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Low temperature Claus reactor studies Besher, Elmarghani M. 1990

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LOW TEMPERATURE CLAUS REACTOR STUDIES By E L M A R G H A N I M . B E S H E R B.Sc. University of Tripoli M.Sc. University of Southern California A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF PH ILOSOPHY in T H E F A C U L T Y OF G R A D U A T E STUDIES CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH COLUMB IA September 1990 © E L M A R G H A N I M . BESHER, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CffeM C /tL- ^ AJ(C The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract A small-scale fluidized bed reactor (0.1m ID, 0.86m high) was used to carry out the Claus reaction 2H2S + SO2 - - 5 X • + 2H20 x at low temperatures (100 to 150°C) where elemental sulphur condensed on the catalyst particles (Kaiser alumina S-501, 195fim mean particle size). The experimental apparatus was similar to that described by Bonsu and Meisen (1985). The feed gas consisted of pure nitrogen mixed with H2S and SO2 in the ratio of 2 to 1. The H2S concentration was varied from 200 to 1300 ppm. The feed gas flow rate ranged from approximately 1.4 to 5.6 m 3 / h . The corresponding U/Umf ranges were approximately 2.2 to 8.8. The bed heights varied from 0.12 to 0.38m. It was found that the experimental conversion efficiencies ranged from 60 to 96% and that they were less than those predicted thermodynamically. The conversion efficiency was found to increase with H2S concentration and catalyst bed height; it decreased with gas flow rate. Contrary to thermodynamic predictions, the conversion efficiency increased with temperature. These results suggest that thermodynamic equilibrium was not achieved in the reactor. The decline in conversion due to catalyst fouling was mea-sured as a function of catalyst sulphur content. The experimental results could be interpreted by means of a bubbling bed model. New analytical expressions for predicting the overall conversion and the concentration profiles were developed for reactions of order n. For the Claus reaction, where n=1.5, good agreement was found between the model predictions and experimental values. The model 11 properly discribed the observed behavior resulting from changes in feed concentration, bed temperature, U/Umf and static bed height. The bubbling bed model was used to predict the effect of particle size on conversion for various operating gas velocities and bed dimensions. The model predictions showed that the canversion improved with decreasing particle size and that the improvement depended on U/Umj. The bubbling bed model was modified for conditions where condensed sulphur fouled the catalyst. A catalyst deactivation function, derived from first principles and based on catalyst sulphur content, was incorporated into the rate expression. The modified model predicted the the experimental measurements well and conclusions are drawn regarding the continuous operation of fluidized bed Claus reactor operating under sulphur condensing conditions. A general procedure is presented to demonstrate the applicability of the bubbling bed model in the design of large scale reactors; examples for specific conditions are given. Attrition tests were performed on the catalyst at U/Umf=5.1 and room temperatures. It was found that most of the attrition occurred in the first few hours when the catalyst particles were rough. The overall test results indicated that attrition of the catalyst was negligibly small thereby suggesting the suitability of the Kaiser S-501 catalyst for long term use in fluidized bed Claus reactors. 1U Table of Contents Abstract ii List of Figures * viii List of Tables xi Acknowledgement xiv 1 INTRODUCTION 1 2 LITERATURE REVIEW 12 2.1 CLAUS REACTIONS 12 2.1.1 Theoretical Studies 12 2.1.2 Fluidized Bed Claus Process 15 2.1.3 Experimental Studies 16 2.1.4 Catalyst Deactivation By Fouling . 18 2.1.5 Low Temperature Industrial Processes 20 2.2 FLUIDIZED BED R E A C T O R M O D E L L I N G 21 2.2.1 Number Of Phases 22 2.2.2 Mass Transfer Between Phases 27 2.2.3 Division Of Flow Between Phases 31 2.2.4 Gas Mixing In The Dense Phase 33 2.2.5 Fraction Of Bed Occupied By Bubbles 34 2.2.6 Reaction In Dilute Phase 35 iv 2.3 C A T A L Y S T ATTRITION 35 3 MODEL FOR FLUIDIZED BED CLAUS REACTOR 38 3.1 M O D E L ASSUMPTIONS 38 3.2 GOVERNING EQUATIONS 41 3.3 SOLUTION OF EQUATIONS 42 3.4 D E T E R M I N A T I O N OF T H E R A T E CONSTANT 52 3.5 M O D E L S FOR CATALYST FOULING 61 3.6 T H E R M O D Y N A M I C CONVERSION 66 4 EXPERIMENTAL APPARATUS AND MATERIALS 69 4.1 R E A C T I O N EQUIPMENT 69 4.1.1 Fluidized Bed Reactor 69 4.1.2 Nitrogen Regeneration System 72 4.1.3 Gas Analysis System 76 4.1.4 Safety Devices 76 4.2 M A T E R I A L S USED 77 5 EXPERIMENTAL PROCEDURE 82 5.1 R E A C T I O N P R O C E D U R E 82 5.1.1 Equipment Start-up 82 5.1.2 Reaction Process 84 5.1.3 Catalyst Regeneration 86 5.1.4 Equipment Shut-down 87 5.1.5 Scrubber Clean-up 88 5.2 C A L I B R A T I O N OF INSTRUMENTS 89 5.2.1 Calibration Of Rotameters 89 v 5.2.2 Calibration Of Analytical Instruments 95 6 RESULTS AND DISCUSSION 108 6.1 E X P E R I M E N T A L RESULTS 108 6.1.1 Minimum Fluidization Velocity 108 6.1.2 Sulphur Conversions 108 6.1.3 Catalyst Attrition 126 6.2 M O D E L PREDICTIONS 127 6.3 Applicability of the two phase model 133 6.3.1 Use of Two Phase Model in Reactor Design: 135 6.3.2 Choice of particle size 136 6.4 E R R O R ANALYSIS . 145 6.5 P R A C T I C A L IMPLICATIONS OF FLUIDIZED BED CLAUS R E A C T O R S 147 7 CONCLUSIONS AND RECOMMENDATIONS 150 7.1 CONCLUSIONS 150 7.2 RECOMMENDATIONS 151 Nomenclature 153 References 159 Appendice 172 A STATISTICAL ANALYSIS 172 A . l ANALYSIS OF V A R I A N C E 172 A.2 C O N F I D E N C E LIMITS ON CONVERSION 181 B COMPUTER PROGRAMME FOR T H E MODEL PREDICTIONS 186 vi C COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 218 D COMPUTER PROGRAMME FOR DATA LOGGING 234 E PURGING-TIME OF REACTOR SYSTEM 250 F PREDICTIONS OF EQUILIBRIUM CONVERSION 251 vii List of Figures 1.1 Modified Claus processes 3 1.2 Fluidized bed Claus process (Meisen, 1977) 9 2.1 Claus reaction equilibrium conversion versus temperature (basis: 1 mole H2S with stoichiometric air) 13 2.2 Schematic representation of Davidson and Murray models 26 3.1 Schematic diagram for the two phase bubbling model 39 3.2 Solution of equation 3.42 (a = 1.701, /32 = 1.387, 7 = 6.36, x0 = 1.307) . 47 3.3 Predicted concentration profiles (a = 1.701, j32 = 1.387, 7 = 6.36, x0 = 1.307) 50 3.4 Rate constant versus temperature 55 3.5 Relationship between Af and E 60 4.1 Flow diagram of the equipment (All dimensions in mm) from Bonsu (1981) 70 4.2 Fluidized bed reactor 71 4.3 NaOH Scrubber and reservoir 74 4.4 Driers 75 4.5 Electric circuit of the equipment 78 5.1 Calibration curve for total N2 rotameter 92 5.2 Calibration curve for H2S/N2 rotameter 93 5.3 Calibration curve for S02/N2 rotameter 94 5.4 Flowsheet for calibrating the analytical instruments 96 V l l l 5.5 Determination of the extinction coefficient, K , due to H2S 97 5.6 Calibration curve for SO2 analyser (ppm selector marked 0-50) 98 5.7 Calibration curve for S02 analyser (ppm selector marked 0-100) 99 5.8 Calibration curve for SO2 analyser (ppm selector marked 0-500) 100 5.9 Calibration curve for SO2 analyser (ppm selector marked 0-1000) . . . . 101 5.10 Calibration curve for H2S (selector #lx, range 0-20 ppm) 103 5.11 Calibration curve for H2S (selector #10x, range 0-100 ppm) 104 5.12 Calibration curve for H2S (selector #100x, range 0-1500 ppm) 105 6.1 Pressure drop versus air velocity for a bed of activated alumina (Kaiser S-501) 109 6.2 Sulphur conversion as a function of H2S concentration in feed I l l 6.3 Effect of temperature on conversion {U/Umf = 4.44, Ht— 0.19m) 115 6.4 Effect of U/Umf on conversion (HB= 0.19m, T= 150°<7) 116 6.5 Effect of sulphur condensation on conversion (H2S= 1000 ppm, S02= 500 ppm, U/Umf=AAA, i/,=0.32m, T=100°C) 120 6.6 External colour of catalyst as a function of sulphur loading 121 6.7 Conversion as a function of time (H2S =1000 ppm, S02 — 500 ppm, U/Umf= AAA, H,= 0.32m, T = 100°<7) 122 6.8 Sulphur loading as a function of time (^7r25'=1000ppm, S02— 500ppm, U/Umf=AAA, #,=0.32m, T=100°C) 123 6.9 Effect of bed height on conversion (H2S=600ppm ,S02 = 300 ppm, U/Umf — AAA, T=100°C) 125 6.10 Particle size distribution 128 6.11 Extent of attrition as a function of time 129 6.12 Initial extent of attrition (expanded scale) 130 ix 6.13 Effect of attrition on particle mean diameter 131 6.14 Predicted versus experimental conversion 134 6.15 Model predictions for large reactors (U=0.25m, T=100°C, H2S=600 ppm, dp=195fim 137 6.16 Effect of particle size on conversion as predicted by the two phase model 140 6.17 Predicted residence time as a function of particle size 141 6.18 Predicted UJUmf as a function of mean particle diameter 142 6.19 Concentrations of hydrogen sulphide and sulphur dioxide in the effluent gas as a function of time 148 A . l Experimental Block (U/Umf = 4.44, H, = 0.19m) 182 A.2 Experimental block for the subtotals defined by equation A.12 185 A.3 Confidence limits on x 185 x List of Tables 1.1 Maximum permissible atmospheric S02 levels (Goar, 1977) 5 1.2 Toxicity effect of H2S on the human body (Archibald, 1977) 6 1.3 Ambient air-quality guidelines for the petroleum and chemical industries in British Columbia (Venables, 1989) 7 2.1 Typical assumptions for two- and three-phase reactor models (Grace, 1987) 23 2.2 Assumption or approaches embodied in some of the principal two- and three phase reactor models 24 2.3 Interphase mass transfer models 28 3.1 Solutions for equation 3.51 at the top of the bed for selected reaction orders 51 3.2 Values of rate constant, kw 54 3.3 Activation energies and frequency factors for Claus catalysts 56 3.4 Calculation of external mass transfer effectiveness factor 57 3.5 Calculation of Thiele modulus 58 3.6 Analysis of equilibrium Claus reaction 66 3.7 Equilibrium conversion (%) 68 4.1 Physical properties of Kaiser S-501 catalyst. . 80 4.2 Chemical properties of S-501 catalyst on a dry basis 80 4.3 Particle size distribution of catalyst used in this study 81 5.1 Operating conditions of present experimental equipment 107 xi 6.1 Sulphur conversion as a function of H2S in feed gas 112 6.2 Conversion as a function of temperature ( r//f/m/=4.44, Hs= 0.19m) . . . 114 6.3 Conversion as a function of U/Umj (T = 150°C, H.= 0.19m) 117 6.4 Conversion as a function of time and sulphur loading (T = 100°C, H2S— lOOOppm, i7,=0.32m) 119 6.5 Conversion at several static bed heights (T = 100°C; U/Umf = AAA; H2S= 600ppm; S02 = 300 ppm) 124 6.6 Model predictions as a function of bed dimensions 143 6.7 Effect of particle diameter on conversion as predicted by the two phase model 144 6.8 Relative error as a function of H2S concentration in the feed 149 A. l Analysis of variance for a Two-Factor block experiment 182 B. l Parameters calculated in the programme for model predictions 188 B.2 Model predictions 207 B.2.1: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Unf = AAA, #,=0.19m 207 B.2.2: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Umf = 8.88, tf,=0.32m 209 B.2.3: Conversion as a function of H2S feed concentration for T=373.0 °K, U/Umf = AAA, #,=0.19m 211 B.2.4: Conversion as a function oW/Umf for T=423.0°i<r, H2S in feed =600ppm, tf,=0.19m 213 B.2.5: Conversion as a function oW/Umf for T=A2Z.0°K, H2S in feed =1300ppm, if.=0.19 214 B.2.6: Conversion as a function of sulphur loading 215 x i i B. 2.7: Conversion as a function of static bed height 217 C l Volumetric flow rates of H2S/N2 222 C. 2 Volumetric flow rate of S02/N2 225 C.3 Volumetric flow rate of total iV"2 228 C.4 Volumetric flow rate of cylinder nitrogen 230 C. 5 Volumetric flow rate of sample 232 D. l Principal experimental measurements made in reaction experiments . . . 240 xm Acknowledgement This work would not have been completed without the great help and support of various people. I would like to take this opportunity to thank all of them for the time and effort they gave to help bring this thesis into being. Firstly, my deep gratitude and appreciation go to my supervisor Dr. Axel Meisen, who was my first syntax teacher when I started my Ph.D. degree program at the Uni-versity of British Columbia, and who, since the beginning, gave generously of his time and effort toward the creation and correction of this work. Many thanks go also to my professors, whose contribution to my background in research, reaction engineering, flu-idization engineering and mathematical operations I will remember and appreciate for the rest of my life. Secondly, I would like to thank the Libyan people represented by Elfateh University in Tripoli, Libya, and The People's Committee for Students of the Socialist People's Libyan Arab Jamahiriya (PCSSPLAJ) in the United States and Canada for their financial support in offering me a scholarship for the period of January 1984 to June 1988. Thanks are also deserved by the personnel of the P C S S P L A J for their tolerance and patience during the period of my sponsorship. Thirdly, thanks go to the personnel of the Chemical Engineering Workshop, Stores and the staff of the Chemical Engineering main office for their cooperation and kindness during my stay at the department. Last but not least, with the help of numerous friends and colleagues in the department and in the university a lot of work was made easier and more enjoyable. I would like to express my appreciation and thanks to Mr. Van Le for assisting me in writing the data xiv logging program. Thanks also go to the personnel in the Mineral Processing Laboratory for use of their grinding facilities. I would like to thank all my other friends for creating a suitable atmosphere in which to work toward the completion of this thesis. xv Chapter 1 INTRODUCTION Large quantities of sulphur compounds such as hydrogen sulphide are present in gas streams arising in refineries and natural gas plants. Removal of sulphur compounds is necessitated by the high demands for clean energy sources, by the value of sulphur (which furnishes the basis for a broad range of chemical industries) and by the need to meet air pollution control regulations. To achieve these goals, sulphur compounds are stripped from sour gas streams by means of selective absorption processes to produce acid gases typically rich in H2S. The objective of the Claus process is the recovery of elemental sulphur from these acid gas streams. In its original version, as developed by Claus in 1883, elemental sulphur is produced by oxidizing hydrogen sulphide with a stoichiometric amount of air over hot iron oxide according to the overall chemical reaction: H2S + \o2 ^ -Sx + H20 (1.1) The subscript x denotes the number of atoms per molecule of sulphur and depends on the temperature. At temperatures less than 150°C, x fa 8 whereas above 800°C, x fa 2. For temperatures between 150 and 800°C, x ranges from 8 to 2. The above reaction is exothermic in nature (AH = —145 to -173 kcal/mole H2S) and, at elevated temperatures, the conversion efficiencies are usually less than 80%. To overcome the restrictions imposed by the exothermic nature of the reaction, several modified Claus processes have evolved. Two variations used world wide were developed by I.G. Farbenindustrie (Gamson and Elkins, 1953). 1 Chapter 1. INTRODUCTION 2 In the first modification, known as the "Split-Stream Process", hydrogen sulphide is split into two streams (see Figure 1.1). One third of the H2S is completely burned to SO2 in a free flame combustion chamber at about 1100 to 1200°C: H2S + \o2 ^ H20 + S02 (1.2) (AH = -124 to -138 kcal/mole H2S, T=1100 to 1200°C, P = l atm) The sulphur dioxide is then used to oxidize the remaining two thirds of H2S to elemental sulphur in catalytic reactors: H2S + 1 S 0 2 ^ H 2 0 + -^SX (1.3) (AiT = -21 to -35 kcal/mole H2S, T=220 to 300°t7, P = l atm.) A significant improvement in this modification can be deduced by comparing the heats of reaction of equations 1.1, 1.2, and 1.3. Over 80% of the total heat from reaction 1.1 may be recovered at the exit of the combustion furnace and upstream of the catalytic reactors. Since reaction 1.3 represents the catalytic stage, it is seen that the operating temperature can be maintained at sufficiently low levels with greatly increased space velocity, and consequently the attainment of high conversion. In the second modification, known as the "Straight-Through Process", all H2S is burned with stoichiometric amounts of air in a free flame combustion furnace at about 1100°C to produce a mixture of sulphur vapour, sulphur dioxide, hydrogen sulphide, water vapour, and nitrogen: 2H2S + 202 ^ 2H20 + S02 + 1/ x Sx (1.4) Chapter 1. INTRODUCTION STRAIGHT SPLIT DIRECT H 2S THROUGH FLOV OXIDATION 50-100% 15-50% E-15% HYDROCARBON <2% <5% >57. FURNACE CONDENSER PREHEATER REACTOR CONDENSER PREHEATER REACTOR CONDENSER TO STACK (or o.ddrttono.1 reactor) HgS AIR H 2S AIR H 2S AIR A LA (ELD a c ) c ) D O _ _ J Figure 1.1: Modified Claus processes Chapter 1. INTRODUCTION 4 The unconverted H2S is then oxidized, according to reaction 1.3, with SO2 in two or more catalytic converters. The elemental sulphur is removed by condensation which shifts the equilibrium to the product side and lowers the sulphur dew point temperature in each converter. The straight-through process has two advantages over the split-stream process. First, about 90 to 95% of the total heat of reaction is recovered in the high temperature, free flame combustion furnace and, second, almost 70% sulphur is recovered prior to the first catalytic stage. The choice of Claus process depends primarily on the concentration of H2S in the feed gas. Well-operated Claus plants using a furnace and two catalytic reactors in series are capable of achieving approximately 95% total sulphur recovery provided the HiS concentration in the feed exceeds 30%. The unconverted H2S is normally incinerated to SO 2 and discharged into the atmospher. However, severe damage of animals and plants may occur upon exposure to even low levels of SO2 (see Tables 1.1 and 1.2). To protect the environment, most industrialized nations have passed regulations restricting SO2 emissions to the atmospher. Air pollution control laws, such as those in effect in Brithish Columbia (see Table 1.3) and other provinces, often necessitate the improvement of Claus plant performance to achieve conversion efficiencies higher than 99%. Chapter 1. INTRODUCTION 5 Table 1.1: Maximum permissible atmospheric SO2 levels (Goar, 1977). Exposure time Approximate SO 2 concentrations hazardous to human health ppmv Approximate SO 2 concentrations hazardous to vegetation ppmv 1 hour 0.5 0.8 1 day 0.2 0.3 4 days 0.15 0.2 1 month 0.07 0.09 1 year 0.01 0.01 Chapter 1. INTRODUCTION 6 Table 1.2: Toxicity effect of H2S on the human body (Archibald, 1977). H2S concentration in air (ppm) Period of exposure 10 Maximum allowable concentration for 8 hours. 70-150 Slight symptoms after exposure of several hours. 150-300 Maximum concentration that can be inhaled for 1 hour. 400-500 Dangerous upon exposure for 30 minutes to 1 hour. 600-800 Fatal after exposure of 30 minutes or less. 4 Chapter 1. INTRODUCTION 7 Table 1.3: Ambient air-quality guidelines for the petroleum and chemical industries in British Columbia (Venables, 1989) (Dry basis, 20°C, 760 mm Hg)  Level A Level B Level C (ppmv) (ppmv) (ppmv) so2 1 hour maximum 0.17 0.34 0.5 24 hour maximum 0.06 0.10 0.14 Annual arithmetic mean 0.01 0.02 0.03 H2S 1 hour maximum 0.005 0.03 0.03 24 hour maximum - 0.005 0.005 New operations are required to meet level A emissions; Existing operations are required to meet level C; Existing operations are required to upgrade emissions to level B and ultimately to level A. Chapter 1. INTRODUCTION 8 Although such high conversions are thermodynamically attainable at temperatures below the sulphur dew point, sulphur condensation leads to catalyst deactivation. To recover deposited sulphur by vaporization, traditional fixed bed reactors cannot be op-erated continuously. Fluidized bed reactors, on the other hand, can be operated with continuous catalyst regeneration and have been proposed for the Claus process operating at low temperatures (Meisen, 1977, see Figure 1.2). 8 •8 CONDENSER FURNACE INCINERATOR STACK 1 PREHEATERS : FLU;IDIZED-BED .REACTORS-CONDENSER A = S U L P H U R - L A D E N C A T A L Y S T B=SULPHUR--FREE C A T A L Y S T o o Figure 1.2: Fluidized bed Claus process (Meisen, 1977) Chapter 1. INTRODUCTION 10 A fluidized bed is formed by passing a gas upward through a bed of a finely divided particles supported by a distributor or grid. The superficial gas velocity at which the fine particles of a fixed bed start to move is known as the minimum fluidization velocity, Umf, and its value depends on the physical properties of the gas and solid particles. At gas velocities above Umf, the bed expands and small gas bubbles form at the distributor and ascend to the surface of the bed where they burst causing splashing of particles into the space known as the freeboard region. During their rise, bubbles may grow by coalescence and may shrink due to splitting. The bed may be notionally divided into a dense and dilute phase. Part of the gas percolates through the dense phase and the remainder passes through the bed in the form of gas bubbles. The main advantages of fluidized beds over the fixed beds for the Claus reactions were summarized by Bonsu (1981): 1. The bed temperature is uniform due to the intense agitation of the catalyst particles by the rapidly rising gas bubbles. 2. Operation at temperatures below the sulphur dewpoint (where thermodynamic yields are high) is possible. Operation even below the sulphur melting point is, in principle, attainable. Catalyst fouling caused by condensed sulphur can be con-trolled by continuously circulating the catalyst through a regenerator. 3. Catalyst deactivation from sulphation and deposition of impurities such as carbon can also be controlled by means of a regenerator. 4. The catalyst activity is enhanced by the large specific surface area of the fine particles. 5. The pressure drop across fluidized beds is moderate. Chapter 1. INTRODUCTION 11 6. Pelletizing, which is an important cost item in the production of Claus catalysts, may not be required for fluidized bed catalysts. However, fluidized beds also have some basic disadvantages such as: 1! Lowering of conversion efficiency due to the fact that some gas by-passes the catalyst in the form of bubbles. 2. Reduction of conversion due to backrruxing. 3. Attrition of catalyst particles and erosion of the reactor walls due to the intense catalyst agitation. 4. Elutriation of catalyst fines from the bed. Detailed literature reviews of Claus reactions and fluidized bed reactors are included in chapter 2. Models for fluidized bed Claus reactors are developed in chapter 3. Description of a small-scale fluidized bed reactor and auxiliary components are summarized in chapter 4. In chapter 5, experimental procedures and calibration of instruments are outlined. The performance of a small scale fluidized bed reactor at low temperature is compared with model predictions and practical implications are discussed in chapter 6. Conclusions are drawn and recommendations for future work are itemized in chapter 7. The final part of this thesis is presented in the form of appendices. The appen-dices contain statistical analyses of the experimental results, computer programmes, and calibration tables. Chapter 2 LITERATURE REVIEW 2.1 CLAUS REACTIONS 2.1.1 Theoretical Studies The first fundamental investigation of the Claus process was published by Gamson and Elkins (1953). Using the thermodynamic data of Kelly (1937), they employed the equi-librium constant method to predict sulphur yields and equilibrium composition for an idealized Claus process. McGregor (1971) used more accurate data compiled by McBride et al. (1963) to calculate Claus conversions. He utilized the free energy minimization approach developed by White et al. (1958). Bennett and Meisen (1973) employed the key component method proposed by Kellogg (1971) and considered up to 44 compounds to be present under equilibrium conditions. Their results agree quite well with those reported by Kellogg but only 25 species were found to have concentrations in excess of 0.1 ppm. The slight discrepancies in the results (see Figure 2.1) are likely caused by the different free energy data used by the various authors (Bennett and Meisen, 1973). Results from the above studies provide basic information for understanding the nature of Claus reactions and serve as a guide for the design and prediction of maximum yields of Claus plants. Despite the differences in the methods employed and the system com-plexity, there is basic agreement that the theoretical conversion efficiencies are high at low temperatures, fall rapidly with increasing temperature and pass through a minimum before increasing again at elevated temperatures. These studies also showed that, at 12 Figure 2.1: Claus reaction equilibrium conversion versus temperature (basis: 1 mole H2S with stoichiometric air) Chapter 2. LITERATURE REV IEW 14 temperatures below 300°C, the dominant sulphur species is Sg whereas at temperatures higher than 1000°if, sulphur occurs essentially in the di- and monoatomic forms (S2 and S). This change in the degree of polymerization is due to the endothermic dissociation reactions of Ss and Se- Hence the overall reaction becomes progressively less exothermic and leads to increased sulphur yields at elevated temperatures. Considering the presence of feed impurities such as ammonia, hydrocarbons, and carbon dioxide and accounting for a large number of chemical reactions, Maadah and Maddox (1978) concluded that large amounts of such impurities in the furnace feed decrease the conversion. The primary reason for this effect appeared to be the decreased H2S concentration in the sour gas. They also found that including sulphur polymers with an odd number of atoms does not significantly affect the equilibrium conversions predicted for Claus processes. However, they observed a notable decrease in the combined H2S and S02 concentration in the tail-gas stream when all sulphur polymers were considered to be present under equilibrium conditions. Bragg (1976) has developed a computer program to predict the performance of Claus plants under both equilibrium and non-equilibrium conditions. His predictions agreed quite well with measured plant performance. In practice, sulphur plants use, whenever possible, a furnace operating in the high temperature region (~ 1000°C) where sulphur yields are about 70%. The thermal stage is followed by a waste heat boiler where most of the heat of reaction is removed. The gases leaving the furnace are passed through a condenser to recover the elemental sulphur before they enter the catalytic stage. Two or three catalytic converters are often used to maximize sulphur recovery and minimize sour gas emissions into the atmosphere. The temperature of the first reactor is normally set in response to the concentration of carbon disulphide and carbonyl sulphide (which may be formed in the furnace) since conversion of these compounds is high at temperatures above 300°C (Pearson, 1973; George, 1975; Grancher, 1978). The downstream reactors are operated at lower temperatures to take Chapter 2. LITERATURE REVIEW 15 advantage of the high conversion of H2S and S02 favoured by thermodynamics. However, at low temperatures, the reactions become kinetically controlled. Moreover, at very low temperatures, condensation of sulphur occurs and causes catalyst fouling. Most catalytic Claus reactors are therefore operated above the sulphur dew point. 2.1.2 Fluidized Bed Claus Process A two stage fluidized bed Claus process (FBCP) was proposed by Meisen (1977) as an alternative to three fixed bed reactors in series used in many conventional Claus plants. The downstream reactor in the F B C P is kept at a temperature below the sulphur dew point. Under such conditions, the catalyst collects the condensed sulphur formed in the reaction. The sulphur laden catalyst is recycled to the upstream reactor, which is oper-ated at an elevated temperature, where vaporization of sulphur occurs and regeneration of the catalyst takes place. The sulphur free catalyst is then recycled back to the second reactor. This novel process represents a sub-dew point process which is truly continuous (see Fig. 1.2). In assessing fluidized bed Claus technology, Bonsu and Meisen (1985) used the equilib-rium constant method to simulate various idealized FBCP 's . Their results indicated that, for a pure H2S feed, an overall sulphur conversion of 99% was attainable by using a Claus furnace and two fluidized bed reactors in series. Such high conversions were independent of the first reactor temperature which varied from 400 to 800°K. The temperature in the downstream reactor was kept constant at 383°jFf thereby always compensating for incomplete conversion in the first reactor. In addition, they reported sulphur conversions for an experimental fluidized bed Claus reactor which exceeded equilibrium conversions predicted from thermodynamic principles. Using the bubble assemblage model developed by Kato and Wen (1969) and a kinetic rate expression referred to as the LIU Model II, Birkholz et al. (1987) simulated the Chapter 2. LITERATURE REVIEW 16 FBCP. They found that the overall recovery efficiency is the same as that achieved in a Claus plant containing three fixed beds. Furthermore, only 50% of the catalyst was required compared with the conventional fixed bed process; the pressure drop was 25% less. It is therefore clear that the F B C P should be capable of achieving sulphur recoveries comparable to those obtained in Claus plants having three fixed bed reactors. 2.1.3 Experimental Studies The first experimental studies of the Claus reactions in fluidized bed reactors were under-taken by Bonsu and Meisen (1985). Using an activated alumina catalyst, they reported that at elevated temperatures experimental conversions are in good agreement with those obtained from fixed bed studies by Gamson and Elkins (1953) and Dalla Lana (1978). For dry feed mixtures consisting of H2S, SO2 and N2, and temperatures ranging from 150 to 300°C, Bonsu and Meisen observed that, for some experiments, sulphur conversions were reduced at low temperatures and high H2S feed concentrations. They also found a weak relationship between sulphur conversion and the ratio U/Umf. They concluded that the performance of fluidized bed Claus reactors is only slightly affected by gas by-passing the catalyst particles in the form of bubbles. Furthermore, they reported that experi-mental conversions are independent of bed height above 0.12m. These observations were attributed to the fact that the Claus reaction is very fast and almost complete conversion occurs near the gas distributor. With the exception" of the work by Bonsu and Meisen, all reported Claus reaction studies were performed with fixed bed reactors. Fixed bed reactor studies are discussed in the following paragraphs. Claus catalysts and reaction kinetics have been the subject of experimental investiga-tion since Tayler and Wesley (1927) recognized that the reaction between H2S and S02 proceeds entirely on solid surfaces. They noted that the reaction rate was proportional Chapter 2. LITERATURE REVIEW 17 to the surface area of their glass reactor and that the reaction order was 1.5 and 1.0 for H2S and SO2, respectively. Using cobalt thiomolybdate catalyst, Murthy and Roa (1951) observed that no reac-tion occurred at temperatures of 25°C or less in the absence of water. They reported an overall reaction order of 2. McGregor (1971) studied, in detail, the kinetics of the Claus reaction using commercial bauxite catalyst and proposed the following rate expression for the disappearance of H2S (gmole/h-g cat): rH2s = k0exp(-E/RT)P^sPbSO2 (2.1) where: fc0 = 2.198 ± 0.564 h~l E=7589±451 cal/mole a=0.963±0.0448 b=0.359±0.135 R=1.987 cal/mole/K. PH2S and Pso2 denote the partial pressures (in mm Hg) of H2S and 502) respectively. T denotes the absolute temperature (in K) . It should be noted that the equation pro-posed by McGregor is not dimensionally consistent. McGregor observed that, while low partial pressures of water vapour had an autocatalytic effect on the reaction, high partial pressures caused marked retardation. The effect of water vapour on the kinetics of the Claus reaction was further investi-gated by Dalla Lana et al. (1972) using commercial bauxite catalyst. They proposed the following rate expression: r . „ = 1 . 1 2 1 e , p ( - 7 4 4 1 / i J r ) T T 5 | ^ _ ( 2 . 2 ) The retarding effect of water vapour is reflected by the denominator of the rate expression. Chapter 2. LITERATURE R E V I E W 18 Dalla Lana et al. (1972) concluded that water vapour competes with either H2S or SO2 - molecules for adsorption sites on the catalyst surface. A similar rate expression was proposed by Dalla Lana (1976) who studied alumina catalysts: ^ ^ . S M - W W , , ^ , , (2.3) Water inhibition was also confirmed by George (1974). He reported 1.0 and 0 as the reaction orders for H2S and SO2, respectively, and found the activation energy to be 5.5 kcal/mole of H2S. Due to the low value of E, George concluded that the Claus reaction is controlled by pore diffusion. Similar conclusions were reached by Grancher (1978) who recommended the use of small catalyst particles. Using activated alumina catalyst, he obtained reaction orders of 1 and 0.5 for H2S and SO2, respectively. The control of the Claus reaction by pore diffusion has also been reported by Landau et al. (1968). They based their conclusions on the fact that the activity of bauxite catalyst increased with decreasing particle size. Pearson (1973) examined the activity of various Claus catalysts. He found that Kaiser S-501 activated alumina and cobalt-molbydenum had the highest resistance to catalyst poisoning. George (1975) studied the catalytic activities of acids and bases for the Claus reactions. He found that, while acidity did not have any effect, basicity considerably improved the catalyst activity for the reactions. 2.1.4 Catalyst Deactivation By Fouling Operating Claus reactors below the sulphur dew point leads to the deposition of sulphur on the external and internal surfaces of the catalyst. This deposit causes a decrease in catalyst activity (termed fouling) and leads to reduced conversions. Pearson (1977) tested the performance of the activated alumina under fouling conditions. His study showed that the alumina S-501 retains its activity (conversion was higher than 98%) even when Chapter 2. LITERATURE R E V I E W 19 loaded up to 50 wt% with condensed sulphur. At a sulphur loading of 80 wt% the sulphur conversion dropped from 80% to 31%. To model reactors with fouling, it is clear that the reaction rate expression must include a deactivation term. There are basically two different procedures for introducing such a term into the rate expression. One procedure is based on the so called "time on stream theory" which envisions the catalyst decay to be a function of the length of time for which the process has been in operation (Pachovsky et al., 1973; Sadana et al., 1971). A second group of workers suggested that the amount of deposit retards the reactants from reaching the active surface of the catalyst and therefore reduces the activity (Froment and Bischoff, 1961; Masamune and Smith, 1966). Froment and Bischoff alluded to the fact that treating the deactivation function in terms of the foulant concentration in solids would allow comparisons between different systems, whereas a correlation with respect to "time on stream" is specific for the conditions and operations under consideration. The accumulation of sulphur in pores of the Claus catalyst such as activated alumina and bauxite may arise from two mechanisms: adsorption of elemental sulphur on the surface since the sulphur is actually produced on the surface or condensation when the temperature is below the dew point. The concentration of the feed gas and the type of reactor are also important. For a dilute feed gas, it takes longer for sulphur to collect in appreciable amounts and catalyst deactivation due to fouling is slow relative to the gas residence time in the reactor. Under such conditions, all catalyst particles in a fluidized bed are exposed to the same extent of fouling. On the other hand, a concentrated feed gas entering a fixed bed reactor creates a fouling front travelling along the axis of the reactor. Hence a transient model is required to describe this situation. Razzaghi and Dalla Lana (1984) showed that fouling of fixed bed Claus reactors is a relatively slow process. They assumed that pseudo-steady state prevailed in order to study cold-bed sulphur recovery processes. Chapter 2. LITERATURE REMEW 20 2.1.5 Low Temperature Industrial Processes The first commercial recovery of sulphur from tail gases leaving Claus process was achieved by the Sulfreen process (Martin and Guyot, 1971; Cameron, 1974). This process is, in essence, an extension of the Claus process described in section 1.1. In the original Sulfreen plants, reaction 1.3 is carried out at temperatures below the sulphur dew point over a fixed bed of activated carbon. As in the Claus process, the ratio of H2S to S02 is set to 2. At the operating temperature (125-135°C), the condensed sulphur remains on the carbon catalyst. Although highly efficient, carbon requires high temperatures (500 - 600°C) to vapourize the sulphur during regeneration. In the process developed jointly by Lurgi Gesellschaft fits Warme und Chemotechnik of West Germany and Societe Na-tional des Petroles d'Aquitaine (recently Societe Elf Aquitaine) of France, four reactors in parallel are used for adsorption while a fifth reactor is in desorption mode and a sixth reactor is cooled to the required reaction temperature. A loop of hot inert gas is used to desorb the sulphur from the saturated carbon bed. Sulphur is recovered from this hot gas in a sulphur condenser. The gas is then passed to a tower where it is further cooled by washing with liquid sulphur and additional sulphur is recovered. Because of the high regeneration temperature, stainless steel is used throughout the plant. Modern Sulfreen plants use activated alumina catalyst which requires a regeneration temperature of about 300°C. In addition, the number and size of the reactors are smaller. The wash tower in the old process is replaced by a sulphur condenser. Another aspect of the modern Sulfreen process is that the activity of the alumina catalyst is restored by introducing a stream of H2S into the regeneration loop when the bed temperature reaches 300°C A similar process was developed by A M O C O Canada Company designated as the Chapter 2. LITERATURE REVIEW 21 C B A (Cold Bed Adsorption) process (Goddin et al. 1974). An alumina catalyst is used for the recovery of sulphur from Claus tail gases at 130°C. This process also requires H2S/S02 ratios of 2 for optimum conversion. However, the regeneration step is different from that of the Sulfureen process. Part of the feed to the first Claus reactor is passed to the saturated C B A reactor where, in addition to the release of sensible heat, heat is generated due to the reaction between H2S and SO2. As a result, the bed temperature rises to about 300° C which corresponds to the outlet temperature of the first Claus reactor. The rise in temperature causes gradual vaporization of sulphur. The regeneration gas is then returned to the first Claus reactor after passing through a sulphur condenser. Once the regeneration cycle is complete, the gas stream from the last Claus reactor is passed through a sulphur condenser and then to the hot C B A reactor to lower its temperature to about 130°C. Other low temperature processes such as JLSC and M C R C use basically the same principles and are described by Kohl and Riesenfeld (1985). A l l of the above processes use fixed bed reactors and have to be operated in cyclic mode. Catalyst regeneration may be performed by taking the reactor out of operation when the catalyst sulphur loading has reached a certain value. To achieve the changes in operations, quite sophisticated process control schemes are needed. 2.2 FLUIDIZED BED REACTOR MODELLING Early fluidized bed models were based on the assumption that the gas and catalyst are in intimate contact and well mixed without segregation into dilute and dense phases. Most fluidized bed models postulated in the 1950's assume that fluidized bed reactors consist of two parallel, single-phase reactors with cross-flow between them. In reality, however, the hydrodynamics of fluidized bed reactors are far more complex; some of the Chapter 2. LITERATURE REVIEW 22 gas flows through the bed in the form of bubbles, thus forming a dilute phase, whereas the remainder percolates through a region of high particle density called the "dense phase". The fact that the gas in the bubbles is in poor contact with the catalyst particles and the gas contact in the dense phase is intimate, has led researchers in the 1960's to the development of fluidized bed reactor models which focus on the properties of the rising bubbles. The complexity of fluidized bed models depends on the assumptions underlying their formulation (see Table 2.1 and 2.2 for common assumptions). Furthermore, model pre-dictions are sensitive to certain assumptions. In the 1970's, experimental evaluations of these models were undertaken to discriminate between the various model parameters and the degree of importance of individual assumptions. Although more than a dozen assumptions (related to bubbling bed reactors) have been invoked to describe mathe-matically the behavior of the gas and solids in fluidized beds, only the principal ones are discussed in the following sections. A number of reviews and model evaluations have been published (Grace, 1971; Pyle, 1972; Chavarie and Grace, 1975; Yates,1975; Horio and Wen, 1977) 2.2.1 Number Of Phases The majority of bubbling bed models are based on the assumption that a fluidized bed may be envisioned to consist of a dilute and dense phase (e.g. Kato and Wen, 1969; Grace, 1984). In some models, the clouds surrounding the bubbles are lumped together with the emulsion phase (Orcutt et al., 1962) whereas in others they are included in the bubble phase (Partridge and Rowe, 1966). Very few models account for the presence of a cloud phase between the bubble and emulsion phases (Kunii and Levenspiel, 1969; Fryer and Potter, 1972). The main advantage of the two phase theory is that it leads to simpler equations and Chapter 2. LITERATURE R E V I E W 23 Table 2.1: Typical assumptions for two- and three-phase reactor models (Grace, 1987) A . Nature of dilute phase: 1. Bubble phase completely free of particles. 2. Bubbles containing some widely dispersed solids. 3. Bubble-clouds are included. B. Division of gas between phases: 1. Governed by two-phase theory. 2. A l l gas carried by bubbles. 3. Some downflow of gas in the dense phase is permitted. 4. Other or fitted parameter. C Axial dispersion in dilute phase: 1. Plug flow. 2. Disperse plug flow. D. Axial dispersion in dense phase: 1. Plug flow. 2. Disperse plug flow. 3. Stagnant. 4. Well-mixed tanks in series. 5. Perfect mixing. 6. Downflow. 7. Bubble-induced turbulent fluctuations. E. Mass transfer between phases: 1. Obtained from independent gas mixing or mass transfer studies. 2. Fitted parameter for case under study. 3. Empirical correlation from previous or pilot plant data. 4. Bubble to dense phase transfer obtained from experimental or theoretical single bubble studies. 5. Transfer across cloud/emulsion boundary due to diffusion. 6. Enhancement due to bubble interaction included. F. Cloud size: 1. Davidson theory. 2. Murray or modified Murray analysis. 3. Wake not specifically included or assumed negligible. 4. Wake added to cloud. 5. Recognized but assumed negligible. G. Bubble size: 1. Not specifically included. 2. One size for entire bed. 3. Increases with height. 4. Obtained from separate measurement, correlation, or estimated. 5. Kept as fitting parameter. Chapter 2. LITERATURE REVIEW 24 Table 2.2: Assumption or approaches embodied in some of the principal two- and three phase reactor models Authors Assumptions A B C D E F G (a) Two-phase models: Shen and Johnstone (1955) 1 1 1 1 or 5 3 N A 1 Lewis, Gilhland, and Glass (1959) 2 2 1 1 or 5 3 N A 1 May (1959) 1 1 1 2 1 N A 1 Van Deemter (1961) 1 4 1 2 1 N A 1 Orcutt, Davidson, and Pigford(1962) 1 1 1 1 or 5 . 4 N A 2,5 Partridge and Rowe (1966) 3 1 1 1 5 2,4 4 Mireur and Bischoff (1967) 1 1 1 2 1,3 N A 1 Kato and Wen (1969) 3 2 1 4 1 1,3 3,4 Bywater (1978) 1 4 1 7 5 5 2,4 Darton (1979) 1 1 1 5 4,5 5 3,4 Werther (1980) 1 1 1 1 3 N A 3,4 Grace (1984) 2 2 1 3 4,6 N A 2,4 (b) Three phase models: Kunii and Levenspiel (1969) 2,1 1 or 2 1 3 4,5 1,4 2,4 Fryer and Potter (1972) 1 3 1 6 4,5 4,5 2,4 Fan, Fan, and Miyanami (1977) 2 1 2 2 4,5 2,3 3,4 Letters and numbers in the table refer to Table 2.1 Chapter 2. LITERATURE REVIEW 25 less computation than the three phase theory. However, the number of phases could be considered as an integral part of other assumptions such as interphase transfer coefficients and the presence of solids in some or all phases. The concept of the cloud phase was based on Davidson's treatment of a rising bubble through a dense phase (Davidson and Harrison, 1963). This model showed that cloud formation depends solely on the relative velocity of the rising bubble to that of the percolating gas [i.e Ub/(Umf /emf)]- The model assumes that the bubbles are spherical and it leads to the prediction of spherical, concentric clouds with radius: C-f = ^ (2.4) where a = ub/'{Umf /'em}). The model also predicts the through flow (i.e. the volumetric gas flow rate that enters and leaves a bubble during its rise): q = ZirUmfr2b (2.5) A more sophisticated mathematical analysis by Murray (1965, 1966) led to smaller and non-spherical clouds with centroids above the centre of the "assumed" spherical bubble (see Figure 2.2). The Murray model predicts that the ratio of the cloud to bubble radius and the through flow are given by: (a- l ) ( - ) 4 - d ( - ) - 4 c o s 0 = O (2.6) q= 1.1857rC/m/rfc2 (2.7) where 8 denotes the angle (in spherical coordinates) measured from the bubble nose. Experimental results by Rowe et al.(1964) indicate that Murray's model gives more ac-curate predictions than Davidson's model. The above equations suggest three situations: Chapter 2. LITERATURE REVIEW 26 a = 1.3 d = 2.0 a. = 5.0 1 Bubble boundary 2 Cloud accbrcllng to Murray's model (1965,1966) 3 Cloud according to Davidson's model (1963) 4 Typical position of wake according to Rowe et al. (1964) Figure 2.2: Schematic representation of Davidson and Murray models Chapter 2. LITERATURE REVIEW 27 For d < 1, often referred to as " slow bubble regime", the bubbles are cloudless and the quickly rising gas uses the bubble as a short cut on its way through the bed. The gas enters the bottom of the bubble and leaves the top with a velocity of the order of Umf. As the gas leaves the top of the bubble, it encounters particles moving tangentially to the bubble with a velocity of order u^. The gas experiences a slight change in direction due to the drag force of the particles but, since the gas velocity is high, the inertial force results in deep gas penetration into the dense phase. Clouds can therefore not form. Hence a bed consisting of only two phases is a more realistic assumption for d < 1. As the bubble velocity approaches the interstitial gas velocity, the drag force on the gas increases and becomes comparable to the inertial force. Hence the gas penetration into the dense phase becomes smaller and leads to gas circulation. Thus the gas emerging from the roof of a bubble is swept back to re-enter it at the bottom. Inspection of the above equations show that for d = 1, the cloud is infinite in size (i.e. the cloud covers the entire emulsion phase). This overlap suggests that a simple two phase model is more appropriate to apply provided other parameters such as interphase transport are properly determined. When d >2, commonly referred to as "the fast bubbles regime", the clouds become very thin and the emulsion phase occupies practically the entire bed except for the fraction occupied by the bubble phase. 2.2.2 Mass Transfer Between Phases The success of a fluidized bed reactor model in predicting reactor performance depends primarily on the proper determination of interphase mass transfer coefficients. Numerous mass transfer models have been proposed in the literature for predicting the overall mass transfer coefficient (see Table 2.1). The majority of these models is based on the single isolated bubble theory. According to this theory, transfer coefficients derived from the Chapter 2. LITERATURE REVIEW 28 Table 2.3: Interphase mass transfer models Model Overall mass transfer coefficient Description 1 Partridge and kgdJDg = 2 + O.mSc^Rel'2 Pure diffusion at Rowe (1966) Rec = pgUbdc/fig cloud boundary. 2 Chiba and kq = lA28^emfDgub/db{(a - l ) / d ] 2 ' 3 Same as in (1). Kobayashi (1970) 3 Kunii and kq = l/[l/fcb + l/fce] Three mass Levenspiel (1969) kb = 0.75f/m / + 0.975 i/D*g/db transfer resistances, ke = l.my/emfDgUb/4 diffusion resistance at cloud boundary is dominant. 4 Davidson and kq = 0.75Umf+0.975^Dlg/db Additive convection Harrison (1963) and diffusion terms at bubble interface. 5 Calderbank kq = 0.75C/m / + l.228y/Dgub/Lb Same as (4), Lb is the et al. (1975) vertical dimension of the bubble. 6 Chavarie and kq = Umf/4 Murray's through Grace (1976) flow for spherical bubble, no diffusion. 7 Sit and kq = Umf/4 + 1 . 1 2 8 ^ 6 ^ / 4 Through flow as Grace (1978) in (6), diffusion from kq = 0.39f/m / + y/lADgemfUb/di penetration theory. 8 Sit and As in (7) for spherical Grace (1978) cap bubble 9 Hovmand and [lA9Fb/(Fb + emfFp)][Umf + Interacton of Davidson (1968) 0 . 7 6 4 F p e m / ^ f f 5 / d f c ] , diffusion and convection terms, Fb = exp(-B2/4.Dg)/[l - erf(B/2Dl'% Fb and Fp are Fp = exp(-B2/ADg)/[l + erf(B/2Dl<% interaction factors; through B = Umf{Z.7ZUblubfl\ flow from Davidson model. 10 Walker kg = [0.472F b/(F b + emfFp)}[Umf+ Interaction as in (9) (1975) +1.93Fpemff/Dgg/db}, with through flow based on B = UmfJl.U5db/ub Murray's analysis. Chapter 2. LITERATURE R E V I E W 29 properties of a single rising bubble and are assumed to apply accurately to freely bubbling beds. There are at least three approaches in modelling single bubble mass transfer (for reviews see Drinkenburg and Rietema, 1972; Walker, 1975; Sit and Grace, 1978): 1. Pure diffusion approach: In this type of model, three principal assumptions are made: (i) A cloud surrounds each bubble, (ii) The cloud is closed with no shedding of par-ticles from the wake behind the bubble, (iii) The resistance to mass transfer resides at the cloud-emulsion interface. Cine photographs by Rowe et al. (1964) and Toei et al. (1969) showed the shedding of gas from the wake to the surrounding continuous phase with the shedded gas elements becoming part of the interstitial gas. Walker (1975) pointed out that the contribution to bulk flow due to the shedding phenomenon is significant and cannot be ignored. Grace (1981) argued that this type does not account for at least three important mechanisms: (i) The shedding mechanism as indicated by the previously mentioned photographs, (ii) Distortion and volume changes of bubbles and their clouds during bubble coalescence and interaction, (iii) The cloud boundary is a streamline for the gas but not for the solid particles; hence particles entering and leaving the cloud con-tribute to the transfer of gas. Chavarie and Grace (1976) injected ozone tracer bubbles and measured concentration profiles near single rising bubbles in a two dimensional bed. They allowed for bubble growth and evaluated published mass transfer models. This technique was also used by Sit and Grace (1978) to measure the overall mass transfer (bubble to dense phase) for different particle sizes ranging from 90 to 390/mi. Their results indicate that diffusion controlled models consistently underestimate the overall mass transfer coefficient by at least one order of magnitude. 2. Convection and diffusion approach: In this approach, transfer models are based on three common assumptions: (i) The principal resistance to mass transfer resides at the bubble boundary, (ii) Mass transfer occurs by diffusive and convective mechanisms, (iii) The overall mass transfer is the sum of the diffusive and convective components. Other Chapter 2. LITERATURE REVIEW 30 assumptions varied among models. In some models, the diffusion term was obtained from the Davidson and Harrison (1963) analysis, whereas in others it was derived from the penetration theory. Assumptions regarding the convective term ranged from those based on the Davidson model for throughflow to Murray's analysis for either spherical or hemi-spherical bubbles. The experimental results by Chavarie and Grace (1976) suggest that models which are based on the concept of additive diffusive and convective transport at the bubble interface overpredict the transfer rate. This conclusion was confirmed later by Sit and Grace (1978). The latter also reported that models with the diffusive component calculated from the penetration theory and the convective component determined by the Murray model showed better agreement with experiments. 3. Interactive diffusion and convective approach: This type of model is similar to the previous ones since the mass transfer is thought to be controlled by diffusion and convection at the bubble boundary. However, unlike the previous models, the diffusion and convection terms are assumed to interact (Hovmand et al., 1971; Walker, 1975). As a result, the overall transfer is less than the sum of the individual components. Although the agreement between predictions from these models and experimental results (see Sit and Grace, 1978) was quite good for some particle sizes, none of these models was accurate over a wide range of particles sizes. In a freely bubbling bed, the shape, size and velocity of a rising bubble is affected by the presence of neighbouring bubbles. Coalescence of bubbles has been described by Toei and Matsuno (1967), Clift and Grace (1970), Grace (1971) and Darton et al. (1977). They found that a trailing bubble elongates and its velocity increases as it is drawn into a leading bubble. Experimental measurements (in two dimentional beds) by Sit and Grace (1981) on pairs of obliquely aligned bubbles indicate that the leading bubble grew 2.5 times as quickly as an isolated bubble, while the trailing bubble increased its area 3.5 times as quickly. They obtained similar results for pairs of bubbles in vertical alignment Chapter 2. LITERATURE REVIEW 31 where the overtaking bubble grew 20-80% more quickly than the leading bubble. This bubble interaction was found to significantly enhance interphase transfer. For example Sit and Grace (1981) reported overall mass transfer coefficients for interacting pairs of bubbles (9.6 and 8.5 cm/s for vertical and oblique alignments) to be 2 to 3 times higher than those obtained by Sit and Grace (1978) from isolated bubble measurements (3.4 cm/s). Based on their experimental results and those obtained by Toei et al. (1969) for interacting bubbles in two dimensional beds as well as the results obtained by Pereira (1977) in three dimensional beds, Sit and Grace (1981) modified their original equation (Sit and Grace, 1978) to account for bubble interaction: * , = % i + / % ^ ( 2 . 8 ) The first term in the above equation represents the throughflow from Murray's analy-sis corrected to account for enhancement due to bubble interaction. The second term represents the flow due to diffusion based on the penetration theory. 2.2.3 Division Of Flow Between Phases Most models rely on the two phase theory (Toomey and Johnstone, 1952), which states that all gas in excess of that required for minimum fluidization flows through the bubble phase and the local emulsion velocity, Ue, is equal to Umj /6mj i.e: Qb = A ( U - U m f ) (2.9) t/e = £Wem/ (2.10) The minimum fluidizing velocity can be measured by plotting the pressure drop across the bed (Ap/l) versus the superficial gas velocity U . It can also be estimated from a Chapter 2. LITERATURE R E V I E W 32 number of correlations, e.g the equation recommended by Grace (1982): RemS = ^ (27 .2 )2+ 0.0408Ar - 0.0408 (2.11) where R e m / = dpUmfpg/pg and Ar = pg(pp - pg)gdHfi2g. The voidage at minimum fluidization may be estimated from the Broadhurst and Becker(1975) correlation: enf = 0 .586V>-°- 7 2 Ar- 0 - 0 2 9 (^) 0 - 0 2 1 (2.12) PP (2.13) It has been reported, however, that the two phase theory overestimates the flow, Qb, and is only valid in shallow beds and near the top of deep beds (Grace and Clift, 1974). The popularity of this theory continues to be the means for flow division between phases for two reasons (Grace, 1981): (i) Lack of a suitable alternative and (ii) Confusion between the flow in the voids (visible flow) and flow resulting from gas exchange with the clouds (invisible or throughflow). The visible flow, Qb, is needed to calculate the hydrodynamic parameters such as bed expansion, bubble diameter and bubble velocity. The total bubble flow is needed for writing the material balances for each phase. The total flow in the dilute phase equals the visible flow plus the flow due to gas short-circuiting through each bubble (i.e the throughflow). When (U — Umf) is small, the throughflow is of order UmftbA but there is evidence that this value may be exceeded considerably when (U — Umf) is large (Valenzuela and Glicksman, 1985). Since the visible flow is agumented by the through flow, it is reasonable to make the simphfying assumption of zero vertical flow in the dense phase (i.e. all gas flows through the dilute phase). The rising bubbles induce circulation of solids in the dense phase which, in turn, modifies the flow pattern of the percolating gas. Analysis by Calderbank et al.(1975) Chapter 2. LITERATURE REVIEW 33 suggests that local circulation of solids occurs in different regions in the bed. They found that particles, just above the distributor, tend to move upward at the centre and downward near the walls. They noticed that bubbles grew during their rise and tended to drift towards the centre of the bed causing solids to move down at the wall. They reported interstitial upward emulsion velocities of about O.lm/s at the center of the bed and about 0.05m/s downward near the walls (U=0.031m/s; Umf — 0.011 m/s; static height=0.48m; dp = 90/xm) Rowe and Partridge (1962) have pointed out that, since particles are carried upward in the wake of rising bubbles, they must move down with the same rate. More work by Rowe and Partridge (1965) indicates that wakes occupy about 30% of the bubble phase. As the bubble velocity increases, solids must move down faster. Sufficiently high solid velocity causes reversal in the direction of the dense phase gas as confirmed by the tracer studies of Kunii et al. (1967). According to Kunii and Levenspiel (1969), the dense phase gas velocity is given by: U e = (1 - emfVJVb) emfVw/Vb 1 - e6 - ebVw/Vb\ Umf U (2-14) (Umf/emf) where Vw/Vb is the ratio of the wake to bubble volume. A similar expression was derived by Fryer and Potter (1972). For typical values of Vw/Vb ~ 0.2 - 0.4 (Rowe and Partridge, 1965), e^/ ~ 0.5 - 0.7 (Kunii and Levenspiel 1969), eb < 0.4 (Grace, 1984), it is reasonable to assume that Ue = 0 for U/Umf — 4.5 - 8.5. The accuracy of models is hardly affected by this assumption (Grace, 1984) and few models were based on the above concept (Lewis et al, 1959; Kunii and Levenspiel, 1969; Kato and Wen, 1969; Grace, 1984). 2.2.4 Gas Mixing In The Dense Phase Several alternatives have been employed to represent the gas flow pattern in the dense phase. Assumptions ranged from upward plug flow (Orcutt et al., 1962; Partridge and Chapter 2. LITERATURE REVIEW 34 Rowe, 1966) to perfect mixing (Davidson and Harrison, 1963) and stagnant gas (Kunii and Levenspiel, 1969; Grace, 1984) to down flow (Fryer and Potter, 1972). Some authors used a dispersed plug flow representation (May 1959) while others assumed well mixed compartments in series (Kato and Wen, 1969). The overall reactor performance is affected by dense phase gas mixing if conversions higher than 90% are sought; it is insensitive to the dense phase flow pattern for lower conversions Grace (1981). 2.2.5 Fraction Of Bed Occupied By Bubbles The bubble volume fraction, eb, depends on the hydrodynamics prevailing in the bed. The bubble size and velocity are essential factors for the predictions of eb. The bubble velocity, ub, can be calculated from the equation: ub = 0.711 Jtfb + (U - U m f ) (2.15) Several expressions were proposed for the estimation of db as function of bed height (Mori and Wen, 1975; Darton et al., 1977). An iterative procedure is required for estimating eb (Grace, 1982). Using a first guess of e^ , the bed height, H, can be calculated from the relation: H = Hmf/(l-eb) (2.16) The bubble diameter is then calculated at 0.4H from Mori and Wen (1975) or the Dar-ton et al. (1977) equations. The Mori and Wen (1975) correlation is widely used for calculating the bubble diameter at any bed height z: db - < k n = e x p r _ Q Z z / D y (2.17) dbo — dhm where the maximum bubble diameter is given by: dbm = 1.64{A(U-Umf)}OA (2.18) Chapter 2. LITERATURE REVIEW 35 and the initial bubble diameter is given by (Miwa et al., 1972): dbo = 0.376([/- U m f f (2.19) Finally, eb is calculated from: eb = Qb/Aub (2.20) 2.2.6 React ion In Di lu te Phase Very few models account for chemical reaction that might take place in the bubble phase (Kato and Wen, 1969; Grace 1984). This is particularly important for fast chemical reac-tions. Catalytic chemical reactions in the bubble phase may be simulated by introducing the volume fraction of bubbles occupied by solid particles, (f)b, as a model parameter. Based on experimental findings, Kunii and Levenspiel (1969) reported that 0.2 to 1% solids are present in the bubbles. The value of in the Grace model was recommended as O.OOleb < <j)b < 0.01e6. (2.21) For slow reactions (f>b may be set equal to zero. The recommended expression for the solid fraction in the dense phase, fa, is given by: & = ( 1 - * ) ( ! - * • / ) , (2.22) 2.3 C A T A L Y S T A T T R I T I O N Catalyst particles in fluidized bed reactors usually collide and rub against each other. They also suffer wall abrasion. These actions cause larger particles to break into finer ones which may then elutriate. It has been reported that the rate of attrition decreases with time (Forsythe and Hertwig, 1949; Vaux and Schruben, 1983) because the attrition Chapter 2. LITERATURE REVIEW 36 resistance increases as the rough edges of the particles are smoothed off and the weaker particles are eliminated (Forsythe and Hertwig, 1949). There is no universally accepted procedure for measuring attrition because there is not a single mechanism of attrition. Various attrition phenomena and attrition tests have been summarized by Zenz (1979) and Vaux and Keairns (1980). Kono determined the attrition rate of relative^ coarse alumina-silica particles by measuring the decrease in weight for a certain period of fluidization. He observed that the attrition rate is constant and concluded that attrition rates are influenced mainly by the superficial gas velocity and the ratio of the bed height at minimum fluidization to the bed diameter. He also found that the effect of particle size on attrition is small. Vaux and Fellers (1981) determined the degree of attrition of granular solid particles in fluidized beds by measuring the changes in particle specific surface area and increase in fines fraction. They concluded that sieve analysis of particles before and after fluidization of solids for one hour discriminates clearly between the attrition tendencies of different bed materials. A number of standard attrition tests have been developed by various manufacturers and users of catalysts. These tests include shaker tests, spouting jets, submerged jets, and Chevron impingement tests. The standard apparatus and procedure for such tests varies among its users. The submerged jet test is used to simulate attrition which can occur in the grid region of deep fluidized beds. The original apparatus consisted of a 0.038m I.D. tube, 0.686 m long fitted with a grid plate having three 0.0004m diameter holes. At its upper end, the tube expands to a diameter of 0.127m. High pressure air is admitted to yield near sonic velocities (274.3 m/s) through the 0.0004m diameter holes. Typically, 0.1 kg samples are used. In the expanded section, the velocity is reduced to about 0.006 m/s which just exceeds the terminal velocity of 16 to 20 micron particles. The weight of particles smaller than 20 microns (including those originally present) is collected over a period of 5 to 45 hours and is expressed as a percentage of the original Chapter 2. LITERATURE REVIEW 37 charge. This percentage, which is called the attrition index, is used to compare different catalysts. In contrast to the submerged jet test, the spouting jet test is used to simulate the attrition under acceleration and impact conditions. In this test, the particles are sub-jected to a high velocity and impacted on a solid surface. The test procedure consists of placing a 0.3 Kg sample in an inverted Erlenmeyer flask having a 0.0254 m diameter hole in its bottom. The hole is covered with a 10 mesh screen. Bone dry air is admitted through a 0.0063m diameter stopper connected to the mouth of the flask. The air enters the flask at a velocity of 91.4 m/s and penetrates the entire catalyst sample as a spout thereby picking up catalyst particles and throwing them up against the base of the flask. The air leaves through the covered 0.0254m diameter hole. After one hour of operation, the material in the flask is screened through a number 10 mesh screen. The catalyst loss during the spouting plus that passing through a 10 mesh grid in the final sieving is reported as the attrition loss. Chapter 3 MODEL FOR FLUIDIZED BED CLAUS REACTOR Based on fundamental hydrodynamic considerations as well as experimental observations, Grace(1984) has proposed a general two phase model to predict the performance of fluidized bed reactors operating in the bubbling regime. This model is used as a basis for simulating fluidized bed Claus reactors. 3.1 MODEL ASSUMPTIONS The basic assumptions underlying this model are: • The bed consists of a dilute phase and a dense phase; • A l l gas enters and flows through the dilute phase and there is no net flow in the dense phase; • Catalyst particles are present in both phases and are well mixed; • Mass exchange takes place between the two phases; • The voidage in the dense phase is the same as that at minimum fluidization; • Chemical reactions take place in both phases. A schematic diagram of the model is shown in Figure 3.1. In addition, the following assumptions are invoked in this work: • Isothermal conditions prevail throughout the bed; 38 Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR \ interphase o o SO d "a. ~o, o transfer Dense Dense 5 t Dilute phase Dense phase Co ^ 2 , 0 UA 0 4>b = o.oi^ ^ = ( 1 - ^ ( 1 -Concentration at z=0 Gas flow rate Fraction of bed accupied by phase Solids associated with phase Voidage Figure 3.1: Schematic diagram for the two phase" bubbling model Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 40 • Quasi-steady state prevails; • The hydrogen sulphide/sulphur dioxide ratio is 2/1. Based on the notion that fouling merely reduces the active catalyst surface, a fouling term is introduced as a multiplying factor in the numerator of the rate equation. The rate of disappearance of H2S for the reversible Claus reaction can then be expressed as the difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction, i.e. VH2S = [paaSPg7 ~ ^ ^ o P j x ] (3.1) where k'w, Ke and $ denote the rate constant, the equilibrium constant and deactivation function, respectively. The present study was confined to the temperature and H2S concentration ranges of 100 to 150°C and 200 to 1300 ppm, respectively. It will be shown subsequently that, under these conditions, the second term in Equation 3.1 is negligible. For a gas mixture containing 1300 ppm H2S and 650 ppm SO2, the first term in the parenthetical expression in Equation 3.1 is PH2SPSO2 = ( 1 3 0 0 x 1 0 x 760)(650 x 10 - 6 x 760)05 = 0.694 (mm Hg) 1 5 . K it is assumed that the reaction goes to completion, then PH2O — PH2S = 1300 x 10~6 x 760 or 0.988 mm Hg. The partial pressure of sulphur cannot exceed the sulphur vapour pressure. At 150°C, the latter is 0.196 mm Hg according to the equation given by Meisen and Bennett (1979). The equilibrium constant, Ke, can be estimated from the free energy data compiled by McBride et al. (1963). At 150°C, Ke = 1.66 x 107and the second term Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 41 in the parenthetical expression in Equation 3.1 therefore becomes: i/„oPir = < i S ^ X o . » « X o . i « > ) " " " = 4.38 x 1(T 8 (mm H g ) 1 5 . The reverse Claus reaction is therefore negligible under the conditions examined in the present study. The rate expression may therefore be rewritten as: rH2s = k'wVPH2SP™2 (3-2) For Pso2 — 0-5Pff25 and assuming ideal gas behavior, the rate expression takes the form: rH2S = kwVC£s (3.3) where kw = k'^RT)1-5/y/2. 3.2 GOVERNING EQUATIONS An H^S mass balance over differential volumes leads to the following equations for a fresh catalyst for which $ = 1. Dilute phase: U ^ l f + k^b<CAh ~ C A d ^ + M b C j i 5 = 0 (3.4) Dense phase: kqabeb(CAb - CAd) = kv<f>dClJ (3.5) These equations must be solved simultaneously subject to boundary conditions at z= 0. In this work, the following boundary conditions are used. Dilute phase: Cxt.o = C 0 (3.6) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 42 Dense phase: KfaC^lo + kqabeb{CAd,0 - Co) = 0 (3.7) These conditions imply that, at z = 0, the dense phase concentration is established by mass transfer from the dilute phase and chemical reaction in the dense phase. It is less than the dilute phase concentration. This assumption is based on the premise that all gas enters the reactor as the dilute phase and that there is no net flow of gas in the dense phase. 3.3 S O L U T I O N O F E Q U A T I O N S The above equations can be made dimensionless by introducing the following variables: C1 = CAb/C0, C2 = CAd/C0, and ( = z/H. (3.8) Equations 3.4 to 3.7 therefore become: ^ = a(C2 - C) - hC\* (3.9) a ( d - C2) = foCl* (3.10) with the boundary conditions at £ = 0: C i = 1 (3.11) /3 2 (7 2 1 - 5 - r a(C7 2 - l ) = 0 (3.12) where: kqabebH a = u (3.13) ft = l^tHVCo. ( 3 1 4 ) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 43 A> = jj • (3-15) If C 2 ) 0 denotes the value of C 2 at £ = 0, then equation 3.12 may be rewritten in the form: (y/cZ)3 + ji\fC^f - J2 = 0 (3-16) It may be shown that the positive real root of the above cubic equation (for <x > 0) is given by V^o" = ( ~ ) 1 / 3 [ ( - + ^ ) 1 / 3 + (*- V^)1/31 - g £ (3-17) where <r = 1 - 2(a//32)/27. Equations 3.9 and 3.1G can be combined by introducing the transformation a v a C 2 = { ^ ( * 2 - 1 ) } 2 P2 (7 1 = (|-)V(x 2-l) 2- (318) Differentiating equation 3.18 yields: ^ = 2 ( £ ) 2 ^ 2 - l ) ( 3 x 2 - l ) ^ . (3.19) It is clear that equation 3.10 is automatically satisfied. Substituting the expressions for C i , C 2 and dCi/d£ into equation 3.9 and simplifying gives: dx = _a_{l-*>Ytf + J) di 2 7 3 t ( 3 z 2 - l ) x f K J where 7 3 = 02/Pi-If » 0 denotes the value of x at £ = 0 and s a the corresponding value at £ = 1, then x0 can be calculated from the value of C 2 at the bottom of the reactor (i.e. C 2 ]o): x° = \l1 + ^ y/c*° (3-21) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 44 where C2to is given by equation 3.17. To find xi, equation 3.20 is integrated (by partial fractions) between the limits XQ and Xi to give: 7 ^ 1 * o ) = 0 (3.22) where f(xi,x0) is the function whose root gives xi at £ = 1. Once Xi is found, C\ and Ci can be calculated at the top of the reactor. The function "f(xi,x0) at f — 1 is given by: (3a;2 - l)x (1 - a; 2 ) 2 ( 7 3 + x 3 ) ' The kernel in the above integral may be rearranged into: (3x 2 - l)x (3a:2 - l)x (1 - x 2 ) 2 ( 7 3 + x3) (1 + x ) 2 ( l - a;) 2( 7 + x)(x2 - 7 a; + 7 2 ) The right hand side may then be rewritten in terms of partial fractions as: (3.24) (3s 2 - l)z A, A2 A3 AA A6 Aex + A7 (1 - x2)2(-j3 + x3) ~ 1 + x^ (1 + a:)2 + 1 - z + (1 - a;)2 + 7 + a; + x2 - -yx + 7 2 ( ' The constants Ai to A7 are evaluated as follow: d x(3x2 - 1) 2 3 7 3 2 ( 7 3 - 1) 2 (3.26) and A2 is given by: •1 2 ( 7 3 - 1) (3.27) . _ d (3a:2 - l ) s 2 A z ~ Si d x ^ l + a;)2(l - x)\j> + x 3 ) K 1 ~ X ) = 3 ^ 2 ( 7 3 + l ) 2 (3.28) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 45 1 (3.29) 2(7 3 + 1) v r ( 3 x 2 - l ) x . A 5 = M { ( x 2 - l ) ( a ; + 7 ) ( x 2 - 7 a ; + 7 2 ) } ( : C + 7 ) 1 3 ^ ^ (3.30) 37 (7 2 - I ) 2 ' To find ^ 6 and A7, the function A(x) is introduced to simplify the notation. The kernel may be rewritten as x ( 3 x 2 - l ) A(x) (1 — x 2 ) 2 ( 7 + x)(x 2 — 7 x -f 7 2 ) x 2 — 7 x + 7 2 where (3.31) AW= ( 1 : ( ^ 1 ) ^ By inspection of equation 3.25, A(x) is also given by: A(x) = A6x +A7 + (x 2 - 7 x + 7 2 ) G ( x ) (3.33) and G(x) denotes the first five terms on the right hand side of equation 3.25. The roots of the expression x 2 — 7 x + 7 2 are x = 7 (1 ± i\/3)/2, where 1 = Substituting for x = 7 (1 -f fc\/3)/2 in equation 3.33 gives: A ( l + l 2 ^ ) = 7 A 6 ( l + t V ^ ) / 2 + ^ l 7 = A, + IA , (3.34) where A, and A R denote the imaginary and real parts of A. Equating the imaginary terms in equation 3.34 gives: A6 = A l / ( 7 v / 3/2) . (3.35) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 46 Similarly, A7 is determined by equating the real term in equation 3.34: A7 = A r - A./V3. It is easy to show (after some algebraic manipulation) that ,7 T * /3v = 1 574 + 3 7 2 + l v /3 676 + 7 7 7 + 7 2 + l 2^ 2 >~ 2 ( 7 4 + 7 2 + l ) 2 6 ( 7 4 + 7 2 + l ) 2 ' (3.36) Hence: and K = - -1 5 7 4 + 3 7 2 + 1 2 ( 7 4 + 7 2 + l ) 2 = v /3 676 -r 777 + 7 2 + l * 6 ( 7 4 + 7 2 + i ) 2 Thus the constants A& and A7 are given by: 1 6 7 6 + 7 7 4 + 7 2 + l 37 (74 + 7 2 + l ) 2 } and 1 3 7 e _ 4 7 4 _ 4 7 2 _ !  7 3* ( 7 4 + 7 2 + l ) ' (3.37) (3.38) (3.39) (3.40) (3.41) Substituting the constants A\ to Ar into equation 3.25 and integrating term by term gives: f(xux0) = A 1 l n ( i ^ ) + A 3 l n ( i ^ i ) + A 5 l n ( l ^ i ) (3.42) I + x0 I — XQ 7 + ^0 I I -- A2( •) + M 1 + X l 1 + x 0 1 — X i 1 - x 0 ) + 2A7 - 7 ^ 6 arctan( ^ ) — arctan( 0 ^ + A e H X \ - 1 X l + / 2 ) -Xo~7a;o + 7 Although this expression is not an exphcit function of X i , it is well behaved except at x a ± 1 (see Figure 3.2). The singularity at x x = 1, arises when C\ and C2 —» 0 (the Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 47 co co o to to II co - I II X CO O o II o o CD d c o o cr d CM d c o o C N I H I 3 cn O CO o o o d o d l o d I Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 48 ratio C1/C2 approaches 1) and hence both the rate of reaction and mass transfer are zero. The root, x 1 } of equation 3.22 can be found within a few iterations provided that 1 < x1 < x0 (see Figure 3.2). A root finding subroutine, which uses the bisection method to calculate any specified number of roots in a given interval and avoids discontinuities, was developed to find x i (see Appendix B). Values of Ci and C\ at £ = 1 are calculated from the relations: Ci = - l ) } 2 (3.43) Pi a Ci = {^f*\{A - l) 2. Pi (3.44) The theoretical conversion is then given by: (3.45) The above equations were formulated for the calculation of the overall conversion and the concentration at the top of the reactor. Concentration profiles for the dilute and dense phases can be predicted by replacing X\ by x(£) in equations 3.42, 3.43, 3.44, and by multiplying the term a/27 3 m equation 3.22 by £ i.e: a 2 ^ + A ^ 1 + *(£)' l + x 0 + A 3 In *(0 1 - XQ + A5ki 7 + x(£) 7 + ^0 + A 6 l n 1 z 2 ( £ ) - 7 * ( 0 + 7 2 «o ~ lxo + 7 2 2 A 7 - jA6 1 - XQ }' + arctan( [ l + x 0 1 + «(£). ^ 7 ) — arctan( + AA{ 2x 0 - 7 = 0 \/37 \/37 Similarly the dimensionless concentrations as a function of £ are given by: 2 <?2(£) = a Wi (*2(0 " 1) a d ( 0 = (^ )V(£ ) x 2 ( £ ) - l (3.46) (3.47) (3.48) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 49 Concentration profiles generated from the above equation are shown in Figure 3.3 for the case where a = 1.701, /3 2 = 1.387, 7 = 6.36 and XQ = 1.307 which were calculated in Appendix B for the conditions U/Umf = 4.44, Hf = 0.19m and T=150°C. The above procedure can be extended to any reaction of order n(= p/q 7^  1) by choosing x = (C1/C2)1/9 to combine the equations for the dilute and dense phases. The resulting equations will be: Pi C2 = (^-f(p~q\xq ~ i) '/fr-«> Pi xq-l(pxq +q-p)' (x2- l)2(<yr + xr) subjected to the boundary condition at £ — 0 dx = —a q{p - qh" di (3.49) (3.50) (3.51) X/\ x p-g 02 a 0 (3.52) where jp = (3i/@2- Partial fractions may be used, in principle, to integrate equation 3.51. The result of the integration of equation 3.51 is a function of x x , x0, 7, and a. The solution may expressed as: ^{xijXOjf, a) = 0. (3.53) Table 3.1 presents expressions for T for reactions of order n. 0 0.2 0.4 0.6 0.8 1 Dimensionless bed height, f Cn Figure 3.3: Predicted concentration profiles (o=1.701, /?2=1.387, 7=6.36, xt=1.307) ° Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 51 Table 3.1: Solutions for equation 3.51 at the top of the bed for selected reaction orders \ ^(1V(,Uir} AM$%) + - J » M g ) + ^[axctan(*i/7) " arctam>0/7)] 2 - ^ ( 1 ^ : ^ + X 2 ) ^ M l S ) + ^ l n ( S ) - ^ ( T ^ - T ^ ) + A 4 ( T ^ - T i ) + ^ ln(fl^J) + f [arctan(x 1/ 7) - arctan(x 0/ 7)] + f 2 - a r c t a n ( ^ ) ] + ^ 2 7 ' n A2 A3 A* . As Ae Aj 3 ^ 1 7 wfo NA N A NA , - 7 ?-3 - 3 nr ' - l 1 - 1 - 2 T 3 N A 4(T* + 1) j 4(T 3-1) 4(-T!+1)= 4( 7' + l) T ( 7 J + 1) J ( 7 j + 1) 5 , -2-^ + 17 - 5 2->8-l 1 -3->-2 -6->'i+2-r4-673-4-y?+3->-2 3T>"-4Tf,'H-12-r!'-4Tfi+37 + 2 J 4(-f»-iP 4(7»-l) 4 ( 7 a + l)3 4(7» + l) S^ S^-lJJ 37(74+12 + l)2 3l2(74+^2+l)2 Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 52 3.4 DETERMINATION OF THE RATE CONSTANT The reaction rate constant used in the bubbling bed model was determined from fixed bed studies. This constant is a function of temperature and catalyst characteristics. Although rate expressions for the Claus reaction over various catalysts have been published (see Section 2.1.3), the rate constant for the catalyst used in this study (known as Kaiser S-501 alumina) has not been reported in the literature. Furthermore, the rate expressions cited in section 2.1.3 were developed under temperature conditions ranging from 200 to 325°C (Dalla Lana et al., 1972, 1976). Therefore, the decision was made to carry out experiments within the temperature range shown in Table 5.1 and at gas velocities lower than the minimum fluidizing velocity. During these experiments, the catalyst weight, WCCLt, and the H2S concentration in the feed were kept constant at 1.2 kg and 600 ppm, respectively. The bed diameter was 0.1 m and its depth was 0.19 m. The ratio of H2S to SO 2 in the feed was fixed at 2. The experiments were performed according to the procedure described in section 5.1.2. Three basic assumptions are invoked in the following analysis: • Constant temperature throughout the bed. • Plug flow of gas through the bed. • Reaction orders are 1 and 0.5 for H2S and S02, respectively. The axial and radial dispersions arising in the fixed bed experiments may be tested by means of the Peclet numbers, Pej, and P e r , defined as: PeL and PeT axial convection DU .„ — r - r - T : = "TT" ( 3 - 5 4 ) axial dispersion DL axial convection DU ^ ^ radial dispersion Dr Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 53 where DL and Dr denote the axial and radial dispersion coefficients, respectively. Dis-persion coefficients in packed beds were reported by Bischoff and Levenspiel (1962). The estimated values of Di and Dr were taken as 9.12 x 1 0 - 6 and 5.58 x 1 0 - 6 m2/s./, re-spectively, and the corresponding values of Pe^ and Per were 219 and 358. According to Levenspiel (1972), deviation from plug flow occurs when Pe < 100. The assumption of plug flow in the present fixed bed reactor was therefore justified. The material balance equation for the plug flow reactor is given by: - = f* - * * L (3.56) UACH2S,O JO -rH2s Substituting equation 3.3 into equation 3.56 and rearranging gives (for $ = 1): UA tx dX UA 1 (3.57) Wcaty/CH2s,0 I V ^ X where kw denotes the rate constant per unit catalyst mass. Values for kw were found to be 0.1834, 0.202, 0.239 (kmole/m 3 )-°- 5 /s.kgcat at 100, 124, 150°C, respectively. Rate constants for other catalysts could be obtained from expressions reported by Dalla Lana et al.(1972, 1976) and by McGregor(1971). For instance when equation 2.2 is evaluated at 373 K and Pso2 — PH2S/2, 1.12 (62.4 x 373) 1 5 , -7440 w s  T H ' S ~ 3600" V2 6 X P ( 1.987 x 3 7 3 ^ = 0 .034Cg 5 (h°^e/m') ) ( } H * s s.kg bauxite ; v ; The kw values are summarized in Table 3.2. It should be noted that equation 2.2 was developed for the temperature range of 481 to 560 K , the reported temperature range for equation 2.3 was 473 to 596 K . Table 3.2 shows that the values of kw determined in Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 54 Table 3.2: Values of rate constant, ku Temperature (K) Rate constant, kw (kmol/m 3 )" 0 - 5 s.kg cat 373 397 423 a b e d , 0.031 0.034 0.055 0.183 0.063 0.069 0.112 0.202 0.135 0.124 0.222 0.239 a) Dalla Lana et al.(1976); b) Dalla Lana et al.(1972); c) McGregor (1971); d) This work. this study are significantly higher than those obtained from equations 2.2 and 2.3 thus indicating that the activity of the promoted alumina S-501 exceeds that of bauxite and 7-alumina. This is consistent with the findings of Pearson (1973) who reported that the S-501 catalyst had led to higher conversions than those obtained with bauxite and an S-201 alumina catalyst. Figure 3.4 shows the Arrhenius plots for various catalysts. Curves 2 to 5 are based on the results of previous studies which were conducted at temperatures greater than 200°C. Extrapolation of these expressions to the lower temperatures used in the present study is not reliable and is provided for comparision purposes only. The corresponding activation energies and frequency factors are listed in Table 3.3. The low value of E determined in this study is associated with a low value of Af thus indicating a compensating behavior. To elucidate these results, the effects of external mass transfer and pore diffusion were calculated. The influence of the external mass transfer effects may be determined from the effectiveness factor, 77, defined by: Reaction rate with mass transfer resistance Reaction rate without mass transfer resistance (3.59) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 4* 0.1 -0. 2.5 2.6 10 3 /T(° Figure 3.4: Rate constants as a function of temperature for various Claus catalysts Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 56 Table 3.3: Activation energies and frequency factors for Claus catalysts Catalyst E (kcal/mole) Af Investigator Bauxite 7.44 807.3 Dalla Lana et al. (1972) 7—alumina 7.35 744.1 Dalla Lana et al. (1976) Cobalt-Molybdate 5.50 - George (1974) on alumina Chemisorb-A 25.0 - George (1975) Chemisorb-A promoted 15.0 - George (1975) with 5.0%NaOH Bauxite 5.02 386.4 Kerr et al. (1976) Bauxite 7.59 1690.8 McGregor (1971) Alumina S-501 1.93 2.43 This work Carberry (1976) presented charts for TJ in terms of the observable quantity, -qDa^ i.e: „ Observed rate r,DaQ = r (3.60) where CH2S& denotes the concentration of H2S in the bulk of the gas phase and Dao represents the Damkohler number, i.e the ratio of chemical reaction velocity to the mass transport velocity. kg denotes a mass transfer coefficient and ap denotes the interfacial area expressed as the particle surface area per unit particle volume. The mass transfer coefficient in packed beds may be calculated from the correlation reported by Sherwood et al. (1975): kg = lA7U(^^-)-0A2(-^-)-0-67 (3.61) y-g PgDg The observed rate can be calculated from the measured conversion: A x Observed rate = Wcat/Fn2s,o X WCat/-r?ff2s,o (3.62) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 57 Table 3.4: Calculation of external mass transfer effectiveness factor Temperature (K) 373 397 423 X 0.93 0.94 0.96 CH2S,O x 10s (kmole/m 3) 1.959 1.841 1.728 Ff l ! S , „x 109 (kmole/s) 3.385 3.181 2.714 Obs. rate x l O 9 (kmole/m 3)/s.kg cat Obs. rate x l O 6 (kmole/m 3)/s.m 3 2.623 2.491 2.16. 2.086 1.9807 1.717 kg (m/s) 0.0208 0.0232 0.0281 T)Da0 x 104 1.664 1.507 1.149 r] (from Carberry, 1976) 1 1 1 Effect of mass transfer Nil Nil Nil where FH2S,O — UACH2si0 (kmole/s) and CH2s,o = ( P P M x 10~6)P/RT (kmole/m 3). The numerical values of the above parameters are presented in Table 3.4. The pore diffusion effect may be assessed by using the generalized Thiele modulus, $. Bischoff (1967) formulated the following criterion for $: Observed rate x llg(CH2s,g) 2DeJoH^ g(CH2s)dCH2S < 1 Negligible pore diffusion (3.63) > 1 Significant pore diffusion where g(CH2s) denotes the concentration term in the rate expression [i.e. g{Cii2s) — C}j2S}, De denotes the effective diffusivity and lc is a characteristic length of the catalyst particle. Aris (1957) showed that for a spherical particle, lc may be taken as dp/6. The effective diffusivity may be estimated from the relation (Sherwood et al., 1975): where 6 denotes the particle voidage and £ denotes the tortuosity factor. Satterfield (1970) recommended, in the absence of experimental values, that 6 = 0.4 and £ = 5. Substituting for g(C) = C 1 ' 5 , equation 3.62 gives: $ = 5 (Observed rate)(^ p/6) 2 4 DeCH2s,g Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 58 Table 3.5: Calculation of Thiele modulus Temperature (K) De x 107 (m 2/s) 373 397 423 7.86 8.9 9.91 $ x 104 1.789 1.596 1.324 $ < 1 < 1 < 1 Effect of pore diffusion negligible negligible negligible Values of $ are presented in Table 3.5 and show that the pore diffusion effects are negligible. Different values of activation energy for a given reaction over a series of catalysts may be attributed to the methods by which such catalysts were prepared. Ashmore (1963) quoted various authors and reported 8 different values of E (for 8 catalysts) for two classical reactions (Methanol synthesis and sulphur dioxide oxidation). For instance the reported activation energy for SO 2 oxidation ranged from 10 to 38 kcal/mole. It is common to find a relationship between the activation energy, E, and the fre-quency factor, Af, for different catalysts promoting a given reaction (Constable, 1925). The form of the relationship is: In Af = a-LE + ai (3.66) This effect was later called the "theta rule" by Schwab (1950) and "the compensation effect" by Cremer (1955). In essence, it states that increases in the activation energy are "compensated for" by increases in Af. The Compensation effect may arise because catalysts have different energy levels (Cremer, 1955). For example, if the adsorption on catalyst 2 is stronger than that on catalyst 1 (i.e. the desorption energy E2 > E{ and the activation energy E-i > E2) then the "activated complex" formed on catalyst 2 possesses less vibrational and rotational freedom than that formed on catalyst 1; in other words the entropy difference between the activated complexes formed on catalyst Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 59 1 and the reactants, ASi, is higher than AS2 (the entropy difference between the acti-vated complexes formed on catalyst 2 and reactants). Since Af is related to the entropy difference, it follows that Aj1 must be higher than Af2. Thomas and Thomas (1967) discussed the importance of lattice imperfections in catalysts and pointed out that the compensation effect may be explained on the basis of lattice defects. The effect has also been observed in other processes such as homogeneous reactions (Fairclough and Hin-shelwood, 1937), viscosity of aqueous solutions (Good and Stone, 1972) and conductivity of inorganic (Roberts, 1974) and organic (Eley, 1967) semiconductors. These example are cited to indicate the generality of the compensation behavior. Several mechanistic models have been proposed to explain the compensation phenomena and were discussed in a comprehensive review by Galwey (1977). George (1975) studied various Claus catalysts and found that the activity of some of the catalysts was improved when they were treated with alkali such as NaOH. His study showed that treatment with NaOH resulted in decreased activation energies. Figure 3.5 shows that, for Claus reaction catalysts, the increase in the activation energy is associated with an increase in Af. Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 60 Figure 3.5: Relationship between A, and E Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 61 3.5 MODELS FOR CATALYST FOULING Several expressions have been suggested for catalyst deactivation (Froment and Bischoff, 1979). Most of these expressions were based on observations of coke deposition on oil cracking catalysts. They contained fitting parameters and need a theoretical justification. A simplified analysis for developing an expression for the deactivation of Claus catalyst is presented in the following paragraphs. An expression for the deactivation function, can be written in terms of the fraction of the sites, <j), fouled by sulphur deposits. Such expression may take the form: * = 1 - <f> (3.67) The dependency of <f> on catalyst sulphur content can be found by considering the depo-sition of sulphur on the vacant sites, s, to form a mono-sulphur layer: S + s S.s t Sulphur may also deposit onto fouled sites to form M multilayers i.e: S + S.s 2S.s | S + 2S.s ZS.s | S + (m — 1)S.S 77X5.3 I S + m5.JS ^ + (TJX + 1)S.S I The net rate of deposition may, in general, be written as: R(m-l)S.* = ^ ^ 5 ' ' = ^ T n - l C ( m _ 2 ) S . « ~ L C ( r a - l ) S . , (3.68) RmS.s = = ^ m ^ m - i J S . , — fcm+lCmS.„ (3.69) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 62 where Cms., denotes the surface concentration of sites fouled by m layers of sulphur. Dividing equation 3.69 by equation 3.68, yields: ^ C ( m - 1 )5 .« _ fcm-iC(m_2)S.< ~ fcmC(m_i)s.g ^ ^ dCmS.t Kn.C(Tn-l)S.s — km+xCmS.t This expression can be simplified by assuming that all rate constants are equal, i.e: fc0 = fc1 = . . . = &„, (3.71) and equation 3.70 reduces to: ^ C ( T n _ i ) 5 . J _ C (m -2)5.« ~ 0 (m- l )5 .« ^ ^ dCmS., C(rn-l)S.» " CmS.a Solution of equation 3.72 may be obtained by introducing a distribution ratio, r: r = C m S > ( 3 . 7 3 ) C{jn-l)S., The distribution ratio relates the surface concentration of the (m-1) layer of sulphur to that of the m layer. The ratio may be regarded as constant over short time intervals. The surface concentration of a mono-layer (i.e. when m = 1) is: Cs, = Cvr (3.74) and that of the m-layer: C m S , = C v r m (3.75) where Cv denotes the concentration of vacant sites. A balance on the total sites leads to: M Ct<f> = £ CmS.. (3.76) m=l C t ( l -<I>) = C V + [ C B 9 S a + CSo2, + CH2o.t] (3.77) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 63 where Ct denotes the concentration of total sites and the terms between the square brackets counts for the sites occupied with H2S, S02 and H20, respectively. Substituting equations 3.74 and 3.73 into equation 3.76, gives: 9i cv M i + E r !> r l - r M m - 1 m=2 (3.78) <f> 1 — r The sites occupied by H2S, S02 and H20 are a small fraction of the total sites and may be neglected compared with those occupied by sulphur and those which are still vacant. Equation 3.77 therefore becomes: ct 1 Cv l-<f> Combining equations 3.78 and 3.79 gives: <t> (3.79) l - r M (3.80) \-<f> v 1 - r Alternatively, the distribution ratio may be expressed in terms of sulphur content. Let A 0 denote the weight of sulphur per site per unit weight of catalyst due to monolayer deposition. The catalyst sulphur content, denoted by A, can readily be obtained: Af A = A 0 rnCmS.s (3.81) m=l Substituting equations 3.74 and 3.75 into equation 3.81 yields: Af * = (AoC„) £ mrT m=l ( A 0C„ )T (1 — r M ) — MrM{\ — r) Ml Eliminating Cv by substituting equation 3.78 into equation 3.82 leads to: (3.82) AoCf Mr M 1 - r (3.83) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 64 Equations 3.80 and 3.83 can be used to eliminate r and to express (f> in terms of A. For the case when M = 1, equation 3.80 reduces to: 4> and equation 3.83 becomes: AoCf - r <j>. (3.84) (3.85) Substituting equation 3.84 into equation 3.67 gives: where K, = l/\0Ct. For the case when M oo, equations 3.80 and 3.83 become: 1 for r > 1 <t> = { r for r < 1 (3.86) (3.87) and ^oCt oo for r > 1 £ for r < 1 (3.88) Since the maximum value of <j> equals 1 and since X is finite, it follows that the distribution ratio, r , must be less than 1. Equations 3.87 and 3.88 may be combined to eliminate r and to express the fraction of fouled sites, <f>, in terms of the catalyst sulphur content, A. Hence for M —» oo, equation 3.87 becomes (since r < 1): r = (f> and equation 3.88 gives: 4> A 0 C t (3.89) (3.90) Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 65 Substituting equation 3.89 into equation 3.90 and rearranging yields: '-•-I+kv (3'91) Using equations 3.91 and 3.67, the deactivation function takes the form: * = TT^ (3'92) Froment and Bischoff (1979) suggested, without theoretical proof, expressions similar to equations 3.86 and 3.92. The mono-layer model (i.e equation 3.86) was also suggested by Masamune and Smith (1966). The multi-layer model was used in this work to predict the performance of a fluidized bed Claus reactor operating under sulphur condensing conditions (see Section 6.2). Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 66 3.6 THERMODYNAMIC CONVERSION Prediction of the Claus equilibrium conversion can be quite complicated due to the num-ber of species that might be present and consequently the number of chemical reactions that take place. However, simplification results when exploring conditions of a specific mixture. Under the conditions used in this study (see Table 5.1), it is reasonable to assume that elemental sulphur is predominantly present as S$. The formed sulphur con-denses and its mole fraction in the gas phase is negligible. For instance the sulphur vapour pressure at 423 K is 0.026 kPa (Meisen and Bennett, 1979). For a feed mixture containing S02, H2S and N2, material balances are formulated and presented in Table 3.6 for the reaction: 2H2S + S02 ^ |s8 i +2H20 (3.93) Table 3.6: Analysis of equilibrium Claus reaction Component Molar flow rate into reactor Equilibrium molar rate of gaseous component Equilibrium mole fraction S02 fi f i - v ih - «0/(/ - «0 H2S 2/ i 2 ( / a - ^ ) 2(/ i - " ) / ( / ~ v) N2 h H hlU - ») H20 0 2v 2u/(f-u) total / = 3 / a + f2 f - v 1.0 The equilibrium constant for the above reaction may be related to the partial pressures Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 67 of the gaseous components by: fi ~H2SRS02 It is also given by the change in free energy of the reacting system i.e: K * = pi H P ° (3-94) The partial pressures of the gaseous components may be calculated from Table 3.6, thus: PH7O = (jZ^)P (3-96) Pso2 = i j ^ ) P (3-97) PH2S = 2PSo2 (3.98) where v denotes the extent of reaction under equilibrium condition, jx and / denote the molar flow rate of SO 2 and the total molar flow rate into the reaction system, respectively. It is easy to show that: v = hP - fPso, ( 3 9 9 ) * — rJS02 and PH2o = 2 ( f l P - f ? S O > ) (3.100) J ~ Ji Substituting for PH2S from equation 3.98 and for PH2O from equation 3.100 into equation 3.94 and rearranging yields: KePlo2 - ( h P ~ [ P f S ° 2 Y = 0 (3.101) where / 2 denotes the molar flow rate of N2. Chapter 3. MODEL FOR FLUIDIZED BED CLAUS REACTOR 68 The above equation was solved numerically for Pso2 ( s e e Appendix F). The equilib-rium conversion may be calculated from the relation: partial pressure of SO 2 at equilibrium 1 1 -partial pressure of SO2 in feed Pso2 (3.102) (fi/f)P Selected values of equilibrium conversion are presented in Table 3.7 and are shown in Figure 6.3. Table 3.7: Equilibrium conversion (%) Temperature (K) SO 2 concentration in feed 300 ppm 650 ppm 373 98.49 98.81 378 98.24 98.19 383 97.97 98.42 388 97.66 98.19 393 97.31 97.92 398 96.94 97.62 403 96.52 97.26 408 96.06 96.93 413 95.54 96.53 418 94.99 96.09 423 94.37 95.61 Chapter 4 EXPERIMENTAL APPARATUS AND MATERIALS 4.1 REACTION EQUIPMENT The experimental apparatus used in this work (shown schematically in Figure 4.1) was basically designed by Bonsu (1981). It consisted of a fluidized bed reactor and supporting facilities for nitrogen regeneration, gas analysis and operational safety. 4.1.1 Fluidized Bed Reactor The reactor was a stainless steel tube (0.86m high x 0.1m ID) with a freeboard section (0.3m high x 0.2m ID). The gas distributor was made from a wire mesh laminate (Dy-napore, Type 401420, made by Michigan Dynamics Inc., Garden City, Mich.). A similar mesh was installed at the top of the reactor to prevent catalyst elutriation (see Figure 4.2). External heating of the reactor was accomplished with shielded nichrome wires (type D/R19S2, made by Pyrotennax Inc., Trenton, Ont.). The total power supplied by the heater was 2 kW. Cooling was provided by passing water in a coil wound outside of the reactor. Insulation consisted of a 0.025m thick thermal blanket (made by Carborun-dum Inc., Niagara Falls, NY)? The temperature inside the reactor was monitored by four Iron-Constantan thermocouples located 0.05m below and 0.075, 0.56, and 1.1m above the distributor. The desired temperature was maintained within ±3°C by the use of two proportional controllers (model 49 made by Omega Engineering Inc., Stamford, Conn.) connected to the second and fourth thermocouples. 69 Figure 4.1:. Flow diagram of the equipment (All dimensions in mm) from Bonsu (1981) Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 71 12' .5 7 T .50" NPT 8 CLEARANCE HOLES FOR 5/16* BOLTS . 45°APART 10' PCD .25' NPT 12 CLEARANCE HOLES EUR .25' BOLTS . 30° APART 4.5' PCD 25' NPT .25* NPT 2 DIAMETRICALLY OPPOSITE 1' NPT 50' NPT .25' NPT 5.5' — — .50' NPT — .25' NPT .25' NPT .50' NPT Figure 4.2: Fluidized bed reactor Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 72 Two mercury-in-glass manometers were installed just below the gas distributor and in the freeboard section to monitor the pressure inside the reactor. The reactor was equipped with a spring loaded relief valve to avoid excessive pressure build-up. This valve, which was connected to the ventilation system, was designed to open slightly at 7.5 psig and open fully at 10 psig. Rotameters were used to measure the flow rates of pure N2 as well as mixtures of H2S and SO2 in N2 to the reactor. The nitrogen and sulphur dioxide feed streams were preheated electrically upstream of the reactor with nichrome wires which were heavily insulated with fiberglass. To avoid sulphur condensation, the line between the reactor and scrubber was similarly heated. The power supplied by the preheater and the exhaust heater was 1.2 and 0.4 kW, respectively. The temperature of these lines were measured by two Iron-Constantan thermocouples and regulated by two proportional temperature controllers. The quality of fluidization was observed through two identical sight glasses located 0.34m above the distributor. The sight glasses were installed diametrically opposite each other with one behind and the other in front of the reactor. The one-inch N P T ports for accepting the sight glasses were inclined at 60° to the reactor axis. Illumination was provided by a 60 w light bulb mounted on the top of the sight glass located behind the reactor. 4.1.2 Nitrogen Regeneration System Reactor effluent gas consisted mostly of nitrogen and traces of H2S, S02 and H20. It also contained sulphur vapour during catalyst regeneration. It was therefore essential to remove extraneous components before recycling the nitrogen. The cleaning was accomplished by passing the reactor outlet gas through an aqueous NaOH scrubber as well as glass columns packed with KOH and CaSO^ pellets. The NaOH scrubber (see Figures 4.1 and 4.3) consisted of a Q V F column packed Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 73 with 1/4" ceramic Berl Saddles. A solution containing 50wt% NaOH was pumped (at 2 L/min) continuously and concurrently with the reactor gas through the scrubber, the gas was then bubbled through the NaOH solution in the reservoir with a sparger to ensure almost complete removal of H2S and S02. The temperature of the NaOH solution was maintained at about 15°C by passing water through a cooling coil located in the reservoir. A glass wool filter was placed at the bottom of the reservoir to prevent entrainment of spray and mist. Two glass columns filled with KOH and CaSO^ pellets were used to remove moisture from the gas. Each drier had a stainless steel bottom section. The pellets were supported by a wire mesh installed between the bottom section and the glass column (see Figures 4.1 and 4.4). The KOH also acted as an absorption medium for water and any residual traces of H2S and S02. The CaS04, on the other hand, removed moisture with very high efficiency. Potassium hydroxide is deliquescent; therefore, a saturated solution was formed after absorbing the moisture. This solution was collected in the stainless steel section and was discharged through a drainage valve at the bottom of the drier. A bellows pump (model MB-302, manufactured by Metal Bellows Corp., Sharon, Mass.) was installed upstream of the reactor. It had a maximum capacity of 85 L/min at 1 atm. A regulating valve and a rotameter were used to control and measure the flow rate of the recycled nitrogen, respectively. When a sample of the regenerated nitrogen was tested, the H2S and S02 concentra-tions were below detectable limits of 2 and 1 ppm, respectively. Therefore, the regener-ation system was more than 99.99% efficient. Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 74 Stf-4S? a 6' 12 HOLES FDR 37V SO4 APART PCD „ HUL£5 *' NBDLTS . 18* I • £5* NPT CC CC 25* NPT 12». .30* KPT •6 HOLES FOR .373" BOLTS . 60° APART . 10* PCD > 6' OVF GLASS COLUMN SS. VIRE MESH &S. PLATE 50* NPT 6' PIPE 6 HOLES FOR 25* BOLTS 60° APART . 450* PCD 3* PIPE • D-R1NG J2S*X 3.73* OJL X X ID &S. 18*X 18*X 50* THJQC 23' COOLING COD. 2* TUBE 12* QVF GLASS COLUMN • 1350* • Figure 4.3: NaOH Scrubber and reservoir Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 75 .SO' NPT 8 HOLES FOR .373' BOLTS 43° APART . 9.30' PCD 6 ' K1MAX GLASS COLUMN S.S. VIRE MESH 6 ' S.S. PIPE LIQUID DISENGAGEMENT PORT £5' NPT 6 ' QVF CLASS COLUMN 6 HOLES FOR .375* BOLTS 60° APART . 10' PCS S.S. VIRE MESH 50* NPT Figure 4.4: Driers Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 76 4.1.3 Gas Analysis System To ensure proper operation of the H2S and S02 analysers, gas samples had to be condi-tioned prior to analysis. Separation of sulphur particulates was accomplished in a sulphur condenser which contained CaCl2 and glass wool. To obtain dry samples, two driers con-taining CaCl2 and glass wool were installed downstream of the sulphur condenser. The first drier was equipped with a water cooling coil. Further conditioning was accomplished by a fine filter which removed particulates larger than 0.3 pm in diameter. A diaphragm pump (Air Codet, model 7530-40, supplied by Cole-Parmer Instrument Co., Chicago, 111.) which had a maximum capacity of 14.75 L/min at 1 atm, was used as the sampling pump. A sample (flow rate of 4.8 L/min) was introduced to two on-line gas analysers. The latter instruments were a Pulsed Fluorescence SO2 Analyser (model 40, made by Thermo Electron Corp., Hopkinton, Mass.) and a Photoionization H2S analyser (model PI 201, made by HNU Systems Inc., Newton, Mass.). These gas analysers were calibrated as described in section 5.2.2. Signals from these instruments and the thermocouples were fed into an analog digital convertor (model ADC-1 , supplied by Remote Measurement Systems Inc., Seattle, Wa.) which was capable of scanning 16 channels and contained a built-in temperature compensator in the reference junction. A Commodore computer (model C64, supplied by Commodore Business Machines, Inc., West Chester, Pa.) was used to record and/or display the data on a monitor (A BASIC programme for data logging is included in Appendix D). 4.1.4 Safety Devices Being aware of the extreme toxicity of H2S and S02 (see Tables 1.1 and 1.2), strict precautions were exercised to ensure the safe operation of the equipment. A l l joints and fittings were tested by applying soap solution to make sure that they were leak-proof. Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 77 To ensure the safe operation of the equipment further, an enclosure was built around the entire equipment including the gas cylinders. A fan capable of creating a small vacuum (approximately 30 mm H20) was also provided. The exhaust from this fan was connected to the building ventilation system. A pressure switch was installed on the control panel. In case of vacuum loss due to fan failure or other reasons, the pressure switch shuts-down the entire equipment including the solenoid valves on the H2S/N2 and S02/N2 cylinders. A complete equipment shut-down was accomplished by switching off the main power supply to the equipment (see Figure 4.5). The H2S concentration in the suction line between the fan and the enclosure was frequently checked with the H2S analyser. When the concentration exceeded approximately 10 ppm, an alarm, which is a built-in feature of the H2S analyser, would sound. A gas mask with H2S absorbing canister (model 457069, made by Mine Safety Appliances Co. of Canada Ltd., Downsview, Ont.) was provided in case the operator had to work in an atmosphere containing high levels of H2S. The allowable H2S hmit for 8-hour exposure is 10 ppm (Archibald, 1977). 4.2 MATERIALS USED The catalyst used in this study was activated alumina designated commercially as Kaiser S-501. It was supplied by Kaiser Aluminum and Chemical Corporation, Baton Rouge, Louisiana. The catalyst contains mostly aluminum oxide promoted with some lithium oxide (see Table 4.2). It is available as small spheres with a size range -3 +6 mesh. To use the S-501 in the fluidized bed, it was ground and sieved to -42 +150 mesh. The mean particle diameter for the particle size distribution shown in Table 4.3 was calculated from the relation recommended by Kunii and Levenspiel (1969): dp = i / £ W < u (4-i) LI L2 L3 N DISCONNECTING MAGNETIC SW. START cjj STOPerf AIR PRESSURE I . s w , r - - z J E CONT.I RJ_ 4 TO ENCLOSURE FROM FAN Z<H 208 30 A MAIN CONT. 2 VARIAC 15 A 0-I20V CONT. 3 R2 CONT. 4 LI L2 L3 N ^ l A J ^ ^ I5A^ 8A|_<gJ 4A| IA£ BLOWER SCRUBBER SIGHT GLASS LIGHT 60 W VARIAC 15 A 0-120 V f lOOOwl 1*408 w l 1 1000 W 120 V. 120 V 120 V 8.7 A 4A 8.7A 816 W 120 V 7 A 400 W 120V 4 A TOP HEATER EXHAUST LINE BOTTOM HEATER PREHEATER Figure 4.5: Electric circuit of the equipment Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 79 where W{ denotes the weight fraction of material in size interval i and dPi denotes the arithmetic mean diameter in interval i. The gases used were mixtures of 10% H2S in 90% N2 and 5% SO2 in 95% N2 by volume. These mixtures were supplied by Canadian Liquid Air Ltd., Vancouver, B .C . The gases were diluted to the desired concentration with pure N2. Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 80 Table 4.1: Physical properties of Kaiser S-501 catalyst. Average particle diameter (dp) 195 fim Particle density (pp) 1843 kg/m3 Particle bulk density 795 kg/m3 True density (Bonsu, 1981) 3160 kg/m3 Table 4.2: Chemical properties of S-501 catalyst on a dry basis. Al203 and inorganic promoters 93.5 Loss on ignition 6.0 Na20 0.45 Fe203 0.02 Si02 0.02 Chapter 4. EXPERIMENTAL APPARATUS AND MATERIALS 81 Table 4.3: Particle size distribution of catalyst used in this study. Diameter range (pm) (pm) Weight fraction Wi 125 - 149 137 0.094 149 - 177 163 0.354 177 - 210 194 0.156 210 - 250 230 0.115 250 - 295 273 0.187 295 - 354 325 0.094 Chapter 5 EXPERIMENTAL PROCEDURE 5.1 REACTION PROCEDURE The Claus reaction was carried out in the fluidized bed and the supporting equipment described in section 4.1. Because H2S and S02 are toxic compounds and due to the fact that 02 may cause catalyst sulphation, it was necessary to avoid any possible leaks. This requirement was accomplished by ensuring that all joints were leakproofed. It was also essential to remove all oxygen from the system prior to each run to avoid catalyst deactivation. Catalyst fouling was a consequence of sulphur deposition on the catalyst within the temperature range shown in Table 5.1; hence it was important to regenerate the catalyst to keep its activity at high levels. To ensure proper operation and achieve accurate and meaningful results, the following procedures similar to those described by Bonsu (1981) were adopted for this work. 5.1.1 Equipment Start-up To meet safety standards and to ensure the smooth operation of the equipment, the following steps were followed: 1. Remove the fluorocarbon panel in the front of the reactor. 2. Dismount the freeboard section. 3. Introduce the required weight of catalyst to give the desired static bed height. 82 Chapter 5. EXPERIMENTAL PROCEDURE 83 4. Check the gasket and remount the freeboard section. 5. Test for leaks by pressurizing the reactor and associated equipment with nitrogen from the N2 cylinder. The pressure in the reactor was maintained at about 10 psig for about 12 hours. Should a drop in pressure occur, leaks where located by applying soap solution to the flanges and joints. 6. Replace the fluorocarbon panel and seal all the edges of the enclosure with 100 mm wide, duct tape. 7. Create a vacuum of about 200 mm Hg by switching on the sampling pump. Main-tain the pressure in the reactor at about 560 mm Hg absolute for about 30 min. 8. Introduce nitrogen into the system until the pressure in the reactor returns to atmospheric levels. 9. Switch on the bellows booster pump to fluidize the bed. 10. Purge about 10% of the total gas flow rate through the reactor for about 24 hours with the sampling pump to ensure that virtually all oxygen is removed from the system (see Appendix E). 11. Switch on the caustic solution circulation pump, gas analysers, C64 Commodore computer and heaters for the sight glass, preheaters, reactor, and reactor-scrubber line. 12. Circulate cold water through the cooling coils in the caustic reservoir. 13. Monitor all thermocouples by watching the displayed readings on the T V screen until the desired steady state temperatures are reached (this procedure usually requires about 1 hour). Chapter 5. EXPERIMENTAL PROCEDURE 84 14. Eliminate the last traces of oxygen and regenerate the catalyst by admitting a small stream of H2S (20 mL/min) into the reactor for about 30 min. 5.1.2 Reaction Process Since it had been decided to perform all experiments at atmospheric pressure, two flow rates were adjusted to achieve a reactor pressure of 1 atm at the desired superficial gas velocity. To ensure proper performance of the gas analysers, their electronic zeros were always checked according to the instruction manuals. Using a sample of known composition from the feed to the reactor, the calibration curves for the analysers were also validated at the beginning of each run. If significant differences were detected, a new calibration curve was generated as described in section 5.2.2. The SO2 analyser performed exceptionally well. The performance of the H2S analyser was excellent provided that the optical windows of this analyser were cleaned with acetone every 8 working hours. It was important to maintain the H2S and SO2 concentrations in the feed at a ratio of 2/1. This ratio had been proved to give maximum sulphur conversions (Bennett and Meisen, 1973). To achieve this ratio, the following procedure was adopted: 1. Choose the flow rate of N2 to give the desired superficial velocity (see Appendix 2. Select the desired concentrations of H2S and SO2 and calculate the corresponding flow rates of H2S and S02 according to the equations: c) . QH2S + Qso2 + QN2 = YH2SQH2S X 10 6/P(H2S)/ (5.1) YH2SQ H2S /Yso2Q so2 = 2 (5.2) p(so2)f = 0.5P(H2S)/ (5.3) Chapter 5. EXPERIMENTAL PROCEDURE 85 where YJI2S and Yso2 denote the volume fractions of H2S and SO2 in the cylinders containing a mixture of H2S/iV2 and S02/N2, respectively. QH2SI QSO2 and QN2 denote the flow rates to the reactor of mixtures of H2S in JV2, SO 2 N2 and pure N2, respectively. P(H2s)f denotes the selected H2S feed concentration in parts per million and P(so2)f denotes the concentration of SO 2 in the feed. 3. Turn on the switch to open the solenoid valves on the H2S/N2 and SO2/N2 cylin-ders. 4. Open the H2S/N2 and S02/N2 cylinders and set the line pressures to 15 psig using the valves on the regulators. 5. Adjust the flow rates (calculated in step 2) using the rotameters located upstream of the reactor. 6. Withdraw a sample of the feed gas to the reactor and use it to check the calibration curves of the gas analysers. 7. Monitor the concentrations of H2S and 1502 in the feed sample as they are being displayed on the T V screen and compare with the desired ones. If the differences are within ±10 ppm, set the H2S and S02 flow rates precisely. K the difference exceeds ±10 ppm, validate the calibration curves. 8. Record the feed concentrations and the thermocouple readings for about 10 min using the Commodore computer. 9. Analyze a sample from the reactor outlet and monitor the readings on the T V screen. 10. Check the the concentrations of SO2 and H2S in the recycled nitrogen stream. Chapter 5. EXPERIMENTAL PROCEDURE 86 11. When steady state readings are established, record the H2S and S02 reactor outlet concentrations and the temperatures for about 10 min. 12. Record the flow rates of the H2S/N2, S02/N2 and N2 streams. 5.1.3 Catalyst Regeneration When sulphur condenses on the catalyst, several types of deactivation may arise (Pearson, 1973). Among these mechanisms are the accumulation of sulphur in the pores of the catalyst and also the formation of sulphates. To keep the catalyst activity at high levels, it was essential to vapourize the sulphur. Although it is unlikely that sulphation took place under the temperature conditions shown in Table 5.1, appropriate catalyst regeneration eliminates sulphates. Pearson (1977) and Grancher (1978) recommended a regeneration temperature of 300°(7 in the presence of H2S to restore catalyst activity. Their technique was used in this work: 1. At the end of step 12 of section 5.1.2 and before equipment shut-down, close the S02/N2 gas cylinder. 2. Switch off the solenoid valves on the S02/N2 cylinder. 3. Close the regulating valves located downstream of the H2S and S02 rotameters. 4. Switch off the caustic pump. 5. Set the temperature controllers to 300°C. 6. Circulate only nitrogen through the reactor for about 4 hours. 7. Admit a small rate of H2S (20 mL/min) into the nitrogen stream entering the reactor. Chapter 5. EXPERIMENTAL PROCEDURE 87 8. Allow the equipment to run under this condition for about 4 hours to regenerate the catalyst. The catalyst sulphur content was tested by heating a sample of the regenerated catalyst at 400°C for 24 hours; the results indicated that no traces of sulphur were present 5.1.4 Equipment Shut-down The main problem likely to occur during equipment shut-down is the sudden loss of pressure in the reactor when the booster pump is switched off. The loss in pressure might cause air to leak into the the reactor and, if there are any sulphur compounds present, sulphation of the catalyst could occur. To avoid this problem, the following procedure was adopted: 1. Close the H2S/N2 cylinder. 2. Switch off the solenoid valve on the H2S/N2 cylinder. 3. Close the regulating valve located down-stream of the H2S rotameter. 4. Switch off the heaters 5. Turn off the cold water for the cooling coils in the caustic reservoir. 6. Turn on the cold water for the cooling coils around the reactor. 7. Circulate only nitrogen until the reactor temperature drops to about 80° C. 8. Increase the A^2 flow rate into the reactor to raise its pressure to about 7 psig. 9. Switch off the booster pump 10. Close the N2 cylinder. Chapter 5. EXPERIMENTAL PROCEDURE 88 11. In preparation for the next series of runs, clean the sampling system and refill the condenser and driers with CaCl2 and glass wool. Also, inspect the filter cartridge in the sampler and replace it if severely contaminated. Discharge the deliquescent solution formed at the bottom of the K O H drier and check if there is any sulphur condensed at the exit of the reactor-scrubber line. Finally, clean the optical windows of the H2S analyser. 5.1.5 Scrubber Clean-up The scrubber temperature was kept at about 10 - 15°C during all experiments by circu-lating cold water through the cooling coils inside the NaOH tank. After a few catalyst regeneration cycles, a yellow sulphur layer appeared at the top of the scrubber. The formation of salts such as Na2S, NaHS, Na2S03 and NaHSOz also took place at the scrubber top. Hence, even though the NaOH solution might not be totally spent, it was necessary to clean the scrubber before blockage occurred. After several runs, the colour of the aqueous sodium hydroxide solution changed to dark red due to the partial solubility of sulphur in the NaOH solution. During washing of the scrubber with water, the solution became diluted and its colour changed to dark green and then to a light green. In addition to the substances listed above, there were also iron, aluminum and silicon compounds in the scrubber due to the elutriation of very small quantities of the catalyst from the reactor. To ensure adequate clean-up of the scrubber the following procedure was adopted: 1. Check to make sure the discharge valve at the bottom of the caustic reservoir is connected, through a pump, to the waste disposal tank. 2. Open the discharge valve and switch on the discharge pump. Chapter 5. EXPERIMENTAL PROCEDURE 89 3. After emptying the tank, close the discharge valve and fill the reservoir with water. 4. Circulate the water through the scrubber for about 30 min. 5. Repeat steps 2 to 4 about four times. 6. Open the top of the scrubber and remove the packing at the top of the column and clean it with a brush to get rid of the condensed sulphur. 7. Clean the inside walls of the top of the column as well as the covering plate to remove condensed sulphur. 8. Replace the top plate of the scrubber and wash the tower again three times using steps 2 to 4. At this stage the solution is very dilute and can be discharged directly into the drain. 5.2 CALIBRATION OF INSTRUMENTS 5.2.1 Calibration Of Rotameters Accurate calibration of the rotameters was essential since the flow rates of the various gases influence the analyser calibrations and the estimation of the various hydrodynamic parameters in the reactor. It was recognized that the rotameters had to be calibrated (depending on the range of the flow rates) with several standard flowmeters such as a soap bubble meter, electronic mass meter and wet-test meter. The accuracy and ranges of these standard meters has been described by Nelson (1971) and Cosidine (1974). The soap bubble flow meter was used to measure flow rates ranging from 10 to 1000 mL/min. This flowmeter uses the simple principle of determining the time required for the displacement of a soap bubble between two Chapter 5. EXPERIMENTAL PROCEDURE 90 marks on a tube of a known volume. At low flow rates the soap bubbles move slowly and the time measured with an electronic timer (activated by two photocells) is very accurate. The electronic mass flowmeter (Model 8160, made by Matheson Co., East Ruther-ford, N.J.) consisted essentially of an electrically heated tube and an arrangement of thermocouples to measure the differential cooling caused by the passing gas through the tube. This flowmeter was used to measure intermediate flow rates ranging from 500 to 2000 mL/min. For the measurement of flow rates between 1 L/min and 100 L/min, a wet-test flowmeter (Model TS-63111, supplied by Precision Scientific, Chicago, 111.) was used. The flow rates at standard state for a given float position in the rotameter were calculated from the equation recommended by Cosidine (1974): Q.. = —= \-p—p- ( 5 - 4 ) where P, T and Q denote the pressure, temperature and volumetric flow rate, respectively. The subscripts r , sm and ss refer to conditions inside the rotameter, standard flowmeter and the standard state, respectively. For safety reasons, air was used to calibrate the rotameters. The actual flow rates of N2, H2S and SO2 were calculated from the equation recommended by Callahan (1974): Qi = Qss/y/Qi (5.5) where Qi denotes the volumetric flow rate of gas i at standard conditions and Qi denotes its specific gravity with respect to air. The computer programme for Chapter 5. EXPERIMENTAL PROCEDURE 91 calculating the flow rates together with calibration tables are presented in Appendix C. Typical rotameter calibration curves are shown in Figures 5.1 to 5.3. ' i I i I • ^ Q P 0 , 0 100 200 300 400 500 Flow rate, Q (mL/min) co Figure 5.2 Ca l ibrat ion curve for H 2S/N 2 rotameter M Chapter 5. EXPERIMENTAL PROCEDURE 95 5.2.2 Calibration Of Analytical Instruments The flow rates obtained in the previous section were used to generate, as shown in Figure 5.4, samples of a gas mixture consisting of N2/H2S, N2/SO2 and N2/ H2S/S02. The concentration of H2S and SO2 in these samples are calculated from the rela-tions: where £ <2i = QH2S + QSo2 + QN2-YH2S and Yso2 denote the volume fractions of H2S in H2S/N2 cylinder and SO2 in SO2/N2 cylinder, respectively. The samples were passed through a Photoionization and Pulsed Fluorescent anal-yser to measure the responses of these instruments, in m.V, due to the presence of the H2S and SO2, respectively. The readings from these instruments were recorded as a function of the sample composition. The Photoionization instrument was built to handle samples with H2S concentra-tions between 1 and 1500 ppm. The Pulsed Fluorescent monitor was designed to measure SO 2 concentrations between 1 and 5000 ppm. It has been observed, however, that the signal from the S02 analyser was affected by the presence of the hydrogen sulphide in the sample (Bonsu and Meisen, 1985). The wavelength of the ultraviolet light source for this instrument ranged from 1900 to 2300A 0. This wavelength falls into the absorption band of H2S, i.e 1900 - 2700A0 (Watanabe and Jursa, 1964). Bonsu and Meisen (1985) used the Lambert-Beer law to correct for the quenching action of the H2S, i.e (ppm)H2s = YH2SQH2s x l O 6 / £ Qi (5.6) (Ppm)s02 = Ys02Qso2 x 1 0 7 £ Q ; (5.7) E = E0exp{-K[H2S}) (5.8) 5. EXPERIMENTAL PROCEDURE Id > 24 <E OJ • 00 Q£ Ld 00 >-_ l <r <: u PQ <c X o I < I •! < I < I' I • I • I • I • 1 • 1 <^>  I • I •! • I I I I I • I I I I I 00 Ld h-Ld < r -• Figure 5.4: Flowsheet for calibrating the analytical instruments O.o * ' 1 1 1 1 1 ' 1 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 H 2 S Concentration (ppm) Figure 5.5: Determinat ion of the coeff ic ient, K, due to H 2S • EXPERIMENTAL POINTS REGRESSED LINE 0 200 400 600 800 1000 Instrument Reading E 0 (mV) Figure 5.6: Calibration curve for SOj analyser (selector marked 0 -50 ppm) 0 200 400 600 800 1000 Instrument Reading E 0 (mV) Figure 5.7: Calibration curve for S0 2 analyser (selector marked 0-100 ppm) co • EXPERIMENTAL POINTS REGRESSED LINE 0 200 400 600 800 1000 Instrument Reading E 0 (mV) Figure 5.8: Calibration curve for S0 2 analyser (selector marked 0-500 ppm) 0 200 400 600 800 1000 Instrument Reading E 0 (mV) Figure 5.9: Colibrotion curve for S0 2 analyser (selector marked 0-1000 ppm) Chapter 5. EXPERIMENTAL PROCEDURE 102 where E and E0 denote the instrument signals for samples with and without H2S, respectively and [H2S] denotes the hydrogen sulphide concentration in the sam-ple. The value of the extinction coefficient, K , was obtained from the slope of InEo /E vs. [H2S] plot. As shown in Figure 5.5, the slope of the straight line was 8.35 X 10~ 5/ppm H2S. Hence, by knowing the H2S readings produced by the photoionization monitor and E from the S02 analyser, ED was calculated. The con-centration of SOi in the samples was then obtained from calibration curves shown in Figures. 5.6 to 5.9. The S02 analyser produces fluorescent light of intensity, F, which is related to the S02 concentration by the equation (Thermo Electron Corporation, 1976): F = B1{X - exp(-B2{S02})} (5.9) [S02] denotes the concentration of the sulphur dioxide and B l and B2 are instru-ment constants. The exponential nature of the above expression causes a small curvature in the calibration curve, especially at high S02 concentrations, as indi-cated in Figures 5.8 and 5.9. At low S02 concentrations, the calibration curve is almost linear (see Figures 5.6 and 5.7) because equation 5.9 can be approximated by: F S B[S02] (5.10) The H2S analyser is based on the photoionization principle. For a compound to be detected, its ionization potential must be less than or equal to the energy of the photons emitted by the ultraviolet light source in the instrument. The energy of the light source of this instrument, i.e 10.2 eV, is lower than the ionization potentials of sulphur dioxide and nitrogen (i.e SO2~12.063 eV and JV2=15.76 e V ) . Hence, there was no interference from any of these gases. The ionization potential of H2S is 10.4 0 1000 2000 3000 4000 Instrument Reading (mV) Figure 5.12: Calibration curve for H 2S (selector #100x, range 0-1500 ppm) Chapter 5. EXPERIMENTAL PROCEDURE 106 eV (Watanabe and Jursa, 1964). The calibration curves for H2S are presented in Figures 5.10 to 5.12 Bonsu (1981) performed rigorous tests of the conditioning system using dry samples containing H2S, S02 and N2. He found no change in the sample concentration upon passage through the conditioning system. To explore the effect of moisture on the instrument readings, he passed dry samples over wet CaCl2 and detected a slight decrease in concentration equivalent to an increase in conversion of 0.5 percentage points. This variation falls within the experimental error (see Section 6.3). However, throughout the present experimental runs, great care was exercised to ensure that the surface of the CaCl2 was dry at all times. Chapter 5. EXPERIMENTAL PROCEDURE 107 Table 5.1: Operating conditions of present experimental equipment Operating Variable Range H2 S feed concentration (ppm) 400 - 1300 SO 2 feed concentration (ppm) 200 - 650 Temperature (°C) 100 - 150 U/Umf at reactor conditions 2.24 - 8.88 Static bed height (m) 0.12 - 0.38 Chapter 6 RESULTS AND DISCUSSION 6.1 EXPERIMENTAL RESULTS 6.1.1 Minimum Fluidization Velocity The minimum fluidization velocity for the catalyst particles was determined from measurements of pressure drop against flow rate of air at ambient conditions (see Figure 6.1). The estimated Umj, based on this plot, is 0.0272 m/s. This result agrees well with value of 0.0266 m/s obtained from equation 2.11. The value of Umf was then corrected to the reactor conditions and was found to be 0.0246 and 0.0225 m/s at 100 and 150°C, respectively. 6.1.2 Sulphur Conversions The experimental conversion was calculated from material balances on nitrogen and sulphur. Assuming a constant flow rate of N2 through the reactor, the following expression was derived: Uout 1 - Vi Vout (6.1) The conversion of H2S and SO2 into elemental sulphur was found to increase (see Figure 6.2) with the reactant concentrations in the feed gas. This result is in general agreement with the previous findings of Bonsu and Meisen (1985). Theoretically, 108 8 Co a co o ^ 10 s < CO Q CO S3 O U„,= 2.72 cm/s. 0.3 S U P E R F I C I A L G A S V E L O C I T Y , U ( c m / s ) 1 0 Figure 6.1: Pressure drop versus oir velocity for a bed of a l u m i n a (Ka i ser S-501) at STP o CD Chapter 6. RESULTS AND DISCUSSION 110 the maximum conversion is dictated by thermodynamic equilibrium. For the tem-peratures used in this study (100 to 150°C), the Bonsu and Meisen model predicts this maximum to be in excess of 99%. As indicated by Figure 6.2 and columns 2 to 4 of Table 6.1, the experimental conversion for feed compositions of 0 to 1300 ppm H2S is generally lower than 97%. For instance at 150°C (see column 4 of Table 6.1), the sulphur conversion rose from 75.7 to 97.7% as the H2S feed concentration increased from 200 to 1300 ppm. The dependency of reaction rate on the reactant concentration is very well known to be first order with respect to H2S and half or-der with respect to S02 (McGregor et al., 1972; Dalla Lana et al., 1976; Grancher, 1978). For low concentrations of H2S and S02 in the feed, the concentrations of the reactants in the reactor are also small, and the lower the concentrations of these components, the greater the reduction in reaction rate. Consequently, a decline in conversion is plausible. The drastic fall in experimental conversion with decreasing H2S and SO2 feed concentrations suggests the likelihood of kinetic limitations on the Claus reaction. These limitations, which are significant as the feed concen-trations approach zero, may be noticed by the sharp decrease in the experimental conversion accompanying the decrease in feed concentration from 800 to 200 ppm. Above 800 ppm, the fall in conversion was very gradual suggesting a lower degree of kinetic hmitation at higher H2S feed concentrations. Closely associated with the effect of the feed concentration on conversion is the role of reaction temperature. Thermodynamic principles suggest that, for the present exothermic reaction, the conversions should rise as the reaction temperature is lowered. Experimental results indicate the opposite trend. Figure 6.3 shows an increase in conversion with increasing temperature. As indicated by Table 6.2, sulphur conversions at H2S feed concentration increased from 79.4 to 82.0% when 100 o Ul > o 90 80 70 60 -50 0 i u T ' C U / U m f H(m) 100 4.06 0.19 150 4.44 0.19 150 8.88 0.32 EXP. MODEL O A + 200 400 600 800 1000 FEED H 2S CONC. (ppm) 1200 1400 CO s Co CO O CO O Figure 6.2: Sulphur conversion as a function of H 2 S concentration in feed Chapter 6. RESULTS AND DISCUSSION Table 6.1: Sulphur conversion as a function of H2S in feed gas H2S in Experimental Predicted %dev feed (ppm) conversion (%) conversion (%) a b c a b c a b c 200 - 70.1 75.3 59.4 68.0 73.4 - -2.99 -2.52 300 64.3 75.2 79.7 67.4 75.5 81.3 +4.82 +0.39 +2.01 400 71.9 81.1 81.0 72.8 80.2 85.8 +1.25 -1.11 +5.93 500 75.6 79.9 86.9 76.6 83.5 88.7 +1.32 +4.51 +2.07 600 79.4 82.9 89.0 79.6 85.9 90.7 +0.25 +3.62 +1.91 700 - 87.2 92.1 81.9 87.7 92.2 - +0.57 +0.11 800 86,3 90.6 93.9 83.7 89.1 93.3 -3.01 -1.66 -0.64 850 86.4 - - 84.6 89.7 93.7 -2.08 - -900 - 93.1 85.3 90.3 94.1 - - +1.07 950 86.7 - - 86.0 90.8 94.5 -0.81 - - . 1000 90.2 91.9 95.6 86.6 91.2 94.8 -3.99 -5.77 -0.84 1100 88.9 - - 87.7 92.0 95.4 -1.35 - -1200 91.9 93.8 96.9 88.6 92.7 95.8 -3.59 -1.17 -1.14 1300 89.4 92.8 97.7 89.4 93.3 96.2 0.0 +0.54 -1.54 a: T = 100°C; U/Umf = AAA, H. = 0.19m; RMS%E=2.55 b: T = 150°C; U/Umf = AAA; H. = 0.19m; RMS%E=2.S6 c: T = 150°C; U/Umf = 8.88; H, = 0.32m; RMS%E=2.Z2 Chapter 6. RESULTS AND DISCUSSION 113 the temperature increased from 100 to 150 °C. A similar increase in conversion (for H2S— 1300 ppm) occurred for the same increase in temperature (i.e. 100 to 150°C). This observation was already reported by Bonsu and Meisen for reactor temperatures below 200°C7. They found conversions at 150°C to be generally lower than those obtained at 200°C. It is conceivable that the reaction rate is adversely affected by the combination of low temperature and reactant concentrations. An additional important variable which effects the performance of the fluidized bed reactor is the gas flow rate. This fact is illustrated in Figure 6.4 where a drop in conversion with increasing U/Umf is evident (see also Table 6.3). Bonsu and Meisen found that the performance of their fluidized bed Claus reactor suffered only slightly from the by-passing of gas in the form of bubbles. The simulation of Birkholz et al. (1987) showed that the performance of such reactors is 4.7% less than that of fixed bed reactors. It therefore seems that the effect of gas by-passing is more severe in the case of low reactant concentrations. The measured conversions of H2S and SO 2 were found to drop gradually as the catalyst sulphur content increased thereby indicating a fall in catalyst activity due to fouling. Figure 6.5 shows the experimental conversion as a function of the sulphur loading, A, defined as the weight of sulphur per unit weight of catalyst. There was no change in colour of the catalyst up to a sulphur loading of approximately 50%. At this value, the conversion had fallen to 55% suggesting that deposition of sulphur had deactivated the catalyst significantly. Beyond sulphur loadings of approximately 50%, a yellow film started to appear on the surface of the catalyst (see Figure 6.6) and the particles agglomerated. It was intended to extend the experiments to higher sulphur loadings to explore whether the fall in conversion continued. However, at 60% sulphur loadings, where the conversion had declined to Chapter 6. RESULTS AND DISCUSSION 114 Table 6.2: Conversion as a function of temperature (U/Umf—AAA, Hs= 0.19m) Temperature °c Experimental conversion (%) Predicted conversion (%) %dev I II I II I II 100 79.4 89.7 79.6 89.4 +0.25 -0.33 110 - 90.7 - - - -0.44 120 81.2 • - - - +0.86 -124 - - 82.3 91.5 - -130 81.4 92.6 - - +1.81 -0.65 150 82.9 92.7 84.4 93.3 +1.81 +0.65 I : H2S feed concentration = 600 ppm ; RMS%E=\.Z7 II: H2S feed concentration= 1300 ppm ; RMS%E=0.5A F—' < ) ) E q u i l i b r i u m H 2 S 6 0 0 p p m H 2 S 1300 p p m E x p e r i m e n t a l O A Bubb l ing m o d e l • • o 90 100 140 150 110 120 130 TEMPERATURE (°C) Figure 6.3: Effect of temperature on conversion (U/Umf=4.44, Hs=0.19 m) 100 o to M W > 2 8 8 0 I" I I I X I •8 S3 CO O o 70 H 2 S Feed Cone. 600ppm EXPERIMENTAL POINTS O MODEL PREDICTIONS 1300ppm 2 3 4 u/u m f (-) Figure 6.4: Effect of U/U m f on conversion (H s : 0.19 m, T: 150°C) 6 er 6. RESULTS AND DISCUSSION Table 6.3: Conversion as a function of U/UmJ (T = 150°C, H,= 0.19m) U/UmJ Experimental conversion (%) Predicted conversion (%) %dev I II I II I II 2.2 96.9 91.9 97.2 93.9 +0.31 +2.18 3.1 96.1 85.9 95.6 90.6 -0.52 +5.47 3.7 93.1 83.6 94.3 87.0 +1.29 +4.07 4.4 92.7 82.9 93.3 86.0 +0.65 +3.74 5.1 91.5 - 92.4 83.8 +0.98 - ' 5.9 - 79.4 91.1 81.6 - +2.77 I : H2S feed concentration=1300 ppm; RMS%E=0.83 II: H2S feed concentration 600 ppm; RMS%E=3.82 Chapter 6. RESULTS AND DISCUSSION 118 38%, fluidizing the catalyst became extremely difficult due to particle agglomeration and stickiness. In addition, uniform temperatures could not be maintained as a result of the poor quality of fluidization. No attempt was made to investigate fouling at temperatures above the sulphur melting point (~ 120° C) where the stickiness would be even more serious. Experimental conversions are shown as functions of time in Figure 6.7 and Table 6.4. For the first few days, the fall in conversion was rather minor. During this period, the rate of sulphur deposition from the dilute gas is very small and the fresh catalyst has a large active surface available for reaction. As time progressed, the sulphur loading increased as indicated by Figure 6.8 resulting in a reduction of active surface; a gradual decrease in conversion followed. To investigate the effect of bed height on conversion, experiments were carried out at several static bed heights. Figure 6.9 demonstrates a substantial increase in conversion as the static bed height increased from 0.19 to 0.32m; only slight improvements in the reactor performance were obtained above this height (see Table 6.5). At the elevated reactor temperatures and feed concentrations examined by Bonsu and Meisen (1985), the effect of static bed height on conversion was hardly noticeable. This suggests an optimum bed height generally exists for each set of conditions. Chapter 6. RESULTS AND DISCUSSION 119 Table 6.4: Conversion as a function of time and sulphur loading (T = 100°C, H2S= lOOOppm, H s=0.32m) Time 00 S. loading (%) Conversion (%) Time 00 S. loading (%) Conversion (%) Exp. Model Exp. Model 2.0 0.01 93.5 95.4 117.0 14.21 79.7 79.6 4.0 0.13 93.5 95.3 125.0 15.13 78.7 78.5 6.0 0.36 93.8 95.1 135.0 16.27 77.4 77.2 9.0 0.53 93.8 95.0 140.8 16.93 76.0 75.2 12.0 0.55 93.9 95.0 151.0 17.90 74.8 75.1 15.0 0.59 93.0 94.9 162.0 18.76 73.8 74.2 18.0 0.72 92.9 94.9 170.0 22.79 73.1 69.6 21.0 0.73 92.9 94.8 178.0 24.99 72.3 67.2 24.0 0.84 92.8 94.7 186.0 25.24 68.9 66.9 27.0 0.89 92.8 94.7 196.0 27.06 68.3 65.1 32.0 1.26 91.6 94.4 207.0 25.22 64.0 66.9 37.0 1.49 92.1 94.1 219.0 29.08 63.4 63.1 42.3 1.52 92.1 94.1 231.0 27.08 61.2 65.1 48.3 1.84 92.4 93.9 243.0 31.97 59.1 60.5 55.0 2.59 90.9 93.1 255.0 37.71 58.1 55.3 60.0 3.51 91.4 92.4 265.0 42.35 57.3 51.9 68.0 4.14 91.7 91.5 277.0 44.44 56.3 50.4 72.0 4.16 90.3 91.5 288.5 45.13 54.2 49.9 80.0 7.05 88.4 88.3 301.0 47.17 52.2 48.6 86.0 6.95 88.0 88.3 313.0 50.81 47.2 46.4 95.0 9.15 81.3 85.8 335.0 54.92 43.0 43.9 99.3 12.02 81.7 82.1 347.0 60.05 39.0 41.3 109.0 13.05 78.8 81.1 Q . U) > a * o-100 80 60 40 20 0 0 v . . Experimental data Model with * =1/(1+0.08X) 20 40 60 SULPHUR LOADING (w/w %) 80 100 Fig. 6.5: Effect of sulphur condensation on conversion (H 2S=1000ppm, T=100*C, U/Um f=4.44, H t = 0.32m) £0 CO 3 ft o to o Chapter 6. RESULTS AND DISCUSSION 121 Figure 6.6: External colour of catalyst as a function of sulphur loading Chapter 6. RESULTS AND DISCUSSION 122 o o o 00 o CD o © Cv? (%) N O l g S B V N O O Chapter 6. RESULTS AND DISCUSSION 123 (% V M ) ONiavoi a i i H d i n s Chapter 6. RESULTS AND DISCUSSION 124 Table 6.5: Conversion at several static bed heights (T = 100°C; U/Umf = 4.44; H2S= 600ppm; S02 = 300 ppm) Height (m) Experimental conversion (%) Predicted conversion (%) 0.12 62.9 63.9 0.19 79.7 79.6 0.25 86.9 87.9 0.32 92.2 92.2 0.38 95.2 94.8 100 80 o . I—I W i > £ . 40 O o 20 -Experimental data Model prediction I CO CO CO a o 0.0 Figure 0.1 0.2 0.3 STATIC BED HEIGHT (m) 0.4 6.9: Effect of static bed height on conversion (H 2S=600ppm, U/Um (=4.44, T=100* C) 0.5 to a t Chapter 6. RESULTS AND DISCUSSION 126 6.1.3 Catalyst At t r i t ion Large spheres of alumina catalyst (Kaiser S-501) were ground and sieved to the desired particle size range. A representative sample (Wo= 0.508 kg) of the sieved catalyst was then loaded into the reactor. The sample contained no particles smaller than 125 pm. An air flow rate of 3.98 m 3 / h (STP) was maintained through the reactor for 1/2 h. The air flow rate corresponded to U/Umf =5.2. Fluidization of the particles was carried out at room temperature and atmospheric pressure. Following the test period the catalyst was recovered, as completely as possible, from the reactor. The collected sample was sieved in a series of screens for 1/2 h. An electronic balance was used to weigh the contents of each screen. The weight of particles smaller than 125 /zm was also determined. There was about 0.02% loss of fines. To investigate the effect of fluidization for longer time, particles with dp < 125pm were discarded and the remaining catalyst mass was returned to the reactor. The catalyst was again fluidized with air for increasing time intervals. The process was repeated up to a total time of 303h. The cumulative mass of particles smaller than 125 pm plus the loss of fines was considered to be the amount of catalyst formed by attrition. The loss of fines occurred only during the first 1/2 h. This loss is probably due to the presence of dust in the newly ground catalyst. The extent of attrition was defined as the mass of particles with dp < 125 fim divided by the total original mass, i.e: Wt A = wn <6-2> The maximum rate of attrition occurred in the first few hours (see Figures 6.11 and 6.12). These figures show that A increased from 0 to 2 % in about 5 hours. During this period, the fresh ground particles had irregular shapes with sharp edges and Chapter 6. RESULTS AND DISCUSSION 127 protruding corners. Such particles may easily undergo attrition due to the colliding and rubbing actions. As time passed, the particles became more rounded and developed smooth surfaces. Rounded particles have high attrition resistance and therefore the extent of attrition levels off. As indicated by Figure 6.11, the extent of attrition reached a constant value of about 2.6% within a short period of time. The constant value of A suggests that the total attrition of the Kaiser S-501 catalyst was quite small. The attrition tendency of this catalyst is also reflected in the sample mean particle diameter (see Figure 6.13). Using equation 4.1, The calculated dp decreased from 199.68 to an almost constant value of 196.20 fim in about 2 hours. 6.2 MODEL PREDICTIONS Conversions predicted by the two phase bubbling model are plotted in Figures 6.2 to 6.5 and in Figure 6.14. Model predictions as a function of H2S feed concentration are presented in columns 5 to 7 of Table 6.1. These predictions may be compared with the experimental values which are included in columns 2 to 4 of the table. For instance, at 100°C as the feed concentration increased from 300 to 1300 ppm both experimental and model conversions increased from 64.3 and 67.4 to 89.4 and 89.4%, respectively. Similarly good agreement between experimental and model conversions can be seen for the second and third sets in Table 6.1 (i.e columns 3 and 4 vs 6 and 7). The three sets of experimental data in this table indicate that a slight deviation from experimental conversions occurs at very low H2S feed concentration. To quantify this deviation, the following definitions may be used: %dev -Pre — Exp x 100 (6.3) Exp 100 150 200 250 300 350 400 PARTICLE SIZE INTERVAL, Ad (/xm) Figure 6.10: Particle size distribution OO Chapter 6. RESULTS AND DISCUSSION (%) N O U I H U V \ 4 0 1 N 3 1 X 3 (%) N 0 I 1 I H 1 I V 4 0 Chapter 6. RESULTS AND DISCUSSION 131 CD CO CO c\? CO C O 00 cv CD o Cv} CD i—( Cv} Cv} OS CD CD o Cv} CD Cv} CO Cv} o o Cv} CO o oo 05 05 CD 05 0) E D TJ C D <D E o o CL c o c o o o <D •4— UJ to* l-(UITY) dp Chapter 6. RESULTS AND DISCUSSION 132 RMS%B = (6.4) where Pre denotes the predicted conversion and Exp denotes the corresponding experimental conversion. N denotes the number of points, %dev denotes the relative deviation and RMS%E denotes the root mean square % error. An RMS%E value of 0 means excellent agreement between model predictions and experimental values whereas RMS%E=100 corresponds to extremely poor predictions. The %dev and RMS% errors are included in Table 6.1 for the three sets of data. Values of RMS%E of less than 3% suggest very good agreement between experimental and predicted conversions. The three sets of data are also plotted in Figure 6.2 which shows good agreement between model predictions and experimental results. In particular, the model clearly follows the sharp fall in conversion in the vicinity of H2S feed concentration of 800 ppm. Model predictions as a function of U/Umf are compared with experimental data in Figure 6.4. The experimental conversions are somewhat less than those predicted by the model at low values of feed concentrations. The RMS%E value of 3.82 for 600 ppm H2S in the feed is slightly higher than that (i.e. RMS%E=0.BZ) for 1300 ppm H2S, but the overall trends are the same and the agreement between model predictions and experimental data is quite reasonable. A better agreement may be noticed for the two sets of data shown in Table 6.2 and plotted in Figure 6.3 where both experimental and predicted conversions increased with increasing temperature. The RMS% errors for these two sets of data are lower than 1.4%. Typical equilibrium conversions are generally higher than 96% (see Figure 6.3 and Table 3.7). It is obvious that predictions by the two phase bubbling model are far superior to predictions based on equilibrium assumptions. To predict the performance of the reactor under fouling conditions, a deactivation Chapter 6. RESULTS AND DISCUSSION 133 function was introduced into the rate equation. A deactivation function with hy-perbolic dependency on the sulphur content was found to lead to the best model predictions. The theoretical justification for such a function was presented in sec-tion 3.5 (i.e. equation 3.92). Values of Ks in equation 3.92 were adjusted to give the model predictions shown in Figure 6.5. A value of if,,=0.08 was found adequate for predicting the sulphur conversions shown in Figure 6.5 and Table 6.4. Hence equation 3.92 may be rewritten as: * = (6.5) 1 + 0.08A v ' The form of this deactivation function suggests that deposition of sulphur on the catalyst has a retarding effect on the Claus reaction. Unfortunately, the experi-ments had to be terminated sooner than desired due to the difficulties mentioned earlier and equation 6.5 could not be tested for catalyst sulphur loading higher than 60%. A final evaluation of model predictions is shown in Figure 6.14. In this graph, conversions predicted by the present bubbling bed model are plotted against the corresponding experimental conversions. The 45° line represents the perfect match between predicted and experimentally determined conversions. Although some of the points deviate, their scatter is close to the 45° line and the agreement is quite reasonable. 6.3 Applicability of the two phase model The two phase model provides a relationship between the reactor conversion, feed concentration, gas velocity and bed height. A knowldege of any three of these Figure 6.14: Model Prediction vs Experimentol conversion Chapter 6. RESULTS AND DISCUSSION 135 quantities permits the fourth to be calculated, provided the physco-chemical char-acteristics of all phases and the reaction rates are specified. For scale-up purposes, this model can be applied to solve two primary problems, i.e: (a) To determine the size of reactor needed to achieve a specific conversion under specified operating conditions. (b) To calculate, for a given reactor, either the conversion for a specified flow rate and feed concentration or the quantity of gas that can be processed to achieve a given conversion. Since the number of variables which enter scale-up calculations is large, it is not possible to present several design charts. The following procedure shows how the two phase model may be applied for the design of industrial units and how to predict the consequences of changes in variables. 6.3.1 Use of Two Phase Model in Reactor Design: (a) For a given gas flow rate, Q, the superficial gas velocity is selected such that Umf < U < Ut, where Ut denotes the terminal velocity of the smallest catalyst particles which should be retained in the bed. Ut can be determined from equations available in the literature (see Kunii and Levenspiel, 1969). Other criteria are needed to avoid gas channeling and catalyst slugging. These cri-teria are presented in section (e) below. (b) The diameter of the cylindrical reactor is calculated from: D2 = AQ/irU. (c) Using the two phase model (Equations 3.22, 3.42, 3.44 and 3.45), Figure 6.15 can be obtained. The calculation is staightforward and a computer programme with input variables Ht, U, Umf, dp, etc. is presented in Appendix B. Chapter 6. RESULTS AND DISCUSSION 136 Figure 6.15 and Table 6.6 show that the conversion decreases with increasing bed diameter. This trend to is due the increased bubble diameter in large beds and hence increased gas by-passing. The Mori and Wen (1975) equation is used in this work to predict the bubble diameter. It should be noted that this equation is based on more than 400 experimental points and that it should only be applied for D < 1.3m, 60 < dp < 450/im, 0.005 < Umf <0.2 m/s and U -Um}< 0.48m/s. (d) Once the conversion versus bed diameter plots are available, the static and expanded bed heights required to achieve the desired conversion can be looked up. (e) The final choice of U, D and H should satisfy the following criteria: (z) U should not exceed the minimum slugging velocity defined as: Umt = Umf + 0.07 Jg~D. (ii) The aspect ratio H/D should not exceed 3.5 to avoid slugging. 6.3.2 Choice of particle size The choice of catalyst particle size affects not only the reactor conversion but also catalyst entrainment. The effect of particle size on conversion may be deduced by examining the relationship between Umf and dp and the two phase theory. Equa-tion 2.11 shows that increasing the mean particle diameter raises the minimum fluidization velocity which, in turn, increases the gas flow from the dilute into the dense phase. Since the dense phase gas is in intimate contact with the catalyst particles, it follows that increasing the particle size should also increases reactor conversion. However; increasing dp reduces the bed expansion (see Section 2.2.5), a O-> © 100 98 96 94 92 i i !'" 1 ' 1 Hs=0.8m, H=1.05m 1 1 f r " -- Hs=0.6m, H=0.80m -Hs=0.5m, H=0.67m -i , i i , i i 0 0.2 1.2 0.4 0.6 0.8 1 Bed diameter (m) Figure 6.15: Model p red ic t i ons for large reactors (U=0.25m, d p=195p.m, 1 = 100' C , H 2 S = 6 0 0 p p m , catalyst: s -501 1.4 9 •8 P3 ft CO CJ § CO Q S o co Chapter 6. RESULTS AND DISCUSSION 138 lowers the gas residence time and thus causes a fall in conversion. Section 2.2.5 and Equation 2.8 show that the particle size affects the interrelated hydrodynamic parameters in a complex manner. The primary advantage of using large particle size is that their terminal velocity is high and the likelihood of particle entrainment is reduced as the terminal velocity is increased. The loss of valuable catalyst is minimized and the cost of gas cleaning equipment to reduce pollution is reduced. However, large particles suffer from the disadvantage that the diffusional resistance encountered by the reacting species in the pores of the catalyst particles is increased which, in turn, lowers the conversion. However, calculations presented in Section 3.5, indicate that diffusion resistance was negligible in this work. Since the present two phase model yielded results which agreed well with experimen-tal measurements, the model may be used to explore the effect of changing particle size. The results should be reliable, even though corresponding experiments were not performed except for dp = 195pm. The model predictions for various particle sizes are presented in Figure 6.16 and Table 6.7. It is clear that in all cases (a to f) that the predicted conversion improves with decreasing particle diameter. The improvement is attributed to the increased residence time which results from the expanded bed height, i.e. H/U rises as shown by Figure 6.17. Curves d, e and f i n Figure 6.16 show increases in conversion for dp > 320pm. These increases occur be-cause Umf increases with increasing particle size and ultimately Uj Umf approaches unity and the bed approaches fixed bed conditions. Hence conversions are high even though H/U is low. On the other hand; for dp < 160pm, the increase in the predicted conversion with deacreasing particle diameter is very gradual despite the increasing H/U. Umf decreases substantially with decreasing dp for particles Chapter 6. RESULTS AND DISCUSSION 139 less than about 160^m in diameter. This results in dramatic increases in U/Umf as shown by Figure 6.18 and consequently, the effect of increasing H/U is counter balanced by the effect of increasing U/Umf. Chapter' 6. RESULTS AND DISCUSSION 140 < VI < E \ E E — o m o CM CN d d d II II II - ZD ZD ZD E E" o o M II n Q o o E" E" E" m in m d d d II n II M - X X X D o / / ' // ' // ' // "/ ' // l» II II II II II II II II II u < <> £ £ 0 0 o o d d d II It II => _ £ £ £ *-d d d II II II Q o O _ £ £ £ m to in 1 d d d II II It M M X X X "D o -tf o o -tf o CM X CO _ CO s o o o u cv CD *« CO T3 O £ d « vt o CO o XL CO • 1—1 Q-cv O JS OJ V 1—1 .c o CJ • (—1 >-n -tf cv • co PH TJ 1_ o Q. o cv o c OJ N «l « o l_ CD o OL o "o • o cv • o CO o o o o 00 o (%) U O I S J 9 A U 0 3 80 120 160 200 ' 240 280 320 360 400 440 Mean particle diameter (/urn) Figure 6.17: Predicted residence t ime of gas as a function of mean part icle diameter Mean particle diameter (Lim) Figure 6.18: Predicted U /U m f as a function of mean particle diameter Chapter 6. RESULTS AND DISCUSSION Table 6.6: Model predictions as a function of bed dimensions U = 0.25m, r = 100°C7, H2S = 600ppm Q (m3/h) 108 180 252 360 468 576 720 864 1008 1188 D (m) 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30. H. H X (m) (m) (%) 0.1 0.15 33.1 32.7 32.5 32.3 32.1 31.9 31.7 31.5 31.4 31.4 0.2 0.28 62.6 62.1 61.3 60.8 60.3 60.0 59.5 59.1 58.8 58.6 0.3 0.42 81.0 80.5 79.9 79.4 78.8 78.4 78.0 77.6 77.2 76.9 0.4 0.55 90.1 89.7 89.3 89.0 88.6 88.3 88.0 87.8 87.4 87.3 0.5 0.67 94.4 94.2 94.0 93.8 93.6 93.4 93.2 93.0 92.8 92.6 0.6 0.80 96.6 96.5 96.4 96.2 96.1 96.0 95.9 95.7 95.6 95.5 0.7 0.92 97.8 97.7 97.6 97.6 97.5 97.4 97.3 97.3 97.2 97.1 0.8 1.05 98.4 98.4 98.4 98.4 98.3 98.3 98.2 98.1 98.1 98.1 0.9 1.17 98.9 98.9 98.9 98.8 98.8 98.8 98.7 98.7 98.7 98.6 D: bed diameter, H„: static bed height, H: expanded bed height, Q: gas flow rate, superficial velocity, x: conversion. Chapter 6. RESULTS AND DISCUSSION 144 Table 6.7: Effect of particle diameter on conversion as predicted by the two phase model dp (pm) Conversion (%) (a) (b) (c) (d) (e) (f) 100. 88.48 85.53 82.82 98.46 98.40 98.44 110. 88.23 85.22 82.53 98.36 98.28 98.33 120. 87.99 84.86 82.05 98.23 98.15 98.18 130. 87.77 84.56 81.64 98.09 98.00 98.03 140. 87.47 84.11 81.17 97.96 97.83 97.86 150. 87.15 83.73 80.79 97.79 97.64 97.65 160. 86.92 83.40 80.22 97.63 97.44 97.43 170. 86.63 83.05 79.77 97.43 97.22 97.18 180. 86.31 82.60 79.29 97.23 96.97 96.91 190. 86.12 82.27 78.80 97.01 96.70 96.63 200. 85.78 81.89 78.29 96.79 96.43 96.32 210. 85.59 81.52 77.77 96.56 96.13 95.98 220. 85.31 81.16 77.36 96.28 95.80 95.60 230. 85.07 80.74 76.96 96.04 95.48 95.22 240. 84.89 80.36 76.49 95.75 95.13 94.80 250. 84.63 80.11 76.06 95.45 94.76 94.35 260. 84.47 79.77 75.56 95.16 94.36 93.90 270. 84.43 79.53 75.16 94.86 93.98 93.90 280. 84.39 79.23 74.88 94.59 93.57 93.43 290. 84.45 79.03 74.45 94.27 93.15 92.96 300. 84.58 78.75 74.10 93.94 92.71 92.42 310. 84.64 78.64 73.86 93.65 92.30 91.90 320. 85.21 78.53 73.50 93.36 91.89 91.35 330. 85.89 78.67 73.28 93.07 91.46 90.84 340. 87.07 78.58 73.10 92.73 91.03 90.30 350. 90.86 78.90 72.88 92.45 90.59 89.76 360. 79.08 72.78 92.20 90.15 89.20 370. 79.87 72.87 91.87 89.79 88.70 380. 81.47 72.86 91.62 89.35 88.12 390. 84.50 73.38 91.38 88.92 87.62 400. 73.62 91.10 88.59 87.07 410. 74.20 90.83 88.18 86.52 420. 75.73 90.69 87.79 86.03 (a): U = OMm/s, Ht = 0.25m, D = 0.1m. (b): U = O.lOm/s, H. = 0.25m, D = 0.1m. (c): U = 0.12m/«, E, = 0.25m, D = 0.1m. (d): U = 0.20ro/«, Hs = 0.75m, D = 1.0m. (e): U = 0.25m/s, H. = 0.75m, D = 1.0m. (f): U = 0.30m/.s, H, = 0.75m, D = 1.0m. Chapter 6. RESULTS AND DISCUSSION 145 6.4 E R R O R A N A L Y S I S The experimental sulphur conversion, x> w a s calculated from the readings of the analytical instruments according to equation 6.1. For every run, a set of instru-ment readings was recorded as explained in section 6.1.2. These measurements may contain instrument errors which could lead to some error in the experimental conversion. This error can be estimated from the following relation: i = 4 8-v A * = E(e£)«;A!fc (6-6) where yx, y2 denote the volume fraction of H2S and SO2 in the reactor effluent stream and y3, y 4 denote the corresponding fractions in the feed. The partial derivatives in equation 6.6 can be obtained by differentiating equation 6.1 i.e: dy\ dy2 (y 3 + j/4)(l - Vi - V2)2 dx_ _ 9x 3/i +V2  dy3 <9y4 (1 - y a - y2)(y3 A y 4 ) 2 Assuming Ax/j = — Si, Ay 2 = —S2, Ay3 - +Si and Aj/4 = +S2 leads to the estimation of the maximum error in conversion. Dividing equation 6.6 by equation 6.1 and substituting for Ay^'s gives an expression for the relative error denoted by S (i.e S = Ax/%): 5 = [(yi + V2) + (a/3 + y 4)] - [(yi + V2? + (ys +1/4)2] ( s . s s ( 6 7 ) ( y s + y 4 ) [ i - ( i n + »>)][(»»+ » 4 ) - ( y i + y * ) ] { } { ' } Values for Si and S2 are chosen as the reliability of the instruments reported by the manufacturers. The manual for the S02 analyser states that the instrument reading is reliable to within ±0.5 ppm. The H2S analyser was designed to detect concen-tration ranges between 1 to 1500 ppm with a sensitivity of 3 ppm. Hence £ 1 and S2 can be assumed as (volume fraction units) 3 x l 0 - 6 and 0 . 5 x l O - 6 , respectively. Chapter 6. RESULTS AND DISCUSSION 146 The relative error estimated from equation 6.7 is presented in Table 6.8 as a function of feed concentration. The relative error for the runs at 100°C ranged from ±0.23 to ±1.63%. Although the error values are small, Table 6.8 shows that the smaller the feed concentration, the larger the relative error. This trend may be expected since small fluctuations in instrument responses to dilute samples were noticed. The fluctuations in the H2S and SO2 outlet concentrations were within ± 4 ppm (see Figure 6.19). The fluctuations in the total outlet concentrations (i.e. outlet concentration of H2S + SO2) were within ± 2 ppm. The fluctuation in conversion ranged from ±0.44% (for feed containing 300 ppm H2S and 150 ppm SO2) to ± 0 . 1 % (for feed containing 1300 ppm H2S and 650 ppm S02). Minimization of these fluctuations were achieved by rigorously calibrating each instrument with gas samples of various degrees of dilution (see Section 5.2.2). Bonsu (1981) used these instruments to measure concentrations from samples rich in H2S and 502- He reported an error ranging from ±0.5 to ±1.0%. Hence a conservative value of the error in this work can be taken as ±1.6% (see Table 6.8). The reliability of the results may be tested statistically. As shown in Appendix A , runs for H2S feed concentrations of 600 and 1300 ppm were duplicated at three temperatures (i.e. 100, 130 and 150°C) and were examined by the t and F tests. The t-test at 95% level showed that confidence limits of ±1.61 may be assigned to the conversion. This value agrees with the error estimated from equation 6.5. Analysis of the variance for these runs are also presented in Appendix A . The F-test showed, for an increase in the H2S feed concentration (e.g. from 600 to 1300 ppm, see column 1 of Table A.2) that there is more than a 999 in 1000 chance that the associated increase in conversion (e.g. at 100°C, see column 2 of Table A.2) from 79.4 to 89.4 is possible. For the increase in temperature from 100 to 150°C (row 1 of Table A.2), this test showed there is only a 1 in 100 chance that the increase in conversion (e.g. at 1300 Chapter 6. RESULTS AND DISCUSSION 147 ppm H2S from 89.4 to 93.1, see row 4 of Table A.2) may be explained on the basis of scatter in data. 6.5 PRACTICAL IMPLICATIONS OF FLUIDIZED BED CLAUS RE-ACTORS Based on the model predictions and experimental findings, it is evident that ther-modynamic conversion efficiencies were not achieved in the present fluidized bed reactor. Furthermore, sulphur condensation led to a substantial decline in reac-tor performance. Operational problems were encountered when catalyst sulphur loadings exceeded about 50%. Because experimental tests were performed in batch mode, regeneration of the catalyst in this study was carried out in situ. Heating the bed at 300°C in the presence of H2S allowed keeping the catalyst activity at high levels. Samples of the regenerated catalyst were further tested for sulphur content in an oven at 400°C. The test results indicated no traces of sulphur. In an industrial unit, the catalyst must be regenerated continuously to keep high levels of conversion and to prevent defluidization. Circulation of the catalyst between the reactor and a regenerating unit was tested by Bonsu (1981) who reported the smooth operation of the small scale apparatus. A . A A — " — 7 J ~ ~ * — — z s — t r -RUN 43.1: HjS OUTLET CONCENTRATION o ^ o °. o o o RUN 13.1: HjS OUTLET CONCENTRATION A A A A A A. A A A A A A RUN 43.1: S 0 2 OUTLET CONCENTRATION RUN 72.0: H 2 S OUTLET CONCENTRATION H 1 1 + 1 1 ^r—**" 1 ^ 1 1 1 + + + O U Q. u 0 Q n O " RUN 13.1: S 0 2 OUTLET CONCENTRATION + + 1 »• + + + •+ + 1 i (•—I • + ± — — RUN 72.0: S 0 2 OUTLET CONCENTRATION 1 1 0 12 14 2 4 6 8 10 TIME (MIN) Figure 6.19: Concentrations of hydrogen sulphide and sulphur dioxide in the effluent gas as a function of time Chapter 6. RESULTS AND DISCUSSION 149 Table 6.8: Relative error as a function of H2S concentration in the feed T = 100°C, u/un f = 4.44, H, =0.19m 2/i (PPm) 300 400 500 600 800 1000 1100 1300 x(%) 64.3 71.9 75.6 79.4 86.3 90.2 88.9 89.7 S(%) 1.63 1.06 0.79 0.61 0.40 0.28 0.27 0.23 Chapter 7 CONCLUSIONS AND RECOMMENDATIONS 7.1 CONCLUSIONS The conversion of hydrogen sulphide and sulphur dioxide into elemental sulphur has been studied in a bubbling fluidized bed reactor. This study has shown that equi-librium conversions could not be achieved within the ranges of the concentration, temperatures and bed heights investigated. The performance of the equipment and associated safety devices was very good. From the experimental and analytical results presented in chapter 6, the following specific conclusions may be drawn: (a) At the low temperatures and feed concentrations studied in this work, the sul-phur conversions are appreciably lower than the thermodynamic conversions on account of kinetic limitations. (b) Sulphur conversions in fluidized beds are reduced by decreasing the feed con-centration and temperature and increasing the superficial gas velocity. (c) Conversions are substantially improved with bed height. However, there exist bed heights beyond which only a slight increase in conversion is possible. (d) Sulphur condensation occurs inside the pores of the catalyst. This conden-sation causes catalyst deactivation which leads to significant reductions in conversion. The activity of the catalyst can be restored by vapourizing the 150 Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 151 condensed sulphur. Heating the fluidized bed to 300°C in the presence of H2S was a successful method to return the activity of the catalyst to high levels. (e) Appreciable amounts of condensed sulphur result in the agglomeration of the catalyst particles. Defluidization of the bed may be avoided by continuous catalyst regeneration. (f) The performance of the fluidized bed Claus reactor under kinetically limiting conditions can be predicted using a two phase bubbling model. (g) Catalyst attrition is negligibly small thereby indicating the suitability of the Kaiser S-501 alumina for fluidized bed operation. 7.2 RECOMMENDATIONS (a) Runs should be undertaken to investigate the effect of moisture in the feed on the performance of fluidized bed Claus reactors. Results from such runs would simulate industrial Claus plants where water vapour formed in the furnace off-gas enters the catalytic stages. (b) Additional runs are recommended to obtain data using continuous catalyst circulation through the reactor. Results from such studies would be useful in the design of industrial units. (c) Ghosh and tollefson (1985) studied the direct oxidation of dilute H2S bearing gas streams over activated carbon. They found that conversion decreased due to catalyst fouling. Exploratory studies should therefore be conducted using a continuously operating fluidized bed. If successful, such an arrangement could be of importance for sulphur recovery from gas streams with very low H2S concentration. Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 152 (d) Pilot plant studies should be carried on fluidized bed Claus reactors to obtain data useful in the scale-up and design of full-scale industrial reactors. The pilot plant should have a diameter larger than 1 m and the effects of feed gas compositon, high gas flow rate and particle size should be studied. Nomenclature A Reactor cross sectional area, m?. A Extent of attrition, kg/kg%. Aj Arrhenius pre-exponential factor. ab Bubble interfacial area, m 2 / m 3 . a p Particle interfacial area, m 2 / m 3 . Ai to A-j Constants defined by equations 3.24 to 3.28 and 3.38 to 3.39. ax constant defined by equation 3.65, (kmole/kcal). a2 constant defined by equation 3.65. B, Bl, Bl instrument constants CAb H2S dilute phase concentration, kmol/m3. CAd H2S dense phase concentration, kmol/m3. CAb.o H2S dilute phase concentration at z = 0, kmol/m3. CA<I,O H2S dense phase concentration at z = 0, kmol/m3. CH2S H2S concentration, kmole/m3. Cli7s,g H2S bulk concentration, kmole/m3. CH2S,O H2S concentration in feed gas, kmole/m3. CmS.s Surface concentration of active sites fouled by m. layers of sulphur, # of active sites fouled/kgcat. Ct Surface concentration of active sites, # of active sites/kgcat. 153 Nomenclature Cv Surface concentration of active sites completly free of sulph # of active sites/kgcat. Co Dimensionless feed concentration. C\ Dimensionless concentration of H2S in dilute phase. C2 Dimensionless concentration of H2S in dense phase. C2to Dimensionless initial dense phase concentration. D Bed diameter, m. Da0 Damkohler number. db Bubble diameter, m. dbm Maximum bubble diameter, m. dbo Initial bubble diameter, m. De Effective diffusivity, m2/s. Dg Diffusivity, m2/s. Dr, Axial dispersion coefficient, m2/s. dp Particle diameter, m. dr,. Particle diameter in size interval i , m. DT Radial dispersion coefficient, m2/s. E Activation energy, kcal/mole. E" Desorption energy, heal/mole, F Instrument flourescence. / Total molar flow rate, kmole/s. FH2S,O Molar flow rate of H2S into reactor, kmole/s. / j Molar flow rate of SO2 into reactor, kmole/s. f2 Molar flow rate of N2 into reactor, kmole/s. g Gravitational constant, m/s2. Nomenclature 155 H Expanded bed height, m. Hmf Bed height at minimum fluidization, m. H, Static bed height, m. K Instrument Extenection coefficient. Ke Equilibrium constant, ( a im) - 1 . Ks Catalyst to sulphur ratio, kgcat/kgS. kg Mass transfer coefficient in packed bed, m/s. km Rate constant governing catalyst fouling, s'1 kq Interphase mass transfer coefficient, m/s/m2. kv Reaction rate constant per unit volume of catalyst, (kmol / m3)~0S/s/m3cat. kw Reaction rate constant per unit mass of catalyst, (kmol/m3)~05/s/kgcat. n Order of reaction. M Number of sulphur layers on active sites. m Layer index. Pei Peclet number based on axial dispersion. Per Peclet number based on radial dispersion. PH2O H20 partial pressure, mm Hg. PH2S H2S partial pressure, mm Hg. P(H2s)f Concentration of H2S, ppm. Pso2 S02 partial pressure, mm Hg. P„ Pressure inside rotameter, psia. Pss Standard state pressure, psia R Gas constant, kcal./kmol/K. RmS.s Rate of formation of active sites fouled by m layers of sulphur, # of active sites fouled/kgcat. Nomenclature 156 r Ratio of surface concentrations. n Bubble radius, m Cloud radius, m rH2S Disappearance rate of hydrogen sulphide, (kmol/m3)/s/kgcat. q Bubble through flow, m3/s. Qb Volumetric flow rate of dilute phase gas, (m3/s). QN2 N2 flow rate, mL/min. QH2S flow rate of mixture H2S/N2, mL/min. Qi Volumetric flow rate of gas i, m3/min. Qso2 flow rate of SO2/N2 mixture, mL/min. Q.T Volumetric flow rate inside rotameter, mL/min. Q.s Volumetric flow rate at standard state, mL/min. T Temperature, K. Tr Temperature inside rotameter, K. T„ Temperature at standard state, K. U Superficial gas velocity, m/s. Bubble velocity, m/s. ue Interstitial superficial gas velocity in dense phase, m/s. Superficial gas velocity at minimum fluidization, m/s. vb Volume of bubble, m3. vw Volume of bubble wake, m3. X Variable defined by equation 3.16. x0 Value of x at reactor inlet. value of x at reactor outlet. YH2S Volume fraction of H2S in the H2S/N2 cylinder. Nomenclature 157 Yso2 Volume fraction of S02 in the S02/N2 cylinder. yin Volume fraction of H2S + S02 in feed stream, yout Volume fraction of H2S 4- S02 in effluent gas. z Height from distributor, m. Greek letters a Dimensionless interphase transfer coefficient. a Ratio of bubble velocity to minimum fluidizatoin velocity. Pi, 02 Modified dimensionless rate constants (defined by Eq's 3.12 and 3.13). 1 Constant, 7 = (P2/fii)*. AG Free energy difference, kcal/kmol. AS Entropy difference, kcal/kmol/K . 6 Relative error in experimental conversion Si, t>2 Errors in the readings of the H2S and SO2 analysers, respectively, (vol.%) Bed volume fraction occupied by dilute phase, m 3/m 3. C m / Voidage at minimum fluidization, m 3/m 3. c Tortuosity factor. V External effectiveness factor e Angle in spherical coordinates. 6 Particle fractional porosity. X Catalyst sulphur content, kgS/kgcat%. Nomenclature 158 Ac Mass of sulphur monolayer per active site, kgS'/active site. A Function defined by equations 3.30 and 3.31. A r Real part of A. A, Imaginary part of A. Pg Gas viscosity, Ns/m2. V Extent of reaction, kmole/s. i Dimensionless height . Pg Gas density, kg/m3. PP Particle density, kg/m3. Qi Specific density of gas i relative to air density. $ Thiele modulus. <t> Fraction of sites fouled by sulphur. <t>b Volume of solids in dilute phase per unit volume of bed, m3/m3 <t>d Solids volume fraction associated with dense phase, m3/m3. X Sulphur conversion. Sphericity. Fouling function. Mass fraction of catalyst with diameter dp{. References Archibald, R.G. , (1977),"Process Sour Gas Safety", Hydro. Proc, 56(3), p.219. Aris, R., (1957), " On Shape factors for Irregular Particles-I The Steady State Problem: Diffusion and Reaction", Chem. Eng. Sci., 6, p.262. Ashmore, P.G., (1963), "Catalysis and Inhibition of Chemical Reactions", But-terworths, London. Bennett, A. and Meisen, A. , (1973), "Hydrogen Sulphide-Air Equilibria Under Claus Furnace Conditions", Can. J. Chem. Eng., 51, p.720. Bennett, H.A. and Meisen, A. , (1981),"Experimental Determination of Air-ily.? Equilibria Under Claus Furnace Conditions", Can. J. Chem. Eng., 59, p.532. Birkholz, R.K.O. , Behie, L .A. , Dalla Lana, I.G., (1987),"Kinetic Modelling of a Fluidized Bed Claus Plant", Can. J. Chem. Eng., 65, p.778. Bischoff, K . B . , (1967), "An Extension of the General Criterion for Importance of Pore Diffusion with Chemical Reactions", Chem. Eng. Sci., 22, p.525. Bischoff, K . B . and 0 . , Levenspiel, (1962), "Fluid Dispersion- Generalization and Comparision of Mathematical Models", Chem. Eng. Sci., 17, p.245 Bonsu, A . K . , (1981), "Fluidized Bed Claus Reactor Studies", Ph.D Thesis, Univ. Of British Columbia, Vancouver, B .C . Bonsu, A . K . and Meisen, A. , (1985),"Fluidized Bed Claus Reactor Studies ", Chem. Eng. Sci., 40, p.27. 159 References 160 Box, G.E.P, Hunter, W . G , Hunter, S.S, (1978), "Statistics for Experimenters: An Introduction to Design, Data, and Model Building", John Wiley &; Sons, New York, p633. Bragg, J.R., (1976), "A Computer Model of the Modified Claus Sulfur Recov-ery Process", AIChE Symp. Series,, 72(156), p.48. Broadhurst, T.E. and Becker, H A . , (1976), "Onset of Fluidization and Slug-ging in Beds of Uniform Particles", AIChE J, 21, p.238. Bywater, R.J. , (1978), "Fluidized Bed Catalytic Reactor According to a Stat-stical Fluid Mechanic Model", AIChE Symp. Series, 74( 1 7 6)> P 1 2 6 -Calderbank, P.H., Pereira, J . , Burgess, J.M^, (1975), " The Physical and Mass Transfer Properties of Bubbles in Fluidized Beds of Electrically Conducting Particles", in Fluidization Technology Vol.1, ed. Keairns, D., Hemisphere Publ. Corp., Washington D . O , p.111. Callahan, F.J.,Jr., (1974), Swadgelok Tube Fitting and Installation Manual, Markad Service Co., Cleveland, Ohio. Cameron, L .C. , (1974), "Aquitain Improves Sulfreen Process for More H2S Recovery", Oil and Gas J., 72, p.H0(June 24). Carberry, J.J., (1976), "Chemical and Catalytic Reaction Engineering", Chap-ter 5, p.194, McGraw-Hill book Co., New York, N . Y . Chavarie, C. and Grace, J.R., (1975), "Performance Analysis of a Fluidized Bed Reactor", Ind. Eng. Chem. Fundam., 14, p.75. Chavarie, C. and Grace, J.R., (1976), "Interphase Mass Transfer in a Gas-Fluidized Bed", Chem. Eng. Sci., 31, p.741. References 161 Chiba, T. and Kobayashi, H. , (1970), "Gas Exchange Between the Bubble and Emulsion Phases in Gas-Solid Fluidized Beds", Chem. Eng. Sci., 25, p.1375. Clift, R. and Grace, J.R., (1970), "Bubble Interaction in Fluidized Beds", Chem. Eng. Prog. Symp. Series, 66(105), p.14. Clift, R. and Grace, J.R., (1972), "Coalescence of Bubbles in Fluidized Beds", Trans. Inst. Chem. Engrs, 50, p.364. Constable, F .H. , (1925), "The Mechanism of Catalytic Decomposition", Proc, Royal Soc. A, 108, p355. Cosidine, D . M . , (1974), " Process Instruments and Controls Handbook", McGraw-Hill Book Co., New York. Cremer, E. , (1955), "The Compensation Effect in Heterogeneous Catalysis", Advances in Catalysis, 7, Ed. Frankenburg, W . G , V.I., Komarewsky and E .K. , Rideal, p.75, Acad. Press Inc., New York, N .Y. Dalla Lana, I.G., (1978), "Catalysis Research on the Modified Claus process", Energy Proc. Canada, 70, p.34. Dalla Lana, I.G., Liu, C L . and Cho, B .K. , (1976), "The Development of a Kinetic Model for Rational Design of Catalytic Reactors in Modified Claus Process", Proc. 6th Euro./^th Int. Symp. Chem. Reaction £n£.,DECHEMA, p.V196. Darton, R . C , (1979), "A Bubble Growth Theory of Fluidized Bed Reactors", AIChE Symp. Series, 74(176), p.126. Darton, R.C., Lanauze, R.D, Davidson, J.F., Harrison, D., (1977),"Bubble Growth Due to Coalescence in Fluidised Beds ", Trans. Inst. Chem. Engrs., 55, p274. References 162 Davidson, J.F and Harrison, D., (1963), "Fluidised Particles", Cambridge Univ. Press, Cambridge. Drinkenburg, A . A . H . and Rietema, K. , (1972), "Gas Transfer from Bubbles in a Fluidized Bed to the Dense Phase", Chem. Eng. Sci., 21, p.1765, also, 28, p.259(1973) Eley, D.D., (1967), "Energy Gap and Pre-Exponential Factor in Dark Con-duction by Organic Semiconductors", / . Polym. Sci., 7, p.73. Fairclough, R.A. and Hinshelwood, C.N. , (1937), "The Functional Relation Between the Constants of the Arrhenius Equation", J. Chem. Soc, p. 538, also p.573. Fan, L.T. , Fan, L.S., Miyanami, K . , (1977), "Reactant Dynamics of Catalytic Fluidized Bed Reactors Characterized by a Transient Axial Dispersion Model With Varying Physical Quantities", Proc. Pachec Conference, p.1379. Fisher, R.A. , (1947), " Statistical Methods for Research Workers", Hafher Pupl., Co., New York. Forsythe, W.L . and Hertwig, W.R., (1949), " Attrition Characteristics of Fluid Cracking Catalysts: Laboratory Studies", Ind. & Eng. Chem., 1(6), p.1200. Froment, G.F. and Bischoff, K . B . , (1961), "Non-Steady State Behaviour of Fixed Reactors Due to Catalyst Fouling", Chem. Eng. Sci., 16, p.189. Froment, G.F. and Bischoff, K . B . , (1979), "Chemical Reactor Analysis and Design", Wily, New York. Fryer, C. and Potter O.E, (1972), "Counter Current Back Mixing Model for Fluidized Bed Catalytic Reactors; Applicability of Simplified Solutions", Ind. Eng. Chem. Fundam., 11, p.338. References 163 Galwey, A . K . , (1977), "Compensation Effect in Heterogeneous Catalysis", dvances in Catalysis, 26, Ed. Eley, D.D., Pines, H. and P.B., Weisz., Acad. Press, N Y , p.247. Gamson, B.W. and Elkins, R.H. , (1953), "Sulfur from Hydrogen Sulfide", Chem. Eng. Prog., 49, p.203. George, Z.M. , (1974), "Kinetics of Cobalt-Molybdate Catalyzed Reaction of SO2 with H2S and COS and the Hydrolysis of COS", J. Cat., 32, p.261. George, Z .M. , (1975). "Effect of Basicity of the Catalyst on Claus Reaction", in Sulphur Removal and Recovery from Industrial Process, Adv. Chem. Series, 139. Ed. Pfeirffer, J.B., Amer. Chem. Soc, Washington, D.C., p.75. Ghosh, T .K, (1985), "Catalytic Oxidation of Low Concentrations of Hydrogen Sulphide", Energy Proc. Canada 77, p.16. Goar, B.G. , (1977), "Chemical Reactors as a Means of Separation: Sulfur Removal, Chapter 5", ed. Crynes, B.L . , Marcell Dekker Inc., New York. Goddin, G.S., Hunt, E.B. , Palm, J.W, (1974), " C B A Process Ups Claus Re-covery", Hydro. Proc, 53(10), p.122. Good, W. and J . Stone, (1972), "Enthalpy-Entropy Relationships in the Fluid Kinetics of Aqueous Electrolyte Solution Containing only Negatively Hydrated Ions", Electrochimica Acta, 17, p.1813. Grace, J.R., (1986), "Fluidized Beds as Chemical Reactors", in Gas Fluidiza-tion Technology, ed. Geldart, D., John Wiley & Sons, New York, Chapter 11. Grace, J.R., (1971), "An Evaluation of Models for Fluidized-Bed Reactors", AIChE Symp. Series, 67(116), p.159. References 164 Grace, J.R, (1981), "Fluidized Bed Reactor Modeling: An Overview", ACS Symp. Series, 168, ed. Fogler, H.S., Wasington D.C., p.3. Grace, J.R., (1982), "Fluidized Bed Hydrodynamics, Chapter 8", Handbook of Multiphase Systems, Ed. Hetsroni, G., Hemisphere Publ. Co., Washington D.C. Grace, J.R., (1984), "Generalized Models for Isothermal Fluidized Bed Re-actors", in Recent Advances in Engineering Analysis of Chemical Reacting Systems, ed. Doraiswamy, L . K , Wiley Eastern, New Delhi. Grace, J.R. and Clift, R-, (1974), "On The Two-Phase Theory in Fluidization", Chem. Eng. Sci., 29, p327. Grancher, P. (1978), "Advances in Claus Technology", Hydroc. Proc, 57(7), p.155. Guenther, W.C. , (1964), " Analysis of Variance", Prentice Hall, Inc, N J , Chap-ter 5, p99. H N U Systems, (1976), "Instruction Manual for PI 201 Photoionization Moni-tor", H N U Systems, Inc., Newton, Mass. Hovmand, S., Freedman, W., Davidson, J .F, (1971), "Chemical Conversion in a Pilot-Scale Fluidized Bed", Trans., Instn. Chem., Engrs., 49, p.149. Horio, M . and Wen, C .Y, (1977), "An Assessment of Fluidized Bed Modeling", AIChE Symp. Series, 73(161), p9. Kato, K . and Wen, C.Y. , (1969), "Bubble Assemblage Model for Fluidized Catalytic Reactors", Chem. Eng. Sci., 24, p.1351. Kelly, K . K . , (1937), "Contribution to the Data on Theoretical Metallurgy: VII Thermodynamic Properties of Sulphur and its Inorganic compounds", U.S. References 165 Bur Mines Bull., 406, p . l . Kellog, H.H. , (1971), "Equilibria in the Systems C-O-S and C-O-S-H as Re-lated to Sulfur Recovery from Sulfur Dioxide", Met. Trans., 2, p.2161. Kerr, R .K. , H.G. Paskall, and M . Ballash, (1976), "Claus Process: Cat-alytic Kinetics Part I-Modified Claus Reaction", Energy Proc./Canada, p.66, (September-October). Kohl, A. , Riesenfeld, F.C., (1985), "Dry Oxidation Process", Chapter 8 in Gas Purification, 4th. Ed., Gulf Pub. Co., Houston. Kono, H. , (1981), "Attrition Rates of Relatively Coarse Solid Particles in Var-ious Types of Fluidized Beds", AIChE Symp. Series, 77(205), p.96. Kunii, D., Yoshida, K. , Hiraki, I., (1967), "The Behaviour of Freely Bubbling Fluidized Beds", Proc. Inter. Symp. on Fluidization, Netherlands Univ. Press., Amesterdam, p243. Kunii, D. and Levenspiel, 0., (1969), " Fluidization Engineering", Wiley, New York. Laundau, M . , Molyneax, A. , Houghton, R., (1968), "Laboratory and Plant Evaluation of Catalysts for Sulphur Recovery from Lean H2S Gas Streams", Inst. Chem. Engrs. Symps. Series, 27, p.228. Lewis, W . K . , Gilliland, E.R., Glass, W., (1959), "Solid Catalysed Reaction in a Fluidized Bed", AIChE J., 5, p.419. Levenspiel, O., (1972), "Chemical Reaction Engineering", John Wiley & Sons, New York, N Y . Maadah, A . G . and Maddox, R.N. , (1978), "Predict Claus Products", Hydro. Proc, 57(8), p.143. References 166 Martin, J .E. and G., Guyot, (1971), "The Sulfreen Process", Paper pre-sented at the Canadian Natural Gas Processors Association meeting, Edmon-ton (June). Masamune, S. and Smith, J .M. , (1966), "Performance of Fouled Catalyst Pel-lets", AIChE J., 12, p.384. May, W.G. , (1959), "Fluidized-Bed Reactor Studies", Chem. Eng. Prog., 55(12), p.49. McBride, B.J . , Hermel, S., Elders, J.G., Gordon, S., (1963), "Thermodynamic Properties to 6000°lf for 210 Substances Involving the First 18 Elements", N A S A SP-3001, Washington, D.C. McGregor, D.E., (1971), "Rate Studies of the Catalytic Reaction of H2S and S02", Ph.D Thesis, University of Alberta, Edmonton, Alberta. Meisen, A. , (1977), "A Novel Fluidized Bed Claus Process", 27th Can. Chem. Eng. Conf., Calgary Alberta, 23-27 October. Meisen, A. and H A . , Bennett, (1979), "Predict Liquid Sulfur Vapor Pressure", Hydro. Proc, 58(12), p.131. Mickley, R.S., Sherwood, T.K. , Reed, C.E. , (1957), "Applied Mathematics in Chemical Engineering", McGraw Hill Book Company, Inc., N . Y . , Chapter 2, p53. Mireur, J.P. and Bischoff, K . B . , (1967), "Mixing and Contacting Models for Fluidized Beds", AIChE J., 13, p.839. Miwa, K. , Mori, S., Kato, T. and Muchi, I., (1972), "Behaviour of Bubbles in Gaseous Fluidized Beds", Int. Chem. Eng., 12, p.1187. References 167 Mori, S. and Wen, C.Y. , (1975), "Estimation of Bubble Diameter in Gaseous Fluidized Beds", AIChE J., 21, p.109. Murray, J.D, (1965), " On the Mathematics of Fluidization", J. Fluid Mech., 21, p.465, also, 22, 57(1966). Murthy, A.R, and Roa, S.B., (1951), " Behavior of Sulfur Compounds-Ill: Kinetics of the Gaseous Reaction Between H2S and S02\ Proc. Ind. Acad. Sci., 24A. p.283. Nelson, G.O., (1971), "Controlled Test Atmospheres: Principles and Tech-niques", Ann Arbor Science Publ. Inc., Ann Arbor, Mich. Orcutt, J.C., Davidson, J.F., Pigford, R .L, (1962), "Reaction Time Distribu-tions in Fluidized Catalytic Reactors", Chem. Eng. Prog. Symp. Series, 58(38), p . l . Pachovsky, R.A., Best, D.A. and Wojciechowski, B.W., (1973), "Application of the Time On-Stream Theory of Catalyst Decay", Ind. Eng. Chem. Proc. Des. Dev., 12, p.254. Partridge, B.A. , Rowe, P.N., (1966) " Chemical Reaction in a Bubbling Gas-Fluidised Bed", Trans. Instn. Chem. Engrs., 44, p.T335. Pearson, M.J . , (1973), "Developments in Claus Catalysts", Hydro. Proc, 52(2), p.81. Pearson, M.J . , (1977), " Alumina Catalysts in Low-Temperature Claus Pro-cess", Ind. Eng. Chem. Prod. Res. Dev., 16, p.154. Pereira, J .A.F, (1977), "The Physical and Mass Transfer Properties of Bubbles in a Fluidised Bed", Ph.D. Thesis, University of Edinburgh. References 168 Pyle, D.L., (1972), "Fluidized Bed Reactors: A Review", Adv. in Chem. Se-ries, 109, Chemical Reaction Engineering, Amer. Chem. Soc, Washington, D . C , p.106. Razzaghi, M . and Dalla Lana, I.G., (1984), "A Model for Predicting Deacti-vation of a Catalytic Claus Reactor by Adsorption of Sulphur", Catalysis on the Energy Scene, Ed., Kahaguine, S. and Maha}', A. , Elsevier Science Publ., Amsterdam, p221. oberts, G.G., (1974), " Activation Energy for Electronic Conduction in Crys-talline Solids", in Transfer and Storage of Energy by Molecules-The Solid State, Chapter 3, Vol. 4, Ed. Burnett, G . M , North, A . M . and J .N. , Sherwood, Wilel & Sons, N Y , p.153. Rowe, P.N. and Partridge, B.A. , (1962), "The Interaction Between Fluids and Particles", Proc. Symp. On Interaction Between Fluids and Particles, Inst. Chem. Engrs., p. 135. Rowe, P.N. and Partridge, B.A. , (1966), " Chemical Reaction in a Bubbling Gas-Fluidised Bed", Trans. Instn. Chem. Engrs., 44, p.T335. Rowe, P.N. and Partridge, B.A. , (1965), "An X-Ray Study of Bubbles in Flu-idised Beds", Trans. Inst. Chem. Engrs. ., 43, p.T157. Rowe, P.N., Partridge, B .A. , Lyall, E . , (1964), "Cloud Formation Around Bubbles in Gas Fluidized Beds", Chem. Eng. Sci., 19, p.973. Sadana, A . and Doraiswamy, L .K. , (1971), "Effect of Catalyst Fouling in Fixed, Moving and Fluidized Bed Reactors", J. Cat, 23, p.147. Satterfield, C N , (1970), "Mass Transfer in Heterogeneous Catalysis", Chapter 1, p . l , M.I.T. press, Cambridge, Mass. References 169 Schwab, G .M. , (1950), "About the Mechanism of Contact Catalysis", Advances in Catalysis, 2, Ed. Frankenburg, W . G , V.I., Komarewsky and E .K. , Rideal, p.251, Acad. Press Inc., New York, N Y . Shen, C Y . and Johnstone, H.F., (1955), " Gas-Solid Contact in Fluidized Beds", AIChE J., 1, p.349. Sherwood, T.K. , R.L., Pigford, and C.R., Wilke, (1975), "Mass Transfer", MacGraw-Hill book Co., New York, N Y . Thomas, J . M . and W.J. , Thomas, (1967), "Introdoction to the Principles of Heterogeneous Catalysts", Chapter 5, p.241, Academic Press, London. Sit, S.P. and Grace, J.R., (1978), "Interphase Mass Transfer in an Aggregative Fluidized Bed", Chem. Eng. Sci., 33, p.115. Sit, S.P and Grace, J.R., (1981), "Effect of Bubble Interaction on Interphase Mass Transfer in Gas Fluidized Beds", Chem. Eng. Sci., 36, p.327. Tayler, H.A. and Wessly W.A. , (1927), "The Gaseous Reaction Between Hy-drogen Sulphide and Sulphur Dioxide", J. Phys. Chem., 31, p.216. Thermo Electron Corportion, (1976), "Instruction Manual for Model HO Pulsed Fluorescent S02 Analyser", TE540-30-76, Thermo Electron Corpo-ration, Hopkintin, Mass. Toei, R. and Matsuno, R., (1967), "The Coalescence of Bubbles in the Gas-Solid Fluidized Bed", Proc. Int. Symp. On Fluidization, Ed. Drinkenburg, A . A . H . , Netherland Univ. Press, Amsterdam, p.271. Toei, R., Matsuno, R., Miyagawa, H. , Nishitani, K. , Komagawa, Y . , (1969), "Gas Transfer Between a Bubble and the Continuous Phase in a Gas-Solid Fluidized Bed", Int. Chem. Eng., 9, p.358. References 170 Toomey, R.D. and Johnstone, H.F., (1952), "Gaseous Fluidization of Solid Particles", Chem. Eng. Prog. 48, P-220. Valenzuela, J.A. and Glicksman, L.R.,(1985), "Gas Flow Distribution in a Bubbling Fluidized Bed", Powder Tech., 44, P103. Van Deemter, J.J., (1961), "Mixing and Contacting in Gas-Solid Fluidized Beds", Chem. Eng. Sci., 13, p.143. Vaux, W.G. and Fellers, A.W., (1981), "Measurement of Attrition Tendency in Fluidization", AIChE Symp. Series, 77(205), p.107. Vaux, W.G. and Keairns, D.L., (1980), " Particle Attrition in Fluidized Bed Processes", in Fluidization, Eds Grace, J.R. and Matsen, J.M., Plenum Press, New York, p.437. Vaux, W.G. and Schruben, J.S., (1983), "Kinetics of Attrition in the Bubbling Zone of a Fluidized Bed", AIChE Symp. Series, 79(222), p.97. Venables, W.N., 1989, "Report on Pollution Control objectives for the Chem-ical and Petroleum Industries of British Columbia as a Result of a Public Inquiry Held by the Director of the Pollution Control Branch", Table VII, p.33, Ministry of Environment, B.C Walker, B.V., (1975), "The Effective Rate of Gas Exchange in a Bubbling Fluidized Bed", Trans. Instn. Chem. Engrs, 53, p.255. Watanabe, K. and A.S., Jursa, (1964), "Absorption and Photoionization Cross Sections of H20 and H2Sn, J. Chem. Phys., 41, p.1650. White, W.B., Johnson, S.M., Dantzing, G.B., (1958), "Chemical Equilibrium in Complex Mixtures", J. Chem Phys., 28, p.751. References 171 Werther, J. , (1980), "Mathematical Modeling of Fluidized Bed Reactors", Int. Chem. Eng., 20, p.529. Yates, J .G. , (1973), "Fluidised Bed Reactors", Chem. Engr., (London), p.671. Zenz, F .A. , (1979), "Studies of Attrition in Fluid- Particle Systems", Proc. NSF Workshop on Fluidization and Fluid-Particles Systems, Ed. Littman, H. , Torry N Y , p.162. Appendix A STATISTICAL ANALYSIS A . l ANALYSIS OF VARIANCE To study the significance of the feed concentration and the reactor temperature on conversion statistically, a variance analysis is presented in the following section (keeping U/Umf and H„ fixed). It should be noted that the term "significance" does not mean "scientific significance". Instead, it means that a hypotheses may be ac-cepted or rejected. A statistically significant effect may or may not be scientifically significant. According to the so called fixed effect model (Box et al., 1978; Guenther, 1964), the observed conversion, in a given run, may be considered as the sum of four effects i.e: XUT = r c + r t + r t c + e^. (A.l) where r c , denotes the pure concentration effect: r c = h{C) (A.2) and r t , denotes the pure temperature effect: It = h(T) (A3) 172 Appendix A. STATISTICAL ANALYSIS 173 r t c denotes the interaction effect due to the combined action of the feed concentra-tion and reactor temperature: r t c = / 3 ( c , r ) (A.4) The term etcr denotes the experimental error which is assumed to be normally distributed. The subscript c refers to the concentration level and the subscript t denotes the temperature level. The number of replications is indicated by the subscript r. Four variances are associated with these effects and they may be denoted by: <r2, erf, erf, and &\ which are measures of concentration, temperature, interaction and error effects, respectively. According to Mickley et al. (1957), the corresponding mathematical expressions are given by: Concentration variance: *l = E ( r c - f C) 2K (A.5) where r c denotes the mean concentration effect and nc is the number of concentra-tions levels. Temperature variance: <^ 2 = E ( r < - f t ) 2 M (A.6) Interaction variance: ^ = E E ( r t c - r ) 2 / n t n c (A.7) where T denotes the grand mean. Error variance: nt Tic al = E E E ( e t o - etcrflntncnT (A.8) where etCf denotes the mean error averaged over nr at fixed concentration, C, and temperature level, T. Appendix A. STATISTICAL ANALYSIS 174 Once these variances are calculated from experimental data, the F test may be used to determine the significance of each of the effects (i.e F i = of/cr 2). Since it is not possible to isolate each variance completely (see Table A . l ) , an estimate of the population variances, (s2)i, may be used in the F test [i.e Fi = Sp)i/sl]. Mickley et al. (1957) recommended that, when the interaction effect is not significant, the F test should be based on a pooled estimate of error variance i.e: Je + 77 where fe and / / denote the degrees of freedom associated with the error and inter-action variances. The general calculation technique used in variance analysis is cumbersome. The rest of the discussion will therefore be presented by means of the experimental data shown in Figure A . l . The details of the following procedure are comprehensively covered by Guenther (1964) and are summarized in Table A . l . Let ST denotes the sum of squares for the totals and fx denotes the degrees of freedom for ST, i.e: ST = EEEXL ~ (EEExtc) 2 Mn c n r (A.IO) and the degrees of freedom associated with ST is: fT=ntncnr-l (A. 11) Referring to Figure A . l , the first term on the right handside of equation A.IO is: E E E x L = 79.82 + 79.92 + 83.32 + --- + 93.32 = 89967.2 Appendix A. STATISTICAL ANALYSIS 175 and the second term is given by: "t nc fir ( E E E ^ ) V w . = (79.8 + 79.9+ 83.3 +••• + 93.3)7(3x2x2) = 89596.8 Hence ST = 89967.2 - 89596.8 = 370.4 The degrees of freedom for ST is (equation A.11): ft = 3 x 2 x 2 - 1 = 11 For convenience, define the subtotal G t c as Gtc = Ex f cr (A-12) Using equation A.10 leads to a new block as shown in Figure A.2. By analogy to equation A. 10, the sum of squares for the subtotals may be defined as: S* = E E ( G * " (EEExicrF/ncn.n, (A.13) The degrees of freedom for S, is f.=ntne-l (A-14) From Figure A.2 it follows that EE(Gtc)7"r = (158.82 + 162.82 + -•• + 186.12)/2. = 89957.7 Appendix A. STATISTICAL ANALYSIS 176 Hence S, = 89957.7- 89596.8 = 360.9 and / . = 6 - 1 = 5 Subtracting equation A.13 from equation A.10 gives an equation similar to equation A.8: n* nc nr nt nc «r ST-S. = E E E x L - E E C E x ^ K f i t nc nT = E E E ( X * c r - Xtcrf] = SE (A.15) Also from equations A. 11 and A. 14 it follows that fe = fr-f. = ntnc(nT - 1) (A.16) where SE is the error sum of squares and fe denotes the degrees of freedom for SE. Substituting for ST and ST gives: SE = 370.4- 360.9 = 9.5 Also Appendix A. STATISTICAL ANALYSIS 177 Using these values for Se and / e , the estimate of the population error variance (also called the error mean square) is given by se = SJU (A.17) = 9.56/6 = 1.58 Now consider the effect of temperature alone. Referring to Figure A.2, define the sum of squares for the temperature ("columns" in Figure A.2) as: st = E ( E c t e ) 2 M - ( E E L xt~)7 w , - (A. i8) and the associated degrees of freedom as: ft=nt-l (A.19) Then from Figure A.2, E ( E G * 0 2 = {(158-8 + 178.7)2 + (167.8'+ 185.3)2 + (165.2 + 186.1)2}/(2 x 2) = 89622.9 Hence: St = 89622.9- 89596.8 = 26.1 and the degrees of freedom for St is: ft = 3 - 1 = 2 Appendix A. STATISTICAL ANALYSIS 178 The temperature estimate of population variance (or temperature "column" mean squares) is obtained from: (*J)« = St/ft (A.20) = 26.1/2 = 13.1 Similarly, the effect of concentration on conversion is investigated by defining the sum of squares for concentration (concentration " row" mean square in Figure A.2) as: Sc = E ( E Gtc)2/ntnT - ( £ E £ Xtcrf/ntncnT (A.21) and the degrees of freedom for Sc as: fc = nc - 1 (A.22) Hence from Figure A.2, the first term on the right handside of equation a.23 is therefore: E ( E Gtc)2/ntnr = {(158.8 + 162.8 -f 165.2)2 + (178.7+ 185.3 + 186.1)2}/3 x 2 = 89930.7 Hence Sc = 89930.7- 89596.8 = 333.9 with degrees of freedom: Appendix A. STATISTICAL ANALYSIS 179 The concentration estimate of population variance is calculated from the values of Sc and fc as: (^ )c = SJfc (A.23) = 333.9 The interaction sum of squares is given by (Guenther, 1964): Sj = S . - S t - Sc (A.24) The interaction degrees of freedom are given by // = f> — ft — fc = ( n t - l ) ( n c - l ) (A.25) Substituting for the various terms yield: Si = 360.9 - 26.1 •- 333.9 = 0.9 and /, = ( 3 - l ) ( 2 - l ) = 2 These values of Sj and / / are used to calculate the interaction estimate of population variance (interaction mean square): (4)i = Silh (A.26) = 0.9/2 = 0.45 (A.27) endix A. STATISTICAL ANALYSIS 180 The interaction hypotheses may be tested by the F test: (A.28) = 0.45/1.58 = 0.28 This value indicates that the interaction effect is not significant. The value of F at 50% limit (with 6 and 2 degrees of freedom) is 0.78 which means that 50% of the time the interaction assumption is rejected. It also means the effect of a change in concentration is most probably independent of the temperature level and vice versa. With reference to Table A . l , o~\ = 0. Hence the interaction estimate of the population variance, (s2)j, provides an independent estimation of s\. To form a better estimate of the error variance, s\ and (s2,)/ may be pooled in accordance with equation A.9; thus: Using this pooled estimate of the error variance, two F tests may be carried out to find the significance of the feed concentration and reactor temperature. For the concentration effect, the F test is: 6 x 1.58 + 2 x 0.45 6-1-2 = 0.865 (A.29) 333.9 0.865 = 386 For 8 and 1 degrees of freedom, the values of F at 0.1 and 1% limits are (Box et al. 1978): Appendix A. STATISTICAL ANALYSIS 181 F=25.42 at 0.1% limit F=11.26 at 1% limit It is clear that the value of Fc falls far below the 0.1% level, therefore, the con-centration effect is highly significant. In other words, there is less than 1 in 1000 chance that the observed differences in conversions may be explained on the ba-sis of a scatter in data. Thus it is concluded that the conversion at the different concentration levels are actually different. The pure temperature effect is treated in the same way, i.e: F< = <§: (A-30) 13.1 0.865 = 15.14 With 8 and 2 degrees of freedom, the values of F at the 1 and 5% levels are F=8.65 and 5.32, respectively. Thus the temperature effect is also significant. A.2 CONFIDENCE LIMITS ON CONVERSION To assign confidence limits to the experimental conversion Xi the Student's t test is used. In this test, the dimensionless quantity, t, is defined as the difference between the measured sample "conversion" mean, x, and the hypothesized "true" (but generally unknown) population mean, %, divided by the sample estimate of the standard deviation i.e: * = (x - x)/'m (A-31) Ordinary t is not known. However, the distribution function for t was derived by Fisher (1946) and this permits probability limits to be assigned to t intervals. Appendix A. STATISTICAL ANALYSIS 182 Table A . l : Analysis of variance for a Two-Factor block experiment Source Sum of squares Degrees of freedom Mean square Estimate of F T-means St [Eq. A.18] ft = nt - 1 W)i = sj ft cr2 + nraj +n Pn ccr 2 {sl)t/sl C-means SC [Eq. A.20] fe = nc - 1 (*&=sc/fc al + nTa] +nTntal W)c/*.a Interaction Sj [Eq. A.24] // = (nc - 1) (nt - 1) ('J)/ = Sr/fj al + nTaj W)//-.a Subtotals S. [Eq. A. 15] f, = ntnc - 1 Error ST — S> fe = ntnc(nT - 1) s2e = SJf. Totals ST [Eq. A.IO] fr — ntncnT — 1 Figure A . l : Experimental Block (c7/C7m/ = 4.44, H, = 0.19m) 100°C 130°t7 150°C 600 ppm H2S 79.8 83.3 82.9 79.0 79.5 82.3 1300 ppm H2S 89.0 93.5 92.8 89.7 91.8 93.3 Appendix A. STATISTICAL ANALYSIS 183 Consequently most statistic books report tables for the probability that the true value lies inside the limits -t and +t (see Box et al., 1978). To apply the t test to the experimental results shown in Figure A.2, a sample calculation is presented in the following paragraphs and the rest of the calculation is presented in Figure A.3. Consider the C\T\ level (600 ppm,100°C). The average conversion is calculated from Figure A.2 for n r=2: Xur = 158.8/2 = 79.4 where the bar above the r means that the conversion is averaged over the number of replicates at fixed C and T levels. The estimate of the standard diviation, sm, can be calculated from the pooled estimate of the error variance, (.s2)f,v, as recommended by Mickley et al. (1964): sm = \ A s 2 W n r (A.32) From the previous section (s2)bv was found to be 0.865 with 6 degrees of freedom. Hence sm = ^0.865/2 = 0.658 From the t-tables (Box et al., 1978) and for 95% confidence limit, t = ±2.447. Substituting in equation A.31 gives: X i i f - X n = ±2.447 X 0.658 = ±1.61 Appendix A. STATISTICAL ANALYSIS 184 Thus for X n f=79.4: 77.8 < xu < 81 Appendix A. STATISTICAL ANALYSIS 185 Figure A.2: Experimental block for the subtotals defined by equation A. 12 100°C 130°C 150°C 600 ppm 158.8 162.8 165.2 1300 ppm 178.7 185.3 186.1 Figure A.3: Confidence limits on x 100°C 130°C 150°C Xctf 600 ppm 79.4 81.4 82.6 Upper limit H2S 81.0 83.0 84.2 Lower limit 77.8 79.8 81.0 Xctf 1300 ppm 89.4 92.7 93.1 Upper limit H2S 91.0 94.3 94.7 Lower limit 87.7 91.0 92.0 Appendix B COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS The performance of the fluidized bed Claus reactor was predicted by the two phase bubbling model described in chapter 3. The following computer programme was written in Fortran IV to compute the conversion as a function of the operating conditions listed in Table 5.1. It is divided into a main programme and five sub-programmes: BISECT, CONSTAN, F U N , G U N and H Y D R O . The subprogramme BISECT is a root finding subroutine which uses an incremental search to bracket the roots of a given function. Then it uses the bisection method to converge on each root with a prespecified tolerance (in this case TOL=10~ 6 ). It also recognizes function discontinouities. The subroutine CONSTN is a dummy subprogramme in which the constants a, / 3 i , 82 and A\ to A7 are computed. The subprogrammes F U N and G U N are functions whose roots are sought. F U N represents equation 3.10 whose root gives C2 )o- G U N represents equation 3.40 whose root gives X\. The subroutine HYDRO computes the bed hydrodynamic parameters. It uses the iteration procedure described in section 2.2.5 to calculate db, H and eb. It also calculates kq. The various parameters appearing explicitly in the model equations were calculated 186 endix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 187 using expressions found in the literature and cited in chapter 2. They are summa-rized in Table B . l . Other parameters, which did not appear in the model equations but were indirectly needed in the conversion computation, are also shown in Table B . l . Constants defined in chapter 3 are also included in the table. endix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS Table B . l : Parameters calculated in the programme for model predictions Parameter Equation Reference A-i to A7 3.24-3.28, 3.38-3.39 Chapter 3 2.17 Mori and Wen, (1975) H 2.16 Grace, (1982) K 2.8 Sit and Grace, (1981) 1.15 Grace (1982) umf 2.11 Grace (1982) a 3.11 Chapter 3 fix 3.12 Chapter 3 02 3.13 Chapter 3 7 3.18 Chapter 3 2.20 Grace, (1982) emf 2.12 Broadhurst and Becker, (1975) fa 2.21 Grace, (1984) fa 2.22 Grace, (1984) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 189 IMPLICIT REAL*8(A-H,0-Z) EXTERNAL GUN,FUN DIMENSION R00T(1) C0MM0N/BLK1/B0AL C0MM0N/BLK3/EQ,AB,EB,H,FIB,FID,DB COMMON/BLK4/YO C0MM0N/BLK5/HS c MODEL PREDICTIONS. c SYMBOLES c A : CROSS SECTIONAL AREA OF THE BED c AB : INTERFACIAL BUBBLE SURFACE AREA/BUBBLE VOLUME c AG : GRAVITATIONAL CONSTANT c ARN : ARCHIMEDES NUMBER c BOAL: BETA2 OVER ALPHA c C1E : DIMENSIONLESS CONCENTRATION IN DILUTE PHASE c C2E : DIMENSIONLESS CONCENTRATION IN DENSE PHASE c CE : EXIT DIMENSIONLESS CONCENTRATION c CF .: ACTUAL FEED. CONCENTRATION c CONV: CONVERSION '/. c DB : BUBBLE DIAMETER c DG : GAS DIFFUSIVITY c DP : PARTICLE DIAMETER c EB : VOLUME FRACTION OF BED OCCUPIED BY DILUTE PHASE c EMF : BED VOIDAGE AT MINIMUM FLUIDIZATION c EQ : GAS EXCHANGE COEFFICIENT Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 190 C F I B : FRACTION OF DILUTE PHASE OCCUPIED BY PARTICLES C F ID : FRACTION OF DENSE PHASE OCCUPIED BY PARTICLES C GD : GAS DENSITY C GV : GAS VISCOSITY C H : EXPANDED BED HEIGHT C HS : STATIC BED HEIGHT C PPM : CONCENTRATION IN PARTS PER MILLION C REMF: REYNOLD'S NUMBER C RGAS: GAS CONSTANT C RK : REACTION RATE CONSTANT C T : ABSOLUTE TEMPERATURE C U : SUPERFICIAL GAS VELOCITY C UMF : SUPERFICIAL GAS VELOCITY AT MINIMUM FLUIDIZATION C URATIO: U/UMF C W : CATALYST WEIGHT IN BED C I F INDEX=-1 THEN CALCULATE CONVERSION AS FUNCTION OF C FEED CONCENTRATION C I F INDEX=0 THEN CALCULATE CONVERSION AS FUNCTION OF C U/Umf C I F INDEX=1 THEN CALCULATE CONVERSION AS FUNCTION OF C STATIC BED HEIGHT C I F INDIX=2 THEN CALCULATE CONVERSION AS FUNCTION OF C SULPHUR LOADING READ(5,2) GD.GV 2 F0RMAT(1X ,F6 .4 ,1X ,F12 .10 ) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS AG=9.8D0 DP=195.0D-6 RP=1843.0D0 RGAS=62.4D0 C CALCULATE MINIMUM FLUIDIZATION VELOCITY: UMF ARN=GD*(RP-GD)*AG*DP*DP*DP/GV/GV REMF=DSQRT(27.2D0*27.2DO+0.0408D0*ARN)-27.2D0 UMF=REMF*GV/DP/GD C CALCULATE BED VOIDAGE AT MINIMUM FLUIDIZATION: EMF EMF=0.586*(GV*GV/GD/AG/DP/DP/DP/(RP-GD))**(0.029) $*(GD/RP)**(0.021)/(0.6D0)**(0.6D)) READ(5,8) INDEX 8 F0RMAT(I2) IF (INDEX. GE. 2) GO TO 70 IF(INDEX)10,30,50 10 WRITE(6,13) 13 FORMATCl',////) WRITE(6,12) 12 . FORMAT (10X,'Conversion as a function of feed, $ concentrat ion') READ(5,14)T,U,W,DG,RK WRITE(6,260) T 14 F0RMAT(1X,F5.1,1X,F5.3,1X,F3.1,1X,F11.9,1X,F6.2) C CALCULATE BED HYDRODYAMICS URATIO=U/UMF CALL HYDRO(UMF,U,W,EMF,DG) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 192 WRITE(6,150) WRITE(6,160)DB WRITE(6,170)H WRITE(6,180)EB WRITE(6,190)F IB WRITE(6,200)F ID WRITE(6,210)EQ WRITE(6,220)UMF WRITE(6,230)HS WRITE(6,240)EMF WRITE(6,250)URATI0 150 FORMAT(/ ,10X , 'Hyd rodynamic p a r a m e t e r s ' ) 160 FORMAT(/ ,10X , ' Bubb le d i a m e t e r ' $ , 2X ,F5 .3 ) 170 FORMAT(/ ,10X , ' Expanded b e d h e i g h t ' $ , 2X ,F4 .2 ) 180 F O R M A T ( / , 1 0 X , ' F r a c t i o n o f bed o c c u p i e d by $ d i l u t e p h a s e ' , 2 X , F 4 . 2 ) 190 F O R M A T ( / , 1 0 X , ' F r a c t i o n o f c a t a l y s t a s s o c i a t e d $ w i t h d i l u t e p h a s e ' , 2 X , F 6 . 4 ) 200 F O R M A T ( / , 1 0 X , ' F r a c t i o n o f c a t a l y s t a s s o c i a t e d ' $ w i t h dense p h a s e ' , 2 X , F 6 . 4 ) 210 F 0 R M A T ( / , 1 0 X , ' I n t e r p h a s e mass t r a n s f e r $ c o e f f i c i e n t ' , 2 X , F 6 . 4 ) 220 FORMAT(/,10X, 'M in imum f l u i d i z i n g gas $ v e l o c i t y ' , 2 X , F 7 . 5 ) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 193 230 F O R M A T ( / , 1 0 X , ' S t a t i c b e d h e i g h t ' $ , 2X ,F4 .2 ) 240 FORMAT(/,10X, ' V o i d a g e a t minimum $ f l u i d i z a t i o n ' , 2 X , F 5 . 3 ) 250 FORMAT(/,10X, 'U/Unrf ' $, 2X . F4 . 2 , //// ) 260 F O R M A T ( / , 1 0 X , ' R e a c t o r t e m p e r a t u r e K ' , 2 X , F 5 . 1 ) WRITE(6,11) 11 F0RMAT(35X , ' PPM ' , 4X , ' CONVERS ION ' , / ) PPM=100.0D0 20 PPM=PPM+100.0D0 CF=PPM*1.0D-6*760.ODO/RGAS/T C CALCULATE COSTANTS IN MODEL EQUATION CALL CONSTN(CF,U,RK) C FIND DENSE PHASE IN IT IAL CONCETRATION CALL BISECT(FUN,O.ODO,1.ODO,1,ROOT,0.01D0, $1.0D-5,NR) Y0=DSQRT(1.ODO+BOAL*DSQRT(ROOT(1))) CALL B ISECT(GUN,1.001D0.Y0.1,ROOT,0.01D0, $1.0D-5,NR) C2E=(ROOT(1)*ROOT(1)-1.ODO)*(ROOT(1)*ROOT(1) $-1.0DO)/BOAL/BOAL C1E=C2E+(B0AL)*C2E**1.5D0 CE=C1E CONV=100.DO*(1.ODO-CE) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 194 WRITE(6,25) PPM.CONV IF (PPM. GE. 1300) GO TO 999 GO TO 20 25 F0RMAT(34X ,F6 . 1 , 5X ,F5 . 1 , / ) 30 WRITE(6,35) 35 F O R M A T ( ' 1 ' , / / / / / / , 1 0 1 , ' C o n v e r s i o n as a $ f u n c t i o n o f U/Umf ' , / ) READ(5,32)PPM,W,T,DG,RK WRITE(6,31)T 31 F O R M A T ( / , 1 0 X , ' R e a c t o r t e m p e r a t u r e K ' , 2 X , F 5 . 1 ) WRITE(6,33)PPM WRITE(6,37)UMF WRITE(6,38)EMF 32 F 0 R M A T ( 1 X , F 6 . 1 , 1 X , F 3 . 1 , 1 X , F 5 . 1 , 1 X , F 1 1 . 9 , 1 X , F 6 . 2 ) 33 FORMAT(/,10X, 'H2S FEED c o n c e n t r a t i o n i n ppm ' $ , 2X , F6 . 1 ) WRITE(6,36) 36 FORMAT(10X, 'U/Umf CONV Db H Eb Kq $ p h i - b P h i - d ' ) 37 FORMAT(/ ,10X, 'M in imum f l u i d i z i n g v e l o c i t y ' $ , 2X , F7 . 5 ) 38 FORMAT (/ , 10X , ' V o i dage a t minimum f l u i d i z a t i o n ' $ , 2 X , F 5 . 3 , / ) CF=PPM*1.0D-6*760.ODO/RGAS/T URATI0=1.ODO 40 URATI0=URATI0+0.5D0 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 195 U=UMF*URATIO CALL HYDRO(UMF,U,W,EMF,DG) C CALCULATE COSTANTS IN MODEL EQUATION CALL CONSTN(CF,U,RK) C FIND DENSE PHASE IN IT IAL CONCENTRATION CALL BISECT(FUN,0.ODO,1.ODO,1,ROOT,0.OlDO, $1.0DO-5,NR) YO=DSQRT(l.ODO+BOAL*DSQRT(ROOT(1))) CALL BISECT(GUN,1.OOIDO,YO,1,ROOT,0.OlDO, $1.05D-5,NR) C2E= (ROOT( l ) * ROOT( l ) - l .ODO) * (ROOT(1 ) *R00T (1 ) $ - l .ODO)/B0AL/B0AL C1E=C2E+(BOAL)*C2E**1.5D0 CE=C1E CONV=100.DO*(1.ODO-CE) WRITE(6,45) URATIO,CONV,DB,H,EB,EQ,F IB,F ID 45 F 0 R M A T ( / , 1 0 X , F 3 . 1 , 2 X , F 5 . 1 , 2 X , F 5 . 3 , 2 X , F 4 . 2 , 2 X , $ F 4 . 2 , 2 X , F 5 . 3 , 2 X , F 6 . 4 , 2 X , F 6 . 4 ) IF (URATIO.LT.6.ODO) GO TO 40 WRITE(6,46)HS 46 F O R M A T ( / , 1 0 X , ' S t a t i c b e d h e i g h t ' , 2 X , F 4 . 2 ) GO TO 999 50 WRITE(6,51) 51 F O R M A T ( » 1 J , / / / / / / ) WRITE(6,52) 52 F O R M A T ( 1 0 X , ' C o n v e r s i o n as a f u n c t i o n Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 196 $of s t a t i c bed h e i g h t 1 ) READ(5 ,55 )PPM,U > T J DG,RK 55 F 0 R M A T ( 1 X , F 6 . 1 , 1 X , F 5 . 3 , 1 X , F 5 . 1 , 1 X , $ F 1 1 . 9 , 1 X , F 6 . 2 ) URATIO=U/UMF CF=PPM*1.0D-6*760.ODO/RGAS/T WRITE(6,57) 57 FORMAT(/) WRITE(6,31)T WRITE(6,33)PPM WRITE(6,37)UMF WRITE(6,59)URATI0 WRITE(6,38)EMF WRITE(6,57) WRITE(6,300) 59 FORMAT(/,10X,>U/Umf ' .2X.F4.2) W=0.4DO 60 W=W+0.4D0 CALL HYDRO(UMF,U,W,EMF,DG) C CALCULATE CONSTANTS IN MODEL EQUATION CALL CONSTN(CF,U,RK) C FIND DENSE PHASE I N I T I AL CONCENTRATION CALL BISECT(FUN,0.ODO,1.ODO,1,ROOT,0.01D0, $1.0D-5.HR) Y0=DSQRT(1.ODO+BOAL*DSQRT(ROOT(1))) CALL B ISECT(GUN,1.001D0,YO,1,ROOT,0.01D0, Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 197 $1.0D-5,NR) C 2 E = ( R 0 0 T ( l ) * R 0 0 T ( l ) - 1 . 0 D O ) * ( R 0 0 T ( l ) * R 0 0 T ( l ) $-1.0DO/BOAL/BOAL C1E=C2E+(BOAL)*C2E**1.5D0 CE=C1E C0NV=100.DO*(1.ODO-CE) WRITE(6,65) HS,CONV,DB,H,EB,EQ,F IB,F ID 65 F 0 R M A T ( / , 1 0 X , F 4 . 2 , 2 X , F 5 . 1 , 2 X , F 5 . 3 , 2 X , F 4 . 2 , $ 2 X , F 4 . 2 , 2 X , F 5 . 3 , 2 X , F 6 . 4 , 2 X , F 6 . 4 ) IF (W.GE.2.4D0) GO TO 999 GO TO 60 300 FORMAT ( 1 I X , ' H S CONV Db H Eb Kq $ P h i - b P h i - d ' ) 70 WRITE(6,80) WRITE(6,85) READ(5,83)PPM,T,U,W,DG,RK CF=PPM*1.0D-6*760.ODO/RGAS/T URATIO=U/UMF CALL HYDRO(UMF,U,W,EMF,DG) WRITE(6,31)T WRITE(6,33)PPM WRITE(6,150) WRITE(6,160)DB WRITE(6,170)H WRITE(6,180)EB WRITE(6 ,190)F IB Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 198 WRITE(6,200)F ID WRITE(6,210)EQ WRITE(6,220)UMF WRITE(6,230)HS WRITE(6,240)EMF WRITE(6,250)URATI0 80 FORMAT( ' 1 ' , / ///// ) 83 F 0 R M A T ( 1 X , F 6 . 1 , 1 X , F 5 . 1 , 1 X , F 5 . 3 , 1 X , F 3 . 1 , 1 X , $ F 1 1 . 9 , 1 X , F 6 . 2 ) 85 F O R M A T ( 1 0 X , ' C o n v e r s i o n a s a f u n c t i o n o f $ s u l p h u r l o a d i n g ' ) WRITE(6,102) SL=0.000D0 90 SLOAD=1.0DO+SL*0.085DO FRK=RK/SLOAD SL=SL+5.OD0 CALL CONSTN(CF,U,FRK) C FIND DENSE PHASE IN IT IAL CONCENTRATION CALL BISECT(FUN,0.ODO,1.ODO,1,ROOT,0.OlDO, $1.0D-5,NR) Y0=DSQRT(1.ODO+BOAL*DSQRT(R00T(l))) CALL BISECT(GUN,1.OOIDO,YO,1,ROOT,0.OlDO, $1.0D-5,NR) C 2 E = ( R 0 0 T ( l ) * R 0 0 T ( l ) - 1 . 0 D 0 ) * ( R 0 0 T ( l ) $-1.0DO)/BOAL/BOAL C1E=C2E+(BOAL)*C2E**1.5D0 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 199 CE=C1E CONV=100.DO*(1.ODO-CE) WRITE(6,101) SL.CONV IF (SL .GE.60.0D0) GO TO 999 GO TO 90 101 F0RMAT(/ ,33X,F5 .1 ,10X,F5 .1) 102 F0RMAT(//,28X, 'Sulphur l o a d i n g c o n v e r s i o n ' ) 999 CONTINUE STOP END DOUBLE PRECISION FUNCTION FUN(X) IMPLICIT REAL*8(A-H,0-Z) C0MM0N/BLK1/A FUN=A*X**1.5D0+X-1.ODO RETURN END DOUBLE PRECISION FUNCTION GUN(X) IMPLICIT REAL*8(A-H,0-Z) C0MM0N/BLK2/AL ,S I ,S2 ,S3 ,A l ,A2 ,A3,A4,A5,A6,A7 C0MM0N/BLK4/Y0 FACT=(2.0D0*A7+S1*A6)/Sl/DSQRT(3.ODO) T1=A1*DLOG((1.ODO+X)/(1.ODO+YO)) T2=-A3*DL0G(DABS((1.ODO-X)/(1.ODO-YO))) T3=A5*DL0G((Sl+X)/(Sl+YO)) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 200 T4=0.5DO*A6*DL0G((X*X-S1*X+S2)/(Y0*Y0-S1*Y0+S2) ) T5=-A2*((1.ODO/(1.ODO+X))-(1.ODO/(1.ODO+YO))) T6=A4*( (1.ODO/(1.ODO-X)) - (1.ODO/(1.ODO-YO)) ) T7=FACT*DATAN((2.ODO*X-S l )/S l/DSQRT(3.ODO)) T8=-FACT*DATAN((2.ODO*YO-Sl )/S l/DSQRT(3.ODO)) Gl=Tl+T2+T3+T4+T5+T6+T7+T8+AL/S3/2. ODO GUN=G1 RETURN END SUBROUTINE HYDRO(UMF,U,W,EMF,DG) IMPLIC IT R E A L * 8 ( A - H , 0 - Z ) C0MM0N/BLK3/Q,AB,EB,H,FIB,FID,DB C0MM0N/BLK5/HS Y=0.7D0 RP=1843.0D0 RB=795.0D0 A=0.007854D0 . D=0.1D0 AG=9.8D0 URATI0=U/UMF HS=H/A/RB EP=1-RB/RP C CALCULATION OF BED HYDRODYNAMICS: C ESTIMATE FLOW RATE, VB . IH BUBBLE PHASE (CORRECTED C TWO PHASE THEORY) Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 201 UDIFF=U-UMF VB0A=Y*UDIFF C ESTIMATE MAXIMUM STABLE BUBBLE DIAMETER USING C MORI ft WEN CORRELATION FOR POROUS PLATE C DISTRIBUTOR DBM=1.64D0*(A*UDIFF)* *0.4D0 DBO=0.376D0*UDIFF*UDIFF HMF=HS*(1.ODO-EP)/(1.ODO-EMF) C GUESS FRACTION OF BED OCCUPIED BY BUBBLES, EB EB=0.1DO C START ITERATION TO FIND CORRECT EB BY CALCULATING C BED HEIGHT (H) 10 H=HMF/(1.D0-EB) C ESTIMATE BUBBLE DIAMETER, DB, AT HALF BED HEIGHT DBDIFF=DBM-DBO DB=DBM-DBDIFF*DEXP(-0.3D0*H/2.DO/D) C ALSO ESTIMATE BUBBLE VELOCITY (UB) USING DB C AT 1/2 BED HEIGHT UB=0.711D0*(AG*DB)**0.5D0+Y*UDIFF C CALCULATE NEW EB USING NEW (UB) EBOLD=EB EB=VBOA/UB C CHECK DIFFERENCE BETWEEN THE NEW AND OLD E B ' S . C I F THIS DIFFERENCE IS >0.001 GO BACK AND GUESS C AGAIN OTHERWISE ESTIMATE THE REQUIRED PARAMETERS. Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 202 I F (DABS(EBOLD-EB) .GT.1 .0D-3 ) GO TO 10 C ESTIMATE GAS EXCHANGE BETWEEN PHASES Q=UMF/3.DO+(4.D0*DG*EMF*UB/DB/3.1459D0) $ * *0 .5D0 C CALCULATE RATIO OF BUBBLE SURFACE AREA C TO ITS VOLUME AB=6.0D0/DB C CALCULATE FRACTION OF SOLIDS IN DENSE PHASE F ID=(1.DO-EMF)*(1.ODO-EB) C CALCULATE FRACTION OF SOLIDS IN DILUTE PHASE FIB=0.010D0*EB RETURN END SUBROUTINE CONSTN(CF,U,RK) IMPL IC IT R E A L * 8 ( A - H , 0 - Z ) COMM0N/BLK3/Q,AB,EB,H,FIB,FID,DB C0MM0N/BLK2/ALFA,S I , S2 ,S3 ,A l ,A2 ,A3 , $A4,A5,A6,A7 C0MM0N/BLK1/B0AL RGAS=62.358D0 C DEFINE CONSTANTS NEEDED TO FIND THE C ROOT OF THE MODEL EQUATION ALFA=Q*AB*EB*H/U DLK=RK*H*CF**0.5D0/U Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 203 B1=DLK*FIB B2=DLK*FID S1=(B2/B1) * * (1 .0D0/3.0D0) S2=S1*S1 S3=S1*S2 S4=S1*S3 S5=S1*S4 S6=S5*S1 S7=S6*S1 S8=S1*S7 A l= l .5D0*S3/ (S3 -1 .ODO)/ (S3 -1 .ODO) A2=-0.5D0/(S3-1.0D0) A3=l.5D0*S3/(S3+1.ODO)/(S3+1.ODO) A4=0.5D0/(S3+1.0D0) A5=- (3.0D0*S2-1.ODO)/(S2-1.ODO)/(S2-1.ODO) $/S l/3.0D0 A6=-(6.0D0*S6+7.0D0*S4+S2+1.ODO)/(S4+S2+1.ODO $)/(S4+S2+1.ODO)/Sl/3.ODO A7= ( 3 . 0D0 *S6 -4 . 0D0 *S4 -4 . O D O * S 2 - l . ODO)./ (S4+S2 $+1.OD))/(S4+S2+1.ODO)/3.ODO B0AL=B2/ALFA RETURN END SUBROUTINE B I SECT(F ,X I ,XF ,NR00T,R ,DX I ,TOL ,NR) C SOLVES EQUATION F(X)=0 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 204 C USES INCREMENTAL SEARCH TO BRACKET NR ROOTS OF THE C FUNCTION F(X) IN INTERVAL (XI,XF) USING INITIAL C INCREMENT DXI C BISECTION METHOD IS APPLIED TO CONVERGE ON EACH ROOT. C THE ROOTS ARE RETURNED IN THE ARRAY R(NROOT). C TOL IS THE ERROR TOLERANCE ON F(X): F(X) .LT.TOL C NROOT= NO. OF ROOTS SOUGHT C NR=N0. OF ROOTS FOUND C METHOD AVOIDS DISCONTINUITIES IMPLICIT REAL*8(A-H,0-Z),INTEGER(I-N) DIMENSION R(NROOT) NR=0 X=XI 4 DX=DXI •1 X2=0.0D0 E2O.0D0 2 IF(X.GT.XF) RETURN E=F(X) E1=E2 E2=E X1=X2 X2=X IF(DABS(E).LT.TOL) GO TO 9 IF(E1*E2.LT.0.D0.AND.DX.EQ.DXI) GO TO 5 IF(El*E2.LT.O.DO.AND.DX.NE.DXI) GO TO 6 X=X+DX Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 205 GO TO 2 5 DY1=DABS(E2-E1) X=X-DX DX=DX/10.DO GO TO 1 6 DY2=DABS(E2-E1) I F (DY2.LT.DY1) GO TO 7 WRITE(6,12)X 12 FORMAT(10X, 'THE FUNCTION IS DISCONTINOUS $At X = , , F 1 0 . 5 ) X=X2 GO TO 4 7 ICOUNT=0 11 IF( ICOUNT.GE. IOO) GO TO 8 X=(X1+X2)/2.D0 E=F(X) ICOUNT=ICOUNT+l I F (DABS (E ) . LT .TOL ) GO TO 9 I F ( E l * E . L T . O . D O ) GO TO 3 X1=X E1=E GO TO 11 3 X2=X E2=E GO TO 11 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 206 8 X=X2 GO TO 4 9 NR=NR+1 R(NR)=X IF(NR.EQ.NROOT) RETURN X=X+DX GO TO 4 END Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 207 Table B.2: Model predictions Table B.2.1: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Umf = 4.44, ff.=0.19m a: Hydrodynamic parameters: Bubble diameter, df, 0.028 Expanded bed height, H 0.25 Fraction of bed occupied by dilute phase, eb 0.13 Fraction of catalyst associated with dilute phase, fa 0.0013 Fraction of catalyst associated with dense phase, fa 0.3347 Interphase mass transfer coefficient, kq 0.0241 Minimum fluidizing gas velocity, Umf 0.0224 Voidage at minimum fluidization, e m/ 0.616 a 1.68 7 6.36 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 208 Table B.2.1: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Umf = 4.44, ff,=0.19m (cont.) b: Conversion H2S Concentration in feed (ppm) Conversion (%) 02 200.0 68.1 0.0034 0.88 300.0 75.5 0.0042 1.08 400.0 80.2 0.0049 1.26 500.0 83.5 0.0054 1.39 600.0 85.9 0.0059 1.52 700.0 87.7 0.0064 1.65 800.0 89.2 0.0069 1.78 900.0 90.3 0.0073 1.88 1000.0 91.2 0.0077 1.98 1100.0 92.0 0.0081 2.09 1200.0 92,7 0.0084 2.16 1300.0 93.3 0.0088 2.25 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 209 Table B.2.2: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Umf = 8.88, #.=0.19m a: Hydrodynamic parameters: Bubble diameter, db 0.063 Expanded bed height, H 0.44 Fraction of bed occupied by dilute phase, eb 0.18 Fraction of catalyst associated with dilute phase, fa 0.0018 Fraction of catalyst associated with dense phase, fa 0.3140 Interphase mass transfer coefficient, kq 0.0215 Minimum fluidizing gas velocity, Umf 0.02248 Static bed height, H, 0.32 Voidage at minimum fluidization, em/ 0.616 u/umf 8.90 a 1.63 7 5.59 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 210 Table B.2.2: Conversion as a function of H2S feed concentration for T=423.0 °K, U/Umf = 8.88, #,=0.19x11 b: Conversion H2S Concentration in feed (ppm) Conversion (%) Pi ft 200.0 73.4 0.0084 1.46 300.0 81.3 0.0103 1.79 400.0 85.8 0.0118. 2.06 500.0 88.7 0.0132 2.308 600.0 90.7 0.0145 2.53 700.0 92.2 0.0157 2.73 800.0 93.3 0.0168 2.92 900.0 94.1 0.0178 3.11 1000.0 94.8 0.0186 3.29 1100.0 95.4 0.0196 3.43 1200.0 95.8 0.0205 3.58 1300.0 96.2 0.0214 3.73 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 211 Table B.2.3: Conversion as a function of H2S feed concentration for T=373.0 °K, U/Umf = 4.44, ff.=0.19m a: Hydrodynamic parameters Bubble diameter, db 0.029 Expanded bed height, H 0.25 Fraction of bed occupied by dilute phase, eb 0.13 Fraction of catalyst associated with dilute phase, fa 0.0013 Fraction of catalyst associated with dense phase, 4>d 0.3353 Interphase mass transfer coefficient, kq 0.0253 Minimum fluidizing gas velocity, Umf 0.0245 Voidage at minimum fluidization, emf 0.613 a 1.701 7 6.36 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 212 Table B.2.3: Conversion as a function of H2S feed concentration for T=373.0 °K, U/Um, = AAA, # s=0.19m (cont.) b: Conversion H2S Concentration in feed (ppm) Conversion (%) 02 200.0 57.0 0.0031 0.801 300.0 65.0 0.0038 0.981 400.0 70.6 0.0044 1.132 500.0 74.7 0.0049 1.266 600.0 77.8 0.0054 1.387 700.0 80.2 0.0058 1.498 800.0 82.3 0.0062 1.601 900.0 84.0 0.0066 1.698 1000.0 85.3 0.0069 1.790 1100.0 86.6 0.0073 1.878 1200.0 87.6 0.0076 1.961 1300.0 88.4 0.0079 2.041 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 213 Table B.2.4: Conversion as a function of U/Umf for T = 423°K, H2S in feed= 600ppm, E,- 0.19m Minimum fluidizing velocity (m/s) 0.02248 Voidage at minimum fluidization 0.616 u/umf X db H K <k to a ft ft 7 1.5 96.9 0.011 0.22 0.03 0.027 0.0003 0.3712 2.88 0.0036 4.44 10.72 2.0 94.9 0.015 0.23 0.05 0.026 0.0005 0.3627 2.66 0.0047 3.40 8.98 2.5 92.9 0.018 0.23 0.07 0.025 0.0007 0.3556 2.39 0.0052 2.67 8.01 3.0 91.0 0.021 0.24 0.09 0.025 0.0009 0.3494 2.29 0.0056 2.28 7.30 3.5 89.0 0.023 0.24' 0.10 0.025 0.0010 0.3438 1.99 0.0059 1.92 6.99 4.0 87.4 0.026 0.24 0.12 0.024 0.0012 0.3389 1.77 0.0059 1.66 6.54 4.5 85.7 0.028 0.25 0.13 0.024 0.0013 0.3343 1.65 0.0059 1.51 6.33 5.0 84.1 0.030. 0.25 0.14 0.024 0.0014 . 0.3300 1.49 0,0057' 1.34 6.17. 5.5 82.7 0.033 0.26 0.15 0.024 0.0015 0.3261 1.38 0.0058 1.26 6.02 6.0 81.4 0.035 0.26 0.16 0.024 0.0016 0.3225 1.27 0.0056 1.14 5.88 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 214 Table B.2.5: Conversion as a function of U/Umf for T=423°K, H2S in feed =1300ppm, # s=0.19m Minimum fluidizing velocity (m/s) 0.0224 Voidage at minimum fluidization 0.616 u/umf X db H Q> K fa fa a Pi P2 7 1.5 98.6 0.011 0.22 0.03 0.027 0.0003 0.3712 2.88 0.0053 6.54 10.72 2.0 97.7 0.015 0.23 0.05 0.026 0.0005 0.3627 2.66 0.0069 5.01 8.98 2.5 96.7 0.018 0.23 0.07 0.025 0.0007 0.3556 2.39 0.0077 3.93 8.01 3.0 95.8 0.021 0.24 0.09 0.025 0.0009 0.3494 2.29 0.0087 3.36 7.30 3.5 94.8 0.023 0.24 0.10 0.025 0.0010 0.3438 1.99 0.0082 2.83 6.99 4.0 94.0 0.026 0.24 0.12 0.024 0.0012 0.3389 1.77 0.0087 2.44 6.54 4.5 93.2 0.028 0.25 0.13 0.024 0.0013 0.3343 1.65 0.0087 2.22 6.33 5.0 92.4 0.030 0.25 0.14 0.024 0.0014 0.3300. 1.49 0.0084 1.97 6.17 5.5 91.7 0.033 0.26 0.15 0.024 0.0015 0.3261 1.38 0.0085 1.85 6.02 6.0 91.0 0.035 0.26 0.16 0.024 0.0016 0.3225 1.27 0.0082 1.68 5.88 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 215 Table B.2.6: Conversion as a function of sulphur loading Reactor temperature (°K) 373.0 H2S feed concentration (ppm) 1000.0 Hydrodynamic parameters: Bubble diameter, d\ 0.041 Expanded bed height, H 0.40 Fraction of bed occupied by dilute phase, e& 0.12 Fraction of catalyst associated with dilute phase, fa 0.0012 Fraction of catalyst associated with dense phase, 0.3427 Interphase mass transfer coefficient, kq 0.0237 Minimum fluidizing gas velocity, Umj 0.02458 Static bed height, H , 0.32 Voidage at minimum fluidization, 0.613 U/Umf . 4.43 a 1.665 ft 0.0093 p2 2.645 7 6.58 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 216 Table B.2.6: Conversion as a function of sulphur loading (cont.) Sulphur loading (%) Conversion (%) 5.0 95.0 10.0 89.8 15.0 83.6 20.0 77.1 25.0 70.9 30.0 65.1 35.0 60.0 40.0 55.4 45.0 51.3 50.0 47.8 55.0 44.6 60.0 41.8 Appendix B. COMPUTER PROGRAMME FOR THE MODEL PREDICTIONS 217 Table B.2.7: Conversion as a function of static bed height Reactor temperature (°K) 373.0 H2S Feed concentration (ppm) 600.0 Minimum fluidizing velocity (m/s) 0.02458 U/Umf AAA Voidage at minimum fluidization 0.613 H . X db H e& kq to to a ft ft 7 0.13 61.6 0.022 0.17 0.15 0.027 0.0015 0.3283 1.88 0.0038 0.83 6.02 0.19 77.8 0.029 0.25 0.13 0.025 0.0013 0.3353 1.68 0.0049 1.25 6.34 0.26 86.8 0.036 0.33 0.12 0.024 0.0012 0.3396 1.58 0.0059 1.68 6.57 0.32 91.6 0.041 0.40 0.12 0.024 0.0012 0.3427 1.69 0.0072 2.05 6.58 0.38 94.3 0.046 0.48 0.11 0.023 0.0011 0.3449 1.58 0.0079 2.48 6.80 0.45 95.9 0.051 0.55 0.11 0.023 0.0011 0.3466 1.64 0.0090 2.85 6.82 Appendix C COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION DIMENSION PR(60),FACTOR(60),QS(50),QR(50,10),SR(50) CHARACTER GAS*3 CHARACTER SFLOAT*10 C THIS PROGRAMME CALCULATES GAS FLOW RATES, INTO THE C REACTOR AT ATMOSPHERIC PRESSURE AND ROOM TEMPERATURE, C AS FUNCTION OF PRESSURE AND TEMPERATURE INSIDE THE C ROTAMETER AND SCALE READINGS FROM GAS FLOW RATES AT C SATANDARD STATE. THIS RATE WAS LATER CORRECTED TO C REACTOR TEMPERATURE. C A,B,C: POLYNOMIAL COEFFICIENTS OBTAINED FROM FLOW C RATES AT STANDARD CONDITIONS C NSR NO. OF SCALE READINGS C GAS: GAS TO BE MEASURED C FLOAT: TYPE OF FLOAT USED C 1,'J: SCALE READING and PRESSURE COUNTERS C PREACR: REACTOR PRESSURE (=14.7 PSIA) C PROTR : ROTAMETER PRESSURE C PS : STANDARD STATE PRESSURE (=14.7PSIA) 218 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 219 C QS : FLOW RATE AT STANDARD STATE C QREACR: FLOW RATE INTO REACTOR AT REACTOR PRESSURE AND C AT ROOM TEMPERATURE C SG : GAS SPECIFIC DENSITY C TREACR: ROOM TEMPERATURE C TROTR : TEMPERATURE INSIDE ROTAMETER=ROOM TEMPERATURE C TS : STANDARD STATE TEMPERATURE=294.15 deg K READ(5,351) SFLOAT READ(5,350) GAS 350 FORMAT(A3) 351 F0RMAT(A12) WRITE(6,352) SFLOAT 352 FORMAT(10X,'Float 5 ,2X,A12, '\\ ') WRITE(6,353) GAS 353 FORMAT(1OX,'Gas measured ',2X,A3,'\\') READ (5,400) NSR.SG READ(5,401) A,B,C READ(5,402) TR,TM,TS,PM,PS 400 F0RMAT(1X,I3,1X,F5.3) 401 F0RMAT(F8.3,F7.3,F9.6) 402 F0RMAT(1X,F6.2,1X,F6.2,1X,F6.2,1X,F4.1,1X,F4.1) FACT=TM*TM*PS/TS/TR/PM/PM/SG PR(1)=14.7 FACTOR(1)=(FACT*PR(1))**0.5 PP=19.7 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 220 DO 10 J=2,6 PR(J)=PP FACTOR(J)=(FACT*PP)**0.5 10 PP=PP+5.0 S=0.0 DO 20 1=1,HSR S=S+10.0 SR(I)=S QS(I)=A+B*S+C*S*S QR(I,1)=QS(I)*FACT0R(1) DO 20 J=2,6 20 QR(I,J)=QS(I)*FACTOR(J) WRITE(6,500) TR WRITE(6,490) 490 FORMAT ('Scale reading ft ft ft Flow rate ft (mL/min) $& ft \\ \hline') WRITE(6,501) (PR(I),1=1,6) DO 30 1=1,NSR WRITE(6,503) 30 WRITE(6,502) SR(I),(QR(I,J),J=l,6) WRITE(6,504) 500 FORMAT(20X,'Temperature= ',F7.2,'\\') 501 FORMAT('Pressure (psia)',6('&',F7.2),'\\ \hline') 502 F0RMAT(F4.0,6('&',F8.2),'\\') 503 F0RMAT(1X,6('&',1X),1X,'\V) 504 FORMAT(IX,6('ft',IX),IX,'\\') Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 221 s t o p end Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 222 Table C l : Volumetric flow rates of H2S/N2 Tube No: 602 Float: GLASS Gas measured H2S/N2 Temperatures 290.15 (K) Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 10.59 12.26 13.72 15.05 16.69 17.40 20. 19.71 22.81 25.54 28.01 30.28 32.38 30. 42.79 49.53 55.46 60.82 65.74 70.32 40. 67.50 78.14 87.50 95.95 103.71 110.93 50. 93.85 108.65 121.66 133.40 144.20 154.23 60. 121.83 141.04 157.93 173.18 187.19 200.22 70. 151.45 175.32 196.32 215.27 232.69 248.89 80. 182.70 211.50 236.82 259.69 280.70 300.24 90. 215.58 249.56 279.44 306.43 331.22 354.28 100. 250.09 289.52 324.18 355.49 384.25 411.00 110. 286.24 331.36 371.04 406.87 439.78 470.40 120. 324.02 375.10 420.01 460.57 497.83 532.49 130. 363.44 420.73 471.11 516.59 558.39 597.26 140. 404.48 468.25 524.31 574.94 621.45 664.72 150. 447.16 517.66 579.64 635.60 687.03 734.86 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 223 Table C l : Volumetric flow rate of H2S/N2 (cont.) Tube No: 602 Float: Stainless steel Gas measured H2S/N2  Temperature= 290.15 (K)  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 18.06 20.90 23.41 25.67 27.74 29.67 20. 86.93 100.63 112.68 123.56 133.56 142.86 30. 155.17 179.63 201.14 220.56 238.40 255.00 40. 222.77 257.88 288.76 316.64 342.26 366.09 50. 289.73 335.40 375.56 411.82 445.14 476.13 60. 356.05 412.18 461.53 506.09 547.04 585.12 70. 421.74 488.22 546.68 599.46 647.96 693.07 80. 486.78 563.52 630.99 691.92 747.90 799.97 90. 551.19 638.08 714.49 783.47 846.86 905.82 100. 614.97 711.91 797.15 874.12 944.84 1010.62 110. 678.10 785.00 878.99 963.86 1041.84 1114.37 120. 740.60 857.35 960.00 1052.70 1137.86 1217.08 130. 802.46 928.96 1040.19 1140.62 1232.90 1318.74 140. 863.68 999.83 1119.55 1227.65 1326.97 1419.35 150. 924.27 1069.97 1198.08 1313.76 1420.05 1518.92 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 224 Table C l : Volumetric flow rate of H2S/N2 (cont.) Tube No: 604 Float Glass Gas measured H2S/N2  Temperature^ 290.15 (K)  Pressure (psia) 14.70 19.70 24.70 29.70 . 34.70 39.70 Scale reading Flow rate (mL/min) 10. 564.89 653.94 732.24 802.94 867.90 928.32 20. 1172.15 1356.93 1519.40 1666.11 1800.90 1926.28 30. 1793.84 2076.62 2325.27 2549.78 2756.07 2947.95 40. 2429.95 2813.01 3149.83 3453.96 3733.39 3993.32 50. 3080.49 3566.10 3993.09 4378.64 4732.88 5062.40 60. 3745.45 4335.89 4855.05 5323.82 5754.54 6155.18 70. 4424.83 5122.38 5735.70 6289.50 6798.34 7271.66 80. 5118.65 5925.56 6635.06 7275.70 7864.32 8411.86 90. 5826.88 6745.45 7553.11 8282.39 8952.46 9575.75 100. 6549.55 7582.03 8489.87 9309.60 10062.77 10763.36 110. 7286.64 8435.32 9445.32 10357.30 11195.23 11974.67 120. 8038.15 9305.30 10419.47 11425.51 12349.86 13209.69 130. 8804.09 10191.98 11412.32 12514.22 13526.66 14468.41 140. 9584.45 11095.36 12423.86 13623.43 14725.60 15750.84 150. 10379.23 12015.44 13454.11 14753.15 15946.72 17056.97 endix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 225 Table C.2: Volumetric flow rate of S02/N2 Tube No: 602 Float: Glass Gas measured S02/N2  Temperature = 290.15 (K)  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 12.61 14.59 16.34 17.92 19.37 20.72 20. 37.73 43.68 48.91 53.63 57.97 62.01 30. 64.04 74.14 83.01 91.03 98.39 105.24 40. 91.53 105.96 118.65 130.11 140.63 150.42 50. 120.21 139.16 155.82 170.87 184.69 197.55 60. 150.07 173.73 194.53 213.31 230.57 246.62 70. 181.12 209.67 234.77 257.44 278.27 297.64 80. 213.34 246.98 276.55 303.25 327.78 350.60 90. 246.76 285.66 319.86 350.74 379.12 405.51 100. 281.35 325.71 364.70 399.92 432.27 462.37 110. 317.13 367.13 411.08 450.78 487.24 521.17 120. 354.10 409.92 459.00 503.32 544.04 581.91 130. 392.24 454.08 508.45 557.54 602.65 644.60 140. 431.58 499.61 559.43 613.45 663.08 709.24 150. 472.09 546.51 611.95 671.04 725.32 775.82 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 226 Table C.2: Volumetric flow rate of S02/N2 (cont.) Tube No: 602 Float: Stainless steel Gas measured S02/N2  Temperatures 290.15 (K)  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 88.32 102.24 114.48 125.53 135.69 145.14 20. 158.01 182.92 204.82 224.60 242.77 259.67 30. 226.86 262.62 294.06 322.46 348.54 372.81 40. 294.86 341.34 382.21 419.11 453.02 484.56 50. 362.01 419.08 469.26 514.57 556.20 594.92 60. 428.32 495.84 555.21 608.82 658.07 703.89 70. 493.78 571.62 640.07 701.87 758.65 811.47 80. 558.40 646.43 723.83 793.71 857.93 917.66 90. 622.17 720.25 806.49 884.36 955.90 1022.46 100. 685.09 793.09 888.05 973.80 1052.58 1125.86 110. • 747.17 864.96 968.52 1062.04 1147.96 1227.88 120. 808.40 935.84 1047.89 1149.07 1242.03 1328.51 130. 868.79 1005.74 1126.17 1234.90 1334.81 1427.74 140. 928.33 1074.67 1203.34 1319.53 1426.28 1525.59 150. 987.02 1142.61 1279.42 1402.96 1516.46 1622.04 Appendix C COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 227 Table C.2: Volumetric flow rate of S02/N2 (cont.) Tube No: 604 Float: Glass Gas measured: S02/N2  Temperature = 290.15  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 528.49 611.80 685.06 751.20 811.97 868.51 20. 1179.25 1365.15 1528.61 1676.20 1811.81 1937.95 30. 1824.43 2112.04 2364.92 2593.27 2803.07 2998.22 40. 2464.03 2852.47 3194.01 3502.40 3785.75 4049.33 50. 3098.05 3586.44 4015.86 4403.60 4759.87 5091.26 60. 3726.49 4313.94 4830.48 5296.88 5725.41 6124.02 70. 4349.35 5034.99 5637.86 6182.21 6682.37 7147.61 80. 4966.63 5749.58 6438.01 7059.62 7630.76 8162.04 90. 5578.33 6457.71 7230.93 7929.10 8570.58 9167.29 100. 6184.45 7159.38 8016.61 8790.64 9501.83 10163.37 110. 6784.99 7854.59 8795.06 9644.26 10424.50 11150.29 120. 7379.95 8543.34 9566.28 10489.94 11338.61 12128.03 130. 7969.33 9225.63 10330.27 11327.69 12244.13 13096.60 140. 8553.13 9901.46 11087.02 12157.51 13141.09 14056.00 150. 9131.36 10570.84 11836.54 12979.41 14029.47 15006.24 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 228 Table C.3: Volumetric flow rate of total N2 Tube No: R7M251 Float: Steel Gas measured: Total N2  Temperature= 290.15  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 2618.55 3031.34 3394.30 3722.03 4023.15 4303.25 20. 4892.75 5664.05 6342.24 6954.61 7517.25 8040.63 30. 7127.80 8251.44 9239.43 10131.53 10951.19 11713.64 40. 9323.67 10793.47 12085.83 13252.76 14324.94 15322.28 50. 11480.37 13290.16 14881.46 16318.32 17638.52 18866.55 60. 13597.90 15741.50 17626.31 19328.20 20891.90 22346.45 70. 15676.26 18147.50 20320.39 22282.40 24085.11 25761.97 80. 17715.45 20508.14 22963.70 25180.93 27218.13 29113.12 90. 19715.47 22823.45 25556.23 28023.77 30290.97 32399.90 100. 21676.32 25093.41 28097.98 30810.95 33303.63 35622.31 . 110. 23597.99 27318.02 30588.96 33542.43 36256.10 38780.34 120. 25480.50 29497.29 33029.16 36218.25 39148.40 41874.00 130. 27323.84 31631.21 35418.59 38838.38 41980.51 44903.29 140. 29128.00 33719.79 37757.24 41402.84 44752.44 47868.21 150. 30893.00 35763.02 40045.12 43911.63 47464.19 50768.76 dix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 229 Table C.3: Volumetric flow rate of total N2 (cont.) Float: S. steel-R7M251 160. 32618.82 37760.91 42282.22 46364.73 50115.75 53604.93 170. 34305.47 39713.45 44468.55 48762.15 52707.14 56376.74 180. 35952.95 41620.64 46604.10 51103.89 55238.33 59084.16 190. 37561.26 43482.48 48688.88 53389.96 57709.36 61727.22 200. 39130.40 45298.98 50722.88 55620.35 60120.18 64305.90 210. 40660.37 47070.14 52706.10 57795.07 62470.84 66820.19 220. 42151.16 48795.95 54638.55 59914.10 64761.30 69270.13 230. 43602.79 50476.41 56520.22 61977.46 66991.56 71655.69 240. 45015.25 52111.53 58351.13 63985.14 69161.69 73976.88 250. 46388.53 53701.30 60131.25 65937.13 71271.56 76233.69 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 230 Table C.4: Volumetric flow rate of cylinder nitrogen Tube No: 603 Float: Glass Gas measured: Make-up N2  - Temperature^ 290.15  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 238.13 275.67 308.68 338.49 365.87 391.34 20. 443.34 513.23 574.68 630.17 681.15 728.58 30. 640.28 741.21 829.96 910.10 983.73 1052.21 40. 828.94 959.62 1074.52 1178.26 1273.59 1362.26 50. 1009.33 1168.44 1308.35 1434.67 1550.74 1658.71 60. 1181.45 1367.70 1531.46 1679.33 1815.19 1941.57 70. 1345.30 1557.38 1743.85 1912.22 2066.93 2210.83 80. 1500.88 1737.48 1945.52 2133.36 2305.96 2466.50 90. 1648.18 1908.00 2136.46 2342.74 2532.28 2708.58 100. 1787.21 2068.95 2316.68 2540.37 2745.89 2937.06 110. 1917.98 2220.33 2486.18 2726.23 2946.79 3151.95 120. 2040.47 2362.13 2644.96 2900.34 3134.98 3353.25 130. 2154.68 2494.35 2793.01 3062.69 3310.47 3540.95 140. 2260.63 2617.00 2930.35 3213.28 3473.24 3715.06 150. 2358.30 2730.07 3056.96 3352.12 3623.31 3875.58 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 231 Table C.4: Volumetric flow rate of cylinder nitrogen (cont.) Tube No: 603 Float: S steel Gas measured: Make-up 7V2 Temperature = 290.15 Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 513.47 594.41 665.59 729.85 788.90 843.82 20. 921.11 1066.32 1193.99 1309.28 1415.20 1513.73 30. 1311.31 1518.03 1699.79 1863.91 2014.70 2154.97 40. 1684.06 1949.54 2182.97 2393.74 2587.40 2767.54 50. 2039.37 2360.86 2643.54 2898.78 3133.30 3351.45 60. 2377.23 2751.99 3081.50 3379.02 3652.40 3906.69 70. 2697.65 3122.92 3496.84 3834.47 4144.69 4433.25 80. 3000.63 3473.65 3889.57 4265.12 4610.18 4931.15 90. 3286.16 3804.19 4259.68 4670.97 5048.87 5400.38 100. 3554.24 4114.53 4607.19 5052.03 5460.75 5840.94 110. 3804.88 4404.68 4932.08 5408.29 5845.83 6252.83 120. 4038.07 4674.64 5234.36 5739.75 6204.11 6636.06 130. 4253.82 4924.40 5514.02 6046.42 6535.59 6990.62 140. 4452.12 5153.96 5771.07 6328.29 6840.27 7316.51 150. 4632.98 5363.33 6005.52 6585.37 7118.14 7613.73 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 232 Table C.5: Volumetric flow rate of sample Tube No: 603 Float: Glass Gas measured: Sample Temperature = 290.15  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 250.79 290.32 325.08 356.47 385.31 412.14 20. 453.19 524.63 587.44 644.16 696.28 744.75 30. 647.88 750.01 839.81 920.90 995.40 1064.71 40. 834.86 966.47 1082.19 1186.68 1282.69 1371.99 50. 1014.14 1174.01 1314.58 1441.51 1558.13 1666.61 60. 1185.71 1372.63 1536.98 1685.38 1821.74 1948.57 70. 1349.58 1562.33 1749.39 1918.30 2073.50 2217.86 80. 1505.73 1743.10 1951.81 2140.27 2313.42 2474.49 90. 1654.18 1914.95 2144.24 2351.27 2541.50 2718.44 100. 1794.93 2077.88 2326.68 2551.33 2757.74 2949.74 110. 1927.96 2231.89 2499.13 2740.43 2962.13 3168.37 120. 2053.29 2376.98 2661.58 2918.57 3154.69 3374.33 130. 2170.91 2513.14 2814.05 3085.76 3335.41 3567.62 140. 2280.83 2640.38 2956.53 3241.99 3504.28 3748.26 150. 2383.04 2758.70 3089.02 3387.27 3661.31 3916.22 Appendix C. COMPUTER PROGRAMME FOR ROTAMETER CALIBRATION 233 Table C.5: Volumetric flow rate of sample (cont.) Tube No: 603 Float: S. steel Gas measured: Sample Temperature^ 290.15 (K)  Pressure (psia) 14.70 19.70 24.70 29.70 34.70 39.70 Scale reading Flow rate (mL/min) 10. 572.98 663.31 742.73 814.44 880.33 941.62 20. 971.72 1124.91 1259.60 1381.22 1492.96 1596.90 30. 1354.73 1568.29 1756.07 1925.62 2081.41 2226.32 40. 1721.99 1993.45 2232.14 2447.66 2645.68 2829.88 50. 2073.52 2400.40 2687.81 2947.33 3185.78 3407.58 60. 2409.32 2789.13 3123.08 3424.63 3701.69 3959.41 70. 2729.37 3159.64 3537.96 3879.56 4193.43 4485.38 80. 3033.69 3511.93 3932.43 4312.12 4660.98 4985.49 90. 3322.27 3846.00 4306.50 4722.31 5104.36 5459.74 100. 3595.11 4161.85 4660.18 5110.13 5523.55 5908.12 110. 3852.22 4459.49 4993.45 5475.59 5918.57 6330.64 120. 4093.59 4738.91 5306.32 5818.67 6289.41 6727.30 130. 4319.22 5000.11 5598.80 6139.38 6636.08 7098.10 140. 4529.11 5243.09 5870.88 6437.73 6958.56 7443.03 150. 4723.27 5467.86 6122.55 6713.71 7256.86 7762.11 Appendix D COMPUTER PROGRAMME FOR DATA LOGGING 1009 poke 6*6,0 1010 rem claus reaction project 1987 1020 r e » invest igator el. besher 1025 ren progran written by van Ie 1030 rem prog, for data logging 10*0 ret* with c64, adc-1 & instruments 1050 ren version l.a <1967) 1060 : 1070 open 2,2,0,chr*<136>+chr$<0>:rem XX open ijo port 2 ' 1209 baud XX 1080 poke 53281,12-.poke 53230,11:print chr$<14>chr$<8) 1090 teS="":gosub 2570:ren XX nl data <teS=input} XX 1100 : 1110 ren XX get data fron user XX 1120 print "\ • U I 1 B CLAUS REACTION PROJECT <1987>" 1130 print:print ' Progran for Data logging With" 11*0 print " C64, ADC-1, Thermocouple & Analyier" 1150 poke 646,0:print -.print -.print' I1A1N nEtiU 1160 print:print " 1) record temperatures" 1170 print " 2> display recorded data" 1189 pr int ; print : print : pr int" Enter your choice: ~}:sys 49152,1:print 1190 if teS="l" then 1229 1200 if te*="2" then 2850 1210 goto 1120 1229 print:print " Do you wish to write data to disk? ~y"',:sys 49152,1 : print 1230 if teS-'n" then dof="n" -.goto 1360 1249 if teS="y" then doX='y':goto 1260 1250 print "WBU" --goto 1229 1269 print "M Enter f i lename: W T T T T ^ ^ T I * ; 1279 sys 49152,16:print 1289 print "• creating f i l e "teS"...." 1290 close 15:close 7:open 15,8,15:open 7,8,9,te$+",s,w":gosub 2819 1300 if e/70 then 1220 1310 print "• enter # of sets of data you wish to" 1320 print " retrieve before recording the 16" 1330 print " latest temperatures to disk." 13-40 print: print" enter * of sets of data: "}:sys 49152,3:print:tn=vaI<teS> 1350 printiprint " Enter run # "f:sys 491S2,8:print:da£=te* 1360 pr int: pr in t ' enter current time <hhmmss>: T ^ ^ V ; : s / s 49152,6 1379 if len<teS><~6 or teS?"240000" then print "mU" -.goto 1360 1380 ti*=te* 234 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 235 1385 tt*=te* 1390 if do*="y~ then printt7.dat 1400 z 1410 din a<6>, b<6> z rem coeff. Array 1420 d in tp< 16) ~- ren temporary array 1430 ca 1=1.0 z ren calib. factor 14-4-0 ag=20 z ren anp gain 1453 z 1460 restorer for i=0 to 5zread a<i)znext 1470 data -0.0489 , 0.01987 , -2.186Ie-7 , 1.1569e-11 , -2.6492e-16 , 2.0184e-21 1480 for p-0 to 5zread b<p>znext p 1490 data 0.02266, 0.92415, 6.7233e-B , 2.2103e-12 , -8.6096e-16 , 4.B351e-20 1500 z 1510 gosub 4000 1511 printzprint'U Enter H2S flange 1,10 or 100: ; : input rl 1512 print'M confirning rl = 'i-.print rl 1513 print -.print"* Enter S02 Range50, 100,500, 1000 : i : input r2 1514 print'M confirning r2= "', z pr in t r2: pr in tz print z pr int i i=0 1515 i = i * l i i f if 100 then 1515 1520 gosub £000 1545 z 1547 print chr*<147> 1548 print "\ " 1558 for lo=l to tnzren loop x tines before writing data to disk 1560 : 1570 cn=48:gosub 2210zgosub 2210 1580 tb=<z/10>-273.16+cal 1590 z 1600 i/c=1019+< tb-20 >X51 .45:ren calculate junction voltage XX 1610 : 1620 ren print current tine at top 1638 pokeS3281 .llzpoke53280,12:poke646, 1 1640 print "I VMS' 1650 print spc< 13 >"Current tine "", leftS< t /"*,2> " z"i n id£<t it, 3,2>"-."rightS<t is,2) 1655 gosub 6200 1668 poke646,l 1670 print "\ "sprint " CLAUS REACTION PROJECT <1987>" -.poke 646,0 1680 print - DATA LOGGING 1681 print:print'WU" 1690 : Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 236 1400 14-19 din a<6>, b<6> z ren coeff. array 1429 dim tp<16) -.rem temporary array 1439 ca1=1.0 zrem calib. factor 1440 ag=20 zren amp gain 1450 z 1460 restorezfor i=0 to Szread a(i)znext i 1470 data -0.3489 , 0.91987 , -2.1861e-7 , 1.1569e-11 , -2.6492e-16 , 2,0184e-21 1480 for p=0 to 5zread b<p)znext p 1490 data 0.02266, 0.02415, 6.7233e-8 , 2.2103e-12 , -8.6096e-16 , 4.8351e-20 1509 z 1510 gosub 4000 1511 print zprint'U Enter H2S Range 1,10 or 190z T V * * ; z input rl 1512 print'U confirning rl= 'izprint rl 1513 printzprint'm Enter S02 Range50, 100,500,1000 z ^ T * ' ; z input r2 1514 print'U confirming r2= 'izprintr2zprintzprintzprintz i=0 1515 i=i*lzif i<100 then 1515 1520 gosub 6000 1545 z 1547 print chrS<147> 1548 print "I ' 1550 for lo-l to tnzren loop x tines before writing data to disk 1560 : 1570 cn=48zgosub 2219zgosub 2210 1580 tb=<z/10 >-273.16+cal 1590 z 1609 vc=1019+<tb-20)XSl.45zren XX calculate junction voltage XX 1616 z 1620 ren print current tine at top 1630 poke53281 ,11 zpoke53280, 12zpoke&46, 1 1640 print ~\ U B ' 1650 print spc< 13) "Current t ine ' ; lef tS < t i S ,2>' z' % m idS< t t'S, 3 ,2) ' z" r i ghtS < t if ,2) 1655 gosub 6200 1660 poke646,1 1670 print "\ '-.print " CLAUS REACTION PROJECT <1987>':poke 646,0 1680 print " DATA LOGGING 1681 print z print'UtL" 1690 z 1700 rem print reference temperature,*! Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 237 1710 z 1720 print a*<1)i" "WXVWV^" i ch rf < 5 > ', in t < t b) ; ch rS (144 > 1730 tp<l)=int<tb) 1740 rem read aid channel 1 (reference) 1750 z 1768 cn=l6z gosub 2210:gosub 2210 1770 z 1780 za-zX<1001ag) : ren XX convert reading to voltage 1798 : 1O08 ren XXX read next 18 channeIs XXX 1310 z 1820 for i=2 to 11 1839 i 1840 cn=15+izgosub 22I0zgosub 2210 1850 zt=zX <100/ag) 1860 z 1870 vd=zt-za-t-vcz ren XX calc. corresponding voltage 1880 z 1890 ren calc. carresp. temperature by 1908 ren using the polynomial function 1918 z 1920 t=0 1930 for J=0 to 5 194-0 t=t+a<j)*v<r~j 1950 if peek<653)=7 then 2530zren XX if sh i f t , c=, ct r I down, abort 1960 next j 1970 z 1980 ren print temp, of next II chs. 1990 print a$<i)i" •wmTW*" ; chr$<5) i in t < t)chrS< 144) 2000 tp<i) =int<t) 2010 next i 2020 rem read chanaI 12<k-thermocouple) 2030 cn=27igosu£>2210i gosub 2210 2035 vc=813+<tb-20)*40.3 2040 zw= zX<100lag) 2050 vq=zw-za+vc 2060 t=0 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 238 2078 2080 2090 2100 2110 2120 2130 2140 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2168 2169 2170 21S0 2190 2200 2210 2220 2230 2240 2258 2268 2270. 2288 2290 2388 for p-0 to 5 t = t+b(p)Xvq^ p if peek<653J=3 nex t p then 2530 rem print temp, of channel 12,chan 13 and 14 are not connected print a$(12)i" T T T T T V W » chrS<5> }int(t)} chrS(144) tp<12) =int(t) rem read h2s channel cn=38:gosub 2210:gosub2210 zbt=- <zX245.8) I <10Xag) : rem convert reading to m.volt ppm=c<1)+c(2)Xzbt+c(3)XzbtXzbt tp(15> = int< ppm) if peek <653)=3 then 2533 print" XX" print aS(15)'r" " T T V r w r * - ; chrS <5) } in t < ppm) i chr$ (144) rem read so2 channel cn=31:gosub2210:gosub2210 e=<51.SSXz)I(10Xag):rem con. reading to m.volt e0=eXexp(k1+k2Xppm):rem correct for h2s effect ppm-dfl)+d(2)*e8+d(3)Xe0Xe0 tp<16)=int<ppm) if peek(653)=3 then 2530 TTVTTm" f chr$(5) ; int (ppm) print at(I6)i" next lo if doS="n" then 1550 gosub 2470:rem goto 1550Jrem rem subrout ine for read ing aid cf=chr&(cn) gosub 2350 cS=chrS<161) gosub 2350 hb=ch if (hb and 128)C70 then 2230 c$=chr$<l45) gosub 2350 lb=ch hm=hb and 15 XX write data to disk XX XX go back and read more temps Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 239 2310 z =lb*256Xhn 2320 if <hb and 16>=0 then x=- z 2338 return 2340 : 2350 f1=0 2360 print*2,cSi 2379 tn=ti 2380 if ti7tm+4 then 2400: rem XX delay of 4 m i 11 i seconds XX 2390 goto 2380 2409 get*2,x* 2410 if peek < 168> <" 10 then f 1=1 : return 2420 if st=0 then 2370 2430 ch=peek<170> 2440 return 2459 : 2469 ren XX write data to f i l e XX 2470 : 2480 print*7,tiS:for wr=l to 11:print*7,aS(wr>;tp<wr>:next wr 2481 print*7,a$<I2> i tp<12> 2482 print*7,aS<15>i tp( 15> 2485 print#7,a$<16>', tp<16> 2490 for lk=l to 10:poke 53289, int<rnd<1>X15>:next Ik:return 2500 : 2519 ren XX abort & go to main menu XX 2520 : 2539 close 7:close 15:run 2540 : 2559 rem XX ml code for input XX 2560 : 2570 for i=0 to 5:read a:next i:for p=0 to 5:readb:nextp 2580' for i=49152 to 49262:read a:poke i,a:next i:goto 2490 2590 : 2600 data 160,0 , 149 , 111, 192,132,204 , 177, 122 ,291 ,44 , 240 ,4 , 162 ,1 , 298, 3, 32 ,241,183 2610 data 142, 112, 192,32,228,255,201,0,240,249,201 , 13,240,53,201,20,208, 10,172 2620 data 111 , 192,240,236,206,111, 192, 16,29, 170,41 , 127,201,32,144,224 ,138, 172 2630 data 111,192,204,112,192,176,215,238,111,192,208,5,206,111,192,43,205,153 2649 data 113,192,32,219,255,169,0,133,212,76,23,192,160,2,173,111,192,145,45 2650 data 200,169, 113', 145,45,200,169,192,145,45,230,204,169,32,76,210,255 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING Table D.l: Principal experimental measurements made in reaction experiments Reactor temperature: 373.0 K Static bed height: 0.19 m YHts- 0.1 YS02: 0.05 Minimum fluidization velocity: 0.0245 m/s Run # Flow rate u/umf Inlet cone. Outlet cone. (mL/min ) (-) (ppm) (pi jm) N2 H2S/N2 S02/N2 H2S SO 2 H2S so2 13-0 51069 154 77 4.44 300 150 108 53 14-0 50990 205 102 4.44 400 200 113 55 11-0 50915 256 128 4.44 500 250 122 61 18-1 50840 310 155 4.44 600 300 121 61 18-2 50840 310 155 4.44 600 300 127 63 15-0 50685 410 205 4.44 800 400 110 50 15-1 50685 410 205 4.44 800 400 111 57 21-0 50645 435 218 AAA 850 425 116 57 20-0 50770 487 244 4.44 950 475 125 65 12-1 50530 515 255 4.44 1000 500 96 51 42-0 50455 565 282 AAA 1100 550 121 62 42-1 50455 565 282 4.44 1100 550 126 65 41-0. 50375 615 308 4.44 1200 600 .101 45 41-1 50375 615 308 4.44 1200 600 99 51 43-0 50300 665 335 4.44 1300 650 140 74 43-1 50300 665 335 4.44 1300 650 136 65 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 241 Table D . l : Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 423.0 K Static bed height: 0.19 m YEas: 0.1 YSo7: 0.05 Minimum fluidization velocity: 0.0225 m/s Run # Flow rate (mL/min) u/umf (-) Inlet cone, (ppm) Outlet cone, (ppm) ^ 2 H2S/N2 S02/N2 H2S so2 H2S S02 24-1 46935 95 47 4.44 200 100 58 32 25-1 46865 140 70 4.44 300 150 72 38 23-1 46795 190 95 4.44 400 200 77 36 26-0 46725 235 118 4.44 500 250 103 58 30-0 46655 280 140 4.44 600 300 104 50 27-0 46580 330 165 4.44 700 350 90 44 40-1 46510 380 190 4.44 800 400 74 39 28-0 46370 470 235 4.44 1000 500 82 40 36-0 46230 565 282 4.44 1200 600 74 36 33-0 46160 610 306 4.44 1300 650 95 49 33-1 46160 610 305 4.44 1300 650 94 46 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 242 Table D . l : Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 423.0 K Static bed height: 0.32 m YHiS: 0.1 YSo7: 0.05 Minimum fluidization velocity: 0.0224 m/s Run # Flow rate (mL/min) u/umf (-) Inlet cone, (ppm) Outlet cone, (ppm) N2 H2S/N2 S02/N2 H2S S02 H2S S02 80-1 93870 190 95 8.88 200 100 49 25 80-0 93730 280 140 8.88 300 150 62 29 78-0 93590 375 188 8.88 400 200 77 37 77-0 93450 470 235 8.88 500 250 66 31 73-0 93310 565 282 8.88 600 300 66 33 76-0 93165 660 330 8.88 700 350 57 27 75-0 93025 755 378 8.88 800 400 47 25 83-0 92880 850 425 8.88 900 450 63 32 74^0 92745 940. 470 8.88 1000 500 45 21 . 79-0 92460 1130 565 8.88 1200 600 37 19 82-0 92320 1225 612 8.88 1300 650 28 17 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 243 Table D.l: Principal experimental measurements made in reaction experiments (cont.) H2S/SO2 concentration: 600 ppm Static bed height: 0.19 m N2 flow rate: H2S/N2 flow rate: S02S/N2 flow rate: YH2S'-Yso2'-48750 mL/min 295 mL/min 148 mL/min 0.1 0.05 Run # Temperature Outlet cone. (°C) (ppm) H2S S02 18-1 100 121 61 18-2 100 127 63 44-0 120 114 55 45-0 130 102 48 30-0 150 104 50 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 244 Table D . l : Principal experimental measurements made in reaction experiments (cont.) H2S/SO2 concentration: 600 ppm Static bed height: 7Y2 flow rate: H2S/N2 flow rate: SO2/N2 flow rate: YH2S-Yso2' 0.19 m 48230 mL/min 640 mL/min 320 mL/min 0.1 0.05 Run # Temperature Outlet cone. (°C) (ppm) H2S SO2 43-0 100 140 74 43-1 100 135 65 47-0 110 122 59 46-1 130 104 56 33-0 150 95 49 33-1 150 94 46 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 245 Table D.l: Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 423.0 K H2S/S02 concentration: 600/300 Static bed height: 0.19 m YH2s: 0.1 YS02: 0.05 Minimum fluidization velocity: 0.0225 m/s Run # Flow rate (mL/min) u/umf (-) Outlet cone, (ppm) N2 H2S/N2 S02/N2 H2S S02 51-0 23585 140 70 2.2 49 24 50-0 33250 200 100 3.1 83 44 49-0 38900 235 118 3.7 99 49 30-0 46655 280 140 4.4 106 56 52-0 61712 375 188 5.9 122 63 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 246 Table D . l : Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 423.0 K H2S/S02 concentration: 1300/650 Static bed height: 0.19 m YH2s: 0.1 YS02: 0.05 Minimum fluidization velocity: 0.0225 m/s Run # Flow rate (mL/min) u/umf (-) Outlet cone, (ppm) N2 H2S/N2 SO2/N2 H2S S02 55-0 23380 310 155 2.2 39 21 56-0 32525 430 215 3.1 51 25 53-0 39370 520 260 3.7 89 45 33-0 46160 610 306 4.4 95 49 33-1 46160 610 305 4.4 94 46 54-0 52900 700 350 5.1 111 54 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 247 Table D . l : Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 373 K Static bed height: 0.32 m H2S/SO2 concentration: 1000/500 ppm N 2 flow rate: 50530 mL H2S/N2 flow rate: 515 mL S02/N2 flow rate: 255 mL YH3S: 0.1 Yso,: 0.05 Time S.Loading | Outlet concentration Time S.Loading Outlet concentration (h.) (8/g%) (ppm) (h.) (g/g%) (ppm) H2S SO 2 H2S SO 2 2.00 0.011 67 31 109.25 13.048 212 106 4.00 0.135 66 31 117.00 14.213 204 100 6.00 0.355 63 30 125.00 15.129 213 106 9.00 0.532 64 29 135.00 16.271 227 112 12.00 0.548 62 30 140.75 16.927 239 121 15.00 0.593 71 34 151.00 17.904 251 126 18.00 0.716 70 36 162.00 18.764 263 130 21.00 0.728 70 37 170.00 22.786 269 134 24.00 0.844 72 35 178.00 24.994 277 138 27.00 0.892 73 36 186.00 25.241 312 154 32.00 1.264 85 39 196.00 27.062 318 157 37.00 1.489 79 39 207.00 25.220 361 179 42.25 1.523 78 41 219.00 29.080 367 181 48.25 1.837 77 37 231.00 27.078 389 192 55.00 2.592 88 48 243.00 31.969 410 203 60.00 3.505 87 42 255.00 37.711 418 210 68.00 4.144 83 41 265.00 42.353 426 214 72.00 4.159 98 47 277.00 44.444 438 217 80.00 7.049 115 59 288.00 45.125 457 230 86.00 6.950 120 60 301.00 47.172 479 237 95.00 9.153 186 94 313.00 50.812 529 263 99.25 12.016 181 93 335.00 54.922 570 284 347.00 60.055 611 303 Appendix D. COMPUTER PROGRAMME FOR DATA LOGGING 248 Table D . l : Principal experimental measurements made in reaction experiments (cont.) Reactor temperature: 100°C H2S/S02 concentration: 600/300 N2 flow rate: 50840 mL/min H2S/N2 flow rate: 310 mL/min S02/N2 flow rate: 155 mL/min Run # Static bed height Outlet concentration (m) (ppm) H2S so2 R-5 0.12 224 110 18-1 0.19 121 61 18-2 0.19 127 63 R-2 0.25 79 - 39 R-4 0.32 48 22 R-3 0.38 28 15 dix D. COMPUTER PROGRAMME FOR DATA LOGGING 249 Table D . l : Principal experimental measurements made in reaction experiments (cont.) H2S/SO2 concentration: 600/300 ppm Y S 0 2 : 0.05 YH2S: 0.1 WCAT: 1.2 Kg Run # Temperature (K) Flow rate (mL/min) Outlet cone, (ppm) N2 H2S/N2 SO2/N2 H2S S02 64-0 373 10275 62 31 44 19 65-0 397 10275 62 31 36 23 63-0 423 9340 57 28 29 12 Appendix E PURGING-TIME OF REACTOR SYSTEM The presence of oxygen in the reactor system could adversely affect the catalyst at high temperatures. In addition, since it did not constitute part of the feed gas, it was absolutely necessary to purge it from the reactor as well as the nitrogen recycle loop. The purging-time, r, for a system of known volume, V, is given by the equation (Nelson, 1971): r = 2.303^ l o g 1 0 ^ (E.l) Where Ci and Cf denote the initial and final concentration of 02 and Q denotes the purge rate. The volume of the system was approximately 90 1. Accordingly, the concentration of oxygen can be reduced from 21% to 1 ppb within a period of about 6 hours at a purge rate of 5 L/min. 250 Appendix F PREDICTIONS OF EQUILIBRIUM CONVERSION IMPL IC IT REAL * 8 (A -H , 0 - Z ) , I NTEGER ( I -N ) EXTERNAL F C0MM0N/BLK1/EC,FS02,FN2.FTOTAL DIMENSION A ( 4 , 7 ) , F R T ( 4 ) , R 0 0 T ( 1 ) DATA A/0.322571D+1,0.3916307D+1,0.4156502D+1, $ 0 .7783897D+1,0 .5655121D-2 , -0 .3513967D-3 , -0 .1724433D-2 , $ 0 .2509982D-1 , - 0 .2497021D-6 ,0 .4219131D-5 ,0 .5698232D-5 , $ - 0 . 3714831D -4 , - 0 . 4220677D -8 , - 0 . 2745366D -8 , - 0 . 4593004D -8 , $ 0 .2615731D-7 ,0 .2139273D-11 ,0 .4858364D-12 ,0 .1423365D-11 , $ -0 .7120913D-11, -0 .3690448D+5, -0 .3609558D+4, -0 .3028877D+5, $ 0.1011458D+5,0.9817704D+1,0.2366004D+1,-0.6861625D+0, $ 0.4762179D+1/ C A : C o e f f i c i e n t s i n f r e e e n e r g y e x p r e s s i o n s C TO i Tempe ra tu r e a t w h i c h e q u i l i b r i u m c o n v e r s i o n C i s sought C PPM : C o n c e n t r a t i o n o f S02 i n p a r t s p e r m i l i o n C Q : V o l u m e t e r i c f l o w r a t e 251 Appendix F. PREDICTIONS OF EQUILIBRIUM CONVERSION 252 C FRT : F r e e ene r gy o f any s ub s t ance/RT C DRET : D e l t a FRT C EC E q u i l i b r i u m c o n s t a n t C F T O T A L : T o t a l m o l a r f l o w r a t e C FS02 : M o l a r f l o w r a t e o f S02 C FH2S : M o l a r f l o w r a t e o f H2S C FN2 : M o l a r f l o w r a t e o f N2 C X I , X F : I n t e r v a l a t w h i c h r o o t b e i n g sought C DXI : I n t e r v a l i n c r e m e n t C TOL : A c c u r a c y i n r o o t C ROOT :Root o f e q u i l i b r i u m e x p r e s s i o n C CON : E q u i l i b r i u m c o n v e r s i o n C PS02 : p a r t i a l p r e s s u r e o f S02 C S p e c i f y t o t a l v o l u m e t r i c f l o w r a t e and S02 C f e e d c o n c e n t r a t i o n 0=49.193D-3 PPM=300.0D0 C S p e c i f y t e m p e r a t u r e r a n g e N=120 TI=90.0DO+273.0DO TF=150.0D0+273.0D0 T0=TI RN=N DT=(TF-TI )/RN C C a l c u l a t e : f r e e e n e r g y , f r e e ene r g y d i f f e r e n c e and C e q u i l i b r i u m c o n s t a n t a t t e m p e r a t u r e TO Appendix F. PREDICTIONS OF EQUILIBRIUM CONVERSION 20 T1=1.0DO-DLOG(TO) T2=T0 T3=T2*T0 T4=T3*T0 T5=T4*T0 DO 30 K=l,4 FRT(K)=A(K,1)*T1-A(K,2)*T2/2.ODO-A(K,3)*T3/6.ODO $ -A(K,4)*T4/12.0D0-A(K,5)*T5*0.05D0+A(K,6)/T2-A(K,7) 30 CONTINUE DFRT=2.ODO*FRT(3)+3.ODO*FRT(4)/8.ODO-2.ODO*FRT(2)-FRT(1) EC=DEXP(-DFRT) C Calculate molar flow rates. FTOTAL=760.0D0*Q/62.4D0/T0 FS02=PPM*1.0D-6*FT0TAL FH2S=FS02*2.0DO FN2=FT0TAL-FS02-FH2S C Find the root of the equilibrium equation XI=0.0D0 XF=1.0D-1 DXI=0.100D-2 TOL=1.0D-9 CALL BISECT(F,XI,XF,1,ROOT,DXI,TOL,NR) C Calculate partial pressure of S02 PS02=R00T(1) C Calculate equilibrium conversion C0N=100.ODO*(1.0D0-FT0TAL*PS02/FS02) Appendix F. PREDICTIONS OF EQUILIBRIUM CONVERSION 254 WRITE(6,200) TO, CON C Increase temperature TO=TO+DT C Check for temperature range IF(TO.LE.TF) GO TO 20 100 F0RMAT(7(1X,D15.7)) 200 F0RMAT(1X,F5.1,1X,F7.3) STOP END DOUBLE PRECISION FUNCTION F(X) IMPLICIT REAL*8(A-H,0-Z) C0MM0N/BLK1/EK,FS,FN,FT T=(FS-FT*X)/(2.0D0*FS+FN) F=EK*X*X*X-T*T RETURN END 

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