective function (17). 30 minφ = w 1 (r CO,cal. r CO,expt. ) 2 + w 2 i=1 30 i=1 (r H2,cal. r H2,expt.) 2 (17) w 1 and w 2 are weighted factors for the main reaction (1) and side reaction (5), respectively: w 1 + w 2 = 1 (18) Using the damped least square method, kinetic parameters were estimated that are functions of the reaction temperature: K i = K 0i exp(e i /RT ) (19) The values of K 0i, E i are reported in Table 3. Figures 2 and 3 show that the conversions of CO and H 2 from experiments at different temperatures agree well with those estimated from the rates of Equation (15) and (16) developed by our research. The absolute errors of X EN and X H2 in most of the experimental runs are below 15%. The random distribution of experimental and calculated values around the diagonal line suggests that those equations describe all the experimental results quite well. The confidence level of the obtained parameters can be evaluated using the determinative factor ρ 2 and F- test. The determinative factor ρ 2 in Equations (15) and (16) are 0.9934 and 0.9887, respectively, and are

148 Fandong Meng et al./ Journal of Natural Gas Chemistry Vol. 11 No. 3 4 2002 both greater than 0.95. When the confidence limits are 95%, the F-test results of Equations (15) and (16) are greater than 10 times F t (F t =2.61), in the sense that the kinetic model is adequate at a 95% confidence level. Table 2. Experimental data of reaction kinetics a,b T(K) N T (mol h 1 ) p(co) p(en) p(h 2 ) X(CO) X(H 2 ) 363 0.1604 0.0724 0.2123 0.0000 0.2973 0.0000 0.1731 0.0987 0.2122 0.0000 0.2856 0.0000 0.1977 0.1329 0.2122 0.0519 0.1048 0.2022 0.1912 0.1871 0.2122 0.0519 0.1263 0.2476 0.3207 0.1871 0.1322 0.0702 0.0949 0.1833 0.4812 0.1871 0.2052 0.0438 0.0817 0.1688 0.3734 0.2524 0.2052 0.0438 0.1824 0.3269 0.4037 0.2526 0.2733 0.0745 0.1342 0.2411 0.4037 0.2833 0.2733 0.0979 0.1463 0.2766 0.2289 0.2089 0.2733 0.0979 0.1977 0.3816 378 0.1604 0.0724 0.2123 0.0000 0.4147 0.0000 0.1731 0.0987 0.2132 0.0000 0.3873 0.0000 0.1977 0.1329 0.2122 0.0519 0.1548 0.2017 0.2412 0.1871 0.2122 0.0519 0.1863 0.2381 0.3207 0.1872 0.1322 0.0702 0.1248 0.1827 0.4812 0.1871 0.2052 0.0438 0.1105 0.1682 0.3736 0.2527 0.2052 0.0438 0.1895 0.2670 0.4037 0.2526 0.2734 0.0745 0.2042 0.3005 0.4037 0.2835 0.2733 0.0979 0.2277 0.3562 0.2289 0.2089 0.2733 0.0979 0.2645 0.4017 393 0.1604 0.0724 0.2123 0.0000 0.4836 0.0000 0.1731 0.0987 0.2132 0.0000 0.5018 0.0000 0.1977 0.1329 0.2122 0.0519 0.2312 0.2617 0.2412 0.1871 0.2122 0.0519 0.2502 0.2713 0.3207 0.1872 0.1322 0.0702 0.2092 0.2214 0.4812 0.1871 0.2052 0.0438 0.1769 0.1978 0.3736 0.2527 0.2052 0.0438 0.2719 0.2976 0.4037 0.2526 0.2734 0.0745 0.2933 0.3100 0.4037 0.2835 0.2733 0.0979 0.3234 0.3656 0.2289 0.1871 0.2733 0.0979 0.3961 0.4577 (a) Data from the experimental runs in the steady-state stage and in the absence of mass transfer resistances. (b) P =1 atm; V = 2 ml; ρ b = 0.8934 (g ml 1 ); d P = 1 mm. Table 3. values of K 0i and E i i K 0i K 0i unit E i (J mol 1 ) 1 9.84 10 8 Pa 1 5.87 10 4 2 3.24 10 2-1.28 10 3 3 4.13 10 3 Pa 1-1.17 10 4 4 2.72 10 6 Pa 1/2 4.65 10 4 5 2.12 10 5 Pa 1/2 4.46 10 3 6 3.57 Pa 3/2 7.02 10 3 7 2.21 10 2 Pa 1 mol kg 1 s 1-1.36 10 4 All other mechanisms were also taken into consideration, including no adsorption and/or dissociation of hydrogen, but negative kinetic constants K i are obtained, indicating that they are unreasonable. Ma et al. [9] studied the kinetics of the coupling reaction over Pd/Al 2 O 3 with 1wt% of palladium. The main differences between the reaction mechanism presented here and the one proposed by Ma et al. [9] are the rate-determining steps and the adsorption of ethyl nitrite. Whereas in the mechanism envisioned here, the surface reaction is the sole rate-determining step and ethyl nitrite cleaves into an ethoxy radical

Journal of Natural Gas Chemistry Vol. 11 No. 3 4 2002 149 and a NO species, those adsorbed on two active sites, Ma et al. [9] suggested that the adsorption of carbon monoxide is the rate-determining step and that ethyl nitrite is adsorbed on a single active site without dissociation. Uchiumi et al. [2] observed that the partial pressure of ethanol does not affect the reaction rate, which cannot be accounted for by the rate expression from Ma et al. [9]. In fact, as mentioned above, an RO NO bond of alkyl nitrite is easily homolitically cleaved. The assumption that ethyl nitrite dissociates into an adsorbed ethoxy radical and NO is more reasonable. In this explanation, the observations in the work of Ma et al. [9] are readily accounted for. 4. Conclusion The chemical reactions and kinetics of the catalytic coupling reaction of carbon monoxide to diethyl oxalate in the presence of hydrogen over supported palladium is presented in this work. The only other byproduct, ethanol, was formed according to reaction (5) in the coupling reaction system. This process did not occur for reactions (4), (6) and (7) under typical coupling reaction conditions. Moreover, it was discovered that the surface reaction of adsorbed hydrogen with the ethoxy radical is the rate-determining step and that ethyl nitrite, due to the rather low dissociation energy of the EtO-NO bond, cleaves into adsorbed EtO and NO species. Furthermore, as shown in Equations (8), (9), (11) and (12), hydrogen competes with carbon monoxide for adsorption, and the reaction between adsorbed hydrogen and the ethoxy radical competes with the reaction between adsorbed carbon monoxide and the ethoxy radical on the surface of the catalyst. All of these factors exert a significant influence on the reaction behavior-a significant decrease in CO conversion and DEO selectivity. Acknowledgment Figure 2. Calculated versus experimentally observed CO conversion. Financial support from the Chinese Development Foundation (96-539-01) is gratefully acknowledged. Nomenclature Figure 3. Calculated versus experimentally observed H 2 conversion. d p diameter of the catalyst pellets, mm E i activation energy or adsorption energy, J mol 1 kinetic constants K i K 0i P P i pre-exponential factors reaction pressure, atm partial pressure of the component i, Pa N T total mole flow rate at the inlet of reactor, mol h 1 -r CO reaction rate(disappearance of CO), mol 1 g 1 s -r H2 reaction rate(disappearance of H 2 ), mol 1 g 1 s R 1 universal gas constant, J mol 1 K T V w 1 reaction temperature, K volume of catalyst bed, ml weighted sum of the squares

150 Fandong Meng et al./ Journal of Natural Gas Chemistry Vol. 11 No. 3 4 2002 w 2 weighted sum of the squares X CO CO conversion (dimensionless) X H2 Z ρ b Φ H 2 conversion (dimensionless) free active site of the catalyst density of catalyst, g ml 1 minimized value of the objective function References [1] Xu G H, Ma X B, He F, Chem H F. Ind. Eng Chem Res, 1995, 34(7): 2379 [2] Nishimura K, Uchiumi S, Fujii K, Nishihira K. Am Chem Soc Prepr Div Pet Chem, 1979, 24(1): 355 [3] Chen Y. CN Patent 1 054 765A. 1991 [4] Song R J, Zhang X H, He D H. Natur Gas Chem Ind, 1987, 12(5): 1 [5] Jing X Z. Platinum Met Rev, 1990, 34(4): 178 [6] Ohdan, Kyoji. EP Patent 0 802 175A1. 1997 [7] Xuan Z J, Yue H S, Bor J L. Appl Cata A. 2001, 211: 47 [8] Meng F D, Xu G H, Wang B W, Ma X B. J Nat Gas Chem, 2002, 11(1-2): 57 [9] Ma X B, Xu G H, Chen J W. J Chem Ind Eng (China), 1995, 46(1): 50