@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Chemical and Biological Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Jamal, Aqil"@en ; dcterms:issued "2009-09-15T18:13:23Z"@en, "2002"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """Absorption and desorption of carbon dioxide (CO₂) and carbon monoxide (CO) in aqueous alkanolamine solutions are modeled and important kinetic and physical property data are obtained using novel experimental methods. The model is based on the principle of diffusional mass transfer accompanied with fast to very slow chemical reactions in the liquid phase. Fast reactions are represented by CO₂ absorption/desorption in aqueous alkanolamines and slow reactions are represented by CO absorption in aqueous diethanolamine (DEA). The experiments for CO₂ absorption and desorption were conducted in a novel hemispherical contactor designed and developed in this work. The absorption experiments were conducted at near atmospheric pressure using pure CO₂ saturated with water at 293 to 323 K with initially unloaded solutions. The desorption experiments were performed at 333 to 383 K for CO₂ loadings between 0.02 to 0.7 moles of CO₂ per mole of amine using humidified N₂ gas as a stripping medium. The experiments for CO absorption were carried out in a 660 mL batch autoclave reactor at 313 to 413 K with amine concentration between 5 to 50-wt% in distilled water. The partial pressure of CO in the reactor was varied from 800 to 1100 kPa. The data for CO₂ absorption and desorption in aqueous amine systems were analyzed using a new, rigorous mathematical model. The model predicts the experimental results well for all amine systems studied. The results indicate that the theory of absorption with reversible chemical reaction could be used to predict desorption rates. The kinetic data obtained show that desorption experiments could be used to determine both forward and backward rate constants accurately. The absorption experiments on the other hand could only be used to determine forward rate constants. The data for CO absorption in aqueous diethanolamine (DEA) solutions were analyzed using the model for mass transfer with extremely slow reactions. The data are consistent with a mechanism by which formyl-diethanolamine (DEAF) is predominantly formed by direct insertion of CO into DEA. The data also confirm that DEAF formation via the DEA-formate reaction is relatively slow and reversible."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/12793?expand=metadata"@en ; dcterms:extent "12194019 bytes"@en ; dc:format "application/pdf"@en ; skos:note "ABSORPTION AND DESORPTION OF C 0 2 AND CO IN ALK AN OL AMINE SYSTEMS by AQIL JAMAL M.Sc, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 1992 M.Tech., Indian Institute of Technology, Madras, India, 1986 B. Tech., Harcourt Butler Technological Institute, Kanpur, India, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE FACULTY OF G R A D U A T E STUDIES Department of Chemical and Biological Engineering We accept this thesis^ as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 2002 © Aqil Jamal, 2 0 0 2 In presenting this thesis in partial fulfillment 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 The University of British Columbia Vancouver, Canada ABSTRACT Absorption and desorption of carbon dioxide (CO2) and carbon monoxide (CO) in aqueous alkanolamine solutions are modeled and important kinetic and physical property data are obtained using novel experimental methods. The model is based on the principle of diffusional mass transfer accompanied with fast to very slow chemical reactions in the liquid phase. Fast reactions are represented by CO2 absorption/desorption in aqueous alkanolamines and slow reactions are represented by C O absorption in aqueous diethanolamine (DEA). The experiments for CO2 absorption and desorption were conducted in a novel hemispherical contactor designed and developed in this work. The absorption experiments were conducted at near atmospheric pressure using pure CO2 saturated with water at 293 to 323 K with initially unloaded solutions. The desorption experiments were performed at 333 to 383 K for C 0 2 loadings between 0.02 to 0.7 moles of CO2 per mole of amine using humidified N2 gas as a stripping medium. The experiments for C O absorption were carried out in a 660 mL batch autoclave reactor at 313 to 413 K with amine concentration between 5 to 50-wt% in distilled water. The partial pressure of C O in the reactor was varied from 800 to 1100 kPa. The data for C 0 2 absorption and desorption in aqueous amine systems were analyzed using a new, rigorous mathematical model. The model predicts the experimental results well for all amine systems studied. The results indicate ii that the theory of absorpt ion with reversible chemica l reaction could be used to predict desorpt ion rates. The kinetic data obtained show that desorpt ion exper iments could be used to determine both forward and backward rate constants accurately. The absorption exper iments on the other hand could only be used to determine forward rate constants. The data for C O absorpt ion in aqueous diethanolamine (DEA) solutions were ana lyzed using the model for mass transfer with extremely s low reactions. The data are consistent with a mechan ism by which formyl-diethanolamine ( D E A F ) is predominantly formed by direct insertion of C O into D E A . The data also confirm that D E A F formation via the DEA- formate reaction is relatively s low and reversible. iii TABLE OF CONTENTS A B S T R A C T ii LIST OF T A B L E S x LIST OF F IGURES xviii A C K N O W L E D G E M E N T xxix CHAPTER 1. INTRODUCTION 1 1.1 Background 1 1.1.1 Commercially Important Amines 2 1.1.2 Acid Gas Treating Process 5 1.2 Importance of Kinetic and Physical Property data in Design and Simulation of Gas Treating Systems 8 1.2.1 Kinetic Data on C0 2 -Amine Systems 9 1.2.2 Kinetic Data on CO-Amine systems 10 1.3 Objectives and Scope of This Work 11 1.3.1 Organization of the Thesis 12 PART I. C 0 2 ABSORPTION AND DESORPTION IN AMINE SYSTEMS CHAPTER 2. LITERATURE EVIEW 14 2.1 Mass Transfer with Chemical Reaction 15 2.2 Reaction Mechanisms of C0 2 -Amine-Water Systems 20 2.2.1 C 0 2 Reactions with Water 20 2.2.2 C 0 2 Reactions with Amines 21 2.2.3 C 0 2 Reactions with Aqueous Amine Blends 26 2.3 Kinetic Data for C 0 2 Absorption/Desorption in Aqueous Amines 27 2.3.1 Kinetic Data for C0 2 -MEA-Wate r System 27 2.3.2 Kinetic Data for C0 2 -DEA-Water System 30 iv 2.3.3 Kinetic Data for C0 2 -MDEA-Wate r System 34 2.3.4 Kinetic Data for C0 2 -AMP-Wate r System 37 2.3.5 Kinetic Data for Amine Blends 42 2.4 Research Needs 46 CHAPTER 3. EXPERIMENTAL APPARATUS AND METHODS 48 3.1 Overview 48 3.2 Hemispherical Contactor 49 3.3 Experimental Setup and Procedure 52 3.4 Data Acquisition and Calibration 57 3.5 Chemicals 60 CHAPTER 4. MATHEMATICAL MODEL 61 4.1 Reaction Mechanism 62 4.1.1 Reactions for C02+AMP+H20 (Base Case) 62 4.1.2 Reactions for 02+MEA+H20 64 4.1.3 Reactions for C02+DEA+H20 64 4.1.4 Reactions for C02+MDEA+H20 65 4.1.5 Reactions for C02+MEA+MDEA+H20 66 4.1.6 Reactions for C02+MEA+AMP+H20 66 4.1.7 Reactions for C02+DEA+MDEA+H20 66 4.1.8 Reactions for C02+DEA+AMP+H20 67 4.2 Reaction Rates 67 4.2.1 Reaction Rates for C02+AMP+H20 System (Base Case) 67 4.2.2 Reaction Rates for C02+MEA+H20 System 68 4.2.3 Reaction Rates for C02+DEA+H20 System 69 4.2.4 Reaction Rates for C02+MDEA+H20 System 69 4.2.5 Reaction Rates for C02+MEA+MDEA+H20 System 70 v 4.2.6 Reaction Rates for C02+MEA+AMP+H20 System 70 4.2.7 Reaction Rates for C02+DEA+MDEA+H20 System 72 4.2.8 Reaction Rates for C02+DEA+AMP+H20 System 72 4.3 Reactive Gas Absorption/Desorption Model 73 4.3.1 Hydrodynamics of Liquid Film 73 4.3.2 Model Equations 76 4.3.3 Liquid Bulk Concentrations 81 4.3.4 Rate of Absorption or Desorption with Chemical Reaction 83 4.3.5 Rate of Absorption or Desorption without Chemical Reaction 83 4.3.6 Enhancement Factor 85 4.3.7 Overall Reaction Rate (r totai) 8 5 4.4 Model Parameters 86 4.5 Numerical Implementation 87 4.6 Parameter Estimation 89 CHAPTER 5. RESULTS AND DISCUSSION 93 5.1 Model Verification 93 5.1.1 CO2 Absorption/Desorption in Aqueous Amines 93 5.1.2 Detailed Profiles in the Hemispherical Film 97 5.1.3 Numerical versus Analytical Solutions 102 5.2 Parametric Sensitivity Analysis 104 5.2.1 Effect of Operating Parameters 104 5.2.2 Effect of Physical Property Parameters 109 5.2.3 Effect of Kinetic Parameters 111 5.3 Henry's Constant and C 0 2 Diffusivity in Amine Solutions 115 5.3.1 Correlation for Henry's Constant of C 0 2 in Amine Solutions 115 5.3.2 Correlation for C 0 2 Diffusivity in Amine Solutions 116 5.4 C 0 2 Absorption and Desorption in Aqueous Amine Solutions 118 5.4.1 C 0 2 Absorption/Desorption in Aqueous Solutions of MEA, DEA and AMP Solutions 120 vi 5.4.2 C 0 2 Absorption/Desorption in Aqueous MDEA Solutions 134 5.4.3 C 0 2 Absorption/Desorption in Aqueous Amine Blends 138 5.4.4 Comparison of the Parameter Estimates with Literature Data. ...142 5.4.5 Predicted Absorption/Desorption Rates Based on Correlations Developed in This Work 147 5.5 Conclusions 155 PART II CO ABSORPTION AND CO INDUCED DEGRADATION IN AMINE SYSTEMS CHAPTER 6. INTRODUCTION AND LITERATURE REVIEW 157 6.1 Background 157 6.2 Literature Review 158 6.3 Objectives 161 CHAPTER 7. EXPERIMENTAL APPARATUS AND EXPLORATORY EXPERIMENTS 163 7.1 Experimental Apparatus 163 7.2 Exploratory Experiments 166 7.2.1 C O Absorption in Aqueous DEA Solutions 166 7.2.2 Material Balance 168 7.2.3 C O Absorption in Pure DEA 170 7.3 Proposed Reaction Mechanism 170 CHAPTER 8. MATHEMATICALMODEL 172 8.1 Reaction mechanism 172 8.2 Reaction Rates 173 8.3 Mathematical Model 173 8.4 Model Parameters 177 8.5 Parameter Estimation 178 vii CHAPTER 9. RESULTS AND DISCUSSION 180 9.1 Absorption and Degradation in CO-DEA System 180 9.1.1 Determination of k La 180 9.1.2 Determination of H C o-D by Nitrogen Analogy 184 9.1.3 Determination of k3 and k.3 188 9.1.4 Determination of k i , k2 and H C o-DEA 195 9.2 Absorption and Degradation in C O - M D E A System 200 9.3 Absorption and Degradation in CO-DEA+DEAF System 202 9.4 Model Predictions 203 9.5 Process Implications 206 9.6 Conclusions 208 CHAPTER 10. OVERALL CONCLUSIONS AND RECOMMENDATIONS 210 10.1 Conclusions on C 0 2 Absorption and Desorption in Amine Systems Kinetics 210 10.2 Conclusions on C O Absorption and C O Induced Degradation in Amine Systems 214 10.3 Recommendations for Future Work 216 NOMENCLATURE 218 REFERENCES 222 APPENDICES 235 A. Determination of C 0 2 Loading in Amine Solutions 235 B. Calibration of Measuring Instruments 240 C. Analytical Solution for Physical Absorption/Desorption Model 252 D. Derivation of Rate Expression for Zwitterion Mechanism 259 E. Density and Viscosity of Aqueous Amine Solutions 262 viii F. Henry's Constant of C 0 2 and N 2 0 in Aqueous Amine Solutions 272 G. Diffusivity of C 0 2 and N 2 0 in Aqueous Amine Solutions 293 H. Equilibrium constants 313 I. Determination of Gas-Side of Gas-Side Mass Transfer Coefficient 319 J . Determination of Formate and DEAF 324 K. Experimental Data 327 ix LIST OF TABLES Table 1.1: Molecular structure of commonly used alkanolamines 3 Table 2.1: Summary of the results reported on the C0 2 -MEA-Wate r system 28 Table 2.2: Summary of the results reported on the C0 2 -MEA-Wate r system 31 Table 2.3: Summary of results reported on the C0 2 -MDEA-Wate r system 36 Table 2.4: Carbamate stability constants for MEA, DEA and A M P by C 1 3 - N M R (Sartori and Savage, 1983) 39 Table 2.5: Summary of results reported on the C0 2 -AMP+Water system 40 Table 2.6: Summary of results reported on C0 2 -MEA+MDEA+Water and C 0 2 -DEA+MDEA+Water systems 44 Table 4.1: Overall reaction rate (rtotai) • 86 Table 4.2: Parameters for absorption/desorption model 88 N—H - C — C — O H H O — C — C H O — C — C N — C H , Diisopropanolamine (DIPA) Methyldiethanolamine (MDEA) C H 3 I I M H O — C — C — N < , , I I ^ C H 3 2-amino-2-methyl-1 -propanol (AMP) N X C H 2 — C H 2 — O H H 2-piperidine ethanol (PE) 3 The reaction of CO2 with a basic solvent is much slower than that of H 2 S. The slower reaction rate of C 0 2 is due to its nature as a Lewis acid, which must hydrate before it can react by acid-base neutralization. It may also react directly with the amine to form a carbamate. The rate of hydration and carbamation are both slow and can be comparable to the rate of diffusion of C 0 2 . The reaction rate may therefore limit the overall absorption for C 0 2 . It is this fact which creates a need for reliable reaction rate data so that the acid gas contactor can be modeled accurately. Aqueous MEA and DEA solutions are generally used for bulk C 0 2 removal when the partial pressure of C 0 2 is relatively low and the product purity requirement is high. DIPA is used primarily in special applications where it is necessary to preferentially absorb H 2 S over C 0 2 . Both primary and secondary amines react fairly strongly with C 0 2 to form stable carbamates and their heats of reactions are substantial. Consequently, these amines require substantial energy for regeneration. The energy is supplied in a stripper at elevated temperatures thereby making the amine susceptible to degradation. MDEA is the most commonly used tertiary amine and it is mostly used for the selective removal of H 2 S from natural gases. The most important difference between primary and secondary amines on the one hand and tertiary amines on the other is that tertiary amines do not directly react with CO2 to form carbamate. Instead, they are believed to catalyze the hydrolysis of C 0 2 to carbonate and bicarbonate ions. This also means that regeneration of C 0 2 rich MDEA solution requires less energy in comparison to primary and secondary amines. 4 In many gas-treating applications one finds that MDEA is too selective towards H 2 S (i.e., it allows too much C 0 2 to slip through the absorber), while DEA and MEA are not selective enough. In MEA and DEA based plants, this lack of sufficient selectivity towards H 2 S causes too much C 0 2 to be removed and pushes up solvent regeneration cost. Therefore, in recent years there has been considerable interest in using blends of MDEA and DEA or MDEA and MEA. The benefit of using such amine blends is that they combine the advantages of higher absorption rates of MEA and DEA and the better stripping characteristics of MDEA. Moreover, they provide an additional degree of freedom in the form of amine composition that can be manipulated to exercise some control on the selectivity of MDEA towards H 2 S over C 0 2 by adjusting the gas-liquid contact time. Recently a new class of amines referred to as sterically hindered amines, has been introduced as a commercially attractive alternative to MEA, DEA and DIPA. Examples are 2-amino-2-methyl-1-propanol (AMP), which is the hindered form of MEA, and 2-piperidine ethanol (PE), which is the hindered form of DEA. In comparison to primary and secondary amines, hindered amines form less stable carbamate and have good selectivity for H 2 S. Exxon Research and Engineering Company have already commercialized a hindered amine based H 2S-selective gas treating process (Goldstein et al., 1986). 1.1.2 Acid Gas Treating Process A typical process schematic for removing acid gases is shown in Figure 1.1. A feed gas containing typical hydrocarbons ( C H 4 , C 2 H 6 , C3H8, etc.) along , 5 with acid gases is contacted countercurrently with the descending amine solution in a packed or plate column to provide favorable conditions for mass transfer and chemical reactions. The absorber operates at high pressure and low temperature (< 40 °C). The purified gas leaves the top of the absorber. The solution discharging from the bottom of the absorber is rich in acid gases and is heated in an exchanger after pressure reduction in a flash drum. The purpose of the flash is to liberate dissolved hydrocarbons. The rich solution is then fed to the stripper (or desorber) where acid gases are removed from the solution by steam stripping. The stripper operates at slightly above ambient pressure and high temperature (> 120 °C). The acid gases in the overhead accumulator are either incinerated or sent to a sulfur plant. The lean amine solution leaving the reboiler is cooled in the lean-rich heat exchanger, before being returned to the absorber. The major energy consumption in this process is in the stripper. The energy supplied to the reboiler is used for two reasons: (1) to produce enough water vapor so that the vapor phase partial pressure of acid gases is reduced to provide a driving force for desorption, and (2) to provide enough energy to reverse the reactions which occur in the absorber. In fact the reactions of CO2 with aqueous alkanolamine solutions are highly exothermic, releasing energy in the absorber and requiring energy in the stripper. 6 Purified Gas Absorber (High Pressure, Low Temperature) Raw Gas and Impuritie (C0 2,H 2S...) Lean Amine Cooler Lean Amine, Solution Dissolved Hydrocarbons (Fuel Gas) Rich Amine Solution Flash Drum Lean-Rich | / ^ ^ H e a t Exchanger • Pump ~ ,_ CO,,H,S.. Overhead z ^ Condenser Reflux Drum Stripper (Low Pressure, Boiling) Steam Reboiler I K DOII IP Figure 1.1: Typical absorber/stripper system for acid gas removal The reboiler heat duty is the most significant operating cost of this type of system (Blauwhoff et al., 1985). It is, therefore, desirable to gain a better understanding of the the underlying principles behind the absorption/desorption process and to find solvents and/or operating modes, which reduce the reboiler heat duty. Stripping is also an area where amine solutions are exposed to high temperatures (-120 °C). This may accelerate certain undesirable irreversible reactions between amine and acid gases resulting in products from which the amine cannot be regenerated under typical operating conditions. As a result, significant amounts of valuable amine may be lost or rendered ineffective. Recently, amine degradation has been the subject of considerable research, but 7 it is still not much fully understood. In fact, amine degradation due to the presence of C O is one of the topics covered in this dissertation. 1.2 Importance of Kinetic and Physical Property Data in Design and Simulation of Gas Treating Systems Gas treating using alkanolamines has been practiced in industry for over half a century. However, it is only recently that substantial progress has been made in developing a fundamental understanding of these seemingly simple processes. Modern computer technology has made it possible to use sophisticated mass transfer rate-based models to design and simulate almost any type of gas treating systems (Katti, 1995; Katti and McDougal, 1986; Yu and Astarita, 1987; Krishnamurthy and Taylor, 1985; Sardar, 1985). These models have been particularly useful in the development and commercialization of mixed solvents, the composition of which can be tailored to specific applications (Katti, 1995). Comprehensive models require calculations of component and energy balances around each phase on every tray or section of packing. This in turn, involves determining the driving forces, mass and heat transfer coefficients, interfacial area, and interaction between mass transfer and chemical reaction. Thus a rate-based model consists of a vapor-liquid equilibrium (VLE) model, reaction kinetics model, hydrodynamic model and a model to describe the effect of reaction on mass transfer. Although these models are robust enough to treat gas-liquid contacting from fundamental principles and therefore have the potential of accurately predicting the performance of chemical absorbers and 8 strippers, the models are ultimately as accurate as the experimental data upon which they are based. While great advances have been made in developing increasingly complex models to simulate gas-treating units, similar advances are lacking for the basic kinetic and physical property data. 1.2.1 Kinetic Data for C02-Amine Systems A comprehensive literature review of basic kinetic data for commercially important amines is given in Chapter 2. Several general observations about the existing literature data are noted here. First, the great majority of data are gathered under absorption conditions. However, in designing and simulating real amine processes, data under stripping conditions are equally important. Second, the studies on absorption and desorption have been performed in isolation and there has never been a major attempt to investigate if data collected under absorber conditions can be utilized to predict desorption rates. Finally and most importantly, the experimental data on reaction kinetics have been mostly analyzed assuming highly simplified pseudo-first-order kinetics and pseudo-first-order or corresponding second-order rate coefficients have been reported. Whereas, this assumption greatly simplifies the mathematics, it does not adequately represent the parallel and reversible reactions that occur in typical acid gas-amine systems. In addition, the simplified approach provides no insight into the actual reactive mass transfer phenomena and the kinetic data have limited reliability for design and optimization and scale-up of industrial units. In real situations, rarely if ever is there a single mass transfer regime throughout column. 9 Therefore, it is highly desirable to develop a comprehensive model that includes all relevant possible reactions in an acid gas-amine system and that can be used to predict both absorption and desorption rates. The development of such a model is the primary objective of this thesis. 1.2.2 Kinetic Data on CO-Am ine Systems In gas treating plants, amine solutions are continuously regenerated and reused for extended periods. Thus, maintaining the quality of amine solution is absolutely critical for efficient and economic operation. Although acid gas-amine reactions are reversible, irreversible reactions may also occur resulting in products from which the amine cannot be regenerated under typical operating conditions. This phenomenon is called amine degradation. Numerous studies have been published on this subject (Dawodu and Meisen, 1991; Kim, 1988; Chakma, 1987; Chakma and Meisen, 1988; Kennard and Meisen, 1985; Kim and Sartori, 1984). However, all these studies are mainly concerned with amine degradation due to C 0 2 , carbon disulfide (CS 2 ) , carbonyl sulfide (COS) and H 2 S / C 0 2 mixtures. However, some sour gas mixtures (e.g., gas mixtures in hydrogen plants and F C C units) may also contain significant concentrations of carbon monoxide that could also contribute to amine degradation. A literature review on this subject (see Chapter 6) reveals that no detailed scientific study has ever been done to investigate the kinetics of CO-induced degradation of alkanolamines. This problem is of considerable commercial importance because in many refinery gas-treating units, where C O partial pressures are high, large quantities of DEA can be lost or rendered ineffective. 10 Therefore, it could be considerable economic benefit to investigate the mechanism by which C O reacts with aqueous DEA solution and estimate relevant solubility and kinetic parameters. These data are essential for estimating DEA losses. Therefore, the second part of this thesis is devoted to investigating the kinetics of the CO-induced degradation of DEA. 1.3 Objectives and Scope of this Work The work presented in this thesis can be divided into two parts. Part 1 deals with the kinetics of C 0 2 absorption/desorption in aqueous amines and Part 2 deals with the kinetics of CO-induced degradation of aqueous DEA. The main objectives of Part 1 were to obtain kinetic and physical properties data that are needed to predict C 0 2 absorption/desorption rates in aqueous amine solutions and to investigate if the theory of absorption with reversible chemical reactions can be applied to predict desorption rates. To accomplish these objectives, a new hemispherical gas-liquid contactor was designed and absorption/desorption rates of C 0 2 into aqueous solutions of MEA, DEA, MDEA, A M P and their mixtures were measured at various temperatures, amine concentrations and C 0 2 loadings. The experimental data were interpreted by developing a comprehensive reactive mass transfer model. This model takes into account the reversibility of the chemical reactions, the effect of the diffusion of reactants and reaction products through reaction zone, and the gas-phase mass transfer resistance. The model is capable of predicting both absorption and desorption rates. l l In Part 2, the knowledge acquired in studying CCVamine kinetics (i.e., very fast reacting systems) was applied to investigate the kinetics of CO-induced degradation of aqueous DEA (i.e., very slow reacting system). This is the first detailed study ever done on this subject and the project grew out of discussion with Equilon Enterprises LLC, Westhollow Technology Center, Houston Texas and Shell Global Solutions International, Amsterdam, The Netherlands. The specific objectives of this study were to: (a) investigate the mechanism by which C O reacts with aqueous DEA, (b) identify major degradation products and (c) estimate the corresponding solubility and kinetic parameters over a range of temperatures and C O partial pressures so that DEA losses could be quantified and managed. To accomplish these objectives, a novel reaction mechanism was proposed and a mathematical model was developed. The model consists of a set of differential and algebraic equations that describes gas absorption with slow chemical reactions in a well-mixed batch reactor. The parameter estimation procedure presented in this work is based on a novel experimental approach that is fast, accurate and suitable for any gas-liquid reaction system. 1.3.1 Organization of the Thesis The thesis is divided into two parts. The first part (Chapters 2 to 5) covers experimental and modeling study of C 0 2 absorption/desorption in aqueous alkanolamine solutions using a novel hemispherical contactor. The second part (Chapters 6 to 9) deals with the kinetics of C O induced degradation of DEA. Chapter 2 presents a comprehensive review of the literature on the kinetics of CO2 absorption and desorption in aqueous solutions of MEA, DEA, 12 MDEA, A M P and their blends. In this chapter, the theory of mass transfer with chemical reactions is presented to highlight the importance of the kinetics of these systems. Major gaps in knowledge are identified and future research needs that form the basis of most of the work presented are recommended. Chapter 3 describes the novel hemispherical contactor and experimental procedures to measure absorption and desorption rates of C 0 2 in aqueous amine solutions. Chapter 4 presents the development of a comprehensive model for gas absorption and desorption over a hemispherical liquid film. This chapter also includes the algorithms for solving the model equations and for parameter estimation. Chapter 5 presents the results of the C 0 2 absorptions/desorption studies. Chapters 6 to 9 present a comprehensive account of the work on C O -induced degradation of aqueous DEA. These chapters also present a novel technique (patterned on the so called \"Nitrogen Analogy\") to measure the physical solubility of C O in aqueous DEA solutions. Major conclusions and recommendations for future work arising from Parts 1 and 2 are summarized in Chapter 10. 13 CHAPTER 2 LITERATURE REVIEW CO2 absorption/desorption in aqueous amines involves mass transfer with multiple reversible chemical reactions. Under typical operating conditions, the rates of these reactions (particularly those involving molecular CO2) are of the same order of magnitude as rate of diffusion in the solution. Therefore, to model the CO2 removal process, an understanding of the mechanism and kinetics of these reactions is essential. A number of studies on the kinetics of C0 2 -amine reactions in aqueous solutions have been reported in the literature. The experimental procedures in these studies typically involve measurements of C 0 2 absorption rates in aqueous amines using laboratory apparatus with known hydrodynamics and interfacial areas. These rates are then interpreted using kinetic models to estimate rate constants. The purpose of this chapter is to emphasize the importance of kinetic data in predicting C 0 2 absorption and desorption rates and review the results and methods reported in literature. The kinetic data for four important amines (MEA, DEA, MDEA and AMP) and their blends (MEA+MDEA, MEA+AMP, DEA+MDEA, DEA+AMP) have been compiled and research needs that are later studied in this work are identified. The discussion in this chapter is limited to reaction mechanisms and kinetics only. A review of important physical property data that are also needed for the process modeling of these systems is given in Appendices E to H. 14 2.1 Mass Transfer with Chemical Reaction From two-film theory (Lewis and Whitman, 1924) the rate of C 0 2 absorption or desorption in aqueous amines can be represented by: N A = - N D = P ; ° 2 ^ C ° 2 (2.1) 1 , Hco 2 k g a Ek°a The term (p c c , 2 - p £ o 2 ) ' n equation (2.1) represents the driving force for mass transfer, p c c, 2 denotes the partial pressure of C 0 2 in the bulk gas and p c c, 2 denotes the equilibrium partial pressure of C 0 2 corresponding to its concentration in the bulk liquid. For absorption p c c, 2 > p c c, 2 and for desorption Pco2 < Pco2 • The value of p°COz depends on the solubility of C 0 2 in the liquid at the prevailing temperature and pressure. It can be calculated by solving thermodynamic equilibrium models. At low temperatures and high C 0 2 partial pressures, the equilibrium favors absorption because most of the C 0 2 in the liquid phase is chemically combined with the amine and water and the value of p C O z is much lower than p C 0 2 . At high temperatures and low C 0 2 partial pressures, the equilibrium favors desorption because most of the C 0 2 in the liquid is in molecular form and the value of p c c . 2 is much higher than p c c . 2 . The equilibrium chemistry that governs the C0 2-Water-Amine system is therefore important in determining the mass transfer driving forces. The most commonly used models for calculating p c o are those of Kent and Eisenberg 15 (1976), Deshmukh and Mather (1981) and Austgen (1989). The main difference among these models is in their description of liquid phase non-idealities. The model of Kent and Eisenberg (1976) does not account for liquid phase non-ideality and is therefore the simplest. The models of Deshmukh and Mather (1981) and Austgen (1989) properly account for thermodynamic non-idealities and, while more accurate, they are also mathematically complex and computationally time consuming. All three models have been used extensively, and comprehensive reviews have been provided by Weiland et al. (1993) and Austgen et al. (1991). The denominator in equation (2.1) represents the resistance to mass transfer and it consists of two terms: the gas-phase resistance (1/kga) and the liquid-phase resistance (H c c . 2 /Ek°a) . Depending on the operating condition, one or both of these resistances are significant. The gas-side resistance to mass transfer is usually important for systems containing highly reactive amines such as MEA and piperazine or when the C 0 2 partial pressure in the gas phase is low. Fortunately, the gas-side resistance to mass transfer can be easily estimated because the only major unknown parameters in evaluating the gas-film coefficient are the gas diffusivities, which are readily available in the literature (Reid etal . , 1987). In C 0 2 removal processes, the liquid-side resistance to mass transfer is generally dominant. The estimation of this resistance requires knowledge of the effect of chemical reaction on mass transfer. The effect is usually expressed in terms of the enhancement factor (E), which is defined as the ratio of the rate of 16 absorption or desorption with chemical reaction to the rate without chemical reaction. In most cases of practical importance, the enhancement factor is a complex function of a dimensionless parameter commonly referred to as the Hatta number (DeCoursey, 1982, 1992) given by: M = V k 2 . C A M D c 0 2 k° v ' Under the assumption that the amine concentration at the gas-liquid interface is not significantly different from that in the bulk solution, Danckwerts, (1970) derived the following expression: E = Vl + M 2 (2.3) When the gas-side resistance to mass transfer is negligible because of the low gas solubility (i.e., Large H C 0 2 ) , then substitution of equations (2.2) and (2.3) into equation (2.1) gives: N A = - N D = J 1 + ( k c n ^ K2 k°a H c o , ( P c o , - P ° c o 2 ) (2-4) Equation (2.4) demonstrates that the kinetic coefficient, k 2 n d, is important in determining absorption/desorption rates. The effect of k2 n d on the mass transfer rate can be examined with respect to the Hatta number (M). When M « 1, the rate of reaction is slow and it does not affect the mass transfer rate; consequently E ~ 1. This regime is called \"slow reaction regime\". In this regime the reaction kinetics have no significant effect on mass transfer, corresponding to the case of physical absorption or desorption. When M » 1, the enhancement factor is 17 approximately M and the mass transfer rate becomes independent of the liquid-film coefficient; i.e., This regime is called the \"fast\" or \"pseudo-first-order regime\" (Levenspiel, 1972). In this regime the reaction is fast enough that it enhances the mass transfer but not so fast that it depletes the amine concentration in the boundary layer significantly. Therefore, in this regime, CAM can be considered constant throughout in the boundary layer and can be taken as equal to the bulk liquid concentration, and an apparent or pseudo-first-order rate constant (k a p p = k2NDCAivi) can be defined. The pseudo-first-order approximation is usually used in the literature to estimate k a p p f rom absorption rate data (see Tables 2.1 to 2.6). In these studies, the experimental conditions are set so that 3 < M « Eco, where Eoo is the maximum possible enhancement factor. For a CC>2-amine reaction, Danckwerts (1970) has derived the following expression for E^: where V A M is the amine stochiometric coefficient. As M - > oo, the implication is that the reactions are so fast that chemical equilibrium prevails everywhere. The transport rate becomes independent of the reaction rate and is limited by the diffusion of the liquid reactant to the interface. (2.5) 18 This regime is called the \"instantaneous reaction regime\" (Levenspiel, 1972). The enhancement factor in this regime represents an upper bound on the potential enhancement of mass transfer. In this regime the interface concentrations of liquid reactants and products may be calculated by solving the chemical equilibrium model. In the transition from the \"fast\" to \"instantaneous regime\" (1 « M < Eoo), the reactions occur largely near the interface and the amine concentration within the boundary layer may become significantly depleted. Consequently, the pseudo-first-order approximation given by equation (2.5) is no longer valid and the reaction rates at any point in the boundary layer must be calculated using the actual amine concentration at that point. This requires solving the mass balances (including chemical reaction terms) for each species throughout the liquid film. Analytical solutions for the enhancement factor (like eq. 2.3) are not possible and the equations must be solved numerically. An important objective of this thesis is to determine mass transfer rates in mixed solvents where the components may react at different rates. Therefore, the transition regime cannot be ignored. A set of conditions that gives the pseudo-first-order regime for one component may well give a transition regime for the other. For this reason we have developed a model that covers all reaction regimes and can be applied to interpret both absorption and desorption rate data. It is clear from the above observations that kinetics plays an important role in the CO2 absorption/desorption process using aqueous amines. A thorough understanding of the reaction mechanism and determination of reliable kinetic 19 data are essential for effective design and simulation of such systems. The remainder of this chapter is therefore devoted to developing an understanding of the mechanism of CO2 reactions with aqueous amines and a review of the literature data on absorption and desorption kinetics. Physical properties such as Henry's constant of C 0 2 in amine solution, diffusivities of C 0 2 and other chemical species in the aqueous solution and density and viscosity of amine solutions are equally important for process modeling. An extensive literature review of each physical property is given in Appendices E to H. 2.2 Reaction Mechanisms of C02-Amine-Water Systems 2.2.1 C 0 2 Reactions with Water In aqueous solution, C 0 2 exists in several forms. First it dissolves: C 0 2 ( g ) - > C 0 2 ( a q ) and then it reacts with water and hydroxyl ions: C 0 2 +H 2 0<->H 2 C0 3 (2.6) C 0 2 + O H -<->HCO-3 (2.7) The bicarbonate ions quickly establish equilibrium with carbonate ions: H C O 3 + O H ' <-> CO*\" + H 2 0 (2.8) The direct reaction of C 0 2 with water (reaction 2.6) is very slow (k = 0.026 s\"1 at 298 K, Pinsent et al., 1956) and usually neglected in interpreting absorption rate data, as its contribution to mass transfer is insignificant (Rinker et al., 1996; 20 Danckwerts, 1979). This is appropriate because the absorption experiments are generally conducted in equipment with short contact time (xc < 1 s). The C 0 2 reaction with hydroxyl ions (reaction 2.7) is fast and can enhance mass transfer even when the concentration of O H \" ions is low. Pinsent et al. (1956) and Read (1975) have reported correlations for the forward rate constant and equilibrium constant of reaction (2.7). Reaction (2.8) is an equilibrium reaction and Read (1975) has reported a correlation for its equilibrium constant. These correlations are presented in Appendix H. 2.2.2 C 0 2 Reactions with Amines Data for C 0 2 reactions with aqueous amines have been interpreted either by the zwitterion mechanism, which was first proposed by Caplow (1968) and later reintroduced by Danckwerts (1979), or by the base-catalyzed hydration reaction mechanism proposed by Donaldson and Nguyen (1980). 2.2.2.1 Zwitterion Mechanism According to this mechanism, C 0 2 in the liquid phase reacts with amine to form a zwitterion intermediate that is subsequently deprotanated by any base in the solution (Danckwerts, 1979; Blauwhoff et al., 1984). Most of the published kinetic data for MEA, DEA and A M P have been analyzed using this mechanism. For the CO2-AMP system, the zwitterion mechanism is described by the following reactions: 21 Zwitterion Formation: C 0 2 + R 4 N H 2 ^ . R . N H + C O O (2.9) -1 Zwitterion Deprotonation: R 4 N H ^ C O O \" + R 4 N H 2 <-> R 4 N H C O Q - + R 4 N H ^ (2.10) R 4 NH^COO\" + H 2 O ^ R 4 N H C O O \" + H 3 0 (2.11) R 4 NH+COO\" + OH ' ^ R 4 N H C O O \" + H 2 0 k - 4 (2.12) Similar reactions have been reported for MEA and DEA. Danckwerts (1979) combined reactions (2.9) to (2.12) and derived the following expression for the C 0 2 amine reaction: where [C0 2 ] e is the concentration of molecular C 0 2 that is in equilibrium with the other ionic and non-ionic species present in the solution. Equation (2.13) suggests two limiting cases (Versteeg and van Swaaij, 1988): (a) when the termk^ /(k 2 [RNH 2 ] + k 3 [H 2 0] + k 4 [ 0 H \" ] ) « 1 (i.e., the zwitterion deprotonation is much faster then its formation), then the rate of C 0 2 reaction with amine can be expressed in terms of simple second-order kinetics: - M R 4 N H 2 ] ( [ C Q 2 ] - [ C Q 2 ] e ) (2.13) co2 22 rCo2 =-MR 4 NH 2 ]JC0 2 ] - [COj] .} (2.14) (b)when k 2 [ R N H 2 ] » k 3[H 20] and k 4 [OH\"]and the term k _ , / k 2 [ R N H 2 ] » 1 (i.e., the zwitterion deprotonates only with the amine and the zwitterion deprotonation is much slower than its formation), then the overall kinetics are third order: rCo2 = - ^ [ R 4 N H 2 ] 2 ( [ C 0 2 ] - [ C 0 2 ] e ) (2.15) K - i The above analysis indicates that the zwitterion mechanism is able to cover the transition region where the reaction order with respect to amine lies between 1 and 2. It may be noted that equation (2.13) is applicable to both absorption and desorption. However, since the majority of research reported in the literature has been focused on absorption into C02-free amine solutions, [C02]e is generally taken as zero. Furthermore, in most cases it was assumed that during the absorption experiments the amine concentration did not change appreciably and the forward reaction dominated (Danckwerts and Sharma, 1966; Sada et al., 1976; Hikita et al., 1977a). As a result, equation (2.14) can be simplified further and the following pseudo-first-order rate expression results (Little et al., 1992a,b): rCo2 = -kappC02 (2.16) where k a p p = k 2 n d[Amine]. In the studies where the full zwitterion mechanism rate expression represented by equation (2.13) was used and combined rate constants (ki, k-|k2/k-i, kik 3/ k.-i and k-ikV k.-i) were reported, the methodology used in estimating 23 rate constants was essentially the same as for the pseudo-first-order approach. Again, [C0 2 ] e was set to zero and equation (2.13) could be simplified to: r C o 2 =-k a p p [ R 4 N H 2 ] [C0 2 ] (2.17) w h e r e : k - = f + k k FT k k ( 2 1 8 ) K i - i ^ [ R 4 N H 2 ] + —!-^-[H20] + ^ - [ O H - ] k _^ k _^ k _ ^ In this approach, k a p p is estimated by using equation (2.17) for various amine concentrations and, from equation (2.18), the individual and combined rate constants are estimated by non-linear regression (Blauwhoff et al., 1984; Versteeg and van Swaaij, 1988; Xu et al., 1996; Xiao et al., 2000; Ko and Li, 2000). The concentrations of amine and water are generally taken as their initial values whereas the concentration of hydroxyl ions is calculated from the dissociation constants of water and amine. In any given experiment, these concentrations were assumed constant. As shown in the next section, most of the recent studies on the kinetics of C 0 2 with MEA, DEA and A M P have used this approach. For aqueous solutions, the contribution of O H \" ions in the deprotonation of zwitterion is generally neglected (Blauwhoff et al., 1984; Versteeg and van Swaaij, 1988; Versteeg and Oyevaar, 1989; Bosch et al., 1990b; Rinker et al., 1996; Xu et al., 1996; and Xiao et al., 2000). This is justified because the concentration of hydroxyl ions in aqueous amine solutions is 2 to 3 orders of magnitude lower than that of water or amine. Furthermore, it falls significantly as a result of C 0 2 absorption. 24 2.2.2.2 Base-Catalyzed Hydration Reaction Mechanism Donaldson and Nguyen (1980) proposed this mechanism for CO2 reaction with tertiary alkanolamines. According to these authors, the tertiary alkanolamines, such as T E A and MDEA, do not react directly with CO2 to form carbamate. Instead they catalyze the CO2 hydration reaction: k K C 0 2 + R 1 R 2 R 3 N + H 2 0 ^ R ^ R g N h T + H C 0 3 (2.19) k_22 The important point to note in this mechanism is that water must be present for the reaction to occur. Most of the data on C 0 2 - M D E A systems have been analyzed based on this mechanism. There is general agreement in the literature (see Table 2.3) that the reaction rate is first order with respect to amine and C 0 2 . Therefore, the rate expression for reaction (2.19) can be written as: rCo2 = - k 2 2 [ R 1 R 2 R 3 N ] [ C 0 2 ] + ^ - [ R 1 R 2 R 3 N H + ] [ H C 0 3 ] (2.20) K 2 2 Except for Rinker et al. (1995), almost all studies on the kinetics of the C 0 2 -MDEA system have assumed that the forward reaction is the dominant one and that the amine concentration does not change appreciably during the experiment. Consequently, equation (2.20) can be simplified as: rCo2 = - k 2 2 [ R 1 R 2 R 3 N ] [ C 0 2 ] = - k a p p [ C 0 2 ] (2.21) Equation (2.21) is identical to equation (2.16) and represents a pseudo-first-order rate expression similar to that for MEA, DEA and AMP. Therefore, the methodology described above was also used to estimate the rate constants for 25 the CO2-MDEA system (Barth et al., 1984; Little et al., 1990a; Ko and Li, 2000). Since the CO2 reaction with MDEA is much slower compared to its reaction with MEA, DEA and AMP, the pseudo-first-order approximation may well be justified. To analyze desorption data, the rate expression given by equation (2.20) must be used. Furthermore, the CO2-MDEA reaction is slow, and reaction (2.7), therefore, must also be considered for interpreting absorption/desorption rate data. Recently, Rinker et al. (1995) have shown that the effect of reaction (2.7) on the mass transfer enhancement of the CO2-MDEA system is quite significant. 2.2.3 C 0 2 Reactions with Aqueous Amine Blends When more than one amine is present (e.g., AMP+MEA or MDEA+AMP), the zwitterion of carbamate-forming amines (such as MEA, DEA and AMP) will also be deprotonated by the second amine present in the solution. For the CO2+AMP+MEA system, the reaction is: In the literature (Glasscock et al., 1991, Xiao et al., 2000) the kinetic data for blended amines are treated in the same way as those for single amines and the approximate rate expression given by equation (2.17) is used. The only difference in this case is that the apparent rate constant (k a p p) is modified to include reaction (2.22): R 4 N H 2 - C O O - + R 1 N H 2 <-> R 4 N H C O C T +R 1NH 3\" (2.22) k 1 1 (2.23) app k.,k2 [R 4 NH 2 ] + l i ^ [ H 2 0 ] + l ^ [ O H - ] + l ^ [ R 1 N H 2 ] 26 As before, the term involving hydroxyl ions is usually neglected since it is negligible compared to other terms (Xiao et al., 2000) 2.3 Kinetic Data for C02 Absorption/Desorption in Aqueous Amines 2.3.1 Kinetic Data for C02-MEA-Water System MEA is the most commonly used alkanolamine in the gas treating industry and has been studied widely. The literature sources with kinetic data on the C 0 2 -M E A reaction are summarized in Table 2.1. Even though different experimental conditions have been used, the agreement between the published data is fairly good. As concluded by Blauwhoff et al. (1984) and later confirmed by Barth et al. (1986), the correlation of Hikita et al. (1977a) fits the data quite well over the temperature range of 288 to 353 K: l og 1 0 ( k 2 M E A ) = 10 .99 -2152 /T where k 2 l M E A is the second-order rate constant in units of m 3 kmol\"1 s\"1 and T is the temperature in Kelvins. The activation energy from this correlation is 41.2 kJ/mol, which agrees well with the values reported by other investigators. Without exception, an overall second-order reaction (first-order with respect to MEA and first-order with respect to C 0 2 ) was found regardless of experimental techniques and conditions (Blauwhoff et al., 1984). 27 Table 2.1: Summary of the results reported on the CCvMEA-Water system Reference T CAM k 2 n d @ 298 K E a Modef Apparatus & (K) (kmol/ m3) (m 3/ kmol s) (kJ/mol) Method Little et al. (1992b) 318, 333 1.0 (3703) + + — g-z stirred cell (A ) + + + Alper (1990) 278-298 0.01-1.5 5545 46.7 ps-1 stopped flow (A) Bosch et al. (1990a) 313-323 1.0 - - ps-1 stirred cell (D) Penny & Ritter (1983) 278-303 0.01-0.06 4990 42.2 ps-1 stopped flow (A) Laddha & Danckwerts (1981) 298 0.5-1.7 5720 ps-1 stirred cell (A) Donaldson & Nguyen (1980) 298 0.03-0.08 6000 ps-1 aq. amine membrane (A) Alvarez-Fuster et al. (1980) 293 0.2-2.0 (5750) ps-1 wetted wall column (A) Hikita et al. (1977a) 278-315 0.02-0.18 5868 41.2 ps-1 rapid mixng (A) Sada et al. (1976) 298 0.2-1.9 8400, 7140 - ps-1 laminar jet (A) Leder et al. (1971) 353 7194 39.7 ps-1 Stirred cell (A) Groothius (1966) 298 2.0 6500,5720 ps-1 Stirred cell (A) Contd. 28 Table 2.1: Summary of the results reported on the C0 2 -MEA-Water system (Contd.) Reference T CAM k 2 n d @ 298 K E a Model Apparatus & (K) (kmol/ m 3) (m 3/ kmol s) (kJ/mol) Method Danckwerts & Sharma (1966) 291-308 1.0 7600, 6970 41.8 ps-1 laminar jet (A) Clarke (1964) 298 1.6-4.8 7500 - ps-1 laminar jet (A) Astarita (1961) 295 0.25-2.0 (6443) - ps-1 laminar jet (A) Jensen et al. (1954a) 291 0.1, 0.2 (6103) - - competition method with 0.1 and 0.2 M NaOH (A) + ps-1 = pseudo-first-order, ps-1-z = pseudo-first-order with zwitterion mechanism, g-z = general model with zwitterion mechanism + + Values in the bracket indicate that k 2 n d was estimated using E a= 41 kJ/moie + + + A = absorption, D = desorption Although the data generally agree well with regard to reaction order and activation energy, it should be noted that most data were acquired under absorption conditions in the temperature range of 293 to 308 K. These data were mostly interpreted using simplified pseudo-first-order models. The more recent data of Little et al. (1992b) were analyzed using a rigorous model based on the zwitterion mechanism but their study was again limited to absorption. An important conclusion from this study was that, for fast reversible reactions like 29 those in the CO2-MEA system, rigorous modeling is the only way to estimate the reaction rate constants from absorption experiments. There has been no significant work on the kinetics of the CO2-MEA reaction under desorption conditions. Bosch et al. (1990a) provided the only published data for C 0 2 desorption rates from rich MEA solutions. However, their data were taken at low temperatures in the range of 313 to 323 K. These authors used pseudo-first-order kinetics with a simplified equilibrium model to predict their CO2 desorption rates. However, they were unsuccessful in interpreting their data. 2.3.2 Kinetic Data for C02-DEA-Water System DEA is the second most common alkanolamine used for bulk CO2 removal. Because of its wide use, the literature on C0 2-absorption is extensive. The principal results, mostly from Blauwhoff et al. (1984) and Rinker et al. (1996), are summarized in Table 2.2. There is general disagreement on the order and rate of reaction with respect to DEA. The reaction order for C 0 2 is generally accepted to be one but the order for the amine varies between 1 and 2. Blauwhoff et al. (1984) explained some of the discrepancies in the reported results by means of the zwitterion mechanism that includes all bases (i.e., [Amine], [H 20] and [OH -1]) for zwitterion deprotonation. However, recently Rinker et al. (1996) using a rigorous approach for data interpretation were unable to find any significant contribution of hydroxyl ions and water in zwitterion deprotonation. 30 Table 2.2: Summary of results reported on the C0 2 -DEA+Water system Reference T (K) C A M (kmol /m 3) k 2 n d @ 298 K (rrrVkmol s) Order w.r.t. Amine E a (kJ/mol) Modef Apparatus & Method Rinker et al. (1996) 293-343 0.25-2.8 4089 1-2 14.1 9-z laminar jet (A ) + + + Davis & Sandall (1993) 293-313 0.25-2.0 351 (no water) 1-2 - ps-1-z Wetted sphere (A) Little et al. (1992b) sos-s i s 0.2-4.0 (1454) + + 1-2 - g-z stirred cell (A) Crooks & Donellan 298 0.1-1.0 2250 2 - - stopped flow (1989) (A) Versteeg & Oyevaar (1989) 298 0.09-4.40 3170 1-2 ps-1 -z stirred cell (A) Versteeg & van Swaaij (1988) 298 5790 1-2 ps-1-z stirred cell (A) Barth et al. (1986) 298 0.02 275 1 ps-1 stopped flow (A) Blauwhoff et al. (1984) 298 0.5-2.3 5800 1-2 ps-1 -z stirred cell (A) Blanc & Demarais (1984) 293-333 0.01-4.0 656 1 43.5 ps-1 wetted wall column (A) Contd. 31 Table 2.2: Summary of results reported on the COrDEA+Water system (Contd.) Reference T (K) CAM (kmol k 2 n a @298 K (m3/kmol s) Order w.r.t. Amine E a (kJ/mol) Model Apparatus & Method Laddha & Danckwerts (1982) 284 0.5-2.0 (1492) 1-2 ps-1-z stirred cell (A) Laddha & Danckwerts (1981) 298 0.46-2.88 1410 1-2 ps-1-z stirred cell (A) Donaldson & Nguyen (1980) 298 0.03-0.09 1400 1 ps-1 aq. Amine membrane (A) Alvarez-Fuster et al. (1980) 293 0.25 0.82 (3006) 2 ps-1 Wetted wall column (A) Hikita et al. (1977a) 278-313 0.17-0.72 3132 2 ps-1 rapid mixing (A) Coldrey & Harris (1976) 292 0.1-1.0 (1636) 1 ps-1 rapid mixing with 0.002-0.005 M NaOH (A) Sada et al. (1976) 298 0.25-1.92 1340 1 - ps-1 laminar jet (A) Leder (1971) 353 - (7870) 1 - ps-1 stirred cell (A) Groothius (1966) 298 2.0 1300 1 stirred cell (A) Contd. 32 Table 2.2: (Contd.) Summary of results reported on the C0 2 -DEA+Water system Reference T CAM k 2 n a @298 K Order E a (K) (kmol (m 3 /kmols) w - r t (kJ/mol) /m 3) A m i n e Model Apparatus & Method Danckwerts 308 &Sharma (1966) Sharma (1964) Jorgensen (1956) Jensen et al. (1954a) van Krevelen & Hoftizer (1948) 291 Jorgensen 273 (1956) 291 291 292-329 1.0 1.0 0.1-0.3 0.2-0.3 0.1-0.2 0.05-3.0 (1317) (1648) (3381) (6595) (8360) 650 1 ps-1 ps-1 laminar jet (A) laminar jet (A) competitive reaction with 0.1, 0.2, 0.3 M NaOH (A) competitive reaction with 0.2, 0.3 M NaOH (A) competitive reaction with 0.1, 0.2 M NaOH (A) packed column (A) + ps-1 = pseudo-first-order, ps-1 -z .= pseudo-first-order with zwitterion mechanism, g-z = general model with zwitterion mechanism + + Values in the bracket indicate that k 2 n d was estimated using E a= 14.1 kJ/mole + + + A = absorption, D = desorption 33 Crooks and Donnellan (1989) suggested a different mechanism for the reaction of CO2 with DEA by proposing a single step termolecular reaction. In this mechanism, DEA is postulated to react simultaneously with one molecule of C 0 2 and one molecule of base. Their mechanism leads to an overall reaction rate, which has the same form as, that of the second limiting case of the zwitterion mechanism discussed above. However, as pointed by Little et al. (1992b) and Rinker et al. (1996), this mechanism does not explain the fractional orders with respect to DEA concentration observed in non-aqueous solvents (Sada et al., 1985; Versteeg and van Swaaij, 1988; Davis and Sandall, 1993). Nevertheless, there is no plausible explanation in the literature as to why a proton transfer step such as base proton extraction would be rate limiting. Since the zwitterion mechanism adequately covers the varying reaction order, it is fairly universally used in the literature (see Table 2.2) to interpret C 0 2 absorption data. Perhaps a different way of confirming the applicability of this mechanism would be to conduct experiments under desorption conditions and see if the kinetic data acquired under absorption conditions and using a zwitterion mechanism, could be used to predict desorption rates. No such study has been reported in the literature. Critchfield and Rochelle (1988) provided the only study that reports C 0 2 desorption rates from rich DEA solutions but their experiments were performed only at 298 K. 2.3.3 Kinetic Data for C02-MDEA-Water System MDEA is the most widely used tertiary amine with major applications in the selective removal of H 2 S from gases containing both C 0 2 and H 2 S. The kinetics 34 of the C 0 2 reaction with MDEA must be known to estimate C 0 2 pickup in the absorber and in designing systems with mixed solvents where MDEA is blended with a fast reacting primary or secondary amine. Many studies dealing with the kinetics of C 0 2 - M D E A reactions have been reported in the literature. Important results from these studies are given in Table 2.3. All these studies confirm the base catalyzed C 0 2 hydration reaction mechanism proposed by Donaldson and Nguyen (1980) for the C0 2-tertiary amine reaction. The reaction order with respect to both amine and C 0 2 has always been found as one. There are some discrepancies regarding the activation energy and the reported values of second order rate constants. The second-order rate constants at 298 K vary by a factor of 2 depending on the authors (see Table 2.3). In most cases, pseudo-first order models were used to interpret the absorption rate data. Recently, Rinker et al. (1996) used the rigorous model to estimate kinetic coefficients and pointed out that in this system, the C 0 2 reaction with hydroxyl ions must be taken into account. C 0 2 desorption from rich MDEA solutions has been studied by Critchfield and Rocheile (1987), Bosch et al. (1990a) and Xu et al. (1995) in the temperature range of 303 to 343 K. In all these studies, the experimental desorption rates are in good agreement with those predicted by simple models for mass transfer with fast pseudo-first-order reaction. These results are important as they indicate that C 0 2 desorption from MDEA solutions is controlled by mass transfer with fast reaction and the rate of desorption could be predicted based on absorption kinetic data. 35 Table 2.3: Summary of results reported on the C0 2 -MDEA-Water system Reference T CAM k 2 n d @298 K E a Model+ Apparatus & (K) (kmol/ m3) (m 3/kmol s) (kJ/mol) Method Ko&L i (2000) SOS-SIS 1.0-2.5 5.41 44.9 ps-1 wetted wall column (A) + + Pacheco et al. (2000) 298-373 2.9-4.3 2.5 49.0 ps-1 wetted wall column (A) Pani et al. (1997) 296-343 0.8-4.4 5.2 44.0 ps-1 stirred cell (A) Rinker et al. (1995) 293-342 0.8-2.5 6.2 38.0 9 wetted sphere (A) Xu et al. (1995) 313-343 2.6-3.9 - - ps-1 Packed column (D) Rangwala eta l . (1992) 298-333 0.8 -2.5 4.4 48.0 ps-1 stirred cell (A) Bosch et al. (1990) 298-323 1.0 - - ps-1 stirred cell (D) Little et al. (1990a) 298 0.2-2.7 5.5 - ps-1 stirred cell (A) Toman & Rochelle (1989) 298-308 4.3 5.5 ps-1 stirred cell (A) Tomcej & Otto (1989) 298-348 1.7-3.5 5.4 42 ps-1 wetted sphere (A) Contd. 36 Table 2.3: Summary of results reported on the C0 2 -MDEA-Water system (Contd.) Reference T C A M k 2 n d @298 K E a Model Apparatus & (K) (kmol/ m3) (m 3/kmol s) (kJ/mol) Method Versteeg &van Swaaij (1988) 293-333 0.2-2.4 4.4 42 ps-1 stirred cell (A) Haimour et al. (1987) 288-308 0.9-1.7 2.4 72 ps-1 stirred cell (A) Critchfield & Rochelle (1987) 282-350 1.7 2.5 56 ps-1 stirred cell (A) Yu et al. (1985) 313-333 0.2-2.5 4.8 39 ps-1 stirred cell (A) Blauwoff et al. (1984) 298 0.5-1.6 4.8 - ps-1 stirred cell (A) Barth et al. (1984) 298 0.02-0.2 3.2 - ps-1 stopped flow (A) + ps-1 = pseudo-first-order, g = general model + + A = absorption, D = desorption 2.3.4 Kinetic Data for C02-AMP-Water System A M P , a relatively new amine, is primarily used for the selective removal of H 2 S from natural gas (Goldstein, 1986). It is a primary amine in which the amino group is attached to the tertiary carbon atom. The reaction rates of C 0 2 with A M P are significantly higher than those with M D E A and considerably less than those with MEA. Like MEA and DEA, A M P reacts directly with C 0 2 to form carbamate, but its carbamate is highly unstable and quickly hydrolyzes to give free amine 37 and bicarbonate as evident from the value of its carbamate stability constant (Kc) given in Table 2.4 (Sartori et al., 1983). As a result, A M P can absorb up to 1 mole of C0 2 /mo le of amine as opposed to 0.5 mole of C0 2 /mole of amine for MEA and DEA. Moreover, the heat of reaction for C 0 2 - A M P is less than those of C 0 2 - M E A and C 0 2 - D E A . It, therefore, requires less energy for regeneration. A number of studies on the kinetics of the C 0 2 - A M P reactions have been reported in the literature. Important results and experimental conditions from these studies are summarized in Table 2.5. A plot of the second-order rate constant of the C 0 2 - A M P reaction as a function of temperature as reported by various investigators is shown in Figure 2.1. Excluding, the data of Chakraborty (1986), who reported a k 2 n d value of 100 nvVkmol s at 313 K and Bosch et al. (1990b), who reported this value to be 10,000 m 3/kmol s at 298 K, the agreement among the reported data is satisfactory. However, the values of k 2 n d at 298 K reported by various authors differ quite significantly (see Table 2.5). The activation energy obtained by regressing the reported data is 36.13 kJ/mole. It is interesting to note that the activation energy of 41.7 kJ/mole calculated from recently published data of Saha et al. (1995) is exactly the same as that reported by Alper (1990) even though the latter author used a different experimental technique. Recently, Xu et al. (1996) and Messaudi and Sada (1996) have reported significantly different activation energies, which are 24.6 and 51.5 kJ/mole, respectively. 38 Table 2.4: Carbamate stability constants for MEA, DEA and AMP by C 1 3 -NMR (Sartori and Savage, 1983) Amine Kc(m 3/kmol)at313K MEA 12.5 DEA 2.0 AMP < 0.1 x Messaoudi and Sada (1996) oShou Xu (1996) A Sana et al. (1995) • Al per (1990) X Bosch et al. (1990) +Yih and Shen (1988) • Chakraborty et al. (1986) A Sharma (1965) 3.0 3.2 3.4 3.6 3.8 1000/T(1/K) Figure 2.1: Comparison of second-order rate constant for C02-AMP reaction. 10000 1000 100 -i n o A A ° o J I L_ 39 Table 2.5: Summary of results reported on the C02-AMP-Water system Reference T (K) C A M (kmol/ m3) k2nd@298 K (m3/ kmol s) Order w.r.t. Amine E a (kJ/mol) Modef Apparatus & Method Messaudi and Sada (1996) 293-313 0.5-2.0 271.8 1 51.5 ps-1 stirred cell (A)++ Xu et al. (1996) 288-318 0.25-3.5 810.4 1.32-1.50 24.3 ps-1-z stirred cell (A) Saha et al. (1995) 294-318 0.5-0.2 563.5 1 41.7 ps-1 wetted wall column (A) Alper (1990) 278-298 0.5-2.0 502.0 1.14-1.15 41.7 ps-1 stopped flow (A) Bosch et al. (1990b) 298 0.2-2.4 10,000 1 - g-z stirred cell (A) Yih &Shen (1988) 313 0.26-3.0 1270.0 (at 313 K) 1 ps-1 wetted wall column (A) Chakraborty etal. (1986) 313 0.5-1.0 100.0 (at 313 K) 1 - ps-1 PD cell (A) Sharma (1965) 298 0.2-2.0 1048.0 1 - ps-1 stirred cell (A) + ps-1 = pseudo-first-order, ps-1-z = pseudo-first-order with zwitterion mechanism, g-z = general model with zwitterion mechanism h + A = absorption, D = desorption 40 The reaction order with respect to C 0 2 was generally found to be one (Alper, 1990; Saha et al. 1995; Xu et al., 1996). However, the order with respect to amine has been reported to be slightly more than one (Alper, 1990; Xu et al., 1996). This suggests that the zwitterion mechanism should describe the data better. There is some disagreement amongst the researchers about the right mechanism. The majority (Sartori and Savage, 1983; Alper, 1990; Bosch et al., 1990b; Xu et al., 1996) is of the view that C 0 2 reacts with A M P to form carbamate by the zwitterion mechanism and that the carbamate is highly unstable, quickly hydrolyzing to bicarbonate. However, according to Yih and Shen (1988), the formation of carbamate in A M P is inhibited due to the bulkiness of the group attached to the tertiary carbon atom and the equilibrium favors bicarbonate formation via a zwitterion intermediate according to the following reaction: R 4 N H +COCT + H 2 0 <-> H C 0 3 + R 4 N H ; Chakraborty et al. (1996) proposed yet another mechanism according to which A M P , like MDEA, does not participate directly in the reaction and acts only as a base catalyst for C 0 2 hydration reaction. Finally, the data are limited to temperatures typical of absorbers (i.e., 298 to 318 K). No desorption data have been reported. Except for Bosch et al. (1990b), the experimental data have been analyzed using simple pseudo-first-order models. More data are required so that discrepancies reported in the literature regarding the mechanism and the reaction order with respect to amine can be resolved. The data should be collected under both absorber and desorber 41 conditions. To analyze the data, a comprehensive model that involves all possible reactions should be developed so that other mechanisms proposed in the literature can be evaluated. 2.3.5 Kinetic Data for Amine Blends Primary and secondary amines (such as MEA and DEA) are fast reacting amines that form stable carbamates by direct reaction with CO2. The tertiary amines, such as MDEA, on the other hand, are slow reacting amines and do not form carbamates. Hindered amines, such as A M P , have moderate reaction rates and can form carbamates, but the latter are highly unstable and quickly hydrolyze to give bicarbonate ions and free amine. Consequently, the regeneration energy requirements for MEA and DEA are quite high compared to those for MDEA and A M P . Blending of primary or secondary amines with tertiary or hindered amines is therefore an attractive option for designing less energy intensive processes for bulk CO2 removal. An additional advantage of blended amines is that, by varying the composition of the amine blend, the selectivity towards H 2 S can be adjusted. Although Chakraborty et al. (1986) introduced this concept over 15 years ago; little fundamental data are available for the rate of absorption/desorption of C 0 2 in amine blends. Important kinetic studies involving blends of MDEA with MEA or DEA and blends of A M P with MEA or DEA are summarized in the next two sections. 42 2.3.5.1 Kinetic Data for Aqueous Blends of MEA+MDEA and DEA+MDEA Previous work on C 0 2 absorption/desorption in MEA+MDEA and DEA+MDEA systems is summarized in Table 2.6. Most of the data reported are for total amine concentrations between 1 and 3 kmol/m 3 and temperatures between 298 and 313 K. Critchfield and Rochelle (1988,1987) and Glasscock et al. (1991) have reported both C 0 2 absorption and desorption rate data but they are limited to low temperatures (i.e., 288-313 K). The effect of tertiary amines on the reaction rates of primary or secondary amines has generally been taken into account by including an additional reaction where the zwitterion is also deprotonated by the tertiary amine. The results of Glasscock et al. (1991) and Hagewiesche et al. (1995) are important, as they have used rigorous diffusion-reaction and equilibrium models to interpret their data. The available data on C 0 2 absorption/desorption from these blends are sparse and more data, especially near stripper temperatures, are need. 2.3.5.2 Kinetic Data for Aqueous Blends of MEA+AMP and DEA+AMP C 0 2 - MEA+AMP-Water System: In recent years, there has been a considerable interest in capturing and sequestering C 0 2 from industrial point sources such as flue gases from power plants. Because of its high reaction rates with C 0 2 , MEA is generally considered as the best solvent for this application. However, there are many technological problems associated with MEA-based process that require further 43 Table 2.6: Summary of results reported on C02-MEA+MDEA-Water and C0 2-DEA+lv1DEA-Water systems Reference Blend T (K) Total Amine Cone. (kmol/m3) Modef Apparatus & Method Hagewiesche eta l . (1995) MEA+MDEA 313 2.6-3.0 g laminar jet (A) + + Rangwala et al. (1992) MEA+MDEA 293 2.0-3.5 ps-1 stirred cell (A) Glasscock et al. (1991) MEA+MDEA DEA+MDEA 288-313 0.0-3.0 g-z stirred cell (A/D) Critchfield & Rochelle (1988) DEA+MDEA 298 2.0 ps-1 stirred cell (A/D) Critchfield & Rochelle (1987) MEA+MDEA 304 2.0 ps-1 stirred cell (A/D) + ps-1 = pseudo-first-order, ps-1-z = pseudo-first-order with zwitterion mechanism, g=general model, g-z = general model with zwitterion mechanism + A = absorption, D = desorption considerations. MEA is highly corrosive to packing and other equipment and its concentration in the aqueous solution cannot exceed 15-17%. Consequently, very high circulation rates are required. Since MEA carbamate is highly stable, the energy requirements for regenerating the MEA are high. MEA is also highly susceptible to degradation, especially when gas streams contain small quantities of oxygen or fly ash as observed by our own research group and recently by Supape ta l . (2001). 44 The above problems can be effectively addressed by designing a novel solvent blend containing MEA and A M P . The A M P has appreciable reactivity with C 0 2 , but adding small quantities of M E A can further enhance it. Being the major constituent of the blend, the higher cyclic capacity and lower heat of reaction of A M P may significantly reduce the regeneration heat requirement of the process. Until the end of 1999, when the experimental work of this dissertation was being completed, no study on either absorption or desorption involving this system had been reported. Very recently, Xiao et al. (2000) have published absorption kinetic data for this system. They studied C 0 2 absorption in aqueous mixtures of A M P and MEA in the temperature range of 303 and 313 K using a laboratory wetted wall column. The concentration of A M P was set at 1.7 and 1.5 kmol/m 3 and the concentration of MEA was varied from 0.1 to 0.4 kmol/m 3. A hybrid reaction rate model (consisting of a first-order reaction for MEA and a zwitterion mechanism for AMP) was used to model the data. Overall pseudo-first-order and corresponding second-order rate constants were reported. More theoretical and experimental work, especially under desorption conditions, is required. C02-DEA+AMP-Water System: No absorption or desorption studies on this system have been reported. This is probably because the reactivities of DEA and AMP with C 0 2 are quite similar and apparently no advantage can be gained by blending these two amines. It will, however, be interesting to see if the capacity and desorption rates 45 of DEA can be increased by adding A M P as the latter does not form a stable carbamate. 2.4 Research Needs The major areas needing further research on C 0 2 absorption/desorption in the eight aqueous amine systems discussed above may be summarized as follows: 1. Most of the available data have been obtained under absorption conditions in the temperature range of 298 to 313 K using lean amine solutions representing typical conditions near the top of the absorption columns. The kinetic data that represent the absorber bottom and stripper conditions (high temperature and high loading) are needed as a function of C 0 2 loading. 2. The studies on absorption and desorption have been done in isolation and there has never been an attempt to investigate if the data collected under absorber conditions can be utilized to predict desorption rates. 3. The experimental data on reaction kinetics have been mostly analyzed assuming simplified pseudo-first-order kinetic models with pseudo-first-order or corresponding second-order rate coefficients being reported. This assumption greatly simplifies the complex mathematics, which govern the reaction-diffusion process in the mass transfer boundary layer. However, the disadvantage of using this approach is that it does not represent the actual concentration profiles of different chemical species in the boundary 46 layer near the gas-liquid interface and the kinetic data obtained may not be reliable. In real situations, it is rare for a single reaction regime to exist throughout the column. Moreover, this approach does not provide any insight into which reactions enhance mass transfer and which reactions do not. A comprehensive model is therefore needed which describes the diffusion-reaction process in the boundary layer and that takes into account all possible reactions under absorption and desorption conditions. 4. The kinetic data for MEA and MDEA from various sources are in good agreement and no further data under absorption conditions are needed. However, it is important to investigate if these data can be used to predict desorption rates. 5. There are discrepancies in the literature regarding the reaction order with respect to amine for the C O 2 -DEA and C 0 2 - A M P systems. More data, especially under stripping conditions, are needed to reconcile these differences. 6. The kinetic data on amine blends are scarce and more data under both absorption and desorption conditions are needed. Only a single study on C 0 2 absorption in an MEA+AMP blend has been reported in the literature, and no absorption or desorption involving AMP+DEA have been published. It would be nteresting to investigate (from both theoretical and experimental perspectives) if the addition of MEA or DEA can substantially enhance A M P reaction rates. If this occurs, such blends would become potential solvents for bulk C 0 2 removal from flue gases. 47 CHAPTER 3 EXPERIMENTAL APPARATUS AND METHODS 3.1 Overview In absorpt ion/desorpt ion studies on C C V a l k a n o l a m i n e systems, kinetic data are typically obtained by conduct ing exper iments using special types of laboratory contactors. The most commonly used contactors are stirred cel ls, single sphere units, wetted wall co lumns and laminar jets. These contactors are des igned in such a way that the interfacial a rea is accurately known and the hydrodynamics are well def ined so that physical mass transfer coefficients can easi ly be obtained from first principles. The advantage of knowing the interfacial area and mass transfer coefficient in advance is that the reaction kinetics and the mass transfer can be decoupled and the measured rate data can be easi ly interpreted to study the kinetics of gas-l iquid reactions. In this chapter, a new laboratory gas-l iquid contactor is descr ibed. The apparatus is, in principle, similar to the wetted sphere units used in many previous studies on C C V a l k a n o l a m i n e kinetics (Davidson and Cul len, 1957; S a v a g e et a l . , 1980; Tseng et a l . , 1988; A l - G h a w a s et a l . , 1989; Tomcej and Otto, 1989; Richard and Sanda l l , 1993; Tamimi et a l . , 1994a,b; Dehouche and Lieto, 1995; Rinker et al . , 1995). However, in this work the conventional design has been improved by replacing the full sphere by a hemisphere and by designing a better liquid feed and receiver sys tem. 48 3.2 Hemispherical Contactor Figure 3.1 depicts the main features of the hemispherical contactor. All parts of the apparatus in contact with the amine solution were constructed from stainless steel, Teflon, or Pyrex glass. The hemispherical contacting surface was constructed from a 76-mm diameter solid, stainless steel sphere. The upper half of this sphere was machined to have shiny and smooth surface and the lower half was machined to fit into a 79-mm ID stainless steel funnel (included angle) leaving a uniform annular space of 1.5 mm. The hemisphere was centered by three equally spaced stainless steel inserts, which were fastened on the inside of the funnel by metal screws inserted from the outside. The hemispherical assembly was enclosed in two concentric cylinders that formed the absorption/desorption chamber. The total height of the chamber was 457 mm. The inner cylinder was made from 19-mm thick Pyrex glass that had a conical shape, 152 mm ID at the bottom and 76 mm ID at the top. The outer cylinder was made from two cylindrical parts of 203 mm ID. The upper part was 152 mm long and constructed from 13-mm thick stainless steel pipe. The lower part was 305 mm long and was made from 13-mm thick QVF Corning glass. The purpose of using Corning glass in the lower part was to permit viewing the film during the experiment. To prevent heat losses, the upper part of the outer cylinder was wrapped in glass wool insulation and the lower part was wrapped in thermolyne electrical heating tape. 49 I Gos In V o -1 H e m i s p h e r i c a l S u r f a c e (SS 316) 2 R e c e i v e r Tube (SS 316) 3 F l e x i b l e Hose (SS 316) 4 Inner C y l i n d e r ( P y r e x G l a s s ) 5 Top O u t e r C y l i n d e r (SS 316) 6 Bot tom O u t e r C y l i n d e r (QVF G l a s s 7 T h r e a d e d Rod ( C a r b o n S t e e l ) 8 Top F l a n g e (SS 316) 9 Bot tom F l a n g e (SS 316) t 1 Li qui d I n Figure 3.1 Schematic Drawing of the Absorption/Desorption with the Hemispherical Contactor 50 The seal on both ends of the absorption/desorption chamber was provided by two 12-mm thick and 305 mm diameter stainless steel flanges and Teflon O-rings between the flanges and the glass. The top flange was compressed on the glass cylinders by means of six equally spaced 10 mm diameter bolts attached to the bottom flange. To avoid breakage of the glass cylinders due to uneven thermal expansion of the glass and metal components, the inner cylinder was connected to the top flange by a flexible stainless steel hose. The hemispherical assembly with the attached receiver tube was installed at the center of the inner cylinder at 228 mm from the bottom flange. The receiver tube was sealed to the bottom flange by means of a compression fitting. The feed liquid is passed through the stainless steel hemisphere by means of a 4-mm ID stainless steel tube and is discharged at the pole of the hemisphere (see Figure 3.1). It flows as a well-defined liquid film over the surface of the steel hemisphere and is collected by the stainless steel funnel at the base of the hemisphere. The effective mass transfer contact area provided by the hemisphere is 98.03 cm 2 . The liquid is discharged to the storage tank via a 10 mm ID stainless steel receiver tube soldered to the base of the funnel. The liquid level in the funnel is maintained by means of a stainless steel constant head tank (76 mm ID and 76 mm height). The constant head tank is moved vertically up or down on a finely threaded rod by means of a jacking mechanism. The receiver tube is connected to a constant head tank by a 4 mm ID stainless steel flexible Teflon tubing. 51 In Figure 3.1, the gas is shown to enter the top of the chamber and exit at the bottom. However, there are also provisions for the gas to enter at the bottom and exit at the top. The down flow of gas is generally preferred to prevent surface rippling due to opposite gas and liquid flow directions. 3.3 Experimental Setup and Procedure Figure 3.2 shows the flow diagram of the experimental equipment. The amine solution was stored in a 40 L stainless steel tank (item number 9 in Figure 3.2) equipped with a stainless steel diffuser for mixing and loading the amine solution with CO2 in case of desorption runs. The amine solution and the gas stream were heated to the desired temperature in a carbon steel tank (item number 10 in Figure 3.2), which had the same dimensions as those of the amine tank. This tank was equipped with a diffuser, an immersion heater and two stainless steel heating coils, one for heating the amine solution and the other for heating the air that flowed through the annular space in the absorption/desorption chamber. Both coils were made from 12 m long, 4-mm ID stainless steel tubing. Inside the tank, these coils were immersed in the water that filled approximately half of the heating tank. The water temperature was raised to the experiment temperature by means of an immersion heater controlled using a PID type temperature controller (Omega CN76000). 52 CL ZI -*—> 0 CO \" r o -4—» C 0 E i -0 CL X LU CN CO 0 i _ D CT) 1/1 a. : l V The experimental setup shown in Figure 3.2 was used for both the absorption and desorption experiments. The procedure in both cases was essentially the same. In the absorption experiments, pure CO2 or N 2 0 was used, whereas in the desorption experiments pure N 2 was used. All absorption experiments were done under atmospheric pressure. Desorption experiments below 343 K were performed at atmospheric pressure and those above 343 K were carried out at 203 kPa. Higher system pressure was required to prevent flashing of the feed solution due to boiling and excessive C 0 2 desorption. The experimental setup was regularly tested for leaks by pressurizing it with N 2 up to 250 kPa and monitoring the system pressure for several hours. The apparatus always held the pressure extremely well. In a typical absorption or desorption experiment, the amine tank was filled with approximately 20 L of freshly prepared solution and then sealed. The solution was circulated through the hemispherical unit kept under pressure by N 2 from a gas cylinder. The solution was initially fed at high flow rates to ensure complete wetting of the hemisphere. When the liquid film was stabilized, the flow rate was reduced to the desired value. The solution flow rate was measured using a Cole-Palmer variable area flow meter (model H03229-31) and controlled manually by a precision needle valve. For each run, the flow rate was checked using the bypass line. The bypass line was also used to withdraw liquid samples (10 mL) to determine C 0 2 loadings as described in Appendix A. Typically, the liquid flow rate ranged between 1.5 to 3.5 mL/s and the exposure time varied between approximately 0.3 to 0.6 s. The solution temperature was measured 54 using a 1.5-mm diameter, K type thermocouple, installed at the center of the liquid feed point. The feed solution temperature was maintained at the desired value by regulating the power input to the immersion heater attached to the heating tank and the electrical tape wrapped around the liquid feed line. After passing over the hemisphere, the liquid flowed into the receiving funnel where it was maintained at a desired level by means of a constant level device. Prior to entering the constant head tank (item 3 in Figure 3.2), the solution temperature was brought down to the ambient temperature by passing it through a water-cooled condenser (item 2). At this point, a liquid sample could also be withdrawn for analysis. From the constant head tank, the liquid ran down to a Pyrex glass drain tank (50 mm ID and 300 mm height). In the drain tank, the liquid level was maintained at a preset value by adjusting its outflow by means of a precision needle valve. The solution from the drain tank was collected in a storage tank for reuse. The CO2 content (loading) in the amine solution was determined using Gastec tubes. The detailed procedure for this method is given in Appendix A. The gas entering the absorption/desorption chamber was saturated with water vapor at the experiment temperature by bubbling it through the water in the heating tank (item 10). The stirring action of the bubbling gas also helped maintain a uniform water temperature in the heating tank. Saturating the gas feed with water vapor reduced water losses from the liquid film and heat imbalances in the chamber. At all times during an experiment, the water in the heating tank was kept saturated with the feed gas. 55 Gases were supplied from gas cylinders with a discharge pressure maintained at 35 kPa above the system pressure. The gas discharge pressure was controlled by means of low-pressure precision regulators (Skeans Model P-16-04-L00). Depending on the mode of operation, solution concentration and amine type, the flow rate of the gases ranged between 200-1200 mL/min. Typically, the gas stream entered the top of the chamber and exited at the bottom. After leaving the chamber the gas stream was diluted with a CO2 free N 2 gas. The flow rate of dilution N 2 typically ranged between 200-1000 mL/min. The gas mixture was cooled to ambient temperature by passing it through a water-cooled condenser. The cooled gas was then flashed into a Pyrex glass tank (100 mm ID and 300 mm height), to separate the gas from the water condensate. The moisture in the gas stream was further lowered by passing it through an acrylic tube (50 mm ID and 30 mm height) filled with anhydrous calcium sulfate beads. The dry gas mixture was then analyzed using an infrared C 0 2 analyzer (Model NOVA 300, NOVA Analytical Systems Inc., Hamilton, ON). In absorption experiments with N 2 0 , the gas samples were collected in 1 L Tedlar gas sampling bags and the gas composition analyzed using a G C (Shimadzu Model G C 8A). In some runs, the gas phase C 0 2 concentration was also measured using the G C to double check the accuracy of the infrared analyzer. The calibrations and procedure for gas phase C 0 2 and N 2 0 measurements using the infrared analyzer and G C are given in Appendix B. The feed and dilution gas flow rates were measured using Cole-Palmer (Model G F M 171) and Brooks (Model 5700) mass flow meters, respectively. The 56 gas flow rates were maintained at the desired value by means of needle valves installed upstream of the mass flow meters. The mass flow meters were calibrated using a soap film meter (see Appendix B). The temperatures of the gas stream in the heating tank and the absorption/desorption chamber were measured by type K thermocouples. In order to maintain the gas stream at the desired temperature, electrical heating tapes were wrapped around the gas feed line and the outer glass wall of the chamber. The power input to these tapes was regulated using two independent PID temperature controllers (Omega CN76000). All temperatures were controlled to within ±0.5 ° C . The pressures in the chamber and heating tank were measured using Omega (Model PX-202-030GV) pressure transducers. In the desorption experiments, the system pressure was controlled manually by a precision needle valve installed on the gas line downstream of the flash tank. The transducers were precisely calibrated using a mercury manometer (see Appendix B). 3.4 Data Acquisition and Calibration The signals from the thermocouples, pressure transducers, mass flow meters and CO2 analyzer were read and recorded by means of an IBM 486 P C equipped with a CIO-DAS08 data acquisition board. The number of analog input channels in the A/D board were expanded using two externally mounted CIO-EXP16 signal-conditioning accessory boards, each with 16 input channels. The output signals from all sensors were calibrated as described in Appendix B. The 57 calibration equations were included in the data acquisition software written in Visual Basic specifically for this application. During data acquisition, the software also displayed (on a real time basis) all measurements as well as the absorption and desorption rates. The absorption or desorption rates at any given time were calculated by the program from the feed and dilution gas flow rates and the exit gas composition using the following mass balance equations: FNd\" x % C 0 2 in Exit Gas N A (mmol /s) = F c o ^ - (3.1) c ° 2 1 0 0 - % C O 2 in Exit Gas) (FN + FND\" x % C 0 2 in Exit Gas N D (mmol /s) = ^ ^ - (3.2) ( 1 0 0 - % C O 2 inExi tGas) where, N A and No denote the absorption and desorption rates in units of mmol/s, and F c c > 2 , F^ e d and F^' denote the flow rates of feed C 0 2 , feed N 2 , and dilution N 2 respectively in units of mmol/s. Figure 3.3 and 3.4 depict typical plots of exit gas compositions and mass transfer rates for C 0 2 absorption and desorption for aqueous MEA. In the absorption experiments (Figure 3.3), the C 0 2 concentration initially drops very rapidly and then increases to a steady value. This behavior results from the fact that the solution is fed initially at a high flow rate to ensure complete wetting of the hemisphere. This causes it to absorb more C 0 2 and the exit C 0 2 concentration consequently falls. However, when the liquid film stabilizes, its flow rate is 5 8 0 _J I I I I I I I I I I I I I I I I I I I I I I l _ _J L _ l I I I 1 I 1_ 0 0 10 20 30 40 Time (min) Figure 3.3: Typical computer output from an absorption experiment (MEA = 14.3 wt%, T = 303 K, P T = 101.2 kPa, Q L = 2.1 mL/s) 50 3 40 T— i— i— i—i— i—i—I—I—|—p—i—i—i—I—I— i—i— i—|—I—I—I—I—I—I— i—i—i—I— i—i— i— i— i—i—i—i—r 10 8 o E 6 w co CD * x 4 LU H 2 CM o o 0 I ' i • i • ' I I I I I i i i I I I I i I I I I 1 I I I I i I i i i i i i I i i I Q 0 10 20 30 40 Time (min) Figure 3.4: Typical computer output from a desorption experiment:(MEA = 20 wt%, a = 0.279 mol/mol, T = 378 K, P T = 202 kPa, Q L = 2.2 mL/s) 59 reduced to the desired rate and the exit gas composition comes back to a steady value. An experiment was considered complete when the C 0 2 concentration in the exit gas remained constant for at least 10 minutes. In the desorption experiments (Figure 3.4), the concentration of C 0 2 in the stripping gas steadily increases until it reaches a constant value, The gradual increase in C 0 2 concentration in the stripping gas occurs because at the start of a desorption run all lines are purged with pure N 2 and it takes a while for the C 0 2 to diffuse into N 2 gas filling the lines downstream of the absorption/desorption chamber. The reproducibility of the absorption and desorption experiments was always within 2%. 3.5 Chemicals All gases had a purity of 99.9% and were supplied by Prax Air Company. The amines had a purity of more than 99% and were supplied by Sigma-Aldrich, van-Waters & Rogers and Travis Chemicals. The aqueous amine solutions were prepared using distilled water. 60 CHAPTER 4 MATHEMATICAL MODEL This chapter presents a mathematical model for C 0 2 absorption and desorption in aqueous amine solutions falling as a laminar liquid film over a hemispherical surface. The model was developed for the general case where the aqueous solution may contain a binary mixture of amines (e.g., MEA+AMP or MEA+MDEA) and where C 0 2 undergoes a series of reversible reactions. This model can be readily modified to accommodate a single aqueous amine (e.g., MEA or AMP) or water by setting the initial concentration of one or both amines to zero. The model reduces to the well-known pseudo-first-order kinetics when all reactions are lumped into a single, overall reaction by setting the rates, of all but one reaction to zero. The important model parameters and physical property data needed to solve the model equations are identified. Correlations are presented for parameters for which data are available in the literature. For cases where data were deficient or not available in the literature (e.g., Henry's constant and diffusivity of C 0 2 in aqueous amine blends), new data were obtained and new correlations were developed. A methodology to solve the model equations and to estimate unknown model parameters using the non-linear regression package G R E G is also presented in this chapter. 61 4.1 Reaction Mechanism The model for CO2 absorption and desorption applies to the following aqueous amine systems: 1. CO2+MEA+H2O 5. CO2+MEA+MDEA+H2O 2. CO2+DEA+H2O 6. CO2+MEA+AMP+H2O 3. CO2+MDEA+H2O 7. CO2+DEA+MDEA+H2O 4. CO2+AMP+H2O 8. CO2+DEA+AMP+H2O Since most of the data presented in this work refers to the C 0 2 + A M P + H 2 0 system, this system was chosen as the base case and the reactions governing this system are presented first. For systems involving other amines, the additional reactions are given subsequently. In accordance with the convention used in the amine literature, MEA is represented as R1NH2, where R1 denotes -CH2CH2OH. DEA is represented as R 1 R 2 N H , where R1 = R 2 = - C H 2 C H 2 O H . MDEA is represented as R1R2R3N, where R1 = R 2 = - C H 2 C H 2 O H and R 3 = - C H 3 . A M P is represented as R4iNH2, where R4 = - C ( C H 3 ) 2 C H 2 O H . 4.1.1 Reactions for C02+AMP+H20 (Base Case) When CO2 is absorbed or desorbed in aqueous A M P solutions, the following reactions may occur in the liquid phase: 62 AMP- Zwitterion Formation: k K C 0 2 + R 4 N H 2 < ! ^ R 4 N H ^ C O O - (4.1) k_, AMP-Zwitterion Deprotonation: k K R 4 NH^COO- + R 4 N H 2 R 4 N H C O O - + H 2 0 (4.4) AMP-Carbamate Reversion: k 5 , K 5 R 4 N H C O O - + H 2 O ^ R 4 N H 2 + H C 0 3 (4.5) k-5 AMP Deprotonation: k K R 4 N H ^ + O H ^ R 4 N H 2 + H 2 0 (4.6) k-e Bicarbonate Formation: k K C 0 2 + O H \\ ^ H C 0 3 (4.7) k - 7 Carbonate Formation: H C 0 3 + O H - ^ C O ^ + H 2 0 (4.8) k - 8 Water Dissociation: 2 H 2 O ^ O H + H 3 0 + (4.9) k_ 8 In the above reactions, the k's denote rate constants and the K's denote equilibrium constants. 63 4.1.2 Reactions for C02+MEA+H20 When C0 2 is absorbed or desorbed in aqueous MEA solutions, reactions (4.7) to (4.9) are the same as those in the base case, but reactions (4.1) to (4.6) are replaced by the following reactions: MEA-Zwitterion Formation: k 1 0 ,K 1 0 COa+RJNHa ^R^H+COCT (4.10) k-10 MEA-Zwitterion Deprotonation: R1NH^COO-+R1NH2 k l51R1NHCOO-+R1NH: (4.11) k K R.NH^COCT + H 20 ^ R^HCOCT + H 3 0 + (4.12) k.12 k K R^H+COCT +OH' ^ R ^ H C O O \" +H20 (4.13) MEA-Carbamate Reversion: k K R 1 NHCOO-+H 2 O^R 1 NH 2 +HC0 3 (4.14) k-i4 MEA Deprotonation: k K RJMH^+OH \"^RJNHa+HaO (4.15) 4.1.3 Reactions for C02+DEA+H20 When C0 2 is absorbed or desorbed in aqueous DEA solutions, reactions (4.7) to (4.9) are once again the same as those in the base case, but reactions (4.1) to (4.6) are replaced by the following reactions: 64 DEA- Zwitterion Formation: k K C 0 2 +R1R2NH ^ 6 RJR 2NH +COCT DEA-Zwitterion Deprotonation: R^NhrCOCr +R 1R 2NH k ,S 7 R ^ N C O O - +R1R2NH2 k_17 R 1R 2NH+COO-+H 20 RJR2NCOO~ + H 3 0 + ^-18 R1R2NH+COO\"+OH\" ^ RJR2NCOO\"+H20 K - , 9 DEA-Carbamate Reversion: ^ 20-^ 20 RJR 2NCOO+H 20 ^ RJR2NH + H C 0 3 k-20 DEA Deprotonation: R ^ N H * + OH\" ^ R ^ N H + H 2 0 4.1.4 Reactions for C02+MDEA+H20 When C 0 2 is absorbed or desorbed in aqueous MDEA solutions, reactions (4.7) to (4.9) are again unchanged, but reactions (4.1) to (4.6) are replaced by the following: MDEA-C02 Reaction: k K C 0 2 + R ^ ^ N + H 2 0 ^ R1R2R3NH+ + H C 0 3 (4.22) k_22 MDEA Deprotonation: k K RJR2R3NH++OH\" ^ \\ R 2 R 3 N + H 2 0 (4.23) 65 (4.16) (4.17) (4.18) (4.19) (4.20) (4.21) 4.1.5 Reactions for C02+MEA+MDEA+H20 When C 0 2 is absorbed or desorbed in aqueous blends of MEA and MDEA, in addition to reactions (4.7) to (4.15) and (4.22) to (4.23), the following reaction occurs: Deprotonation of MEA-Zwitterion to MDEA: R ^ H + C O O \" + R 1 R 2 R 3 N k 2 < i 2 4 R 1 N H C O O - + R 1 R 2 R 3 N H + (4.24) k_24 4.1.6 Reactions for C02+MEA+AMP+H20 When C 0 2 is absorbed or desorbed in aqueous blends of MEA and AMP, in addition to reactions (4.1) to (4.15), the following reactions must be included: Deprotonation of AMP-Zwitterion to MEA: k K R 4 N H ^ C O O \" + R 1 N H 2 2 ^ 5 R 4 N H C O C T + R 1 N H ; (4.25) k-25 Deprotonation of MEA-Zwitterion to AMP: R 1 N H ^ C O O - + R 4 N H 2 <-> R ^ H C O C T + R 4NH+ (4.26) ^ - 2 6 4.1.7 Reactions for C02+DEA+MDEA+H20 When C 0 2 is absorbed or desorbed in aqueous blends of DEA and MDEA.in addition to reactions (4.7) to (4.9) and (4.16) to (4.23), the following reaction occurs: Deprotonation of DEA-Zwitterion to MDEA: R^Nr - rCOCr + R 1 R 2 R 3 N k 2 i 2 7 R 1 R 2 N C O O \" + R 1 R 2 R 3 N H + (4.27) 66 4.1.8 Reactions for C02+DEA+AMP+H20 When C 0 2 is absorbed or desorbed in aqueous blends of DEA and AMP, the following reactions occur in addition to reactions (4.1) to (4.9) and (4.16) to (4.21): Deprotonation of AMP-Zwitterion to DEA: k 2 8 , K 2 8 R ^ H + C O C T + R ^ N H <-» R 4 N H C O C r + R 1 R 2 N H 2 - (4.28) k_ 2 8 Deprotonation of DEA-Zwitterion to AMP: k 2 9.K 2 g R 1 R 2 N H + C O O - + R 4 N H 2 <-> R 1 R 2 N C O O \" + R 4 N H ^ (4.29) 4.2 Reaction Rates In the above reaction schemes, all reactions are considered to be reversible. Some of these reactions proceed at finite rates while others (that involve only a proton transfer) occur almost instantaneously. This section presents the rate expressions for reactions with finite rates. For convenience, the chemical species in reactions (4.1) to (4.29) are renamed as follows: C, = C 0 2 , C 2 = R 4 N H 2 , C 3 = R 4 N H ^ , C 4 = R 4 N H C O O \" , C 5 - H C 0 3 , C 6 = C O \" 2 , C 7 = O H \" , C 8 = H 3 0 + , C 9 = H 2 0 , C 1 0 = R , N H 2 > C „ = R ^ H * . C 1 2 = RJNHCOCT, C 1 3 = R 1 R 2 N H , C 1 4 = R 1 R 2 N H J , C 1 5 = R 1 R 2 N C O O \" > C 1 6 = R 1 R 2 R 3 N , C 1 7 = R 1 R 2 R 3 N H + (4.30) 4.2.1 Reaction Rates for C02+AMP+H20 System (Base Case) This case includes reactions (4.1) to (4.9). Among these, only reactions (4.1) to (4.4) and (4.7) have finite rates. The latter are expressed as follows: 67 where: \"\"l-4 = - k ' i C , C 2 ~ C 4 1+ r7 = -k7C,C7 +—C5 K 7 A = ' JO v k - i y K 1 K ; + v k - i y K 1 K 3 + v k - i y K 1 K 4 (4.31) (4.32) (4.33) B = i\\2 c 2 + c q + i k _i , l k-1 > y Ik-1 J c 7 (4.34) Equation (4.31) is based on the assumption that pseudo-steady state is valid for the zwitterion. The detailed derivation of the base case equations is given in Appendix D. The derivations for other systems involving zwitterion mechanisms are similar and therefore not presented separately. 4.2.2 Reaction Rates for C0 2+MEA+H 20 System This case includes reactions (4.7) to (4.15), with reactions (4.7) and (4.10) to (4.13) having finite rates. The rate expression for reaction (4.7) is given by equation (4.32). The rate for reactions (4.10) to (4.13) is given by: \"10-13 (AY _ k 1 0 IBJ. f 4 \\ (4.35) 1 + vBj 68 where: A V k - i o y K10 K11 • + k1 v x - i o y K 1 0 K 1 2 • + ^ k13 ^ C 0 v , x- io y K i 0 K 1 3 (4.36) B = k ^ Vk-10 , C 1 0 + ^k N vk-10 y C 9 + v k - i o y C 7 (4.37) 4.2.3 Reaction Rates for C02+DEA+H20 System This case includes reactions (4.7) to (4.9) and (4.16) to (4.21), with reactions (4.7) and (4.16) to (4.19) having finite rates. The rate expression for reaction (4.7) is given by equation (4.32). The rate for reactions (4.16) to (4.19) is given by: (A) _k16 C i C 1 3 -c15 •16-19 1 + B (4.38) where: A = 'k N K 1 7 v k - i e y ' 1 4 K 1 6 K 1 7 • + M 8 v k - i e y K 1 6 K 1 8 • + k i v k - i e y ^ 1 6 ^ 1 9 (4.39) B = v k - i e y C 1 3 + /k ^ * 1 8 v k - i e y | C 9 + 1'k ^ * 1 9 v k - i e y C 7 (4.40) 4.2.4 Reaction Rates for C02+MDEA+H20 System This case includes reactions (4.7) to (4.9) and (4.22) to (4.23), with reactions (4.7) and (4.22) having finite rates. The rate expression for reaction 69 (4.7) is given by equation (4.32) and the rate for reaction (4.22) can be obtained from: r22 - - k ^ C p ^ + — C 5 C 1 7 K 2 2 (4.41) 4.2.5 Reaction Rates for C02+MEA+MDEA+H20 System This case includes reactions (4.7) to (4.15) and (4.22) to (4.24), with reactions (4.7), (4.10) to (4.13), (4.22) and (4.24) having finite rates. The rate expressions for reactions (4.7) and (4.22) were already defined by equations (4.32) and (4.41), respectively. The rate of reactions (4.10) to (4.13) and (4.24) can be expressed as: 10 ^ 1 ^ 1 0 — ' 10-13,24 1 + B (4.42) where: A = vk-10 j K 10 K 11 • + 1 k ^ K 1 2 vk-10 j K 1 0 K 1 2 • + * 1 3 V K - 1 0 J K i 0 K 1 2 • + ^ 2 4 k-i ' 1 7 V ,x-10 J K 1 0 K 2 4 (4.43) B = f k A vk-10 j C 1 0 + ' k ^ K12 k-10 !C 9 + f k A * 1 3 vk-10 j C 7 + , X 2 4 v k - ioy ' 1 6 (4.44) 4.2.6 Reaction Rates for C02+MEA+AMP+H20 System This case includes reactions (4.1) to (4.15) and (4.25) to (4.26), with reactions (4.1) to (4.4), (4.7), (4.10) to (4.13) and (4.25) to (4.26) having finite 70 rates. The rate expression for reaction (4.7) is defined by equation (4.32). The rate of reactions (4.1) to (4.4), (4.25) and (4.10) to (4.13) and (4.26) are given by: where: and 11-4,25 1+ B (4.45) A r i. \\ • + K,K 3 [k_jK,K k25 25 (4.46) (k \\ B = l \\ 2 C 2 + C 9 + 4 c 7 + ^25 ^ k - i , Lk-1 J y l k-1 J ^k_i J '10 (4.47) - k i o C i C 1 0 - C 1 2 '10-13,26 1 + B (4.48) where: ( k ^ vk-10 j '11 • + v12 V k -10 J K 1 0 K 1 2 • + k13 V k -10 J K 1 0 K 1 3 • + ^26 V k -10 J ^10^26 (4.49) B = f k A V k- io J l c 1 0 + 1 k ^ *12 V k- io J l c 9 + A k ^ V k -10 J C 7 + ' k ^ *26 v k - ioy (4.50) 71 4.2.7 Reaction Rates for C02+DEA+MDEA+H20 System This case includes reactions (4.7) to (4.9), (4.16) to (4.23) and (4.27), with reactions (4.7), (4.16) to (4.19), (4.22) and (4.27) having finite rates. The rate expressions for reactions (4.7) and (4.22) are defined by equations (4.32) and (4.41), respectively. The rate for reactions (4.16) to (4.19) and (4.27) is given by: - k i e C i C 1 3 \"16-19,27 1 + '1^ vBy (4.51) where: ( k 1 7 1 C 1 4 k-16 7^16^17 + 1^8 f I, \\ Vk-16 J K 16 K 18 + k i Vk-16 J • \\ 2 7 K i 6 K 1 s Vk-16 ) c 1 7 K 1 6 K 2 7 (4.52) B = f k ^ K17 vk-ie j C 1 3 + vk-ie j IC9 + r k ^ ^19 vk-ie j r k ^ k- i V,x-16 J (4.53) 4.2.8 Reaction Rates for C02+DEA+AMP+H20 System This case includes reactions (4.1) to (4.9), (4.16) to (4.21) and (4.28) to (4.29), with reactions (4.1) to (4.4), (4.7), (4.16) to (4.19) and (4.28) to (4.29) having finite rates. The rate expression for reaction (4.7) is defined by equation (4.32). The rates for reactions (4.1) to (4.4), (4.28), and (4.16) to (4.19) and (4.29) are given by: 72 11-4,28 c.|C 2 ~ C 4 1+ (4.54) where: A = K K , K 3 ^k_ i y • + K i K - i + k28 v^-1 j '14 28 (4.55) f l O (y \\ B = 1 \\ 2 c 2 + C 9 + c 7 + •^ 28 v k -1 J l k_ i J l k - 1 J l k - 1 ) '13 (4.56) and M6 C i C 1 3 - C 1 5 LB J \"16-19,29 (4.57) where: A = k17 Vk-16 J '14 K 1 6 K 1 7 + 1 k ^ *18 v k - i e y ^k A N 19 K 1 6 K 1 8 V k - 1 6 J K 1 6 K 1 9 • + K 29 vk-ie j ^16^29 (4.58) B = K 17 V k - 1 6 J C 1 3 + M8 V k - i e y C Q + *19 V k - 1 6 J :c7 + ' k A K 29 V k - 1 6 J (4.59) 4.3 Reactive Gas Absorption/Desorption Model 4.3.1 Hydrodynamics of Liquid Film Figure 4.1 is a schematic diagram of the hemispherical film described in Chapter 3. The liquid descends in the form of a laminar film from the pole of the 73 hemisphere towards its equator where it is collected in the funnel. The gas, depending on the operating conditions, is either absorbed into the liquid film or is desorbed from it. Gas-Liquid Interface Figure 4.1: Schematic of the Liquid Film This system can be mathematically modeled to calculate the rate of gas absorption or desorption over the exposed area of the film provided the film thickness and the velocity profile are known as a function of position (0). Lynn et 74 hemisphere towards its equator where it is collected in the funnel. The gas, depending on the operating conditions, is either absorbed into the liquid film or is desorbed from it. Gas-Liquid Interface Figure 4.1: Schematic of the Liquid Film This system can be mathematically modeled to calculate the rate of gas absorption or desorption over the exposed area of the film provided the film thickness and the velocity profile are known as a function of position (9). Lynn et 74 al. (1955) have studied the hydrodynamics of laminar liquid films flowing over a sphere. They assumed that the thickness of the liquid film at any latitude on the sphere is the same as it would be for the same flow rate per unit length on a plane surface making the same angle with the vertical. Based on this assumption, the film thickness at latitude 9 (A9) is given by: A e = A 0 ( s i n 9 ) - 2 / 3 (4.60) where A 0 is the film thickness at the equator (9 = nl2) of the sphere and is given by: A 0 = ' 3vQ ,27iRgy ,1/3 (4.61) It follows from the above assumption that a half parabolic velocity profile will exist at all latitude on the sphere so that the velocity distribution, V e , in the film can be approximated by the following equation: V e = V 0 [ l - x 2 J (4.62) where x is the dimensionless distance from the gas-liquid interface, i.e, x = (R + A e - r)/ A e (see Figure 4.1). V 0 is the velocity at the film surface: V 0 = 3Q 47 iRA o y (s in9)- 1 M (4.63) Note that at 9 = 0 (i.e., at the pole of the hemisphere), equation (4.60) is not valid because at that point the thickness of the liquid film becomes infinite. However, this is a physical impossibility because only a finite amount of liquid 75 (about 2 mL/s) flows through the liquid feed tube of 3 mm I.D. We calculated the thickness of the liquid film at different 9 values for water and amine solutions using equation (4.60) and we found that we get reasonable values at 9 very close to the pole. For numerical solution of the model equations, the liquid film in 0 direction was divided into 200 points to integrate the absorption rate over the entire hemispherical surface. This means that the first point at which the concentration gradient was calculated lies at 9 = 0.45° (0.008 radian). For water at 298 K and liquid flow rates of 2, 3 and 4 mL/s, the film thickness at 9 = 0.45° (near the pole) calculated from equation (4.60) are 3.31, 3.80 and 4.17 mm respectively. The corresponding values at 9 = 90° (at the equator) are 0.13, 0.15 and 0.17 respectively. The thinning of the liquid film from the pole to the equator occurs because the same amounts of liquid flows through the increasing cross sectional area as it descends from the pole to the equator. 4.3.2 Model Equations The mathematical model presented below is based on the concept of gas absorption or desorption accompanied by multiple reversible chemical reactions in a hemispherical liquid film. The main assumptions involved in the model derivation are: • The interfacial concentration of dissolved (molecular) C 0 2 corresponds to the physical solubility as determined by Henry's law (i.e., p., = H,C\\). 76 • Mass transfer in the direction of the liquid flow is dominated by bulk convection and diffusion in the 9 direction is negligible. • The flow field is uniform in the O direction (V 0 and x = 0, fdC^ and i Pi A ( c ; -v k g H A (sine) 2/3 ' a c ^ v dx j dx V Vj=2-8,10-12 = 0 (4.82) 80 at G > 0 and x = 1. <3x V ^=1-8,10-12 = 0 (4.83) For the case where the gas side resistance to mass transfer is negligible (kg -» oo), the boundary condition given by equation (4.82) reduces to: fdC } at 9 > 0 and x = 0, C\\=^- and —>- = 0 (4.84) H 1 v e x y j=2-8,10-12 Note that the model equations (4.64) to (4.74) are general and applicable to any of the aforementioned systems by substituting corresponding chemical species, reaction rates and diffusivities. The model equations were solved numerically using a commercial software package called Athena Visual Workbench (see Section 4.5). 4.3.3 Liquid Bulk Concentrations In order to solve the model equations (4.64) to (4.74), the bulk concentrations (C°) , must be known. They can be obtained by writing the following balances: Total C02 Balance: C° +C°4 + C° +C° +C° 2 = a i n i t i a l ( [R 4 NH 2 ] i n i t i a l +[R 1NH 2 ] i n i t i a l) (4.85) Total AMP Balance: C ° + C ° + C ° 4 = [ R 4 N H 2 ] i n i t i a l (4.86) 81 Total MEA Balance: C? 0 +C^+A 2 =[RiNHJ i n i t i a l (4.87) Electron Neutrality Balance: C° + C° + C° - C° - C° - 2C° - C° - C° 2 = 0 (4.88) Equilibrium Equations: * a = ^ (4-89) K e = c^\" ( 4 \" 9 0 ) 7 C°C° K 8 = - ^ - (4.92) c°c° K 9 = C ? C ° (4.93) /~»0 /->0 K 1 4 = ^ P (4.94) u 1 2 ^ 1 5 r~*o (4.05) C°C° 82 4.3.4 Rate of Absorption or Desorption with Chemical Reaction The rate of gas absorption or desorption over the hemispherical film at any latitude 0 can be calculated by invoking the Fick's law of diffusion: N A(6) = -N D (9) = -[2n(R + Aj S i n e ] 5 i f ^ - 1 (4.96) Ae V CD -4—» CO DZ c o o 00 XI < 25 20 h 15 10 h 5 h ~i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r •Numerical •Analytical 0 1 — 1 — 1 — 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i_ 285 295 305 315 325 Temperature (k) Figure 5.11: Absorption rates of CO2 in pure water predicted from analytical and numerical solutions (Q L = 2.0 mL/s, p c o = 87-97 kPa) The analysis presented above verifies that the present model accurately describes the absorption and desorption of a gas in and from the hemispherical film. It further confirms that the experimental technique and the numerical scheme used to solve the model equations are accurate and reliable. 103 5.2 Parametric Sensitivity Analysis The present model consists of three types of parameters: (a) the operating parameters such as amine concentration, temperature, total pressure, CO2 partial pressure, CO2 loading and liquid and gas flow rates, (b) physical property parameters such as density, viscosity, gas-side mass transfer coefficient, liquid phase diffusivities and Henry's constants and (c) kinetic parameters such as rate constants and equilibrium constants. In this section we examine the effect of these parameters on the rate of absorption and desorption of C 0 2 into and out of aqueous amine solutions. 5.2.1 Effect of Operating Parameters In order to study the effect of operating parameters on C 0 2 absorption and desorption rates, a series of simulation runs were carried out with C 0 2 - A M P as the example system. The simulation results are plotted in Figures 5.12 to 5.17. These results were obtained for the base case conditions listed in Table 5.1. To demonstrate the effect of each operating variable separately, only one of the operating parameters in Table 5.1 was varied while the others were fixed at their base value. The physical properties and the equilibrium constants were calculated from the correlations given in Appendices E to I and the rate constants were calculated from the correlations developed in this work. 104 Table 5.1: Base case operating conditions for parametric sensitivity analysis Parameter Value Absorption Desorption T (K) 303 373 P t o t a l ( kPa ) 101.3 202.6 p C 0 2 ( kPa ) 97.0 1.5 CAM (wt%) 20.0 20.0 ocinitiai (mole/mole) 0.0 0.2 Q L (mL/s) Z 0 2.0 The results presented in Figures 5.12 to 5.17 are plausible and self-explanatory with the exception of the effect of amine concentration given in Figure 5.12. This figure shows that both the absorption and desorption rates increase with increase in amine concentration. However, it should be noted that this increase in desorption rate is not because of the increase in amine concentration itself but because of the increase in total C 0 2 present in the solution. As this plot was generated at a fixed C 0 2 loading, which in our case is defined as moles of C 0 2 (in all its forms) per mole of amine. Figure 5.12 also shows that the rate of increase in the absorption rate diminishes when the amine concentration exceeds 30-wt%. This is likely, because at higher amine concentrations, the kinetic effects are offset by the reduced water content, higher solution viscosity and lower physical solubility of C 0 2 in the solution. The results presented in Figures 5.12 to 5.17 clearly demonstrate that the absorption rate is most sensitive to changes in amine concentration, C 0 2 partial pressure and temperature and the desorption rate is most sensitive to 105 temperature, C 0 2 loading and C 0 2 partial pressure in the stripping gas. Similar trends were observed for other systems studied in this work and for the sake of brevity those results are not included here. As will be discussed later in this chapter, the same trends were observed experimentally. Based on these observations, it was decided to conduct absorption experiments by varying mainly the amine concentration and temperature, and desorption experiments by varying the C 0 2 loading and temperature. Figure 5.12: Effect of amine concentration on C 0 2 absorption and desorption rates in aqueous A M P system 106 0.0 0.1 0.2 0.3 0.4 C 0 2 Loading (mol of C0 2 /mo l of amine) Figure 5.13: Effect of C 0 2 loading on C 0 2 absorption and desorption rates in aqueous A M P system 270 290 310 330 350 370 390 Temperature (K) Figure 5.14: Effect of temperature on C 0 2 absorption and desorption rates in aqueous A M P system 107 250 CO 15 200 E E, o 150 x CD CO 100 c o o CO -O < 50 0 0 T 1 1 1 1 1 1 1 1 1 r Desorption Absorption -i 1 1 1 r _ l I L . 20 40 60 C0 2 Partial Pressure (kPa) 20 CO o 15 | X 10 0) ro or c o \"-+-» r CL 5 o CO CU Q 0 80 Figure 5.15: Effect of C0 2 partial pressure on C0 2 absorption and desorption rates in aqueous A M P system 300 CO \"o E 250 E, CO O o 200 ro UL c g Qr 150 o CO -Q < 100 - i 1 1 1 — i — i — i — i 1 — r -i—i—i—r • Desorption Absorption _i i i I _ I i i_ _ l I L 100 150 200 250 Total Pressure (kPa) 20 CO X 10 OJ ro CU c o CO CU Q 0 300 Figure 5.16: Effect of total pressure on C 0 2 absorption and desorption rates in aqueous A M P system 108 300 - i — i — i — i — i — i — | — i — i — i — | — i — i — i — i — i — i — i — i — i — i — r 40 JO o E £ CO O CD -*—< CO CC c o o < 250 200 • •Absorption • Desorption o 30 CO O X 20 a) CO CC A 10 o %LU ert Q CL o < £1 LU CL TO 4 — O o CO CO hy E CL CD •4—' _C CO >» c CO g CO \"CD o \"> CD CD T3 4 — aq o c o CO CD CD Eff 2 o CO CD Q o CO < < < LU Q < 111 Q < LU < < LU Q < LU Q < LU 5 CD 25 CD Q — Q_ E CD i _ CD C L CD i O •4—» co + o CM CO 1 + 2 O Oi co i LO CM • CN i CM • LO CM CM O 4—' O O O 4—» i o co +~ CM + CM + O +~ LO + CO CM i • CM T -LO i O O -*—> o 1 o o CD +~ LO + LO + + CM + •<- CM 1 + ^ o CD + CD CM i CO 1 CM O o O 4—• 4—» •4—« CO CM CM + + + CD + + o CD + i o LO + co + o 4—» CM CM O CM + I O •4—' + CM O + o o CD O • + •2 p LO CO + d o co co CM + co d o o co + co + o •4—» CM CM LO O •4—' co a o + CD d + o -c—» LO d CM 1 + H LO CM i O -4—« O CO CM d o o d i co Q co CD + CD CM CO + CO co N-CO + CM CM + o CO o o 1^ . o 4—• co + CM LO CO CM i CM CM CM i O O O O o •4—» \"<* T — CM T— + + CM X — + + + o o o o o o o CM CM LO LO LO LO LO +1 +1 +1 +1 +1 +1 +1 This table does not show a significant effect of the gas side mass transfer coefficient on the predicted desorption rates. This is because, in the case examined here, the CO2 partial pressure in the stripping gas was less than 1 mol%. However, it can easily be shown that under certain operating conditions this effect may also become significant. As is discussed later in this chapter, in all our desorption experiments, we kept the C 0 2 partial pressure in the stripping gas well below 5 mol%. From the above analysis we find that, in order to predict absorption and desorption rates accurately, it is important that the values of the C 0 2 diffusivities and Henry's constants in amine solutions are known fairly accurately. For this reason we developed new correlations for these parameters that are applicable for both single and blended amine systems and cover wider temperature ranges than the available literature data. These correlations are presented in Section 5.3 (see also Appendices F and G). 5.2.3 Effect of Kinetic Parameters Table 5.3 lists all possible reactions with their associated kinetic parameters for the eight systems considered in this work. Most of these parameters are important to calculate absorption and desorption rates using our model. However, from our sensitivity analysis, we observed that, for carbamate-forming amines such as MEA, DEA and A M P , the contribution of reactions involving the deprotonation of amine-zwitterion to water and hydroxyl ions ill CO L_ 0) OD E CD s , m ID-o * CD C Ik CO c o o E ZJ To Z 3 -g > T3 C =5 : CT ILU io o £ JZ o co II - o T- CD CM T-o co CM T-CO - CO CM 00 - CO CD LO O t— T— o * * * - o o ^ C O o - CD T- CM . V C M T-* - m LO T-- C O IO v-£ ^ i- CD CM T-O CO CM T-CD c5 £ - CD CD O CM CO CD ' co CO c o * CM LO CM - 0) r» C M X . CD CO 1 -- di CO i-J S . CD CO c o o CD A—* CD L— T3 CD C IXI E , o O o C O o C M o j£ CD -Mi OJ JZ co CO CD CO CM C O C D C M C M C O V - 6 CD a T— CD CD CD T~ JH ^ f-- CM ~~co - CD T- CM ^ ^ ^ ^ L O n CM CM T-j*: T- C M oo cn N M T-J±L ^ J£ CO CO Zl c > CD CM jsc: CM - CM f~- CM o T JXL r~- C M CD JUL CO C o o CD or CO E CD 00 i f f o TT + O CM I + < L U O O oc3 . CM 0 3 ^ ^ CN 05 ^ CD Tf' TT r-~ eg in CM ^ CM h - CM in\" CD CM LO CM oc3 -^ t ^ CM ° ? TT ^ \" - ^ O ° ---CD 1J r - TI-°8 ca CD + + + < LU Q + CM o o o CM I + < L U Q + CM o o X + Q_ < + CM o o + + o CM X + < LU Q + < LU + CM o o TT Tl-+ T f T l -+ 0 « + o C M X + D_ < + < LU + C M o o X + < UJ Q + < L U Q + CM o o . CM CM -TT' TT' CD 00 T - T - CM TT' TT' TT' + + o CM X + D_ < + < LU Q + CM o o (reactions 4.3 and 4.4 for AMP, 4.12 and 4.13 for MEA and 4.18 and 4.19 forDEA) to absorption and desorption rates is insignificant. As shown in Table 5.4, a change of four orders of magnitudes in the values of the rate constants associated with these reactions produce no significant change in the predicted rate of absorption. Therefore, these reactions can be ignored without significant loss of accuracy. Similar conclusions were arrived at previously by Rinker et al. (1996) in their work on the kinetics of C 0 2 absorption in aqueous DEA solutions. This simplification greatly reduces the complexity of the kinetic rate expressions and cuts down the time required for parameter estimation by one third as the number of unknown parameters in each expression reduces from 5 to 3. With the present model, parameter estimation with 5 unknowns is extremely time consuming. It takes about 15 to 20 hours to obtain the estimates for a single data set even with the fastest P C (Pentium 4, 1700 Mhz, 256 RAM) available to us. This is because each function call to solve the model equations takes about 2 to 3 minutes and a typical parameter estimation run makes hundreds of such function calls. After this simplification is implemented, the reactions and kinetic parameters that remain are summarized in Table 5.5. Table 5.4: Effect of reactions involving zwitterion deprotonation to water and hydroxyl ions on the rate of absorption (see reactions 4.3, 4.4, 4.12, 4.13, 4.18, 4.19) Parameters Calculated Absorption Rates x 10 3 (mmol/s) Value MEA DEA A M P ki2/k_io & ki2/k_io kis/k.16 & ki 9/k-i6 k3/k.i & Wk-i 0-0 525.99 309.02 263.37 1-1 555.19 309.09 274.76 10-10 556.88 309.31 276.40 100-100 557.06 309.44 276.58 1000-1000 557.08 309.46 276.59 113 CO £ \"CD E co ICL o CO c I* ~o . CD c CO ~ c -Q o E \" o E \" .2 °^ .Q lo 1= zs '5 ^ C7 > UJ 'TJ c o i n T— c n 00 co C N cn CO C N cn CO 1^ cn 00 C O i n o cn co , y C N - O . co * o c 5 * . C N co i n T-co C N o C N cn oo . > C N - C D . cn •<- C N C N V * ^ o C N c n * c o * * o5 „ C N co i n T-0 -I—» co i _ TJ *i CD CO o C O C N o I \\— in cvi C N o C N T-C O C N C O t~-J2 C O _ I V — > . C N ob ^ C O C N T-CO CO 3 c •o o > o =5 a) 2 o C O o V - C N C N O C O CO c o » o co or T t Tt' T £ o ® C N C D CM h- T -T t o -T t T t CM CM T £ ST h~ CM LO T t T t T t 5,-2 <^CM\" CM X LO T t t^ - T — CM T t T t T t + LO LO CM T t CO . i - CM 1 T t T t CO CD CM O CM ^ T t ^ T - LO T — X CM T t T t T t + I T - CM T t T t T t + o \" S CN T t ^ ^ ^ ^ CO + < LU O o o CN X + < LU Q + CN o o o C N X + < LU Q + C N o o o C N X + < + C N o o o C N X + < LU Q + < UJ + C N o o + o C N X + < + < LU + C N o o + o C N X + < LU Q + < UJ Q + C N o o + o CN X + CL < + < UJ Q + CN o o 5.3 Henry's Constant and C 0 2 Diffusivity in Amine Solutions With the help of Table 5.2, it was shown earlier that, in order to predict absorption and desorption rates accurately, fairly accurate values of C 0 2 diffusivities and Henry's constants in amine solutions are required. In this section we examine existing literature data for these properties and present new data and new correlations that are applicable for both single and mixed amine systems and cover wider temperature ranges. 5.3.1 Correlations for Henry's Constants of C 0 2 in Amine Solutions Since C 0 2 reacts with aqueous amine solutions, it is not possible to determine its physical solubility in these solutions by direct measurements and an indirect method based on the N 2 0 analogy is commonly used. According to this method, the ratio of the Henry's constants of C 0 2 and N 2 0 in an aqueous amine solution is the same as that in water at the same temperature: H H° C 0 2 _ C 0 2 (5 1) L l 110 ' ' n N 2 0 n N 2 0 where H c c . 2 and H N 2 0 denote the Henry's constants of C 0 2 and N 2 0 in the aqueous amine solution, and H c c , 2 and H£ 0 denote the Henry's constants of C 0 2 and N 2 0 in water. A large amount of data is available in the literature for the Henry's constant of C 0 2 in water and N 2 0 in water and various amine solutions as a function of temperature. These data are summarized in Tables F.1 to F.10. It can be seen from these tables that most of the existing data are in the low 115 temperature range (293-323 K) typical of an absorber, and the data at stripper operating temperatures (373-393 K) simply do not exist. In this work new data for the Henry's constant of C O 2 in water and N 2 O in water and N 2 0 in aqueous amine solutions were obtained. These results are also listed in Tables F.1 to F.10. The details of the experimental apparatus and procedure are given in Appendix F. The data for H°C02, H^o and H N 2 0 (from this work and from the literature) were correlated as a function of temperature. These correlations are given in Appendix F (see equations F.2 to F.4). The correlations represent the experimental data well. The absolute average percent deviation was within 7% (see Figures F.1 to F.4). 5.3.2 Correlations for C 0 2 Diffusivities in Amine Solutions Like Henry's constant, the diffusivity of C O 2 in amine solutions cannot be determined directly and an indirect method based on the N 2 0 analogy was used again. According to this method, the ratio of the diffusivities of C O 2 and N 2 O in an aqueous amine solution is the same as that in water at the same temperature: D c o D c o D D° where D c c , 2 and D N 2 0 denote the diffusivities of C O 2 and N 2 0 in the amine solution, and D°COz and D ^ 0 denote the diffusivities of C 0 2 and N 2 0 in water. As shown in Appendix G, good quality data are available in the literature for D c c , 2 , D^o and D N z 0 . Some correlations for these data as a function of 116 temperature and amine concentration also exist in the literature. However, most of these correlations, specifically for D N 2 0 , are based on the data collected by individual authors valid only for narrow concentration and temperature ranges. Furthermore, in most of the published literature on CGramine kinetics, D N 2 0 at various temperatures and amine concentrations is calculated using the following modified Stokes-Einstein relation: DN>°.2 - D° 2 0 l a° 2 8 0 • (5.3) In order to check the validity of equation (5.3), we compiled all the available diffusivity data for pure water, and single and mixed amine systems from various sources (see Tables G.1 to G.10) and prepared Stokes-Einstein plots as shown in Figures G.3 and G.4. The data from our own diffusivity measurements using the hemispherical contactor were also included in these plots. It can be seen from these plots that the Stokes-Einstein type relationship does not represent the experimental data well. The average deviation (AAD%) for single amine systems is about 20% and that for mixed amine systems is about 30%. Therefore, in this work, new correlations were developed which are valid over a wider range of temperatures and amine concentrations. These correlations are discussed in detail in Appendix G (see equations G.5 and G.6). Figures G.5 and G.6 show a comparison of the measured and calculated diffusion coefficients using new correlations. In general, the agreement is very good. The overall A A D % for single amine systems is about 13% and that for mixed amine systems is about 9%. In light of the fact that different sources have used different absorption apparatus to measure diffusivities, this much deviation 117 is expected and the correlations can be safely used. Note that for CAM = 0, these correlations (equations G.5 and G.6) reduce to the correlation for N 2 0 - H 2 0 system (equations G.3). This unique and very important feature does not exist in other similar correlations proposed in the literature (Li and Lai, 1995; Li and Lee, 1996). 5.4 C02 Absorption and Desorption in Aqueous Amine Solutions This section presents the experimental and theoretical results from the work on C 0 2 absorption and desorption in aqueous amine solutions. The experimental data are given in Tables K.11 to K.27 and the experimental conditions for each system studied are summarized in Table 5.6. The bulk of the experiments were focused on desorption because the purpose of these experiments was to estimate kinetic parameters under desorption conditions. The absorption experiments were carried out mainly to verify experimental techniques, as for most amines, good quality absorption data already exist in the literature. The data were analyzed using the diffusion-reaction model presented in Chapter 4. Based on the sensitivity analysis results presented above, it was assumed that for carbamate-forming amines (i.e., MEA, DEA, AMP), the contribution of reactions involving zwitterion deprotonation to water and hydroxyl ions is negligible. In all cases, the physical properties and equilibrium constants were calculated from correlations given in Appendices E to I. In all cases, the values of 118 o CD 0_ CM O in o CO o c o | Q LO CO no LO t 7 J CO £ o _ o I E o L L CL o ^ I— * CD T f oo T f o CO LO Is-T f CO CD CO Is-CM T f CO O o d d d d d q O CM 4 o CD q d CM CD CM CM LO T — d d d d d d d d o o o q o q o o Tl-\" LO T f LO LO LO T f T f LO CM c o LO CO 06 Is-o d d d d LO d LO d LO d LO o CM LO CM o CM LO CM o CM CM +~ LO CM +~ LO CM +~ LO CM T LO CM CM CM CM T — 00 Is-c o CM 00 op CO LO c o 00 Is-c p c o Is-c p CO Is-c p CO Is-00 oo Is-c o c o CO CO CO T f c o CO T f c o c o CO CO c o LO c o c o LO c o c o LO c o c o LO CO CO CL c ^ I-B CM (II O CO l-Q -Q_ O E \"o E o CL IS o o d d o o d d o d o d Is-CD • CD CD Is-CD Is-CD Is-CD CO oo CD oo o op op c p op 4 oo 4 CN c o c o c o CM CO CM CO 1 CO 1 o o c o c o CO CD o CD CO CM CO CO O o CO CO q d co o co CO E \"55 >> o CM X + < o CM X + < UJ LU Q O CM X + < LU Q + CM + CM o o o o X + CL < + CM o o o o o CM X + < LU Q + < o CM X + CL < + < + CM LU LU + + CM CM o o o o o d Is- Is- Is- Is-CD CD CD CD LO LO LO LO CM CM CM CM CO O CO + < LU Q + < LU Q + CM CM o o o o o CM X + < + < UJ Q + the forward rate constant for the CO2 hydration reaction (k7) were calculated from the correlation reported by Pinsent et al. (1956) and corrected for ionic strength using an equation developed by Astarita et al. (1983) (see equation H.2). 5.4.1 C 0 2 Absorption/Desorption in Aqueous Solutions of MEA, DEA and The data interpretation for C 0 2 absorption and desorption in aqueous solutions of MEA, DEA and A M P is discussed together as each of these amines forms carbamate and their reactions with C 0 2 can be discussed based on the zwitterion mechanism. The major difference between A M P and MEA or DEA is that AMP-carbamate is not very stable and quickly hydrolyzes to give bicarbonate and free amine. The experimental results for the CO2-MEA system are reported in Tables K.11 and K.20, for the CO2-DEA system in Tables K.12, K.13 and K.21 and for the CO2-AMP in Tables K.15 and K.23. The simplified rate expressions for each of these systems are: CO2-MEA System: AMP 10-11 _ (5.4) CO2-DEA System: k 16 V f X i 6 , x i 7 y (5.5) 16-17 1 + V *17 J w 1 3 120 C C V A M P System: 1^ ] C 3 C 4 V K 1 K 2 J C 2 (5.6) 1-2 Equations (5.4), (5.5) and (5.6) are essentially the same and therefore the procedure for parameter estimation is identical. In order to see if the kinetic parameters obtained under absorption conditions could be used to predict desorption rates we first used literature correlations for the rate constants involved in equations (5.4) to (5.6). For the combined equilibrium constants (i.e., K1K2, K10K11 and K16K17), the correlations given in Appendix H were used. For AMP, ki and k_i/k2 were calculated from the correlations given by Xu et al. (1996), for DEA, k 1 6 and k_ 1 6 /k 1 7 were calculated from the correlations given by Rinker et al. (1996) and for MEA, k-io was calculated from correlation of Hikita et al. (1977a) and k.i 0/kn was set equal to zero because no such correlation is available in the literature. The results are plotted in Figures 5.18 to 5.26. These plots clearly demonstrate that the predictions based on literature correlations are fairly good for absorption rates (see Figures 5.18 to 5.20), but those for desorption rates are consistently higher than the experimental values by a factor of 2 to 6 (see 5.4.1.1 Predicted Rates using Literature Correlations 121 Figures 5.21-5.26). This was expected because the literature correlations have been developed based on the absorption data only. Also, desorption rates are very sensitive to the rate constants for the reverse reactions and accurate values of these constants are not available in the literature. 800 -J\" 700 o E E, 600 CO T< 500 | 400 c 300 o CO § 200 -i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—r 100 0.0 Figure 5.18: Experimental Predicted (Literature) Predicted (This Work) _ i i i i i i i_ 1.0 2.0 3.0 4.0 C M E A (kmol/m3) 5.0 6.0 Predicted and experimental absorption rates for C 0 2 absorption in aqueous MEA solution at 303 K. 122 500 CO I 400 E, °° 300 x cu ro 200 c g o. 8 100 < 0 - i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r Experimental Predicted (Literature) Predicted (This work) i i i i l \\ i i i _l I I I I I I l_ 0.0 Figure 5.19: 1.0 2.0 C D E A (kmol/m3) 3.0 4.0 Predicted and experimental absorption rates for CO2 absorption in aqueous DEA solution at 303 K. 600 .CO o E E «T 400 o v— X 2 cr I 2 0 0 Q . \\ O CO JO < 0 ~ i — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — r Experimental Predicted (Literature) Predicted (This work) _i 1 1 1 1 1 1 1 I |_ 1 1 1 1 • 1 1 0.0 Figure 5.20: 1.0 2.0 3.0 4.0 5.0 C A M P (kmol/m ) Predicted and experimental absorption rates for CO2 absorption in aqueous A M P solution at 303 K. 123 500 CO I 400 E, ? 300 x ro * 200 c o co 100 CD Q 0 ~1 1 1 1 1 1 r-Experimental (this work) Predicted (literature) Predicted (this work) -i i t_ 0.20 Figure 5.21: 100 0.30 0.40 Loading (mole of C0 2 /mole of MEA) 0.50 Predicted and experimental desorption rates for C 0 2 desorption from aqueous MEA solution at 378 K. CO o 80 E E ~> o 60 X \"co CU 40 c o CL O CO 20 CD Q 0 ~i 1 1 — i — i — i — i 1 1 1 1 — i — i — r i Experimenta (this work) - - Predicted (literature) -i 1 r / Predicted (this work) 0.00 Figure 5.22: 0.05 0.10 0.15 Loading (mole of C0 2 /mo le of DEA) 0.20 Predicted and experimental desorption rates for C 0 2 desorption from aqueous DEA solution at 382 K. 124 400 CO o I 300 CO O J2 200 co or ! 1 0 0 CO CD Q 0 Experimental (this work) Predicted (literature) Predicted (this work) 0.20 0.30 0.40 Loading (mol of C0 2 /mo l of AMP) 0.50 Figure 5.23: Predicted and experimental desorption rates for C 0 2 desorption from aqueous A M P solution at 378 K. 400 ~o E E x CD -I—' CO or c 200 o C L O CO CD Q 100 •a CD o CD 0 i i i T r •' 'i T •• A • i i i i i \"i 1^ r — i 1 r — A -A -'_ A -: / -• V / + T = 333 K • T = 343 K -r i i i i i i i x T = 353 K • T = 363 K -A T = 373 K i i i i i i A T = I i i 378 K ; i i i 0 100 200 300 Experimental Desorption Rates x 10 3 (mmol/s) 400 Figure 5.24: Predicted and experimental desorption rates for C 0 2 desorption in aqueous MEA solution at 333 to 378 K using literature correlations 125 .CO ~o E E CO O X CD CO CL. cz o o CO CD Q T3 CD -+—1 O T J CD CL 300 200 h 100 h 0 • T = 343 K x T = 353 K • T = 363 K A T = 373 K A T = 382 K i i i i i i i_ 0 100 200 300 Figure Experimental Desorption Rates x 10 (mmol/s) 5.25: Predicted and experimental desorption rates for C 0 2 desorption in aqueous DEA solution at 343 to 382 K using literature correlations 5f 300 o E E, o O T— X 200 £ ro or c o -1—» C L t O CO 100 CD Q • D £ O T3 CD L_ C L 0 + T = 333 K x T = 353 K A T = 3 7 3 K • T = 343 K • T = 363 K A T = 378 K 0 100 200 300 Experimental Desorption Rates x 10 (mmol/s) Figure 5.26: Predicted and experimental desorption rates for C 0 2 desorption in aqueous A M P solution at 343 to 378 K using literature correlations 126 Minor deviations in the predicted absorption rates are understandable, as different authors have used different experimental techniques to measure absorption rates (see Tables 2.1 to 2.5). Note that, for MEA, the predicted absorption rates based on literature correlations are about 5 to 10% higher than the measured rates, for DEA they are about 20 to 25% less than the measured rates and for AMP, they vary from -10 to +20% of the measured rates (see Figures 5.18 to 5.20). This strongly suggests that the variation in predicted rates is due to the differences in experimental apparatus and the methods used for data interpretation and not due to some consistent error in our measurements. For example, Hikita et al. (1977a) used a pseudo-first-order model, Rinker et al (1996) used a rigorous model and Xu et al. (1996) used the zwitterion mechanism to analyze their data. 5.4.1.2 Parameter Estimates for MEA, DEA and AMP The absorption and desorption rate data for MEA, DEA and A M P were regressed using our model and the kinetic parameters were estimated. These estimates are presented in Tables (5.7) to (5.9) and plotted as a function of temperature in Figures (5.27) to (5.35). Note that all three parameters (e.g., k-i, k 1 / K 1 K 2 and k_ 1 /k 2 ) were easily estimated from the desorption data. However, we were unable to obtain good estimates of combined rate constants (i.e., k 1 / K 1 K 2 a n d k_ 1 /k 2 ; k 1 0 /K^K. , . , and k_i0/ku; k 1 6 / K 1 6 K 1 7 and k_ 1 6 /k 1 7 ) , which represent the reverse reaction in the zwitterion mechanism, from absorption data. This is understandable, because for 127 initially unloaded solutions, the values of these parameters are so close to zero that it becomes impossible to obtain reliable estimates. Therefore, in this work, we first estimated all three parameters for each case using desorption data and then used the correlations for combined constants based on these estimates to obtain forward rate constants under absorption conditions (see Tables 5.7 to 5.9). Table 5.7: Estimates of rate constants in eq. (5.4) from absorption and desorption data T ^10 k_i0 / k^ Method (K) (m3/kmol s) (1/s) (kmol/m3) 303.4 6,828.6 - - Absorption 333.2 45,108.0 14.6 23.0 Desorption 343.2 65,248.0 36.2 44.3 Desorption 353.4 149,720.0 198.1 148.9 Desorption 363.3 276,760.0 523.7 333.1 Desorption 373.2 364,820.0 1,512.8 776.4 Desorption 378.3 540,670.0 3,732.9 1,297.6 Desorption Table 5.8 Estimates of rate constants in eq. (5.5) from absorption and desorption data T k-i6 / K 1 6 K 1 7 k_16 / k 1 7 Method (K) (m3/kmol s) (1/s) (kmol/m3) 303.2 3,055.8 - - Absorption 313.2 4,085.8 - - Absorption 323.2 7,290.7 - - Absorption 343.2 9,139.0 33.9 1.2 Desorption 353.4 12,271.0 122.4 8.7 , Desorption 363.3 15,119.0 531.3 43.2 Desorption 373.2 17,058.0 1,515.6 110.0 Desorption 382.3 21,898.0 3,288.7 257.9 Desorption 128 Table 5.9: Estimates of rate constants in eq. (5.6) from absorption and desorption data T ki k_ 1/k 2 Method (K) (m3/kmol s) (1/s) (kmol/m3) 296.1 924.3 - - Absorption 303.5 1,288.9 - - Absorption 308.3 1,368.1 - - Absorption 313.2 1,868.4 - - Absorption 318.2 2,427.2 - - Absorption 322.9 3,234.9 - - Absorption 333.4 4,264.2 108.5 4.5 Absorption 343.4 6,838.5 374.6 10.4 Desorption 353.5 8,561.9 1,480.6 22.5 Desorption 363.4 10,039.0 3,578.9 47.8 Desorption 373.3 15,386.0 9,651.1 94.4 Desorption 378.4 20,678.0 14,728.0 184.9 Desorption I I I I I I I I I I I I I I I I I • I I I I I f • From desorption data -| £+3 i i i i i i i • i i i i i i i i i i i i i <—i—i—i—i 2.4 2.6 2.8 3.0 3.2 3.4 1000/T(1/K) Figure 5.27: Arrhenius plot of the estimates for k 1 0 from absorption and desorption data 129 10000 00 o 1000 k 100 t 10 - i — i — i — l — i — i — i — i — I — i — i — i — i — i — i — i — i — i — I — i — i — i — r k<° = 9 . 5 3 9 x 1 0 \" e x p f - 1 6 ' 0 6 1 ' K 1 0 K 1 1 E = 133.53 kJ/mol FT = 0.9917 T J *l I i i i i i i i i i_ j i i_ J i i i i _ 2.6 2.7 2.8 2.9 1000/T(1/K) 3.0 3.1 Figure 5.28: Arrhenius plot of the estimates for k ^ / K ^ K ^ from absorption and desorption data 10000 1000 o J 100 -2> 10 t \" 1 — i — i — i — I — i — I — I — i — I — I — I — i — i — i — I — i — i — i — I — i — i — i — r ^ = 4 . 2 3 1 x 1 0 \" e x P r - 1 2 ' 6 4 7 \" V T E = 105.15 kJ/mol R 2 = 0.9943 -I I I I I I I I I I I I I I I I I I I I I I I l_ 2.6 2.7 2.8 2.9 1000/T(1/K) 3.0 3.1 Figure 5.29: Arrhenius plot of the estimates for k^o/k^ from absorption and desorption data 130 1E+5 F ^ 1E+4 o E CO CO * 1E+3 1E+2 i i i I i 1 r- I i — r — i 1 1 1 i 1 1 1 1—: • From absorption data -• From desorption data -Z - k 1 6 = 3x107 exp 2759 ; \\ E = 22.94 kJ/mol -; R 2 = 0.979 • i i i i i i i i i • i • i i i i • i 2.5 2.7 2.9 3.1 1000/T(1/K) 3.3 3.5 Figure 5.30: Arrhenius plot of the estimates for k 1 6 from absorption and desorption data CO CO 1E+5 1E+4 h 1E+3 k * 1E+2 \\E 1E+1 h ~l 1 1 1 1 1- ~I I | I ! ! I'1 \"|\"\"\"' f—-|——\"| • | | | I I \" ' I k.e o..,n2i_J-15,638^ K 1 6 K 1 7 2x10^ exp v J E = 130.01 kJ/mol R^ = 0.9952 *| £+0 I i • i i I • i i i i i i i i i i i i i I 1 i i >-2.5 2.6 2.7 2.8 2.9 3.0 1000/T(1/K) Figure 5.31: Arrhenius plot of the estimates for k 1 6 / K 1 6 K 1 7 from absorption and desorption data 131 10000 1000 k ^ 100 Lr E 10 h 1 t n i i i i i i i i | i i i i i i \" i i i | i i i k_ie o ,^ 22 f -17,920^ 1 6 - 8 x 1 0 exp E = 148.99 kJ/mol VX = 0.9805 Q I i I i I I i I I i I i I I I I I I i I I I [ i I I i I i i I i • i i 2.6 2.7 2.7 2.8 2.8 2.9 2.9 3.0 1000/T(1/K) Figure 5.32: Arrhenius plot of the estimates for k_ 1 6 /k 1 7 from absorption and desorption data 1E+5 « 1E+4 o E 1E+3 : i i i i —r i 1 1 1 — ~ r i 1 1 1 1 1 1 1 — : . *r,9 f - 4 1 1 7 . 2 ^ ! k1 =1x10 exp ; V t ) -E = 34.23 kJ/mol R 2 = 0.9924 : • • From absorption data - • From desorption data • i i i • i i i i • i i i i i i i i i 1E+2 2.5 2.7 2.9 3.1 3.3 3.5 10007T(1/K) Figure 5.33: Arrhenius plot of the estimates for ki from absorption and desorption data 132 CM - I — i — i — i — | — i — i — r 1E+5 1E+4 1E+3 t 1E+2 •j I—'— i—i—\" i < i • • i i i i i i i i i i i • • • • 2.6 2.7 2.8 2.9 10007T(1/K) 3.0 3.1 Figure 5.34: Arrhenius plot of the estimates for k 1 / K 1 K 2 from absorption and desorption data 1E+4 1E+3 o § 1E+2 CM 1E+1 ~ \\ — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — • k , _ , r t 1 3 f -10,041^ - ^ - = 5 x 1 0 1 3 e x p k, E = 83.48 kJ/mol FT = 0.9936 •\\ r £ + f j ' — 1 — 1 — 1 1 1 • • 1 1 ' • 1 1 1 ' 1 1 1 1 ' 1 1 1 *-2.6 2.7 2.8 2.9 3.0 3.1 1000YT(1/K) Figure 5.35: Arrhenius plot of the estimates for k_ 1/k 2 from absorption and desorption data 133 5.4.2 C 0 2 Absorption/Desorption in Aqueous MDEA Solutions The experimental results for the C 0 2 - M D E A system are reported in Tables K.14 and K.22. As stated earlier in Chapter 4, MDEA does not react directly with C 0 2 but catalyzes the C 0 2 hydration reaction. The rate expression for this reaction is given by: k r22 =-l<22C1C16 + — C 5 C 1 7 (5.7) K 2 2 Equation (5.7) has two unknown parameters (i.e., k 2 2 , k_22 or k 2 2 / K 2 2 ) , which were determined from the absorption and desorption rate data given in Tables K.14 and K.22. Here again, first, the existing correlations for these parameters were used to compare the predicted absorption and desorption rates with our experimental data. The correlation to calculate K 2 2 was taken from Appendix H and that for k 2 2 was obtained from Rinker et al. (1995). The latter was developed based on absorption data only. These results are presented in Figures 5.36 to 5.38. In this case, the predictions based on the literature correlations are fairly good for both absorption and desorption rates. This is probably because the rate of the C 0 2 reaction with MDEA is much slower compared to that MEA, DEA and A M P . In the next step, we used our model to estimate k 2 2 and k.22 by using the parameter estimation technique implemented earlier for MEA, DEA and A M P . These estimates from absorption and desorption data are listed in Table (5.10) and plotted as a function of temperature in Figures 5.39 and 5.40. 134 100 In -(mmol 80 -CO O 60 -X -CD -ion Ral 40 -C L Absoi 20 -0 ~i i i i 1 I 1 I I 1 i i i 1 1 1 i 1 r 0.0 Predicted (Literature) Predicted (This work) Experimental - I I I I I I L_ 1.0 2.0 C A M P (kmol/m3) 3.0 4.0 Figure 5.36: Predicted and experimental absorption rates for C 0 2 absorption in aqueous MDEA solution at 303 K. 200 CO o 160 E ^ 120 h x CD -f—' * 80 I-c g S 40 h o E E, CO O X CD CD or c o 100 75 h 50 h fr 25 CO CL) Q 0 0.0 Figure 5.53: 0.1 0.2 0.3 0.4 0.5 Loading (mole of C0 2 /mo le of DEA) Predicted and experimental desorption rates for CO2-DEA system as a function of temperature and C 0 2 loading o E E 80 x CD 60 0T c o o. 40 o co CD Q -o o \" 0 • 0 CD 20 0 • I I I , 1 1 . . . . ] — — , . , ^ , . 1 1 1 1 1 1 v -• - • T = 343 K x T = 353 K \" • T = 363 K A T = 373 K -/ * ' 1 A T = 382 K 1 1 i 1 1 1 1 1 1 • 1 1 1 1 1 0 20 40 60 80 100 Experimental Desorption Rates x 10 (mmol/s) Figure 5.54: Predicted versus experimental desorption rates C 0 2 - D E A system calculated from the correlation developed in this work 149 1 00 I — i — i — i — i — | — i — i — i — i — i — i — i — i — i — | — i — i — i — i — i — i — i — i — i — I — i — i — i — r 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Loading (mol of C0 2 /mo l of AMP) Figure 5.55: Predicted and experimental desorption rates for C 0 2 - A M P system as a function of temperature and C 0 2 loading «T 100 80 h E 60 Q. 40 20 0 0 -i 1 1 1 1 1 1 1 1 1 1 1 1 r + T = 333 K x T = 353 K A T = 373 K • T = 343 K • T = 363 K A T = 378 K 20 40 60 80 100 Experimental Desorption Rates x 10 (mmol/s) Figure 5.56: Predicted versus experimental desorption rates C 0 2 - A M P system calculated from the correlation developed in this work 150 T I I I | 1 1 1 | | \"|- . .| • T • | ' | | | i | | | J | I | I I I I J I I r~~T • T = 3 4 3 K ; x T = 3 5 3 K -• T = 363 K -A T = 3 7 3 K ; A T = 3 7 8 K \" — Model • Q I I t I I 1 1 i • i i i i i i • i i i i i i i i • i i 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Loading (mol of C0 2 /mo l of MDEA) Figure 5.57: Predicted and experimental desorption rates for C 0 2 - M D E A system as a function of temperature and C 0 2 loading 0 20 40 60 80 100 Experimental Desorption Rates x 10 3 (mmol/s) Figure 5.58: Predicted versus experimental desorption rates C 0 2 - M D E A system calculated from the correlation developed in this work 151 When the MEA concentration was 20% of the 25 wt% MEA+MDEA blend, the absorption rate increased by about a factor of 5. Similarly, when the DEA concentration was 20% of the 25 wt% DEA+MDEA blend, the absorption rate went up by about a factor of 3. Addition of MEA to 25 wt% A M P blend does improve the absorption capability of A M P , however, this improvement is nominal. No improvement in the C 0 2 absorption rate was observed when DEA was added to 25 wt% A M P blends. This is reasonable because the reactivities of these amines are comparable. The results for MEA+MDEA and DEA+MDEA mixtures are important. With the help of the model, an optimal mixture concentration could be obtained so that the desired amount of C 0 2 slip could be achieved in the absorber column. This is significant in natural gas treating applications where one may not want to absorb too much C 0 2 in the absorber to avoid unnecessary dilution of the acid gas going to the sulfur recovery plant. 152 800 100 •L 80 H 60 o cc c cu E CU 40 ° cco JZ. c UJ A 20 0 0 20 40 60 80 100 Cone, of MEA in 25 wt% MEA+MDEA Blend (% of total amine) Figure 5.59: Predicted versus experimental absorption rates for CO2-MEA+MDEA system at 303 K based on the correlation developed in this work ( p c o =97 kPa) 500 to o 400 h 0 Experimental Model 100 80 60 40 H 20 0 o -*—» o CO c cu E CD O c CO JZ c LU 0 20 40 60 80 100 Cone, of DEA in 25 wt% DEA+MDEA Blend (% of total amine) Figure 5.60: Predicted versus experimental absorption rates for CO2-DEA+MDEA system at 303 K based on the correlation developed in this work ( p c o =97 kPa) 153 800 -52 o £ 600 [• J2 400 h or c o e-200 h 00 < 0 \"I 1 1 1 1 1 1 1— • Experimental -I 1 1 1 1 1 1 1 1 r-Model E \"V\" -I I l _ _ l I I l _ 100 1 80 60 40 20 0 0 20 40 60 80 100 Cone, of MEA in 25 wt% AMP+MEA Blend (% of total amine) Figure 5.61: Predicted versus experimental absorption rates for C 0 2 -MEA+AMP system at 303 K based on the correlation developed in this work ( p c o =97 kPa) 400 £ 200 CO or c o o CO < 100 0 \"T 1 1 1 1 1 1 1 1 1 1—-1 1 r—I 1 1 1— • Experimental Model E _i i i i • i i i_ _i i i i i i i _ i i _ 100 80 60 40 20 0 20 40 60 80 100 Cone, of DEA in 25 wt% AMP+DEA Blend (% of total amine) Figure 5.62: Predicted versus experimental absorption rates for C 0 2 -DEA+AMP system at 303 K based on the correlation developed in this work ( p c o =97 kPa) 154 5.5 Conclusions The parametric sensitivity analyses indicate that accurate values of C O 2 diffusivity, and the physical solubility of C O 2 given by the Henry's law constant are essential for predicting accurate absorption and desorption rates. An extensive literature search was undertaken and all available property data were compiled. It was found that the values of these parameters at stripping temperatures are not available. A series of experiments involving IS^O-water and N 2-alkanolamine systems were conducted to measure the G 0 2 diffusivities and Henry's constants in water using the N 2 0 analogy. Using data obtained in this work and those available in the literature, correlations were developed that can be used for pure water, as well as for single and binary amine systems covering a wide range of temperatures and amine concentrations. Such correlations are not available in the literature. The absorption and desorption rates of C 0 2 in aqueous solutions of MEA, DEA, MDEA, A M P and their mixtures (MEA+MDEA, MEA+AMP, DEA+MDEA and DEA+AMP) were measured for amine concentrations in the range of 2 to 35 wt%. The absorption experiments were carried out at near atmospheric pressure using pure C O 2 saturated with water at 293 to 323 K with initially unloaded solutions. The desorption experiments were performed at 333 to 383 K for C O 2 loadings between 0.02 to 0.7 moles of C 0 2 per mole of amine using humidified N 2 gas as a stripping medium. The data were analyzed using the rigorous diffusion-reaction model developed in this work. The model predicts the experimental results well for all eight different amine systems discussed above. 155 The results indicate that the theory of absorption with reversible chemical reaction could be applied to predict desorption rates. The zwitterion mechanism adequately describes the reactions between CO2 and carbamate-forming amines such as MEA, DEA and A M P under both absorption and desorption conditions. The reactions between C 0 2 and aqueous MDEA solutions are best described by a base-catalyzed hydration reaction mechanism. The kinetic data obtained show that desorption experiments can be used to determine both forward and backward rate constants accurately. The absorption experiments on the other hand could only be used to determine forward rate constants. For MEA, DEA and AMP, the kinetic data obtained under absorption conditions do not extrapolate well to desorption temperatures. Therefore, kinetic data at higher temperatures should be obtained from desorption experiments. The existing absorption data for the CO2-MDEA system can be extrapolated to desorption temperatures with reasonable accuracy. This is probably because MDEA is very slow reacting amine and does not form carbamate. For the blended amine systems, it was found that small additions of MEA or DEA (< 5 wt%) significantly enhance the absorption rates of CO2 in 25 wt% MDEA solutions. Addition of small quantity of MEA (< 5 wt%) to 25 wt% A M P blend, on the other hand, was found to have very nominal effect on the C 0 2 absorption rates of A M P . No improvement in absorption rates was observed when DEA was added to 25 wt% A M P solutions. 156 CHAPTER 6 INTRODUCTION AND LITERATURE REVIEW 6.1 Background In Part 1 of this thesis, we focused mainly on determining the kinetic parameters for fast-reacting gas-liquid systems by measuring the absorption and desorption of C 0 2 in aqueous amine solutions using a novel hemispherical contactor. In Part 2, we present a novel approach to determining kinetic coefficients for extremely slow reactions. The system under consideration is carbon monoxide absorption and its subsequent reactions with aqueous diethanolamine. The solubility of C O in pure water at 298 K and 1 bar is about 40 times less than that of C 0 2 in water and its reactions with aqueous DEA at 298 K are a few orders of magnitude less than those of C 0 2 with aqueous DEA. Why is it important then to study the kinetics of such slow reactions in gas treating applications? The answer to this question lies in the fact that, in gas treating units, the solvents are regenerated and reused over extended periods and are exposed to varying temperatures, about 313 K in the absorber and about 393 K in the stripper, reboiler and heat exchangers. Thus, feed gases containing appreciable quantities of C O (e.g. gas mixtures from hydrogen plants and fluid catalytic cracker units) may lead to significant absorption of C O in the amine solution at absorber temperatures that in turn may cause reactions of C O with 157 hydroxyl ions and DEA to form formate ions and formyl-diethanolamine (DEAF) respectively. These reactions may become particularly important at stripper and reboiler temperatures resulting in significant losses of DEA. The degradation of DEA is costly and it interferes with the proper running of gas treating units. Therefore, it is quite important to understand how C O reacts with aqueous DEA solutions and what major degradation products it forms, so that DEA losses can be quantified and preventive measures taken. Since the reactions between C O and aqueous DEA solutions are extremely slow, a short contact time apparatus like the hemispherical contactor cannot be used to study the kinetics of these reactions. The best way to monitor the progress of these reactions is to conduct experiments in a batch autoclave reactor of the type described in Chapter 7. Although the subject matter of Part 2 is slightly different from that of Part 1, the modeling and parameter estimation approach is similar. The knowledge acquired during the C 0 2 absorption/desorption study was extremely useful in approaching this second problem. This work was funded by Equilon Enterprises LLC, Westhollow Technology Center, Houston Texas and Shell Global Solutions International, Amsterdam, The Netherlands. 6.2 Literature Review Aqueous solutions of diethanolamine (DEA) are widely used to remove acid gases, such as C 0 2 and H 2 S, from sour gas mixtures including natural gas, synthesis gas, flue gas and various refinery gas streams. The efficiency of these 158 processes largely depends on the performance of the amine solution, which is continuously regenerated and used over extended periods. Although the principal acid gas-amine reactions are reversible, irreversible reactions may also occur resulting in products from which the amine cannot be regenerated under typical operating conditions. This phenomenon is called amine degradation. Numerous papers are available on the degradation of alkanolamines under the conditions typical of gas purification plants. However, most papers focus on alkanolamine degradation due to C 0 2 , carbon disulfide (CS 2 ) , carbonyl sulfide (COS) and H 2 S / C 0 2 mixtures. Some sour gas mixtures (e.g. gas mixtures from hydrogen plants and catalytic crackers) contain significant quantities of carbon monoxide (CO) that may also cause amines degradation. A survey of the literature reveals that C O is a strong reducing agent which is only slightly soluble in water and other physical solvents (< 0.001 mole CO/mole of water at 298 K and C O partial pressure of 101.325 kPa, Kirk Othmer, 1993; Fogg and Gerrad, 1991). An industrially significant process is the reaction of C O with secondary amines to produce formamides. For example, the industrial solvent dimethylformamide (DMF) is manufactured by reacting C O with dimethylamine at 423-428 K and C O partial pressures of 7.5-10.3 MPa in the presence of a catalyst (Duranleau and Lambert, 1985): ( C H 3 ) 2 N H + C O m e t a l c a t a | y s l ) ( C H 3 ) 2 N C H O Similar reactions occur between alkanolamines and C O to produce formylalkanolamines. For instance, DEA is known to react with C O at high pressure ( p c o = 6.2 MPa) and temperature (423 K) over a 5 hour period to 159 produce ( C 2 H 4 O H ) 2 N C O H , i.e. formyldiethanolamine or DEAF (Lambert and Duranleau, 1985). These conditions are very severe and are not likely to be met in normal refinery and gas plant operations. However, DEAF has been found in DEA solutions used to treat gases from fluid catalytic crackers (FCC units). Koike et al. (1988) have suggested that DEAF is formed by the reaction between formic acid (or formate ions) and DEA according to: HCOOH + ( H O C 2 H 4 ) 2 N H - ^ ( H O C 2 H 4 ) 2 N C O H + H 2 0 The formic acid (or formate ions) may be present in the amine solution because of the reaction between C O and O H - ions, and by the hydrolysis of HCN generally present in the F C C dry gas. In another study, Kim et al. (1988) examined the absorption rate of C O into aqueous solutions of potassium carbonate ( K 2 C 0 3 ) , methyldiethanolamine (MDEA) and diethylethanolamine (DEAE) in a stirred tank reactor at 348-398 K and C O partial pressures of 0.75-3.1 M P a . There were no mass transfer limitations and the reaction between C O and hydroxyl ions (OH\") to produce formate ions (HCOO\" ) was found to control the rate of absorption. It was concluded that the rate of C O absorption into aqueous solutions of K 2 C 0 3 , D E A E and MDEA are much slower (by a factor 10 8) than the corresponding rates of C 0 2 absorption. The activation energy for the C O - O H \" reaction in aqueous K 2 C 0 3 solutions was reported to be 122.9 kJ/mol, which is significantly higher then that of 55.4 kJ/mol for the liquid phase CO2-OH\" reaction reported by Pinsent et al. (1956). This suggests that 160 temperature is one of the most important parameter for the C O - O H \" reaction in basic solutions. Eickmeyer (1962) gave a brief account of the deactivation of DEA promoted potassium carbonate solutions in commercial gas treating plants. The formates were claimed to result from the very slow reaction between C O and O H \" ions. Traces of oxygen were believed to catalyze the reaction. From the above information it is clear that little is known about the role of C O in amine degradation. Nonetheless, there is clear evidence from refineries using DEA, which suggests that C O is the leading cause for the buildup of DEAF and formate in the gas treating system. As a result, considerable amounts of valuable DEA are lost or rendered ineffective, and efficiency and cost effectiveness are compromised. The purpose of this study was therefore to investigate the mechanism by which C O reacts with aqueous DEA and to estimate the corresponding solubility and kinetic parameters over a range of temperatures and C O partial pressures, so that one could quantify DEA losses and take preventive measures. 6.3 Objectives The specific objectives of this part of the work were to: (a) identify the dominant DEAF formation route, (b) estimate the kinetic rate coefficients and (c) determine the physical solubility of C O in aqueous DEA solutions. To accomplish these objectives, a reaction mechanism was proposed and a mathematical model was developed. The model consists of a set of differential and algebraic 161 equations, which describe gas absorption with slow chemical reaction in a well-mixed batch reactor. The reason for using a batch reactor was due to the low C O solubility and its slow chemical reaction with aqueous DEA solutions observed in the series of exploratory experiments described in Chapter 7. 162 CHAPTER 7 EXPERIMENTAL APPARATUS AND EXPLORATORY EXPERIMENTS This chapter describes the experimental apparatus for studying the kinetics of CO-induced degradation of aqueous diethanolamine as well as some exploratory results obtained using this equipment. 7.1 Experimental Apparatus and Procedure All experiments presented in this study were carried out in a 660 mL stainless steel autoclave reactor (Model 4560, Parr Instrument Co. Moline, IL). The experimental setup, which mainly consists of a gas bomb and an autoclave, is shown in Figure 7.1. The autoclave was equipped with a variable speed magnetic stirrer with three impellers mounted at 4, 10 and 16 cm from the bottom of a common shaft (20 cm long), a heating jacket controlled by a PID temperature controller (Omega CN76000, Omega Eng. Co., Stamford, CT), gas and liquid sample lines, pressure transducer and a thermocouple inserted into the liquid phase. To ensure proper mixing of the gas and liquid phases, the liquid volume was selected such that the top impeller was always in the gas phase and the bottom two impellers were submerged in the liquid phase. The autoclave could be operated between 283-623 K and at pressures up to 13.8 MPa . The gas bomb was made of stainless steel and could be pressurized up to 20 MPa. 163 Pressure Sensor Gas Bomb Magnetic Stirrer Pressure Sensor j-{9 333 K), chemical reactions become important and the loading is predominantly due to the reaction products. 7.2.2 Material Balance At the end of each experiment presented in Figure 7.2, liquid samples were withdrawn and the main reaction products were identified according to the procedure given in Appendix I. The analyses showed that, in all cases where reaction was significant, DEAF and formate ions were the only reaction products. The presence of DEAF was confirmed by analyzing the liquid sample using G C / M S and comparing the results with those reported by Koike et al. (1988). To ensure that DEAF and formate were the only principal reaction products, material balances were made for experiments in which C O was brought in contact with 30 wt% aqueous DEA solutions at 353, 393 and 413 K at initial C O partial pressures ranging from 650 to 850 kPa. The final solutions were analyzed for DEAF and formate according to the procedure given in Appendix I. Table 7.1 gives the corresponding C O material balances. The deviations 168 between the initial and final amounts of C O are less than 15% and fall well within the range of experimental error. No additional degradation product was observed from the analysis of liquid samples using G C and G C - M S . Table 7.1: Overall C O balance as a function of temperature for C O absorption in 30 wt% aqueous DEA solutions Temperature (K) 353 393 413 Initial Solution (g) 199.16 199.14 198.99 Conditions p c o (kPa) after 5 min 852 654 711 Initial C O introduced (g) 3.368 2.394 2.642 Final Time (h) 48 5 23 Conditions Pco ( k P a ) 661 435 123 C O loaded (g) Formate (wt%) C O in formate (g) DEAF (wt%) C O in DEAF (g) Molecular C O in solution 2 (g) Final C O in all forms (g) 0.827 0.224 0.270 1.061 0.445 0.132 0.847 0.842 0.267 0.324 0.811 0.340 0.091 0.757 2.204 1.106 1.340 1.292 0.541 0.026 1.907 Deviation (%)n -2.4 +10.1 +13.5 1 Defined as 100x(CO loaded-Final C O in all forms)/CO loaded 2 Based on Henry's constant values obtained by N2-analogy Table 7.2: Formate and DEAF concentrations of solutions resulting from exposing pure DEA to C O for 5 hours at p ° Q = 690 kPa T Formate DEAF (K) (wt%) (wt%) 313 0.0 0.0 393 0.0 2.4 169 7.2.3 CO Absorption in Pure DEA To identify the pathways of the C O - D E A reactions, experiments were undertaken where C O was absorbed in 99.8% pure DEA solution at 313 and 393 K for 5 hours at an initial C O partial pressure of 690 kPa. At the end of each of these experiments, liquid samples were taken and analyzed by IC for DEAF and formate ions. The results of this analysis are presented in Table 7.2, which shows that at low temperature (313 K) neither DEAF nor formate ions are formed, whereas at higher temperatures (>393 K) no formate was detected although a significant amount of DEAF was formed. This suggests that C O may react directly with DEA to form DEAF similar to the industrial process for the manufacture of DMF (Duranleau and Lambert, 1985). The absence of formate ions in the sample solution also indicates that water plays an important role for the buildup of formate in the system. 7.3 Proposed Reaction Mechanism The exploratory experiments show that C O reacts with aqueous DEA solutions to form formate ions and DEAF. These experiments also indicate that two pathways may form the DEAF: (i) via direct insertion of CO into DEA and/or (ii) via formate formation. Based on these results, we propose that the C O reacts with aqueous DEA solution according to the following reaction mechanism: Formate Formation: C O + OH ' k 1 ) H C O O \" (7.1) 170 Direct Insertion: C O + R ^ N H ^ ^ R ^ N H C O (7.2) DEA-Formate Reaction: k K R ^ N H * + HCOO- R 1 R 2 N H C O (8.2) DEA-Formate Reaction: R 1 R 2 N H 2 +HCOO\" R ^ N H C O + HjO (8.3) DEA Protonation: R 1 R 2 NH 2 +OH- ^ R ^ N H + HaO (8.4) Water Dissociation: 2 H 2 O ^ O H + H 3 0 + (8.5) 172 where R ^ N H a n d R 1 R 2 N H C O denote DEA and DEAF, respectively. Also, for DEA, Ri = R 2 = -CH2CH2OH. 8.2 Reaction Rates For convenience, the chemical species in reactions (8.1) to (8.5) are renamed as follows: C ^ C O , , , , C 2 = R 1 R 2 N H , C 3 = R 1 R 2 N H 2 - , C 4 = R ^ 2 N H C O (8.6) C 5 = H C O C r C 6 = O H \" , C 7 = H 3 0 + , C 8 = H 2 0 Reactions (8.1) and (8.2) are considered to be irreversible and to proceed at finite rates. The latter are given by the following expressions: r ^ - k t C A (8.7) r2=-k2C,C2 (8.8) Based on the experimental evidence presented below, reaction (8.3) was considered to be reversible with the overall rate given by: r 3 = - k 3 C 3 C 5 + k _ 3 C 4 (8.9) Reactions (8.4) and (8.5) are regarded as reversible equilibrium reactions since they involve only proton transfers. 8.3 Mathematical Model The mathematical model is based on the concept of gas absorption with slow chemical reaction in a well-mixed batch reactor as shown in Figure 8.1. The following equations govern the mass transfer with chemical reaction in a batch autoclave (liquid volume = V L , gas volume = VQ): 173 Vapor, V G Figure 8.1: Schematic diagram of chemical reaction autoclave 174 Gas Phase CO Balance: ^ = - ^ I v L E k L a dt V ' L Pco h i ^ CO-DEA j Liquid Phase CO Balance: dC, _ dt = Ek L a Pco H C O - D E A + r1+r2 DEAF Balance: dC dt - = - r 3 - r 2 Overall CO Balance: V^dpco + dC, d C ± + dC^ RT dt L dt L dt L dt Total DEA Balance: Electron Neutrality Balance: DEA Protonation: dC 2 | dC 3 [ dC 4 = Q dt dt dt dC 3 dC7 dC 5 dC6 _ ^ dt dt dt dt X _ ^2 Water Dissociation: 175 The model equations (8.10)-(8.17) were derived based on the following assumptions: • The concentration of dissolved (molecular) CO at the gas-liquid interface corresponds to the physical solubility as determined by Henry's Law (i.e., Pco =HC,) . • Both the gas and liquid phases are well mixed. • The gas phase resistance to mass transfer is negligible. The last assumption follows because pure C O was used. Also, this assumption was verified experimentally and by simulation. Consequently, there are eight ordinary differential and algebraic equations (equations 8.10-8.17) with eight unknown chemical species. The equations must be solved subject to the following initial conditions: p c o = p ° c o and C i = C ° fori =1-7 (8.18) For the present experiments, the initial C O loading of the DEA solution is zero. Therefore, at t=0, C° = C° = C° =0 . The values of C° , C° , C° and C° can be obtained by solving the equilibrium equations shown below. When the C O loading is zero, it follows that: Overall DEA Balance: C ° + C ° = [ R ^ 2 N H ] i n i t i a l (8.19) Electron Neutrality Balance: C ° + C ° - C ° = 0 (8.20) 176 DEA Protonation: K 4 = - ^ - (8.21) 4 C°C° Water Dissociation: K 5 = C°C° (8.22) For a given initial DEA concentration, the concentrations C°2, C°3, Cg and C° can be calculated by solving equations (8.19) to (8.22) simultaneously. 8.4 Model Parameters The parameters needed to solve the model equations (8.10) to (8.17) are listed in Table 8.1 and their determination is outlined below. Since the present reactions are very slow, one can safely assume that the enhancement factor (E) for the C O - D E A - H 2 0 system is unity. Olofsson and Hepler (1975) reported the following correlation for the water dissociation constant (K 5) in the temperature range of 293-573 K: log 1 0 (K 5 ) = 8909.483 - 1 4 2 ^ . 1 3 6 - 4229.195 log 1 0 (T) + 9.7384T - 0.0129638T 2 + 1 . 1 5 0 6 8 x 1 0 \" 5 T 3 - 4 . 6 0 2 x 1 0 \" 9 T 4 (8.23) Bower et al. (1962) correlated their data for ( K 4 K 5 ) over the temperature range of 273-323 K according to the following equation: log 1 0 ( K 4 K 5 ) = -4.0302 - 1 8 3 ° - 1 5 + 0.0043261T (8.24) 177 Table 8.1: Model parameters Param. Definition Remarks E Enhancement factor For slow reactions, E = 1 K 4 DEA protonation constant Bower et al. (1962) K 5 Water dissociation constant Olofsson and Hepler(1975) k L a Mass transfer coefficient To be estimated HCO-DEA Henry's constant for C O To be estimated ki Rate constant for Rxn. (1) To be estimated k2 Rate constant for Rxn. (2) To be estimated k3 Rate constant for Rxn. (3) To be estimated k-3 Rate constant for reverse Rxn. (3) To be estimated The volumetric mass transfer coefficient (k L a) , Henry's constant of C O in aqueous DEA solution (HCO-DEA) a r | d the reaction rate constants (ki, k2, k 3 and k3) were obtained as part of this work. In addition to the parameters listed in Table 8.1, the densities and viscosities of the aqueous amine solutions must also be known as a function of temperature. These properties were obtained from the correlations given by Hsu and Li (1997a, b). 8.5 Parameter Estimation The model was solved using an algorithm called DDASAC (Caracotsios and Stewart, 1985). DDASAC is an extension of DASSL (Petzold, 1983; Brenan et al., 1989), which uses an implicit integrator for non-linear initial value problems containing ordinary differential equations with or without algebraic equations. The parameter estimation was carried out using the software package G R E G (Stewart et al. 1992). 178 The six unknown parameters ( k L a , H C 0 _ D E A , ki , k2, k3, k.3) were determined by minimizing the following objective function: S(k) = £ & l - y ( k ) ] Q , | y l - y ( k ) ] (8.25) i=i where k = ( k L a , H C 0 _ D E A , k i , k2, k3, k.3)T is the unknown parameter vector, y js the measured value of the state variable (in the present case, it is the partial pressure of CO) and y(k) is the calculated value of the state variable which is obtained by solving the model equations (8.10) to (8.17) for some assumed values of k L a , H C 0 _ D E A , ki , k2, k3, k_3. N denotes the number of experimental data and Q is the weighting matrix. For least squares estimation, Q is taken as the identity matrix. Note that not all six parameters were estimated simultaneously. First, k L a and k3 and k_3 were estimated from the data obtained in a separate series of experiments. Then using these known values k L a , k 3 and k.3, the rest of the unknown parameters (ki, k2, and H C 0 _ D E A ) were estimated. However, the same methodology was used in all three cases. The optimization was carried out using G R E G (Stewart et al. 1992). 179 CHAPTER 9 RESULTS AND DISCUSSION This chapter presents the results and main conclusions from the experimental and theoretical studies on the kinetics of CO-induced degradation of aqueous diethanolamine. 9.1 Absorption and Degradation in CO-DEA System 9.1.1 Determination of k, a In order to obtain accurate CO partial pressure profiles in the batch absorption experiments using the reaction model given in Chapter 8, it is essential to know the values of kLa in each case. A series of experiments were conducted where pure N 2 was absorbed into 30 wt% aqueous DEA solutions over the temperature range of 283-413 K in a batch autoclave. The experimental setup was exactly the same as that shown in Figure 6.1. In a typical experiment of this series, about 300 mL of a 30 wt% aqueous DEA solution were fed into the autoclave, a vacuum was drawn and the liquid solution along with the gas bomb containing pure N 2 was brought to the desired temperature. Once this temperature was reached, a known amount of pure N 2 was released from the gas bomb to the autoclave and the total pressure in the autoclave was recorded with time. Each experiment was run for about 105 minutes, which was found to be sufficient to completely saturate the liquid with nitrogen. To study the effect of 180 agitation on k L a , each experiment was performed at the two stirrer speeds of 1,035 and 1,550 rpm. Since N 2 does not react with aqueous DEA, the data can be analyzed using a physical absorption model, which is obtained by setting the reaction rates in the reaction model to zero. Physical absorption in a batch autoclave (see Figure 8.3) can then be represented by the following equations: Gas Phase N 2 Balance dp N ? RT , R dt V G V L k L a PN 2 N Liquid Phase N 2 Balance d C N , = k L a ^ N j - D E A P n ' - - a (9.1) |_| ^ N 2 - D E A j (9.2) dt Initial Conditions at t = 0 p N 2 = p ° 2 and C N j =0 (9.3) In this model, there are two ordinary differential equations and two unknown parameters (k L a and H N 2 _ D E A ) , which can be determined from the partial pressure (p N 2 ) versus time data by applying the parameter estimation technique described earlier. Figures 9.1 and 9.2 show the experimental and predicted N 2 partial pressures using the optimized k L a and H N 2 _ D E A values at 1,035 rpm and 283-413 K. An excellent agreement between experimental and fitted values demonstrates the accuracy of the experimental procedure. The same set of experiments was 181 2000 Experimental Model 1900 ro Q_ CM z Q. 1800 h 1700 0 20 40 60 80 Time (min) 100 120 Figure 9.1: Nitrogen absorption in 30 wt% aqueous DEA solution at 1050 rpm and 284-333 K 2000 Experimental Model ; | } 3 g^ ;373K 393 K •413K 1200 '—1—1—1 1—1—1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 20 40 60 80 100 120 Time (min) Figure 9.2: Nitrogen absorption in 30 wt% aqueous DEA solution at 1050 rpm and 353-413 K 182 done at 1,550 rpm and similar agreement was found. The estimates of k L a so obtained were correlated by the following equation: D M k L a = 0 .297 - ^Re° - 7 7 Sc 0 - 5 (9.4) djmp where the Reynolds number (Re) and Schmidt number (Sc) are defined as follows: Re = ^ E £ L and S c = (9.5) m. P L D N 2 The impeller diameter (d j m p ) was 3.1 cm and the diffusivity of N 2 in aqueous DEA solution (D N 2 ) was calculated using Wilke and Chang's correlation given in Perry et al. (1963). Note that the exponent of Sc in equation (9.4) was assumed not fitted. This value is the same as reported previously (Critchfield and Rochelle, 1988; Haimour et al, 1985, Hikita et al., 1975; Danckwerts, 1970). A plot of the predicted and estimated k L a values is shown in Figure 9.3. The agreement between the measured and correlated k L a values at both stirrer speeds is within ± 25%. Consequently, equation (9.4) can be used to calculate k L a in the reaction model. 183 0 0.04 0.08 0.12 0.16 Measured k L a (1/min) Figure 9.3: Measured and predicted volumetric mass transfer coefficient 9.1.2 Determination of HCO-DEA by Nitrogen Analogy The second unknown parameter in the reaction model is the Henry's constant of C O in aqueous DEA solutions (H C 0 _ D E A ) . Since C O reacts with aqueous DEA, it is not possible to measure HCO-DEA by conventional techniques used for physical absorption and a new technique called the \"N 2-Analogy\" method was developed. This technique is based on the same principal as the \"N 20-Analogy\" approach used previously for measuring the Henry's constants of C 0 2 in alkanolamine solutions (Laddha et al., 1981). Like C 0 2 and N 2 0 , the molecular masses of C O and N 2 are nearly equal and the ratio of their Henry's constants in water is about 0.70 ± 0.02 over the temperature range of 273-413 K (Fogg and Gerrard, 1991; Perry et al., 1963). If it is assumed that this ratio 184 remains the same even in aqueous amine solutions, then H C O - D E A can be calculated from the following equation: H C O - H 2 0 H i H C O - D E A H (9.6) N 2 - H 2 0 N j - D E A The values of H C 0 _ H 2 0 and H N 2 _ H 2 0 were obtained from the correlations given in Fogg and Gerrald (1991) and the H N _ D E A data were measured in this work using using the N 2-Analogy (equations 9.6) are listed in Table 9.1. A comparison of the values of Henry's constant of nitrogen in water and in aqueous DEA solution indicates that nitrogen is several times more soluble in aqueous DEA solutions than in water and its solubility increases with temperature above 313 K. This trend is not surprising because the literature data on CO and N 2 solubility (see Table 9.2) show that the solubility of these gases in pure organic solvents is 10 to 100 times higher than that in pure water, and in almost all cases, it increases with temperature above 298 K. The solubility measurements presented here were repeated at least three times and the reproducibility was within ± 3%. Due to our concern about the accuracy of the H C 0 _ D E A values obtained from the N 2-Anology, we did not use them in the reaction model to estimate the rate constant ki and k2. Instead, we considered H C 0 _ D E A as one of the unknown parameters and found it directly from the reaction model (see section on determination of k i , k 2 and H C 0 _ D E A ) . As indicated later, the agreement between the H C 0 _ D E A values obtained the procedure described in the previous section. The H C O - D E A values obtained by 185 using both methods is fairly good. This suggests that our measurements of H C O - D E A by the N 2-Anology method are fairly accurate. Table 9.1: Henry's constant of C O in 30 wt% aqueous DEA solution from N 2-Analogy T I_I + n N 2 - H 2 0 I_I + n C O - H 2 0 ^ C O - H j O ^ N 2 - H 2 0 I_J ++ N 2-DEA ^ C O - D E A (K) (MPa) (MPa) - (MPa) (Mpa) 313 10,133 7,072 0.70 4,519 3,154 333 11,429 8,187 0.72 2,371 1,698 353 12,048 8,613 0.72 2,047 1,463 363 11,926 8,582 0.72 1,986 1,429 373 11,683 8,400 0.72 1,834 1,319 383 11,348 8,096 0.71 1,895 1,352 393 10,943 7,701 0.70 1,976 1,390 + Obtained from correlations given in Fogg and Gerrad (1991) Measured in this work 186 Table 9.2: Henry's constants of C O and N 2 in water and organic solvents (Fogg and Gerrad, 1991) Solvent Temp. H co H N 2 H co (K) (MPa) (Mpa) H N 2 Water 298 5,857 8,552 0.68 313 7,072 10,133 0.70 333 8,187 11,429 0.72 353 8,613 12,048 0.71 363 8,582 11,926 0.72 373 8,400 11,683 0.72 383 8,096 11,348 0.71 393 7,701 10,943 0.70 413 6,708 9,960 0.67 Methyl acetate 298 119 173 0.69 303 118 170 0.70 313 116 163 0.71 2-propanone 298 130 187 0.69 303 129 184 0.70 313 126 177 0.71 1-1'-oxybisethane 293 60 82 0.74 298 60 81 0.74 303 60 80 0.75 313 59 78 0.76 Tetrachloromethane 298 117 159 0.74 303 116 156 0.74 313 114 151 0.75 323 111 146 0.76 333 109 141 0.77 Chlorobenzene 298 161 238 0.68 303 159 233 0.68 313 157 225 0.70 323 154 217 0.71 333 150 209 0.72 343 147 202 0.73 353 144 194 0.74 Benzene 298 157 228 0.69 333 135 191 0.71 Hexadecane 298 58 83 0.70 Methanol 298 308 371 0.83 Ethanol 298 220 284 0.77 1-Propanol 298 196 250 0.78 187 9.1.3 Determination of k3 and k.3 It was not possible to estimate k3 and k_3 together with ki , k 2 and H C 0 _ D E A by regressing the pressure versus time data obtained from C O absorption experiments. This was mainly because molecular C O is not directly involved in reaction (8.3). Consequently, the latter exerts no or little effect on the overall change in CO partial pressure due to reaction. Therefore, it was decided to estimate k3 and k_3 separately by following the liquid phase reaction between formic acid and aqueous DEA. In this series of experiments, 0.5-0.65 M formic acid was added to a 30 wt% aqueous DEA solution and the mixture was allowed to react in a stirred autoclave under a nitrogen blanket for about 40-170 hours in the temperature range of 303-413 K. Liquid samples were withdrawn at regular intervals from the autoclave and analyzed for formate and DEAF using IC. The initial formate concentration was set at about 5 times the maximum concentration predicted from the CO-DEA reaction model. 9.1.3.1 DEA-Formic Acid-Water Reaction Model To estimate k 3 and k_3 from the data obtained by means of the above experiments, the following liquid phase reactions can be postulated: R ^ N H * + HCOO- K363 K), amine degradation will occur. Al though the rates of these degradat ion react ions are quite s low our simulation results show that, over time, one can expect substant ial D E A F and formate ion buildup in the sys tem. For the purpose of illustration, the data shown in Figures 9.13 and 9.14 were obtained using very high initial C O partial pressures. Us ing the parameters est imated in this work one can easi ly demonstrate the implication of C O induced degradation under real plant condit ions. It should, however, be noted that translating these data to real plant condit ions is not straightforward. The influence of p rocess condit ions and a totally different gas composit ion on the var ious parameters must be taken into account. 206 Figure 9.13: Predicted concentration profiles for C O absorption in 30 wt% aqueous D E A solution at T = 313 K and p c 0 = 1000 k P a 80 60 h x o b o o X 5 140 LL < LU Q d 20 h 0 Figure 0 2 4 6 T ime (h) 9.14: Predicted concentrat ion profiles for C O absorption in 30 wt% aqueous D E A solution at T = 393 K and p ° 0 = 1,000 k P a 207 9.6 Conclusions T h e kinetics of CO- induced degradat ion of D E A were studied over the temperature range of 313-413 K and D E A concentrat ions of 5-50 wt%. A reaction mechan ism was proposed and a mathematical model was developed to est imate previously unknown kinetic and solubility parameters from batch absorpt ion experiments. T h e experimental data are best descr ibed by reactions (8.1) to (8.5). Numer ica l simulation results, based on the est imated parameters, indicate that the primary D E A degradation reaction is the direct reaction of D E A with molecular C O (reaction 8.2). The fo rma te -DEA reaction (reaction 8.3), on the other hand, is relatively s low and reversible. Compar i son of the simulation results with and without reaction (8.3) show that, at temperatures higher than 343 K, some of the D E A F formed by reaction (8.2) is hydrolyzed back to form formate ions and protonated D E A by reverse reaction (8.3). However, at temperatures lower than 343 K, reaction (8.3) s e e m s to have no significant effect on the net formation of D E A F and formate ions in the sys tem. The data from the experiment on C O absorpt ion in aqueous solution containing 30 wt% D E A and 18.4 wt% D E A F , further confirms the reversibility of reaction (8.3). Parameter est imates of the rate constants suggest that the reaction rates are quite s low but, over t ime, nevertheless lead to substantial D E A F and formate ion buildup in the system. The Henry 's constant of C O in aqueous D E A solution was determined by the N 2 -Ano logy and from the reaction model . The results are in fairly good agreement. Compar ison of the values of H C 0 _ D E A over the temperature range of 208 313-343 K shows that the value of H C 0 _ D E A dec reases with increasing temperature. This trend is similar to that of C O solubility in pure organic solvents reported in the literature (Fogg and Gerrard, 1991). A n experiment conducted by absorbing C O in 30 wt% aqueous M D E A solution shows that, unlike D E A , M D E A does not react with C O . There was no experimental ev idence suggest ing the formation of d iethanolacetamide (R1R2NCOCH3) even after 20 hours at 393 K. The rate constant for the formate ion formation reaction was found to be in excel lent agreement with that obtained from C O - D E A - H 2 0 sys tem. Th is further val idates the proposed reaction mechan isms and the experimental technique used to est imate the kinetic parameters. The D E A F and formic ion concentrat ions found at the end of each experiment agreed well with those predicted from the present mathematical model . In most c a s e s the relative error was within ± 30%. 209 CHAPTER 10 OVERALL CONCLUSIONS AND RECOMMENDATIONS 10.1 Main Conclusions from C 0 2 Absorption/Desorption Work A comprehensive mathematical model governing the diffusion-reaction process of C 0 2 absorption and desorption in aqueous amine solutions falling as a laminar liquid film over a hemispherical surface has been developed. The model applies to a general case where the aqueous solution may contain a binary mixture of amines (e.g., MEA+AMP or MEA+MDEA) and where C 0 2 undergoes a series of liquid phase reversible reactions. The model readily reduces to a single aqueous amine (e.g., M E A or AMP) or physical absorbent system by setting the initial concentration of one or both amines to zero. The model can also be reduced to the well-known pseudo-first-order kinetics when all reactions are lumped into a single, overall reaction by setting the rates of all but one reaction to zero. The predicted absorption and desorption rates from the model at various amine concentrations, C 0 2 partial pressures, temperatures and C 0 2 loadings are consistent with the experimentally observed rates. A numerical procedure was developed to solve the model equations and to estimate unknown model parameters using experimental data. To do this a computer code was written that performs four different tasks involving (a) calculation of physical-chemical properties for a given set of condition, (b) solution of equilibrium model for setting the initial conditions, (c) solution of 210 diffusion-reaction model to calculate concentration gradients at different latitudes 6, and (d) calculation of total absorption or desorption rate by integrating over the entire hemisphere. The Fortran code for tasks (a) and (d) were written as part of this study and that for tasks (b) and (c) were generated using Athena by implementing the model equations in the Athena Visual Workbench environment. These subroutines were compiled together to calculate absorption or desorption rates using the Compaq Visual-Fortran Developer Studio in Windows environment. For the purpose of parameter estimation using the present model and experimental data, the subroutines for tasks (a) to (d) were linked with an additional subroutine generated from Athena that uses weighted least squares and Bayesian estimators with single as well as multi-response data. The computer code has been successfully used to simulate a variety of different operating conditions and to estimate reaction parameters for a number of C 0 2 -amine-water systems. The model was solved analytically for the simple case of physical absorption of a gas over a hemispherical liquid film and a correlation was developed for the physical mass transfer coefficient as a function of dimensionless numbers. The correlation was later used to estimate the diffusivities of C 0 2 in water and N 2 0 in water and amine solutions. The calculated diffusivities are in good agreement with those reported in the literature. The analytical solution was also compared with the numerical solution and good agreement was found. 211 A novel hemispherical contactor was developed to measure absorption and desorption rates of C 0 2 in aqueous amine solutions under a variety of different operating conditions encountered in actual absorption-stripping processes for gas treating. This contactor is, in principle, similar to the wetted sphere units used in many previous studies on C0 2-alkanolamine kinetics. However, the present design offers significant improvements over the conventional designs with respect to surface rippling commonly encountered in the lower half of the full sphere unit. The unit was built in-house with a computerized data logging system and was used successfully to measure absorption and desorption rates to calculate diffusivities and kinetic parameters for both physical and chemical solvents. The diffusion-reaction model developed in this work involves many physical chemical property parameters. A parametric sensitivity analyses indicated that accurate values of C 0 2 diffusivity and C 0 2 solubility given by a Henry's law constant are essential for predicting accurate absorption and desorption rates. An extensive literature search was undertaken and all available property data were compiled. It was found that the values of these parameters at stripping temperatures are not available. A series of experiments involving N 2 0 -water and N 2-alkanolamine systems were conducted to measure diffusivities and Henry's constants of C 0 2 in water using the N 2 0 analogy. Using data obtained in this work and others available in the literature, correlations were developed that can be used for pure water as well as single and binary amine systems covering 212 a wide range of temperatures and amine concentrations. Such correlations are not available in the literature. The absorption and desorption rates of C 0 2 in aqueous solutions of MEA, DEA, MDEA, A M P and their mixtures (MEA+MDEA, MEA+AMP, DEA+MDEA and DEA+AMP) were measured for amine concentrations in the range of 2 to 35 wt%. The absorption experiments were carried out at near atmospheric pressure using pure C 0 2 saturated with water at 293 to 323 K with initially unloaded solutions. The desorption experiments were performed at 333 to 383 K for C 0 2 loading between 0.02 to 0.7 moles of C 0 2 per mole of amine using humidified N 2 gas as a stripping medium. The data were analyzed using the rigorous diffusion-reaction model developed in this work. The model predicts the experimental results well for all eight different amine systems studied (see Chapter 4). The results indicate that the theory of absorption with reversible chemical reaction could be applied to predict desorption rates. A zwitterion mechanism adequately describes the reactions between C 0 2 and carbamate forming amines such as MEA, DEA and AMP under both absorption and desorption conditions. The reactions between C 0 2 and aqueous MDEA solutions are best described by a base-catalyzed hydration reaction mechanism. The kinetic data obtained show that desorption experiments can be used to determine both the forward and backward rate constants accurately. The absorption experiments on the other hand could only be used to determine forward rate constants. 213 For MEA, DEA and A M P , the kinetic data obtained under absorption conditions do not extrapolate well to desorption temperatures. Therefore, kinetic data at higher temperatures should be obtained from desorption experiments. The existing absorption data for the C 0 2 - M D E A system can be extrapolated to desorption temperatures with reasonable accuracy. This is probably because MDEA is very slow reacting amine and does not form carbamate. For the blended amine systems, it was found that small additions of MEA or DEA (< 5 wt%) significantly enhance the absorption rates of C 0 2 in 25 wt% MDEA solutions. Addition of small quantity of MEA (< 5 wt%) to 25 wt% A M P blend, on the other hand, was found to have very nominal effect on the C 0 2 absorption rates of A M P . No improvement in absorption rates was observed when DEA was added to 25 wt% A M P solutions. 10.2 Main Conclusions from the Work on CO-lnduced Degradation of DEA The kinetics of CO-induced degradation of DEA was studied over the temperature range of 313-413 K and DEA concentrations of 5-50 wt%. A reaction mechanism was proposed and a mathematical model was developed to estimate previously unknown kinetic and solubility parameters from batch absorption experiments. The experimental data are best described by reactions (8.1) to (8.5). Numerical simulation results, based on the estimated parameters, indicate that the primary DEA degradation reaction is the direct reaction of DEA with 214 molecular C O . The formate-DEA reaction, on the other hand, is relatively slow and reversible. Comparison of the simulation results with and without the DEA-formate reaction shows that, at temperatures higher than 343 K, some of the DEAF formed by the direct insertion reaction is hydrolyzed back to give formate ions and protonated DEA. However, at temperatures lower than 343 K, the DEA-formate reaction seems to have no significant effect on the net formation of DEAF and formate ions in the system. The data from the experiment on C O absorption in aqueous solution containing 30 wt% DEA and 18.4 wt% DEAF confirms that the DEA-Formate reaction reversible. Parameter estimates of the rate constants suggest that the reaction rates are quite slow but, over time, nevertheless lead to substantial DEAF and formate ion buildup in the system. The Henry's constant of CO in aqueous DEA solutions was determined by the N 2-Anology and from the reaction model. The results are in fairly good agreement. Comparison of the values of H C 0 _ D E A over the temperature range of 313-343 K shows that the value of H C 0 _ D E A decreases with increasing temperature. This trend is similar to that of C O solubility in pure organic solvents reported in the literature. An experiment conducted by absorbing C O in 30 wt% aqueous MDEA solution shows that, unlike DEA, MDEA does not react with C O . There was no experimental evidence suggesting the formation of diethanolacetamide 215 ( R 1 R 2 N C O C H 3 ) even after 20 hours at 393 K. The rate constant for the formate ion formation reaction was found to be in excellent agreement with that obtained from CO-DEA-H2O system. This further validates the proposed reaction mechanisms and the experimental technique used to estimate the kinetic parameters. The DEAF and formic ions concentrations found at the end of each experiment agreed well with those predicted from the present mathematical model. In most cases the relative error was within + 30%. 10.3 Recommendations for Future Work This work provides important correlations for physical properties and kinetic parameters that cover both absorption and desorption conditions applicable to both single and blended amine systems. These correlations should be implemented in process simulators such as Aspen-Plus, T S W E E T and Hysis to simulate industrial gas treating processes involving MEA, DEA, MDEA, A M P or their mixtures and the -model predictions should be compared with pilot plant or industrial plant data. Further work on C 0 2 absorption in partially loaded amine solutions should be carried out to obtain accurate data representing the rich end of the absorber column. More experimental data on C 0 2 absorption/desorption in mixed amine system are desirable. Special attention should be focused on the MEA+MDEA system. The presence of small amounts of MEA in aqueous MDEA solutions significantly improves the capacity of M D E A to absorb C 0 2 . To explore optimum 216 MEA concentrations, more experiments should be conducted with solutions containing less than 10 wt% MEA. Blends of MEA and MDEA could be used to economically capture CO2 from flue gases for the purpose of sequestration or enhanced oil recovery, as the regeneration cost of such solvent systems will be significantly lower. It will be useful to implement the kinetic mechanisms and the correlations of the kinetic parameters obtained from the work on CO-induced degradation of DEA in existing process simulators to estimate DEA losses for processes where significant amounts of C O is present in the feed gas. Innovative scheme could be developed to avoid or minimize DEA losses, which may run into millions of dollars in industry. The hemispherical contactor could easily be used to screen new physical or chemical solvents for C 0 2 and/or H 2 S removal. 217 NOMENCLATURE PART I. a Interfacial area (m2) C A M Concentration of amine (kmol/m3) Cj Concentration of various ionic and non-ionic species as defined by eq. (4.30) Dj Diffusivity of ionic and non-ionic species in aqueous amine solution (m2/s) D c 0 Diffusivity of C 0 2 in amine solution (m2/s) D£02 Diffusivity of C 0 2 in pure water (m2/s) D N 2 0 Diffusivity of N 20 in amine solution (m2/s) D° 2 0 Diffusivity of N 20 in pure water (m2/s) E Enhancement factor E A Absorption enhancement factor E D Desorption enhancement factor Ec* Maximum possible enhancement factor F c o Flow rate of feed C 0 2 (mmol/s) F^* Flow rate of feed N 2 (mmol/s) F^1 Flow rate of dilution N 2 (mmol/s) g Gravitational constant (m/s2) Ga Grashof number as defined by eq. (4.77) H C 0 2 Henry's constant of C 0 2 in amine solution (kPa-m3/kmol) H° 0 2 Henry's constant of C 0 2 in pure water (kPa-m3/kmol) HM n Henry's constant of N 20 in amine solution (kPa-m3/kmol) 3/ H° Henry's constant of C 0 2 in pure water (kPa-m /kmol) N20 J ka p p Apparent rate constant (1/s) k| Rate constant for reaction (i) k2nd Second order rate constant as defined by eq. (2.2) (m3/kmol s) kg Gas-side mass transfer coefficient (kmol/kPa m2 s) k° Physical mass transfer coefficient (m/s) M Hatta number as defined by eq. (2.2) N A Rate of absorption (kmol/s) No Rate of desorption (kmol/s) Pco2 Partial pressure of C 0 2 in the gas bulk (kPa) Pco2 Equilibrium partial pressure of C 0 2 corresponding to its concentration in the liquid bulk (kPa) Q Liquid flow rate (m3/s) r, Rate of reaction number (i), (kmol/m3 s) S Least square optimization objective function 218 R Radius of the hemisphere (m) Re Reynolds number as defined by eq. (4.75) Sc Schmidt number as defined by eq. (4.76) Sh Sherwood number as defined by eq. (4.101) T Temperature (K) V 0 Velocity at the surface of the liquid film (m/s) V 9 Velocity distribution in the liquid film (m/s) x Dimensionless distance from the gas-liquid interface y. Measured value of the state variable y(k) Calculated value of the sate variable z Zwitterion Greek Symbols a CO2 loading (mol of COVmol amine) A e Liquid film thickness as a function of latitude 0 (m) Ao Liquid film thickness at the equator (m) u. Viscosity of aqueous amine solution, (kg/m s) v Kinematic viscosity (m2/s) VAM Stochiometric coefficient p Density of aqueous amine solution, (kg/m3) 0 Angle from the pole x c Contact time (s) PART II. a Gas-liquid interfacial area, (m\"1) C D E A DEA concentration, (wt%) C| Liquid phase concentrations of various chemical species as defined in Eq. (6), (kmol/m3) D N z Diffusivity of nitrogen in aqueous DEA solution, (m2/min) d i m p Impeller diameter, (m) E Enhancement factor in Eqs. (10) and (11) E Activation energy, (kcal/mol) H Henry's law constant, (kPa/m 3 kmol) ki Rate constant for reaction (1), (m3/kmol h) k 2 Rate constant for reaction (2), (m3/kmol h) k3 Rate constant of forward reaction (3), (m 3/kmol h) L 3 Rate constant of reverse reaction (3), (1/h) K3 DEAF hydrolysis constant of reaction (3), (in Eq. 53 m 3/kmol, dimensionless in Eq. 54) K4 DEA protonation constant as defined in Eq. (16) K 5 Water dissociation constant as defined in Eq. (17) K6 Formic acid dissociation constant as defined in Eq. (42) K7 MDEA protonation constant as defined in Eq. (60) k L Liquid side mass transfer coefficient as defined by Eq. (29), (m/min) 219 N Stirrer speed, (rpm) n'co' Total number of moles of C O transferred from gas bomb to autoclave (mol) n^ o Number of moles of C O in the headspace of the autoclave (mol) n D E A Number of moles of DEA in the solution (mol) Pco Initial partial pressure of C O , (kPa) p c 0 Partial pressure of C O , (kPa) P N 2 Initial partial pressure of N 2 , (kPa) p N 2 Partial pressure of N 2 , (kPa) r. Rate of reaction, (kmol/m3 h) S Least square optimization objective function R Gas constant Re Reynolds number as defined by Eq. (30) S c Schmidt number as defined by Eq. (30) T Temperature, K V G Gas volume in the autoclave, (m3) V L Liquid volume in the autoclave, (m3) V Measured value of the state variable j i y(k) Calculated value of the sate variable Greek Symbols u.L Viscosity of aqueous DEA solution, (kg/m-min) p L Density of aqueous DEA solution, (kg/m3) Abbreviations (Part I and II) A M P 2-amino-2-methyl-1-propanol DEA Diethanolamine D E A E Diethylethanolamine DEAF Formyl-diethanolamine DMF Dimethylformamide F C C Fluid catalytic cracking HCN Hydrogen cyanide MDEA Methy-diethanolamine MEA Monoethanolamine RT - C H 2 C H 2 O H R 2 - C H 2 C H 2 O H R 3 - C H 3 R4 -C (CH 3 ) 2 CH 2 OH R - i N H 2 MEA R ^ N H DEA R 1 R 2 R 3 N MDEA R 4 N H 2 A M P 220 R I N H ; R ^ N H ; R 1 R 2 R 3 N H + R 4 N H 3 RuNHCOO\" R ^ N C O O R 4 N H C O O \" RiRzNHCO Protonated MEA Protonated DEA Protanated MDEA Protanated A M P MEA carbamate DEA carbamate AMP carbamate DEAF REFERENCES Al-Ghawas, H.A., Ruiz-lbanez, G. and Sandall, O.C., 1989a, Absorption of carbonyl sulfide in aqueous methyldiethanolamine, Chem. 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Sci. , 42, 425 234 APPENDIX A DETERMINATION OF C 0 2 LOADING IN AMINE SOLUTIONS A.1 Detection Principle The total CO2 content in the liquid phase or the CO2 loading was determined by a novel method developed by Shell Technology Center, Houston, Texas. In this method a small amount of liquid sample (0.1-1.0 gm) is injected into a solution of 30 wt% hydrochloric acid which instantly frees the CO2 chemically combined with the amine. The nitrogen gas carries the total C 0 2 to a Gastec tube filled with an indicating layer of a pale white color substance that contains hydrazine. In the Gastec tube, CO2 reacts with hydrazine to form carbonic acid monohydrazide, which changes the color of redox indicator to a bluish-violet according to following reaction: C 0 2 + N 2 H 4 -> N H 2 N H C O O H The length of the stain formed is directly proportional to the C 0 2 concentration in the sample. A. 2 Experimental Setup and Procedure Figure A.1 shows the experimental setup for determining CO2 in amine solution. The gas analysis vessel shown in Figure A.1 was specifically designed for this type of experiments and was supplied by Shell Technology Center, 235 Houston, Texas. The Gastec tubes used in this work were type 2HH and were obtained from Gastec Corporation, Fukaya, Japan. N 2 In (120 mL/min @ 5 psig) Cone. N a O H Solution Vesse A Cone . HCL 15 mL •!v' M m Drying Tube Gastec Tube N 2 Out Amine Sample (-0.1-1 gm) Gas Ana lys is V e s s e l Figure A.1 Experimental setup for CO2 measurement in Liquid Samples In a typical run, the gas analysis vessel was thoroughly rinsed with distilled water and 15 mL of 30-wt% HCL solution was dispensed into the vessel and the cap was tightened. A low-pressure nitrogen supply line was attached to the inlet of the analysis vessel. Before entering the analysis tube, the nitrogen stream was first bubbled through a tube containing concentrated NaOH solution and then to drying tube. This was done to remove any traces of CO2 or water vapor present in nitrogen gas from the supply cylinder. The N 2 supply was turned on and the upstream pressure was adjusted to 5 psi. The entire system was sparged for 5 minutes and checked for leaks using snoop. After breaking the tips off both ends, the Gastec tube was inserted at the outlet of the analysis vessel and kept in horizontal position by a metal stand. The nitrogen gas was allowed to sparge through the tube for 5 minutes to make sure there was no C 0 2 236 contamination. During this period If there was any stain, the tube was discarded and a new tube was used. Once the system was C 0 2 free, small amount of sample (0.1-1.0 gm, depending on C 0 2 loading) was withdrawn from the air-tight sample bottle using a Hamilton gas-tight syringe, weighed in an electronic balance and injected into the sample port through the septum. At this stage nitrogen flow was adjusted to 120 mL/min and was kept at this throughout the run. The sparging was continued for exactly 40 mins. The nitrogen flow rate and the sparge time were determined by conducting a number of trial runs during the development of the procedure. In the analysis, if the stain over ranged the tube, it was repeated using smaller sample size. If there was no stain, the analysis was repeated using larger sample size. For each run, the vessel was drained and rinsed with water. Also, each analysis was repeated at least twice using a new tube every time. After each run, the Gastec tube was quickly removed from the system and the stain length was measured using a Vernier scale. If the stain length was not uniform, the maximum and minimum lengths were measured and an average was taken. The amount of C 0 2 in a liquid sample was calculated using the following equation: C 0 2 Loading ( m o l s o f C Q 2 >^ ^mols of Amine R f x Stain Length(cm)/44 Amine wt%xSample Size(mg)/Amine mol. wt. The response factor, R f, was obtained from the calibration curve prepared by injecting a liquid sample with known amount of C 0 2 . To do this a standard solution that contained 10,000 ppm (weight) as C 0 2 stock was prepared using 237 sodium carbonate (24.1 gm N a 2 C 0 3 up to 1000 gm) in water. The relationship between the C 0 2 content and the stain length was obtained by injecting standard samples ranging from 0 to 2.5 gm. Each injection was repeated at least twice and the responses were averaged. The raw data are reported in Table A.1 and the calibration curve is presented in Figure A.2. The value of the correlation coefficient (R 2 = 0.9956) indicates that reproducibility of the measurements is excellent. 40 • Measurements Regression y = 6.3278x Gastec Tube No. = 2HH N 2 Flow = 120 mL/min Sparge Time = 40 mins J L 0 2 3 4 5 6 Stain Length (cm) Figure A.2 Calibration Curve for Gastec Detector Tube No. 2HH for C 0 2 Measurement in Liquid Samples 2 3 8 Table A.1: Calibration Data for Gastec Detector Tubes No. 2HH (Standard Solution: 10, 000 ppm (by weight) N a 2 C 0 3 , N 2 Flow = 120 ml/min, Sparge Time = 40 min) Sample Volume Sample Weight C 0 2 i n Sample Tube Reading (Avg. of 2 tubes) ml gm mg cm 0.0 0.00 0.00 0.00 0.5 0.51 5.10 1.03 1.0 1.02 10.20 1.63 1.5 1.53 15.30 2.54 2.0 2.04 20.40 3.14 2.5 2.55 25.50 3.95 3.0 3.06 30.60 4.84 2 3 9 APPENDIX B CALIBRATION OF MEASURING INSTRUMENTS B.1 Pressure Transducers The calibration of pressure transducers installed on the heating tank and absorption/desorption chamber was done by pressurizing the apparatus from ambient to 20 psig and then bringing it back to ambient pressure in a stepwise manner. The calibration curve was generated using the average values. The actual pressure was measured in mm of Hg using mercury manometer and the output signal from the transducer was measured in volts using the computer data acquisition system. The calibration curves and corresponding correlations are shown in Figure B.1 and B .2. B.2 Mass Flow Meters The mass flow meters were calibrated for C O 2 , N 2 0 and N 2 by means of a soap film meter. A soap film assembly as shown in Figure B.3 was set up and the ambient temperature and pressure was recorded. The time taken for a soap bubble to travel between two marks was noted using a stopwatch. For each flow at least three measurements were collected and average was used in generating the calibration curve. The output signal from the mass flow meter was measured using the computer data acquisition system. The same procedure was adopted 240 Figure B.1 Calibration Curve for Pressure Transducer on Absorption/Desorption Chamber(Omega Model PX202-030GV) 20 .9? 15 to l o Q. !<]—J Data Acquisition Gas Out Mass Flowmeter Soap Film Meter Figure B.3 Setup for Mass Flow Meter Calibration using a Soap Film Meter 2000 I E 1000 500 0 i y = 4 0 2 . 2 6 X - 60.821 : R 2 = 0.9981 T = 22.5 °C P = 1 atm • Measurements • i i i l • • i i l i i Regression 0 1 2 3 4 5 Output Signal after Zeroing (volt) Figure B.4 Calibration Curve for Measuring Dilution N 2 Flow Rate using Mass Flow Meter (Brooks Model 5700) 242 for all mass flow meters. The calibration curves for the three mass flow meters used in this apparatus are plotted in Figure B.4 to B.7. Figure B.5 Calibration Curve for Measuring Stripping N 2 Flow Rate using Mass Flow Meter (Colepalmer Model GFM171) c E E o 1500 1000 „ 500 O O \"y = 876.59x + 63.531 '. R 2 = 0.9997 y T = 23.4 °C P = 1 atm JT • Measurements • • i i i i i i—i—i — Regression i i i i i i i i—i—i— 0.0 0.5 1.0 1.5 Output Signal after Zeroing (volt) 2.0 Figure B.6 Calibration Curve for Measuring C 0 2 Flow Rate using Mass Flow Meter (Colepalmer Model GFM171) 243 1500 h y = 854.28X + 59.257 i i • • • 0.0 0.5 1.0 1.5 2.0 Output Signal after Zeroing (volt) Figure B.7 Calibration Curve for Measuring N 2 0 Flow Rate Using Mass Flow Meter (Colepalmer Model G F M 171) B.3 C02 Analyzer The C 0 2 absorption or desorption rate were determined by the difference of the C O 2 flow rate in the gas stream into and out of the hemispherical contactor. The flow rate of C 0 2 into the unit were determined using the mass flow meter as described in the previous section. To determine the flow rate out of the unit a calibration of the gas analyzer was required. NOVA 300 Infrared analyzer that had a range of 0-20% (volume basis) was used in this work. The calibration was carried out in the configuration used in the actual experiment. Two mass flow meters one calibrated for N 2 and other for C O 2 were used in the setup shown in Figure B.8. To calibrate the analyzer, N 2 flow rate was fixed at a certain value and the C O 2 flow rate was varied so that a gas mixture with C 0 2 244 composit ion ranging from 0 to 2 0 % (mole basis) was sent through the analyzer. The analyzer output signal was adjusted to zero by subtracting from it the output s ignal value at zero C 0 2 concentrat ion. A t e a c h setting the s teady state reading of the analyzer output signal and the inlet gas mixture composit ion were recorded by the computer. The calibration curve obtained is plotted in Figure B.9 Throughout this work, before starting an experiment the calibration was checked by sending the gas through the by pass line to the C 0 2 analyzer as shown in Figure 3.2. CO N 2 Mass Flowmeter - 4 C O , Analyzer 1 1 , •1 1 °°° 1 Mass ] W Nova 300 u l r -Data Acquisition Figure B.8 Setup for C 0 2 Ana lyzer Calibrat ion Gas Out 245 25 0 1 2 3 4 5 Output S igna l after Zeroing (volt) Figure B.9 Calibration Curve for G a s - P h a s e C 0 2 Measurement using Infrared Analyzer (Model N O V A - 3 0 0 ) BA Gas Chromatograph In absorption experiments with N 2 0 , the exit gas composit ion was determined using a gas chromatograph (Sh imadzu Model G C 8A) that was equipped with a thermal conductivity detector. The principal operating condit ions are summar ized in Table B.1. The G C was cal ibrated by injecting gas mixtures of known composi t ion. The gas mixtures were prepared by mixing N 2 0 and N 2 gases in various proportions using m a s s f low meters. The standard gas samp les were stored 1-liter Tedlar sampl ing bags . E a c h sample was injected at least three t imes and peak areas of N 2 0 , N 2 and the total area were noted from the strip chart recorder. Average of the three values was used in generat ing the calibration curve. To compensate for error due to injection vo lume, the ratio of 246 N2O peak area to total peak area was plotted against the N 2 0 mole fraction in the standard sample . The calibration data obtained are l isted in Tab le B.2 and the calibration curve is shown in Figure B.10. The G C method descr ibed above was also used for measur ing CO2 in the exit gas. Th is was done only for a few randomly se lec ted runs to check the accuracy of the Infrared Analyzer . The co lumn and operating condit ions were identical to those used for N 2 0 measurement (see Tab le B.1). The calibration data for CO2 are listed in Tab le B.3 and corresponding calibration curve is shown in Figure B.11. 0.20 0 0.18 CM z 1 0.16 o I 0.14 o ^ 0.12 0.10 -y y = 0.8932X - • R 2 = 0.9988 - • Measurements • 1 1 1 1 1 1 1 1 — Regress ion 1 1 1 1 1 1 1 1 1 1 1 1 0.10 0.14 0.18 0.22 0.26 Peak Area Ratio ( N 2 0 Area/Total Area) Figure B.10 Calibration Curve for G a s P h a s e N 2 0 measurement using G C (Shimadzu Model G C 8A, Co lumn : Chromosorb 102) 247 0.5 r y = 0.8987x • Measurements 0.0 0.1 0.2 0.3 0.4 0.5 Peak Area Ratio ( C 0 2 Area/Total Area) Figure B.11 Calibration Curve for G a s - P h a s e C 0 2 Measurement using G C (Shimadzu Model G C 8A, Co lumn : Chromosorb 102) Table B.1 G C operating condit ions for gas phase N 2 0 / C 0 2 measurement Item Descript ion Co lumn Chromosorb 102, mesh s ize 80/100, 20 'x1/8\" S S packed column (supplied by Supe lco Inc. Oakvi l le, O N ) Detector Thermal Conductivity Detector(TCD) Co lumn temperature 40 °C Injector temperature 60 °C Carr ier gas He (20 cm 3 /min) Injection volume 0.25 c m 3 248 Table B.2 Calibrat ion Data for N 2 0 measurement using G C Ref. No. N 2 0 in S td . Samp les (mole fraction) N 2 0 P e a k A r e a Total P e a k A rea Peak A r e a Ratio (N 2 0/Tota l ) N 2 OCa l ib1 0.186 19715 94539 0.2085 19892 95505 0.2083 19580 94260 0.2077 N 2 O C a l i b 2 0.177 18795 94158 0.1996 18946 95046 0.1993 18943 95251 0.1989 N 2 O C a l i b 3 0.166 17346 93568 0.1854 17442 94098 0.1854 17411 94008 0.1852 N 2 O C a l i b 4 0.155 16160 93307 0.1732 16140 93400 0.1728 16055 92836 0.1729 N 2 0 C a l i b 5 0.141 14728 93316 0.1578 14758 93649 0.1576 14560 92791 0.1569 249 Table B.3 Calibration Data for C 0 2 measurement using G C Ref. No . C 0 2 in S td . Samp les (mole fraction) C 0 2 P e a k A r e a Total P e a k A r e a P e a k A r e a Ratio (C0 2 /To ta l ) C 0 2 C a l i b 1 0.401 45017 102002 0.4413 45859 103847 0.4416 45600 103212 0.4418 C 0 2 C a l i b 2 0.350 39432 101738 0.3876 39647 102160 0.3881 39638 102043 0.3884 C 0 2 C a l i b 3 0.300 34027 100098 0.3369 34241 101731 0.3366 34489 102486 0.3365 C 0 2 C a l i b 4 0.2504 28213 100217 0.2815 28411 101089 0.2810 28431 101124 0.2811 C 0 2 C a l i b 5 0.200 22343 99410 0.2248 22596 100552 0.2247 22566 100514 0.2245 C 0 2 C a l i b 6 0.170 18889 98872 0.1910 18847 98828 0.1907 18776 98279 0.1910 C 0 2 C a l i b 7 0.140 15792 98675 0.1600 15814 98786 0.1600 15763 98605 0.1598 C 0 2 C a l i b 8 0.110 12151 97658 0.1244 12241 98647 0.1240 12201 98512 0.1239 250 Table B.3 Calibration Data for C 0 2 measurement using G C (Contd.) C0 2 Cal ib9 0.0801 8601 96902 0.0887 8670 98095 0.0884 8637 97649 0.0885 0.0651 6694 95439 0.0701 CO 2 Cal ib10 6785 97096 0.0698 6758 96683 0.0699 0.0447 4742 95268 0.04977 C0 2 Cal ib11 4730 95063 0.04975 4745 95435 0.04972 C0 2 Cal ib12 0.0324 3438 95411 0.03603 3453 96065 0.03594 3434 94917 0.03618 C0 2 Cal ib13 0.0159 1698 95946 0.01769 1713 96050 0.01783 1692 95737 0.01767 251 APPENDIX C ANALYTICAL SOLUTION FOR PHYSICAL ABSORPTION/DESORPTION MODEL C. 1 Model for Physical Gas Absorption/Desorption The model equation for gas absorption/desorption over a hemispherical liquid film without chemical reaction is given by Initial Condition: at 9 = 0 f o r r>R C,=C° (C.2) Boundary Conditions: atr = R f o r 0 > O ^ 1 = 0 (C.3) atr = R + A e for 0>O C ^ C 1 , (C.4) C . l . l Model Equations in Dimensionless form Equations (C.1) to (C.4) can be written in dimensionless form by substituting the following dimensionless variables (Wild and Potter, 1968): x = R + A ° ~ r (C.5) A 9 252 C = ^ and C ° = - ^ c; (C.6) dr) -V 0 A 9 2 de = 47tR 2D 1 . . 5/3 . . - ( s m 5 M 0)d0 3QA„ (C.7) and performing some algebraic manipulations ( 1 \" X >*T ^ (C.8) Initial Condition: at TI = 0 for x > 0 C = C° (C.9) Boundary Conditions: at x = 0 for T | > 0 C = 1 (C.10) a tx = 1 for r |>0 = 0 (C11) The differential equations (C.8) to (C.11) must be integrated from r\\ = 0 (i.e. 6 = 0) to ri = r|2 (i.e. 6 = K/2). The upper limit of integration is defined by the following equations: \"Ha 4TTR 2r\\ it/2 A-rrR^n = ± J s i n 5 / 3 e d e = 1 (0.84133) (C.12) 3QA o 0 3QA 253 it/2 The fraction 0.84133 in the above equation is the value of Js in 5 ' 3 0d9 and was 0 obtained by numerical integration. The total rate of absorption/desorption of a gas over a hemispherical film can then be computed from the following equation: 2 o v 3 x y(x=ofl) dt| (C.13) Note that the concentration gradient 3 C , is positive quantity for absorption and negative for desorption. The physical mass transfer coefficient can be obtained as follows: N° N° k°= ^ = =-2 (C.14) L 2 T C R 2 ( C ; - C ? ) 2 J I R 2 ( C ? - C 1 ) C.2 Analytical solution In order to obtain an expression for physical mass transfer coefficient we need to solve the model equations (C.8) to (C.11) analytically. A quick analytical solution is possible if we assume that the penetration depth of the gas is much smaller compared to the thickness of the liquid film. Under this assumption, the liquid film can be treated as if it were infinitely deep and boundary condition at x = 1 ( Eq. C.11) can be replaced boundary conditions at x = ~ and the governing equations can be written as: fr=0 254 Initial Condition: atr| = 0 f o r x > 0 C = C° (C.16) Boundary Conditions: a t x = 0 f o r r | > 0 C = 1 (C.17) a tx = o o f o m > 0 C = C° (C.18) Equations (C.15) to (C.18) can be solved using Laplace transform. Taking the Laplace transform of Eq. (C.15) with respect to rj and denoting the transform of C a s C : s C - C ( 0 , x ) = - ^ (C.19) From the initial condition Ci(0,x) = C° , which upon substitution in equation (C.19): dx Particular solution of Eq, (C.20): d 2 r -sC = -C° (C.20) C = - — (C.21) p s Homogenous solution of Eq. (C.20): C7(x,s) = A . e ^ + A2e'rsx (C.22) 255 where A i and A 2 are the arbitrary constants. From boundary condition at x = 0, A ^ A 2 = 1/s and from boundary condit ion at x = oo, A i = 0. Therefore the general solution is: C ( X , S ) = * s s (C.23) or C(x,-n) = L -1 . - V s x 91 s (C.24) From the inverse Lap lace transform table: L-1 -Vsx = 1 - e r f < x ^ and L\"1 v V . J 9L s = C° (C.25) Combin ing equations (C.24) and (C.25): C(x,T|) = 1 - e r f - C ° (C.26) Recal l ing the definition of error function: erf(c;) = A j e ^ d < t ) Vrc o (C.27) Applying the definition of error function from equation (C.27) to equation (C.26): C(X,TI) = 1—±= f e ^ - C 0 V 7 C J 0 (C.28) 256 c c° Substituting C = — 1 and C° = into equation (C.28): c ; c ; 2C r 2 c 1 (x, 1 l ) = c;—p- Je-* d«t>-C? Vrc o (C.29) Differentiating equation (C.29) with respect to x, obtaining y 3 x y(x=o,n) and substituting it into equation (C.13): 2 o V^l (C.30) or - 0 _ f r B _ 3 Q ( C ' 1 - C ? ) ^ A _ _ 2 Vic (C.31) Substituting for r\\2 from equation (C.12) into equation (C.31): N° =-N D° =3.1774, QR D., (c ' i - c? ) (C.32) Substituting forN° or from equation (C.32) into equation (C.14): k° =1.5887 D, ( A -D2 \\ rt A0%R< Q v y (C.33) Equation (C.33) can be written in terms dimensionless numbers as follows: 0.5 o~0.5 Sh = 1.26758 R e u Sc (C.34) 257 where, S h J ^ , R e = - 5 - . S c ^ (C.35) D , 2TIRV D , From Higbie's penetration theory the liquid phase mass transfer coefficient, k°, for physical absorption is given by k?=2 ^ - (C.36) \"c where, xc is the gas-liquid contact time and can be obtained by comparing equations (C.33) and (C.36): T c =1.58487tR' (C.37) Equation (C.37) is similar to that given by Wild and Potter (1968) for complete sphere. 258 APPENDIX D DERIVATION OF RATE EXPRESSION FOR ZWITTERION MECHANISM This appendix gives the derivation for rate expression representing C 0 2 reactions with a mixture of AMP and MEA in aqueous solution via zwitterion mechanism. The reactions involved are: AMP- Zwitterion Formation: k K C 0 2 + R 4 N H 2 < ! 4 R 4 N H ^ C O O - (D.1) AMP-Zwitterion Deprotonation: k K R 4NH^COO\" + R 4 NH 2 R 4 NHCOO\" + R 4 NH: (D.2) k ,K R 4NH^COO\" + H 2 0 ^ 4 R 4 N H C O O \" +H 3 0 + (D.3) k.3 k K R 4NH^COO- + OH\" ^ R 4 N H C O C T + H 2 0 (D.4) Deprotonation of AMP-Zwitterion to MEA: k26.K26 R ^ H ^ C O O ' + R ^ H , <-> R 4 NHCOO\"+R 1 NH^ (D.5) k -26 Reactions (D.1) to (D.5) are same as reactions (4.1) to (4.4) and (4.25) respectively. The nomenclature used to denote chemical species and rate constants involved in these reactions is the same as in Chapter 4. The letter Z represents the zwitterion intermediate. 259 Rate of Accumulation of Z = Rate of formation of Z - Rate of consumption of Z — - k ^ C j + k _ 2 C 4 C 3 + k _ 3 C 4 C 8 + k _ 4 C 4 C 9 + k _ 2 5 C 4 C 1 1 - ^ 10 dZ Assuming a steady state exist, then — = 0 and equation (D.6) can be solved for dt Z as follows: Z = k^C^C2 + k _ 2 C 4 C 3 + k _ 3 C 4 C 8 + k _ 4 C 4 C 9 + k _ 2 5 C 4 C 1 1 k_, - i -k 2 C 2 -i-k3Cg H-k4Cy 4-k2gC (D.7) 10 Rate expression for reaction (D.1) is: *i (D.S) Substituting for Z from equation (D.7) into equation (D.8) gives: ri = -k^C^C2 + — k , C , C 2 + k _ 2 C 4 C 3 + k_ 3C 4Cg + k_ 4C 4Cg +k_ 2gC 4C^ k_, - t-k 2C 2 -i-k 3Cg -f~k4Cy -i\"k2gC 10 (D.9) or r i=-k iCA + k 1 C 1 C 2 + k _ 2 C 4 C 3 + k_ 3C 4Cg + k _ 4 C 4 C g + k _ 2 5 C 4 C 1 1 1 + P 2 + , x 3 C 9 + k-i + K 2 5 v k_ 1 y '10 (D.10) Let B = (k 2 k_\"i P 2 + ' k ^ A k-i C 9 + K 2 5 '10 (D.11) Combining equations (D.10) and (D.11) and rearranging gives: 260 -k, CjCgB — C .^ k^ k^ 4 c 9 + - -25 '11 1 + B (D.12) or k 2 ^ k.i v - 1 j K,K; - C 3 + K,K. - C 8 + K 1 K 4 c 9 + *25 k 1 v \"1 J '11 25 1 + B (D.13) f i r \\ Let A = f i r ^ K 1 K : - C 3 + V k - V K i K -- c 8 + k-, - C 9 + ^25 v k - 1 y • C ^ (D.14) 25 •k, C , C 2 - C 4 B 1 + 2 B (D.15) Since r, is derived from reactions (4.1) to (4.4) and (4.25), in Chapter 4 r, is denoted as r ^^ . When the reaction mixture has only A M P and water then k25 will be zero and r^^ will reduce to r,_4 261 APPENDIX E DENSITY AND VISCOSITY OF AQUEOUS AMINE SOLUTIONS E.1 Density The densities of binary and ternary aqueous amine mixtures were calculated using the correlation of Hsu and Li (1997a). According to this correlation the density of a liquid mixture, p m can be obtained from the following equation: where, Xj is the mole fraction of each component in the mixture, Mi is the molar mass of pure component i, and V m is the molar volume of the liquid mixture. The molar volume of the liquid mixture is calculated from the following equation: where, v ° is the molar volume of the pure fluid at the temperature of the system and V E is the excess volume of the liquid mixture which for a ternary system is assumed to be: (E.1) (E.2) V E = V E + V E + V E v — v 1 2 -i- v 1 3 T v 2 3 (E.3) 262 The excess volume of the binary liquid mixture, v , | can be calculated using the following Redlich-Kister type equation: V 1 E 2 = x 1 x 2 ^ A i ( x 1 - x 2 ) i (E.4) i=0 where, Aj are the binary interaction parameters which are assumed to have the following temperature dependence: A ^ a + bT + cT 2 (E.5) The densities of pure fluids needed to calculate v ° in eq. (E.2) were obtained from the correlation of the type: p = a, +a 2 T + a 3 T 2 (E.6) The correlation coefficients a, b, c, a-\\, a 2 and a 3 in eqs. (E.5) and (E.6) determined by Hsu and Li (1997a) are listed in Table E.1 and E.2. The parameter values are based on 686 data points measured in the temperature range of 303-353 K, including pure fluids, single-amine aqueous solutions, and ternary aqueous solutions of blended amines. The data include both their own density measurements and those reported in the literature. The overall average absolute percentage deviation for the density calculations was reported to be 0.041%. To check the accuracy of this correlation, we measured the density of various aqueous amine mixtures at 303 and 323 K. These values are listed in Table E.3 and a cross plot is presented in Figure E.1. The agreement between 263 our measurements and the estimates using eq. (E.1) is excellent. The relative error is within ± 1%. Table E.1 Binary Parameters of the Redlich-Kister Equation of the Excess Volume (eq. E.4 and E.5) Binary Pair Param. MEA+H2O DEA+H2O MDEA+H2O A M P + H 2 O A 0 a -5.92024 x HT 2 -3.31562 x 10 -2 .88774x10 -6.51042 b -1.77290 x 10\"4 8.11654 x 10\"2 6.95810 x 1 0 \" 2 5.02584 x 10\"3 c -1.10780 x 10' 6 6.15156 x 10\"6 -5.03040 x 1 0 ' 7 1.08578 x IO - 6 Ai a 2.17490 -3.52516 x 10 -2 .06623x10 5.55560 b 1.10385 x 10\"5 9.75694 x 10\"2 6.36707 x 10\"2 -1.1325 x 10~2 c 0 0 0 0 Binary Pair MEA+MDEA MEA+AMP DEA+MDEA DEA+AMP Ac a -2.42756 x 10 5.53222 -1 .24706x10 1.75649 x 10 3 b 1.89797 x 10\"1 1.62914 x 10\"1 1.00561 x 10\"1 -1 .06202x10 c -2.88250 x 10\"4 -6.44380 x l O \" 4 -1.62790 x l O - 4 1.59224 x 10\"2 Ai a 0 0 0 0 b -1.05682 9.86571 x.10\" 1 9.63470 x 10\"2 -1.28358 c 4.28233 x 10\"3 -2.39399 x 10\"3 1.02886 x IO - 5 4.86136 x 10\"3 A 2 a 0 0 0 0 b -1.49472 x 10 -2.70341 x 10 -7.53195 x 10\"3 -6.44203 x 10 c 1.52253 x 10\"2 5.68765 x 1 0 \" 2 -3.65100 x 1 0 ' 3 2.35996 x 10\"1 Based on data from: Al-Ghawas et al. (1989b), Xu et al. (1991), Xu et al. (1992), Li and Shen (1992), Rinker et al. (1994), Li and Lie (1994), Hagewiesche et al. (1995b), Hsu and Li (1997a). 2 6 4 Table E.2 Parameters of the Density Equation for Pure Fluids (eq. E.6) Pure Fluid ai a 2 a 3 H 2 0 0.863559 1.21494 x IO' 3 -2.57080 x 10\"6 MEA 1.19093 -4.29990 x 10 - 4 -5.66040 x 10' 7 DEA 1.20715 -1.51200 x 10 - 4 -7.66530 x 10' 7 MDEA 1.22864 -5.44540 x 10 - 4 -3.35930 x10 \" 7 A M P 1.15632 -6.76170 x 10^ -2.67580 x 10~7 Based on data from: Kell (1975), Perry and Chilton (1984), Al-Ghawas et al. (1989), Xu et al. (1991), Diguillo et al. (1992), Li and Shen (1992), Wang et al. (1994), Xu et al. (1992), Li and Lie (1994). 0.98 1.00 1.02 1.04 Calculated Density (g/cm3) Figure E.1 Measured and calculated densities at 303 and 323 K 265 Table E.3 Density of Aqueous Amine Blends at 303 K and 323 K (Total Amine = 25 wt%, Water = 75 wt%) Blend Density (g/crn^) T = 303 K T = 323K This From Error This From Error + work eq. (E.1) (%) work eq. (E.1) (%) M E A + A M P 0 + 25 1.000 0.995 0.53 0.987 0.983 0.36 5 + 20 1.000 0.998 0.25 0.987 0.986 0.02 10 + 15 1.000 1.000 0.02 0.987 0.989 -0.22 15 + 10 1.000 1.002 -0.21 0.990 0.992 -0.18 20 + 5 1.005 1.005 0.05 0.990 0.994 -0.45 25 + 0 1.010 1.006 0.36 0.997 0.996 0.02 DEA + A M P 0 + 25 1.000 0.995 0.53 0.987 0.983 0.40 5 + 20 1.000 1.000 -0.05 1.000 0.990 1.03 10 + 15 1.010 1.006 0.35 1.000 0.996 0.36 15 + 10 1.015 1.012 0.25 1.000 1.003 -0.29 20 + 5 1.015 1.018 -0.34 1.010 1.009 0.08 25 + 0 1.020 1.025 -0.46 1.006 1.016 -0.97 M E A + MDEA 0 + 25 1.010 1.018 -0.80 1.006 1.008 -0.18 5 + 20 1.015 1.016 -0.07 0.997 1.005 -0.89 10 + 15 1.010 1.013 -0.32 0.997 1.003 -0.65 15 + 10 1.010 1.011 -0.09 0.997 1.001 -0.42 20 + 5 1.000 1.009 -0.88 0.997 0.999 -0.22 25 + 0 1.010 1.006 0.36 1.000 0.996 0.36 DEA + MDEA 0 + 25 1.010 1.018 -0.80 1.006 1.008 -0.18 5 + 20 1.020 1.019 0.08 1.010 1.009 0.08 10 + 15 1.016 1.020 -0.44 1.006 1.011 -0.47 15 + 10 1.020 1.022 -0.17 1.010 1.012 -0.23 20 + 5 1.020 1.023 -0.31 1.010 1.014 -0.39 25 + 0 1.020 1.025 -0.46 1.020 1.016 0.42 + Error = 100 x (measured-calculated)/measured 266 E.2 Viscosity The viscosities of binary and ternary aqueous amine mixtures were calculated using the correlation of Hsu and Li (1997b). According to this correlation the kinematic viscosity of a liquid mixture, v m , can be obtained from the following equation: n lnv m =5v + £ x i l n v i (E.7) i=1 where, Xj is the mole fraction of each component in the mixture, Vj is the kinematic viscosity (|Oj/pi) of pure fluid i, and 5v is the deviation in kinematic viscosity, which for a ternary system is assumed to be: 5v = 5vf 2 +5vf 3 +5vf 3 (E.8) For a binary system, the 5vf2 is a function of temperature and mole fraction and can be calculated using the following Redlich-Kister type expression (Hsu and Li, 1997b): m 5v*2 = x 1 x 2 £ A i ( x 1 - x 2 ) i (E.8) i=0 where, Aj are the binary interaction parameters which are assumed to have the following temperature dependence: A : = a + — — (E.9) T + c 267 The viscosity of pure fluids required to calculate vi in eq. (E.7), is assumed to be the following expression: lnv = a 1 + — ^ — (E.10) T + a 3 The correlation coefficients a, b, c, a ^ a 2 and a 3 in eqs. (E.9) and (E.10) determined by Hsu and Li (1997b) are listed in Table E.4 and E.5. The parameter values are based on 499 data points measured in the temperature range of 303-353 K, including pure fluids, single-amine aqueous solutions, and ternary aqueous solutions of blended amines. The data include both their own viscosity measurements and those reported in the literature. The overall average absolute percentage deviation for the viscosity calculations was reported to be 1%. To check the accuracy of eq. (E.7), we measured the viscosity of aqueous amine mixtures at 303 K using a falling ball viscometer (Colepalmer Model P-08701-00). These measurements are listed in Table E.6 and a cross plot is presented in Figure E.2. The agreement between our measurements and the estimates from eq. (E.7) is within + 12%. 268 Table E.4 Binary Parameters of the Redlich-Kister Equation for the Viscosity Deviation (eqs. E.8 and E.9) Binary Pair Param. MEA+H 2 0 DEA+H2O MDEA+H2O AMP+H2O Ao a 2.58323 x 10' 1 2.76655 -6.26493 4.01239 b 5.05207 x 10 2 3.64795 x 10 3 1.59158 x 1 0 3 2.49856 x 10 2 c -2.23155 x 10 2 6.78430x10 -1.79649 x 10 2 -2.65712 x 1 0 2 A i a -7.20106 1.71593 x 10 2.87926 -2.68462 b 2.30838 x 10 3 -4.75487 x 10 3 -4.03039 x 1 0 3 0 c 0 0 0 0 Binary Pair MEA+MDEA MEA+AMP DEA+MDEA DEA+AMP Ao a 2.45414 x 10 -1.27691 x 10 2 -3 .71143x10 -5.71403 b -7.79167 x 10 3 4.00392 x 10 4 7.70451 x 10 3 0 c 0 0 0 0 A i a -1.56256 x 10 1.10232 x 10 2 -1.33407 x 10 -6.48408 x 10 b 0 0 0 0 c 0 0 0 0 Based on data from: Al-Ghawas et al. (1989), Xu et al. (1992), Rinker et al. (1994), Li and Lie (1994), Hagewiesche et al. (1995b), Song et al.(1996), Hsu and Li (1997b). 269 Table E.5 Parameters of the Viscosity Equation for Pure Fluids (eq. E.10) Pure Fluid ai a 2 a 3 H 2 0 -3.28285 4.56029 x 10 2 -1.54576 x 10 2 MEA -3.51312 8.93173 x 10 2 -1.59612 x 10 2 DEA -4.99689 1.58400 x 10 3 -1.57449 x 1 0 2 MDEA -4.06399 1.20196 x 10 3 -1.54419 x 1 0 2 A M P -4.36785 9.96598 x 10 2 -1.92984 x 10 2 Based on data from: Yaws et al. (1976), Al-Ghawas et al. (1989), Diguillo et al. (1992), Xu et al. (1992), Li and Lie (1994), Song et al. (1996). 1.5 2.0 2.5 3.0 Calculated Viscosity (cp) Figure E.2 Measured and calculated viscosities at 303 K. 270 Table E.6 Viscosity of Aqueous Amine Blends at 303 K (Total Amine = 25 wt%, Water = 75 wt%) Blend Viscosity Viscosity Error + (cp) (cp) (%) (This Work) (From eq. E.7) MEA + A M P 0 + 25 2.455 2.363 3.8 5 + 20 2.250 2.224 1.2 10 + 15 2.120 2.103 0.8 15 + 10 2.081 1.991 4.3 20 + 5 1.972 1.877 4.8 25 + 0 1.872 1.754 6.3 DEA + A M P 0 + 25 2.455 2.363 3.8 5 + 20 2.215 2.296 -3.7 10 + 15 2.372 2.228 6.1 15 + 10 2.155 2.162 -0.3 20 + 5 2.105 2.100 0.2 25 + 0 1.994 2.046 -2.6 MEA + MDEA 0 + 25 1.924 2.094 -8.9 5 + 20 1.927 2.014 -4.5 10 + 15 2.084 1.940 6.9 15 + 10 1.993 1.872 6.1 20 + 5 1.939 1.810 6.7 25 + 0 1.942 1.754 9.7 DEA + MDEA 0 + 25 1.924 2.094 -8.9 5 + 20 2.374 2.079 12.4 10 + 15 2.229 2.066 7.3 15 + 10 2.226 2.056 7.6 20 + 5 2.128 2.049 3.7 25 + 0 1.994 2.046 -2.6 + Error = 100 x (measured-calculated)/measured 271 APPENDIX F HENRY'S CONSTANT OF C 0 2 AND N 2 0 IN AQUEOUS AMINE F.1 N20 Analogy In order to predict the rate of absorption and desorption of C 0 2 in aqueous amine solutions or analyze the rate measurements in terms of reaction kinetics, it is essential to estimate the physical solubility of C 0 2 at various amine concentrations and temperatures. This physical solubility is calculated by multiplying the partial pressure of the gas above the solution with the inverse of the Henry's law constant. Since C 0 2 reacts with aqueous amines, its physical solubility in these solutions cannot be determined by direct measurements and an indirect method based on the N 2 0 analogy is commonly used. The analogy is based on the assumption that the ratio of the solubilities of N 2 0 and C 0 2 is the same in aqueous amine solutions as in water at the same temperature. In view of the similarities of N 2 0 and C 0 2 with regard to configuration, molecular volume and electronic structure, this assumption is considered reasonable and the physical solubility represented by Henry's constant can be estimated as follows: SOLUTIONS H H (F.1) 272 where H c c , 2 and H N 2 0 denote the Henry's constants of C 0 2 and N 2 0 in aqueous amines, and H£ 0 2 and H^o denote Henry's constants of C 0 2 and N 2 0 in water. F.2 Henry's Constant of C02 and N20 in Water The data for Henry's constant of C 0 2 in water and N 2 0 in water from the present work and those reported in the literature are presented in Tables F.1 and F.2. These data were correlated as a function of temperature according to the following correlations: Q C C 7 V Q O Log 1 0 (H C O 2 ) = 69.39562 - ^ -22.29261log 1 0(T)+0.003941096 T (F.2) 4373 35 Log 1 0 (H° 2 0 ) = 85 .8485- ^ - 27.716621 log 1 0 (T) + 0.003397123 T (F.3) where T is in Kelvin and H°C02 and H° 2 0 are in the units of kPa-m 3/kmol. The correlation for C 0 2 is valid over the temperature range from 273 to 523 K and the correlation for N 2 0 is valid from 278 to 393 K. As shown in Figures F.1 and F.2, these correlations represent the solubility data reasonably well. The average absolute percent deviation (AAD%) for C 0 2 - H 2 0 and N 2 0 - H 2 0 is 2.32% and 4.1% respectively. Figures F.1 and F.2 also indicate that there is a good agreement between literature results and those of the present study particularly in the temperature range of 293-350 K where historically most of the data are reported. 273 F.3 Henry's Constant ofN20 and C02 in Aqueous Amine Solutions To estimate the Henry's constant of C 0 2 in aqueous amine solutions at various amine concentrations and temperatures using N 2 0 analogy (eq. F.1), corresponding data for N 2 0 are needed. Therefore, an extensive literature survey was conducted and the data for the Henry's constant of N 2 0 in aqueous solutions of MEA, DEA, MDEA, A M P and their mixtures (i.e., MEA+MDEA, MEA+AMP, DEA+MDEA and DEA+AMP) were complied. These data are listed in Tables F.3 to F.10. It can be seen from these tables that the published data are limited to absorber temperatures (i.e. 293-333 K) only. The data corresponding to stripper temperatures do not exist in the open literature and are usually obtained by extrapolating the low temperature data. However, in the present study it was found that these extrapolations might lead to inaccurate prediction of mass transfer rates as the literature correlations for H ^ 0 and H N z 0 proposed by Versteeg and van-Swaaij (1988), Li and Lai, (1995) and Li and Lee, (1996) over predict the Henry's constant value at stripper temperature by a factor of 3. Note that these correlations have been developed based on the solubility data up to 323 K. Consequently, in this work the solubility of N 2 0 in aqueous solutions of MEA, DEA, MDEA, AMP, MEA+MDEA, MEA+AMP, DEA+MDEA and DEA+AMP were measured in the temperature range of 293-393 K and amine concentration of 10-30 wt%. These data are presented in Tables F.3 to F.10. The experimental apparatus and procedure used was identical to that described in Chapter 6 (see Figure 6.1). 274 To correlate the solubility of N2O in amine solutions, a semiempirical model proposed by Wang et al. (1992) was used. According to this method the Henry's constant of N2O in mixed solvent system can be obtained from the following equation: l nH N 2 0 =H E + X o i l nH^ 0 (F.4) i=i where H N 2 0 is the Henry's constant of N 2 0 in the mixed solvent, H E is the excess Henry's constant, H' N 2 0 is the Henry's constant of N 2 0 in pure solvent i, and 4>j is the volume fraction of solvent i. The volume fraction is calculated as * . = ^ - (F-5) i=1 where Vj is the molar volume of pure solvent i, and Xj is the mole fraction of solvent i. Wang et al. (1992) measured the Henry's constants of N2O in pure amines such as MEA, DEA, MDEA and A M P in the temperature range of 293-355 K and correlated their data as H S n e = a i e x p (F.6) where ai and a2 are correlation coefficients and are listed in Table F.11. The densities of pure solvents were calculated according to the method described in Appendix E. The Henry's constant of N 2 0 in pure water was calculated using eq. (F.3). The excess Henry's constant for binary system was correlated as: 275 (F.7) and that for ternary solvent systems was correlated as: Hyk =®&laii +0 ,O k a I k +OjCDka j k + 0>ikaijk (F.9) where CCJJ, aik, oijk and 0% are the interaction parameters. For ternary systems (e.g. H 2 0-MEA-MDEA) , the parameters ay and ccik represent the water-amine interactions (e.g. H 2 0 - M E A and H 2 0-MDEA) , cqk represent the amine-amine interaction (e.g. MEA-MDEA) and ayk represent the amine-amine-water interaction (e.g. H 2 0-MEA-MDEA) . As in the work of Wang et al. (1992), ap was set to be constant and ay, aik, % were assumed to have the following temperature dependence: where is T in Kelvin and ai and a 2 are constants. In this work, first the constants for binary systems (i.e. H 2 0+MEA, H 2 0+DEA, H 2 0+MDEA and H 2 0+AMP) were determined by regressing the data presented in Tables F.3 to F.6 and then using those values the constants for ternary systems (i.e. H 2 0+MEA+MDEA, H 2 0+MEA+AMP, H 2 0+DEA+MDEA and H 2 0+DEA+AMP) were estimated by regressing the data given in Tables F.6 to F.10. The regression was done using the software package G R E G supplied by Stewart & Associate Engineering Software Inc. The estimates of the regression coefficients for both binary and ternary systems are presented in Table F.12. The comparisons of the calculated and experimental Henry's constants of N 2 0 in binary and ternary aqueous amine a y = a 1 + a 2 / T (F.8) 276 solutions are shown in Figures F.3 and F.4 respectively. The estimates of the average absolute percent deviation (AAD%) for each system are reported in Table F.12. The results are satisfactory. The rather large deviation may be because the regression was performed using data from all sources. Also, the solubility data for mixed amine systems studied here are not plenty. The regression results indicate that the N 20 solubility data for H20+DEA+MDEA and H20+DEA+AMP reported by Li and Lee (1996) do not correlate well with the experimental data obtained in this work and those reported by other sources as indicated by Figures 3 and 4. Overall, the N 20 solubilities in the aqueous amine systems studied in this work are well correlated using the method of Wang et al. (1992). The correlations coefficients obtained in this study are valid over the temperature range of 293-393 K and the amine concentration of 10-30 wt%. With all the other quantities in eq. (F.1) estimated, the Henry's constant of C 0 2 in unloaded aqueous amine solutions can be calculated. For the sake of brevity the results of these calculations are not presented here. 277 Table F.1 Henry's constant of C 0 2 in water T (K) H c o 2 (kPa m3/kmol) Reference T (K) H c o 2 (kPa m 3/kmol) Reference 293 2630 This work 318 4854 Versteeg & 304 3500 it 323 5155 van Swaaij (1988) 313 4234 if 333 6135 II 323 5179 ti 344 7143 II 333 6233 II 350 7576 II 343 7296 if 355 8333 II 353 8305 II 360 9259 II 363 9302 II 298 2889 Malinin (1974) 373 10056 II 308 3723 II 383 10828 II 323 5192 II 393 11225 II 348 7257 II 303 3420 Li & Lee (1996) 373 9829 II 308 3835 II 423 12485 II 313 4226 II 473 11913 II 303 3382 Li & Lai (1995) 523 9760 II 313 4227 it 383 9971 Takenouchi & 323 5136 II 423 12513 Kennedy (1964) 298 2993 Saha et al. (1993) 473 12652 II 293 2744 II 523 11984 n 313 4572 II 373 9895 Ellis & Golding 333 6476 II 423 13108 (1963) 353 8600 it 450 14362 it 303 3394 Al-Ghawas et al. 473 13496 it 313 4250 (1989) 523 12099 II 323 5167 II 273 1328 Perry et al. (1963) 291 2469 Versteeg & 278 1598 II 292 2410 van Swaaij (1988) 283 1897 II 292 2571 II 288 2225 II 293 2632 II 293 2590 II 298 2967 if 298 2991 II 298 3040 ii 303 3392 II 303 3571 II 308 3812 II 308 3937 ti 313 4249 it 311 4098 it 318 4687 it 313 4219 it 323 5161 II 313 4202 it 333 6219 II 278 Table F.2 Henry's constant of N 2 0 in water T HN,O Reference T H N 2 0 (kPa m3/kmol) Reference (K) (kPa m3/kmol) (K) 293 3701 This work 291 3344 Versteeg & 304 4903 II 292 3484 van Swaaij (1988) 313 5849 i t 293 3333 II 323 7117 « 293 3425 n 333 8461 i t 298 4132 II 343 9780 i t 299 3774 i i 353 10911 i t 303 4950 II 363 11845 II 308 5263 i i 373 12745 II 313 5917 II 383 13534 II 313 6061 i t 393 14013 II 318 6993 II 303 4465 Li & Lee (1996) 323 7143 i t 308 4813 i t 323 7407 II 313 5822 II 340 10309 t i 303 4406 Li & Lai (1995) 353 12821 II 313 5725 i t 359 14085 i t 323 7264 II 298 4173 Haimour (1984) 298 4234 Browning (1994) 298 4132 Sada et al. (1977) 293 3694 Sandall et. al. 298 4154 Joosten (1972) 313 6339 (1993) 298 4171 Sada&Kito (1972) 333 9104 II 298 3906 Duda and Vrentas 353 11223 II 313 6211 (1968) 298 4176 Xu et al. 278 2134 Perry et al. (1963) 323 7254 (1991) 283 2572 II 348 12348 II 288 3029 II 293 3393 Al-Ghawas et al. 293 3617 i t 298 3879 (1989) 298 4114 II 303 4321 i t 303 4743 II 308 4703 i t 308 5539 II 313 5009 t i 298 4212 Markham & Kobe (1941) 279 Table F.3 Henry's constant of N 2 0 in aqueous MEA solutions T (K) CMEA (wt%) H N 2 0 (kPa m3/kmol) Reference T (K) CMEA (wt%) H N 2 0 (kPa m3/kmol) Reference 293 10.0 3944 This work 303 19.6 4920 Lttel et al. 303 10.0 5146 \" 303 19.7 4901 (1992c) 313 10.0 6296 \" 318 1.2 7223 II 323 10.0 7324 \" 318 2.6 6976 II 333 10.0 8720 \" 318 5.4 6957 II 353 10.0 11193 \" 318 10.0 7013 II 373 10.0 12840 \" 318 15.1 7088 u 393 10.0 13925 \" 318 19.9 6921 u 293 20.0 4250 318 21.6 7184 u 303 20.0 4998 333 1.4 9107 u 313 20.0 6205 \" 333 3.6 9137 u 323 20.0 7373 u 333 5.4 9018 It 333 20.0 8494 u 333 9.8 9077 a 353 20.0 10460 u 333 10.9 8817 u 373 20.0 12104 a 333 16.0 8817 u 393 20.0 12764 a 333 20.4 9167 u 293 30.0 4189 u 333 22.8 8264 u 303 30.0 5165 u 348 1.3 11001 u 313 30.0 6220 u 348 2.6 10445 u 323 30.0 7222 u 348 5.5 10755 u 333 30.0 8322 u 348 11.2 10676 a 353 30.0 10081 u 348 16.6 10715 a 373 30.0 11175 u 348 18.0 9774 u 393 30.0 12597 u 348 22.7 9807 u 303 30.0 4362 Li & Lai 348 24.3 9333 u 308 30.0 4696 (1995) 298 6.7 4132 Ladha et al. 313 30.0 5127 u 298 12.5 4202 (1981) 303 1.1 4564 Lttel et al. 303 2.4 4910 (1992c) 303 4.8 4780 it 303 9.5 4717 it 303 13.2 4863 II 280 Table F.4 Henry's constant of N 2 0 in aqueous DEA solutions T (K) CDEA (wt%) H N 2 0 (kPa m3/kmol) Reference T (K) CDEA (wt%) H N 2 0 (kPa m3/kmol) Reference 293 10.0 3810 This work 303 2.6 5018 Littel et al. 303 10.0 4768 ii 303 3.2 4872 (1992c) 313 10.0 5772 II 303 6.3 5028 II 323 10.0 6982 II 303 6.3 5120 II 333 10.0 8272 II 303 8.3 4949 II 353 10.0 10971 II 303 9.0 5079 II 373 10.0 12352 II 303 12.6 5110 II 393 10.0 12984 II 303 17.9 5226 II 293 20.0 4108 n 303 26.6 5429 II 303 20.0 5111 ti 303 36.8 5699 n 313 20.0 6333 ti 318 2.8 7088 n 323 20.0 7267 u 318 4.4 7050 a 333 20.0 8291 a 318 7.1 7050 u 353 20.0 10743 u 318 8.6 7204 a 373 20.0 12006 u 318 14.3 7323 u 393 20.0 13681 a 318 15.9 7145 u 293 30.0 4064 u 318 25.2 7323 a 303 30.0 5128 u 318 34.6 7685 a 313 30.0 6824 u 333 4.3 8733 u 323 30.0 7975 u 333 8.9 8545 II 333 30.0 9169 u 333 17.8 8679 II 353 30.0 11156 u 333 25.4 8733 it 373 30.0 12875 u 333 33.2 8873 ii 393 30.0 14197 u 298 2.0 4235 Versteeg & 303 30.0 6890 Li & Lee 298 2.1 4206 Oyeaar 308 30.0 9613 (1996) 298 4.0 4286 (1989) 313 30.0 14377 u 298 5.5 4272 u 288 10.8 3293 Haimour 298 7.7 4362 u 288 21.3 3597 (1990) 298 11.2 4546 a 288 31.5 4205 u 298 15.4 4505 il 293 10.8 5016 a 298 29.0 4496 ii 293 21.3 3577 u 298 36.0 4764 il 293 31.6 3779 u 298 37.0 4848 n 298 10.8 4499 u 298 43.8 4985 u 298 21.4 5826 u 298 56.3 5151 a 298 31.6 3972 a 298 57.3 5140 u 303 10.8 4124 u 298 75.8 6132 u 303 21.4 5076 u 298 78.3 4719 a 303 31.7 7103 u 298 80.8 4424 u 298 80.8 4563 u 281 Table F.4 Henry's constant of N 2 0 in aqueous DEA solutions Continued T (K) CDEA (wt%) ^N 2 0 (kPa m3/kmol) Reference T (K) CDEA (wt%) H N 2 0 (kPa m3/kmol) Reference 298 4.7 4164 Versteeg & 298 4.7 4164 Sada et al. 298 14.5 4393 van Swaaij 298 10.4 4213 (1977) 298 14.7 4432 (1988) 298 20.9 4385 it 298 16.1 4324 \" 298 23.7 4456 it 298 20.9 4385 298 31.3 4631 it 298 22.9 4571 298 5.2 4149 Ladha et al. 298 23.7 4456 \" 298 10.4 4202 (1981) 298 24.2 4666 \" 298 20.6 4367 it 298 24.5 4480 298 31.3 4631 \" 282 Table F.5 Henry's constant of N 2 0 in aqueous M D E A solutions T (K) CMDEA (wt%) H N 2 0 (kPa m 3 /kmol) Reference T (K) CMDEA (wt%) H N 2 0 ( kPa m 3 /kmol) Reference 293 10.0 3960 This work 298 30.0 4565 A l - G h a w a s 303 10.0 5167 \" 298 40.0 4840 et a l . 313 10.0 6410 \" 298 50.0 5229 (1989a) 323 10.0 7422 \" 303 10.0 4483 \" 333 10.0 8845 \" 303 20.0 4892 \" 353 10.0 11210 \" 303 30.0 5101 •* 373 10.0 13025 \" 303 40.0 5429 \" 393 10.0 14039 \" 303 50.0 5631 293 20.0 4110 \" 308 10.0 4940 \" 303 20.0 4965 \" 308 20.0 5172 313 20.0 6410 \" 308 30.0 5376 •* 323 20.0 7558 u 308 40.0 5668 333 20.0 8615 a 308 50.0 5970 \" 353 20.0 10363 u 313 10.0 5205 \" 373 20.0 11389 u 313 20.0 5630 a 393 20.0 12951 a 313 30.0 5898 u 293 30.0 4246 u 313 40.0 6206 u 303 30.0 5179 u 313 50.0 6426 u 313 30.0 6065 u 323 10.0 5563 u 323 30.0 6770 u 323 20.0 5841 u 333 30.0 8311 u 323 30.0 6074 u 353 30.0 10089 u 323 40.0 6220 u 373 30.0 11495 u 323 50.0 6370 u 393 30.0 12339 u 293 15.3 3663 A l - G h a w a s 303 30.0 5169 Li & Lai 293 20.1 3800 et a l . 308 30.0 5585 (1995) 293 30.2 4128 (1989b) 313 30.0 6188 u 298 15.3 4173 u 288 10.0 3103 A l - G h a w a s 298 20.1 4308 u 288 20.0 3273 et a l . 298 30.2 4623 u 288 30.0 3654 (1989a) 303 15.3 4638 u 288 40.0 4036 u 303 20.1 4769 u 288 50.0 4154 u 303 30.2 5070 it 293 10.0 3497 u 308 15.3 5039 a 293 20.0 3658 u 308 20.1 5167 a 293 30.0 4039 u 308 30.2 5453 a 293 40.0 4349 a 313 15.3 5363 u 293 50.0 4616 a 313 20.1 5490 it 298 10.0 3996 a 313 30.2 5762 u 298 20.0 4289 u 283 Table F.5 Henry's constant of N 2 0 in aqueous MDEA solutions Continued T (K) CMDEA (wt%) (kPa m3/kmol) Reference T (K) CMDEA (wt%) ^ N 2 0 (kPa m3/kmol) Reference 293 4.1 3566 Versteeg & 318 6.0 6994 Versteeg & 293 4.9 3588 van Swaaij 318 11.3 6609 van Swaaij 293 8.5 3663 (1988) 318 11.9 7126 (1988) 293 9.4 3685 318 22.2 6994 \" 293 11.8 3702 318 30.4 6976 \" 293 13.0 3719 318 31.0 7364 \" 293 16.3 3818 333 6.0 8873 \" 293 17.7 3794 333 9.2 8624 293 21.9 3873 333 12.0 8931 \" 293 30.6 4289 333 15.4 9167 298 7.3 4235 333 18.0 8545 \" 298 10.0 4164 u 333 22.4 8733 \" 298 14.6 4316 a 333 24.6 8571 298 14.8 4464 u 333 30.7 8733 n 298 19.3 4546 a ' 333 31.3 9077 \" 298 19.5 4529 u 288 10.0 3207 Haimour 298 20.3 4480 M 288 15.0 3272 et al. 298 21.9 4596 a 288 20.0 3386 (1984) 298 22.2 4728 u 288 30.0 3773 u 298 28.2 4858 u 288 40.0 4162 u 298 29.3 4955 u 293 10.0 3662 tt 298 31.9 6057 a 293 15.0 3737 tt 308 7.4 5391 u 293 20.0 3830 tt 308 9.7 5414 u 293 30.0 4218 a 308 11.8 5495 u 293 40.0 4541 tt 308 14.8 5483 u 298 10.0 4273 u 308 15.6 5507 tt 298 15.0 4404 u 308 17.2 5542 tt 298 20.0 4561 u 308 17.8 5483 u 298 30.0 4846 u 308 19.7 5615 if 298 40.0 5126 u 308 21.0 5653 u 308 10.0 5530 u 308 21.8 5678 u 308 15.0 5602 tt 308 22.1 5628 u 308 20.0 5772 u 308 30.8 5941 u 308 30.0 5984 tt 318 5.8 6295 u 308 40.0 6285 u 284 Table F.6 Henry's constant of N 2 0 in aqueous A M P solutions T (K) C A M P (wt%) HN2O (kPa m3/kmol) Reference T (K) C A M P (wt%) H N 2 0 (kPa m3/kmol) Reference 293 10.0 3456 This work 288 4.5 3243 Saha et al. 302 10.0 4489 tt 293 4.5 3737 (1993) 313 10.0 5858 \" 298 4.5 4216 tt 323 10.0 7293 n 303 4.5 4751 tt 334 10.0 8952 II 288 8.9 3413 ti 353 10.0 10796 II 293 8.9 3941 II 373 10.0 13391 298 8.9 4446 II 393 10.0 14886 it 303 9.0 5006 I I 294 20.0 3857 I I 288 13.3 3550 II 304 20.0 4931 » 293 13.4 4098 it 312 20.0 5936 it 298 13.4 4613 it 323 20.0 7230 u 303 13.4 5179 ti 333 20.0 8440 a 288 17.8 3717 II 353 20.0 10431 u 293 17.8 4293 II 373 20.0 12423 u 298 17.9 4826 II 393 20.0 13360 u 303 17.9 5405 it 294 30.0 5159 a 303 1.7 4863 it 303 30.0 6032 u 303 3.5 4910 u 313 30.0 6729 a 303 6.9 4988 u 323 30.0 7516 a 303 14.0 5038 u 333 30.0 8429 u 303 17.6 5237 a 343 30.0 9301 u 303 22.2 5383 u 353 30.0 10222 u 303 28.2 5686 u 363 30.0 10988 u 303 29.1 5712 u 373 30.0 11929 u 283 17.8 3213 Xu et al. 383 30.0 12973 u 288 17.8 3683 (1991b) 393 30.0 12861 u 298 17.9 4617 u 303 30.0 5856 Li and Lai 310 18.0 5986 u 308 30.0 6545 (1995) 283 26.6 3518 u 313 30.0 7531 u 288 26.7 4020 u 298 26.8 4842 u 310 27.0 6313 a 285 Table F.7 Henry's constant of N 2 0 in MEA+MDEA+H 2 0 T (K) CMEA (wt%) CMDEA (wt%) H N 2 0 (kPa m3/kmol) Reference 293 12.5 12.5 3660 This work 303 12.5 12.5 4791 a 313 12.5 12.5 5764 a 323 12.5 12.5 6645 H 333 12.5 12.5 7899 ii 353 12.5 12.5 9606 ii 373 12.5 12.5 10802 li 393 12.5 12.5 11697 II 303 24.0 6.0 4481 Li & Lai (1995) 303 18.0 12.0 4580 II 303 12.0 18.0 4696 II 303 6.0 24.0 4868 II 308 24.0 6.0 4860 II 308 18.0 12.0 4957 it 308 12.0 18.0 5156 u 308 6.0 24.0 5392 a 313 24.0 6.0 5277 u 313 18.0 12.0 5396 tt 313 12.0 18.0 5624 tt 313 6.0 24.0 5935 tt 303 1.5 28.5 5140 Hagewiesche et al. 303 3.0 27.0 5270 (1995b) 303 4.5 25.5 5360 u 303 2.0 38.0 5580 a 303 4.0 36.0 5670 u 303 6.0 34.0 5850 a 313 1.5 28.5 6100 u 313 3.0 27.0 6290 u 313 4.5 25.5 6480 u 313 2.0 38.0 6270 u 313 4.0 36.0 6340 u 313 6.0 34.0 6440 u 323 1.5 28.5 6350 u 323 3.0 27.0 6550 u 323 4.5 25.5 6590 tt 323 2.0 38.0 6290 it 323 4.0 36.0 6320 It 323 6.0 34.0 6430 it 298 10.0 40.0 5680 Browning & 298 20.0 30.0 5465 Weiland (1994) Table F.8 Henry's constant of N 2 0 in MEA+AMP+H 2 0 T CMEA CAMP H N 2 0 (kPa m3/kmol) Reference (K) (wt%) (wt%) 293 12.5 12.5 3919 This work 303 12.5 12.5 4920 a 313 12.5 12.5 5977 u 323 12.5 12.5 7054 if 333 12.5 12.5 8114 II 353 12.5 12.5 10049 II 373 12.5 12.5 11570 ll 393 12.5 12.5 12565 II 303 24.0 6.0 4548 Li & Lai (1995) 303 18.0 12.0 4911 II 303 12.0 18.0 5415 II 303 6.0 24.0 5597 II 308 24.0 6.0 5000 II 308 18.0 12.0 5656 it 308 12.0 18.0 5961 tt 308 6.0 24.0 6304 u 313 24.0 6.0 5545 u 313 18.0 12.0 6131 u 313 12.0 18.0 6813 u 313 6.0 24.0 7145 tt 287 Table F.9 Henry's constant of N 2 0 in DEA+MDEA+H 2 0 T (K) CDEA (wt%) CMDEA (wt%) H N 2 0 (kPa m3/kmol) Reference 293 12.5 12.5 5106 This work 303 12.5 12.5 6313 a 313 12.5 12.5 7879 u 323 12.5 12.5 9140 II 333 12.5 12.5 10774 II 353 12.5 12.5 12927 it 373 12.5 12.5 14670 M 393 12.5 12.5 15264 II 303 24.0 6.0 6586 Li & Lee (1996) 303 18.0 12.0 6081 II 303 12.0 18.0 5938 it 303 6.0 24.0 5422 it 308 24.0 6.0 8480 it 308 18.0 12.0 7663 u 308 12.0 18.0 6797 tt 308 6.0 24.0 6090 it 313 24.0 6.0 11537 if 313 18.0 12.0 9632 tf 313 12.0 18.0 7979 u 313 6.0 24.0 6887 u 298 10.0 40.0 5680 Browning & 298 20.0 30.0 5465 Weiland (1994) 288 Table F.10 Henry's constant of N 2 0 in DEA+AMP+H 2 0 T CDEA C A M P HN2O (kPa m3/kmol) Reference (K) (wt%) (wt%) 293 12.5 12.5 6048 This work 303 12.5 12.5 7450 u 313 12.5 12.5 8654 a 323 12.5 12.5 10008 II 333 12.5 12.5 11334 11 353 12.5 12.5 13970 II 373 12.5 12.5 15917 it 393 12.5 12.5 16543 II 303 24.0 6.0 6579 Li & Lee (1996) 303 18.0 12.0 6293 II 303 12.0 18.0 6164 II 303 6.0 24.0 6037 II 308 24.0 6.0 8580 II 308 18.0 12.0 7970 u 308 12.0 18.0 7439 u 308 6.0 24.0 7007 u 313 24.0 6.0 11520 u 313 18.0 12.0 10174 u 313 12.0 18.0 9054 u 313 6.0 24.0 8194 u 289 Table F.11: Parameters in eq. (F.6) for Henry's constant of N 2 0 in pure amines (Wang et al., 1992) System a i a 2 No. of data A A D % + M E A 1.207 x 10 5 -1136.5 6 1.39 DEA 1.638 x 10 5 -1174.6 5 2.43 MDEA 1.524 x 10 5 -1312.7 5 0.90 A M P 8.648 x 10 4 -1205.2 6 1.55 + A A D % = average absolute percent deviation Table F.12: Parameters in excess Henry's constant of N 2 0 in binary and ternary solvent systems (this work) System ai a 2 0C123 No. of data A A D % + M E A + H 2 0 -2.14841 1034.851 59 3.95 D E A + H 2 0 -2.697683 1263.981 97 7.73 M D E A + H 2 0 -2.72350 1342.437 147 5.64 A M P + H 2 0 -1.367139 1089.998 62 3.88 M EA+M D EA+ H 2 0 33.68282 -1436.122 -47.71418 40 5.18 MEA+AMP+H 2 0 93.32045 -5199.785 -110.8438 20 4.53 DEA+MDEA+H 2 0 -27.38076 2762.749 42.73698 22 7.63 DEA+AMP+H 2 0 -50.12477 4131.152 72.02965 20 7.08 + A A D % = average absolute percent deviation 2 9 0 16000 — 12000 F o E CD D_ x • CM O O X 8000 F 4000 0 • This work o Literature data (Table F.1) — Correlation (Eq. F.2) _ i i _ _ J I L i I i i i i 250 300 350 400 450 500 550 Temperature (K) Figure F.1 Henry's constant of C 0 2 in water 16000 — 12000 o E 2 8000 o CM X I i 4000 F o • This work o Literature data (Table F.2) — Correlation (Eq. F.3) - i i i _ j i _ i i 250 275 300 325 350 Temperature (K) 375 400 Figure F.2 Henry's constant of N 2 0 in water 291 0 4000 8000 12000 16000 Measured H N 2 C - A M (kPa n r v V k m o l ) Figure F.3 Measured and calculated values of Henry's constant of N 2 0 in aqueous amine solutions between 288 to 393 K. 0 4000 8000 12000 16000 Measured H N 2 0 . A M (kPa m3/kmol) Figure F.4 Measured and calculated values of Henry's constant of N 2 0 in aqueous amine blends between 288 to 393 K. 292 APPENDIX G DIFFUSIVITY OF C 0 2 AND N 2 0 IN AQUEOUS AMINE SOLUTIONS G.3 N2Q Analogy Since CO2 reacts with aqueous amines, its diffusivity in these solutions cannot be measured by direct absorption experiments and an indirect method based on N 20-Anology is frequently used. This analogy is based on the assumption that under identical conditions, the ratios of the diffusivities of C0 2 and N 2 0 in water and aqueous amine solutions are equal: where D C 0 2 and D N 2 0 denote the diffusivity of C 0 2 and N 2 0 in amine solution, and Dco2 and D£ 2 0 denote the diffusivity of C 0 2 and N 2 0 in water. In order to calculate D c c . 2 using eq. (G.1), the values of D°C02, D£ 0 and D N 2 0 are required which were calculated from the correlations given below. G.2 Diffusivity of C02 and N20 in Water Diffusivities of C 0 2 and N 2 0 in water were calculated using the following equations: D (G.1) D D° L - 'M (G.2) 293 5.2457 x10 \" 6 exp -2388.9 (G.3) where T is in Kelvin and D°CCl2 and D^o are in the units of m 2/s. These correlations were developed from the data acquired in this work and those reported in the literature. These data are tabulated in Tables G.1 and G.2; also, they are plotted on Figures G.1 and G.2. Evidently, the agreement between the measured and predicted values is good. The average absolute percent deviation (AAD%) for CO2-H2O system is 4 .1% and for N 2 0 - H 2 0 system is 10.9%. The rather large deviation for N 2 0 - H 2 0 system is because the data reported by A l -Ghawas et al. (1989a, 1989b) are about 10-70% lower then those measured in this work and those reported in other sources (see Table G.2). In general, the diffusion coefficients measured in this work are in good agreement with the literature values. G.3 Diffusivity of N20 and Aqueous Amine Solutions Historically, the diffusivity of N2O in aqueous amine solutions at various temperatures and amine concentrations is calculated using the following modified Stokes-Einstein relation: In order to check the above relationship, N 2 0 diffusivity data for MEA, DEA, MDEA, A M P and their mixtures (MEA+MDEA, MEA+AMP, DEA+MDEA & DEA+AMP) were compiled from various literature sources. These data along with those obtained in this work are tabulated in Tables G.3 to G.10. The NjOM-sol — '-'N2OM'H20 (G.4) 294 corresponding Stokes-Einstein plots for single and mixed amine systems are presented in Figures G.3 and G.4 respectively. It can be seen from these plots that the Stokes-Einstein type relationship does not represent the experimental data well. The average deviation (AAD%) for single amine systems is about 20% and that for mixed amine systems is about 30%. Therefore, in this work new correlations were developed. The data for single amine systems were correlated as: D N z 0 =(5.2457x10\"6 + A i 1 C A M + A i 2 C A M ) e x p | 2388.9 (G.5) and the data for mixed amine systems were correlated as: DN 2o = '5.2457X10-6 + A L 1 C A M , + A 1 2 C A M , + A 2 1 C A M 2 ^ + A 2 2 C A M 2 + B 1 2 C A M ' C A M 2 J exp 2388.9 (G.6) where T is in Kelvin, CAM is in kmol/m 3 and D N 2 Q are in the units of m 2/s. The interaction parameters An, A i 2 , and B i 2 were assumed to have the following temperature dependence: A j^A j j .B^ - a , (G.7) where T is in Kelvin and ai and a 2 are constants. In this work, first the constants for single amine systems were determined by regressing the data given in Tables G.3 to G.6 and then using these results, the constants for mixed amine systems were estimated by regressing the data given in Tables G.7 to G.10. The regression was done using the software 295 package G R E G supplied by Stewart & Associate Engineering Software Inc. The estimates of the regression coefficients for single and mixed amine systems are presented in Table G.11 and Table G.12. A comparison of the measured and calculated diffusion coefficients is shown in Figures G.5 and G.6. In general, the agreement is satisfactory. The overall A A D % for single amine systems is about 13% and that for mixed amine systems is about 9%. In light of the fact that different sources have used a different absorption apparatus to measure diffusivity, this much deviation is expected and the correlations can be safely used. Note that for C A M = 0, these correlations (eqs. G.5 and G.6) reduce to the correlation for N 2 0 - H 2 0 system (eq. G.3). This unique and very important feature does not exist in other similar correlations proposed in the literature (Li and Lai, 1995 and Li and Lee, 1996). G.4 Diffusivity of C02 and Aqueous Amine Solutions Once the diffusivity of C 0 2 in water, N 2 0 in water and N 2 0 in aqueous amines are known, the diffusivity C 0 2 in aqueous amine solution was calculated using N 20-analogy given by eq. (G.1). G.5 Diffusivity of the Alkanolamines in Aqueous Solutions The diffusion coefficients of various amines in their aqueous solutions were calculated using the correlation developed by Glasscock (1990): D A M = 2 . 5 x 1 0 - 1 0 Mw 298 ] u ^ l n y (G.8) 296 The density of pure amine at 298 K ( p A ^ ) was calculated using eq. (E.6) and the viscosities of pure water (|iH20) and aqueous amine solutions (u.^,) were calculated from eqs. (E.10) and (E.7) respectively. The diffusion coefficients of all other ionic species were set equal to D A M -2 9 7 10.0 _C/3 CM E x O CM o o o Q 1.0 b 0.1 o Data from Table G.1 — Eq. (G.2) _ l I L J I I I 1 I 1_ 1 2 3 4 I 1000/T (1/K) Figure G.1 Diffusivity of C 0 2 in water as a function of temperature 10.0 .CO CM E x a> O O CM z o Q 1.0 0.1 o Data from Table G.2 — Eq. (G.3) - i i i i • • • i i i i_ 1 2 3 4 5 1000/T (1/K) Figure G.2 Diffusivity of N 2 0 in water as a function of temperature. 298 7.0 6.0 5.0 J 4 . 0 CN O Q z 3.0 2.0 1.0 0.0 o MEA+H20 • D E A + H 2 0 x MDEA+H20 A AMP+H20 x X X X X X A X ^x x x x x x x x 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 (Viscosity of Amine Sol.A/iscosity of Water) 0 ' 8 Figure G.3 Stokes-Einstein plot for diffusivity of N 2 0 in aqueous alkanolamine solutions. 8.0 6.0 o CM z Q ^5 4.0 CNJ z o Q 2.0 0.0 ; oMEA+MDEA+H20 : x MEA+AMP+H20 : • DEA+MDEA+H20 cP • ' a ; A DEA+AMP+H20 CO • n > • LJ / S< ' 1 1 ! : l 1 ' 1 1 ' ' 1 ' ' i f \\ 1 I 1 I ! 1 1 . . . i i 1 , 1 1 1 1 0.0 2.0 4.0 6.0 8.0 (Viscosity of Amine Sol.A/iscosity of Water) 0 ' 8 Figure G.4 Stokes-Einstein plot for diffusivity of N 2 0 in aqueous alkanolamine blends. 299 Figure G.5 Measured and calculated diffusivities of N 2 0 in aqueous amine solutions. 3.0 u ra O CO E x cn O O CN z a •a cu 2.0 IS 1.0 0.0 : o MEA+MDEA+H20 ; x MEA+AMP+H20 : • DEA+MDEA+H20 O >r [ A DEA+AMP+H20 DWK ° I I I ! I 1 ! 1 i ! 1 i 1 1 • 0.0 0.5 1.0 1.5 2.0 Measured D N 2 o (10 9 xm 2 / s ) 2.5 3.0 Figure G.6 Measured and calculated diffusivities of N 2 0 in aqueous amine blends. 300 Table G.1 Diffusivity of C 0 2 in water T 1 0 9 x D ° C O 2 (m2/s) Reference T 1 0 9 x D ° C O 2 (m2/s) Reference (K) (K) 298 1.75 This work 292 1.65 Versteeg & 308 2.12 t i 293 1.68 van Swaaij (1988)+ 318 3.11 i i 293 1.64 II 328 3.65 i t 293 1.60 II 298 2.03 Rowley et al. (1998) 293 1.77 II 303 2.23 Li & Lee (1996) 298 1.98 tt 308 2.51 u 298 1.87 II 313 2.80 i t 298 1.95 II 303 2.12 Li & Lai (1995) 298 2.05 II 308 2.46 i t 298 1.85 t i 313 2.78 u 298 2.00 t t 293 1.76 Tamimi et al. (1994a) 298 1.94 t t 298 1.94 u 298 1.87 n 303 2.20 u 298 1.90 i t 313 2.93 tt 298 1.74 t l 333 4.38 II 303 2.29 u 353 6.58 u 303 2.15 II 368 8.20 u 308 2.41 II 298 1.93 Xu et al. (1991b) 308 2.18 i t 273 0.96 Versteeg & 313 2.80 tt 280 1.15 van Swaaij (1988) + 318 3.03 f l 283 1.46 n 325 3.61 u 288 1.60 328 3.68 i f 288 1.39 338 4.40 ft 289 1.57 II 338 4.30 It 291 1.71 • i 348 5.40 II +Versteeg & van Swaaij (1988) includes data from 30 different sources. 301 Table G.2 Diffusivity of N 2 0 in water T (K) 1 0 9 x D ° 2 O (m2/s) Reference T (K) 1 0 9 x D ° 2 O (m2/s) Reference 297 1.59 This work 288 1.39 Versteeg & 303 2.19 » 290 1.70 van Swaaij (1988)+ 313 2.61 ft 291 1.47 II 323 3.00 u 292 1.56 II 303 2.11 Li & Lee (1996) 293 1.48 i i 308 2.34 n 293 1.52 ft 313 2.70 u 293 1.92 ft 303 2.01 Li & Lai (1995) 293 1.74 ft 308 2.30 u 293 1.45 \" 313 2.65 « 293 1.65 293 1.84 Tamimi et al. (1994a) 298 2.09 \" 298 1.88 tt 298 1.86 303 1.93 tt 298 1.69 313 2.61 tt 298 1.92 333 4.51 t i 298 1.78 353 6.50 t f 298 1.88 368 7.30 u 298 1.80 294 1.59 Saha eta l . (1993) 303 2.27 302 1.95 tf 304 2.35 \" 312 2.51 308 2.03 \" 318 2.93 t i 308 2.34 u 288 1.29 Al-Ghawas et al. 313 2.35 u 293 1.44 (1989a) 313 2.55 u 298 1.57 tt 313 2.58 II 303 1.61 u 318 3.17 II 308 1.63 u 340 5.33 u 313 1.68 u 343 5.43 u 323 1.87 u 353 6.32 a 293 1.40 Al-Ghawas et al. 298 1.49 (1989b) 303 1.58 308 1.66 313 1.73 u \"Versteeg & van Swaaij (1988) includes data from 30 different sources. 302 Table G.3 Diffusivity of N 2 0 in aqueous MEA solutions T (K) CMEA (wt%) 1 0 9 x D N 2 O (m2/s) Reference 303 25.0 1.70 This work 313 25.0 2.18 u 323 25.0 2.74 a 303 30.0 1.56 Li and Lai (1995) 308 30.0 1.73 313 30.0 1.88 u 298 4.5 1.74 Sada et al. (1978) 298 8.3 1.63 a 298 12.3 1.46 u 298 16.8 1.24 a 298 20.4 1.15 tt 303 Table G.4 Diffusivity of N 2 Q in aqueous DEA solutions T (K) CDEA (wt%) 1 0 9 x D N 2 O (m2/s) Reference 303 25.0 1.32 This work 313 25.0 1.66 u 323 25.0 2.10 u 303 30.0 1.16 Li & Lee (1996) 308 30.0 1.32 » 313 30.0 1.50 u 293 10.0 1.23 Tamimi et al. (1994b) 298 10.0 1.31 M 303 10.0 1.51 a 313 10.0 1.71 u 333 10.0 2.91 u 353 10.0 3.95 a 368 10.0 4.23 u 293 20.0 0.96 u 298 20.0 0.98 u 303 20.0 1.19 u 313 20.0 1.57 u 333 20.0 2.40 u 353 20.0 3.48 u 368 20.0 3.73 u 293 30.0 0.57 u 298 30.0 0.69 u 303 30.0 0.78 a 313 30.0 1.17 u 333 30.0 1.88 u 353 30.0 2.88 u 368 30.0 3.44 u 298 3.1 1.66 Sada et al. (1978) 298 6.0 1.56 u 298 11.6 1.40 u 298 16.9 1.26 u 298 20.7 1.04 u 304 Table G.5 Diffusivity of N 2 0 in aqueous MDEA solutions T C MDEA 1C 9 x DN 2o Reference T C MDEA 1 09 x D N 2 O (m2/s) Reference (K) (wt%) (m2/s) (K) (wt%) 303 25.0 1.23 This work 293 50.0 0.12 Tamimi et al. 313 25.0 1.54 it 298 50.0 0.19 (1994b) 323 25.0 1.95 u 303 50.0 0.23 ft 303 30.0 1.08 Li & Lai (1995) 313 50.0 0.41 it 308 30.0 1.18 333 50.0 0.97 it 313 30.0 1.29 « 353 50.0 1.23 i i 303 30.0 1.03 Hagewiesche 368 50.0 1.56 tf 303 40.0 0.82 et al. (1995b) 288 10.0 1.05 Al-Ghawas et al. 313 30.0 1.24 cc 293 1.0.0 1.16 (1989) 313 40.0 1.11 cc 298 10.0 1.33 it 323 30.0 1.42 11 303 10.0 1.43 tt 323 40.0 1.27 (1 308 10.0 1.48 Cf 293 10.0 1.36 Tamimi et al. 313 10.0 1.61 Cf 298 10.0 1.41 (1994b) 323 10.0 1.76 Cl 303 10.0 1.60 u 288 20.0 0.84 ft 313 10.0 1.93 u 293 20.0 0.99 Cl 333 10.0 3.20 it 298 20.0 1.15 it 353 10.0 4.13 u 303 20.0 1.29 tl 368 10.0 4.86 ti 308 20.0 1.41 CI 293 20.0 1.06 u 313 20.0 1.50 Cf 298 20.0 1.11 u 323 20.0 1.67 CC 303 20.0 1.25 u 288 30.0 0.71 Cl 313 20.0 1.67 Cl 293 30.0 0.82 ti 333 20.0 2.71 11 298 30.0 0.97 U 353 20.0 3.93 CI 303 30.0 1.03 it 368 20.0 4.29 11 308 30.0 1.16 tt 293 30.0 0.61 Cl 313 30.0 1.24 it 298 30.0 0.72 Cl 318 30.0 1.30 it 303 30.0 0.81 tl 323 30.0 1.42 tt 313 30.0 1.27 tl 288 40.0 0.59 it 333 30.0 2.02 It 293 40.0 0.64 CC 353 30.0 3.02 II 298 40.0 0.75 CC 368 30.0 3.71 i i 303 40.0 0.82 Cf 293 40.0 0.26 ft 308 40.0 0.99 CC 298 40.0 0.38 Cf 313 40.0 1.11 tf 303 40.0 0.49 u 318 40.0 1.17 Cf 313 40.0 0.80 if 323 40.0 1.27 ft 333 40.0 1.77 It 288 50.0 0.33 tt 353 40.0 2.58 tt 293 50.0 0.43 tf 368 40.0 2.97 tf 298 50.0 0.51 ft 305 Table G.5 Diffusivity of N 2 0 in aqueous MDEA solutions Continued T C MDEA 1C 9 x DN 2o Reference T CMDEA 1 09 x D N 2 O (m2/s) Reference (K) (wt%) (m2/s) (K) (wt%) 303 50.0 0.56 Al-Ghawas et al. 298 11.7 1.64 Versteeg et al. 308 50.0 0.64 (1989) 298 12.5 0.95 (1988) 313 50.0 0.75 u 298 13.3 0.77 u 318 50.0 0.84 it 308 3.9 1.98 u 323 50.0 0.93 u 308 5.0 1.87 u 293 2.1 1.46 Versteeg et al. 308 7.6 1.64 a 293 2.6 1.32 (1988) 308 8.1 1.64 u 293 4.4 1.22 u 308 8.9 1.54 u 293 4.8 1.16 u 308 10.2 1.43 u 293 6.7 1.26 u 308 10.8 1.38 u 293 8.4 0.81 a 308 11.3 1.31 it 298 1.5 1.88 u 318 3.0 2.46 a 298 2.5 1.32 u 318 5.8 2.18 u 298 3.1 1.44 u 318 9.1 2.06 u 298 4.3 1.36 u 318 12.2 1.68 a 298 5.9 1.32 a 318 15.8 1.47 a 298 6.5 1.32 u 318 17.5 1.10 u 298 6.5 1.25 u 333 4.7 3.34 u 298 7.2 1.16 u 333 8.0 3.13 a 298 8.8 1.02 u 333 12.7 2.37 u 298 9.7 1.06 u 333 15.9 2.09 u 306 Table G.6 Diffusivity of N 2 0 in aqueous A M P solutions T (K) CAMP (wt%) 1 0 9 x D N a O (m2/s) Reference T (K) CAMP (wt%) 1 0 9 x D N 2 O (m2/s) Reference 303 25.0 1.13 This work 298 12.2 0.81 Xu et al. 313 25.0 1.71 u 300 12.3 0.91 (1991b) 323 25.0 2.25 u 301 12.3 0.97 u 303 30.0 1.05 Li & Lai (1995) 304 12.3 1.02 it 308 30.0 1.16 u 313 12.3 1.47 it 313 30.0 1.30 a 323 12.4 2.09 u 294 3.1 1.57 Saha et al. 334 12.5 2.82 ft 294 6.1 1.30 (1993) 344 12.5 3.88 If 294 9.2 1.09 u 348 12.6 4.44 If 294 12.2 0.88 a 294 18.3 0.59 ff 302 3.1 1.83 u 296 18.4 0.62 If 302 6.1 1.55 u 308 18.5 1.06 ff 302 9.2 1.30 (( 319 18.6 1.57 ff 302 12.3 1.10 tl 328 18.7 2.27 ff 312 3.1 2.30 tl 338 18.8 3.00 f 312 6.2 1.98 a 348 18.9 4.07 ff 312 9.2 1.68 a 349 18.9 4.17 u 312 12.3 1.45 u 318 3.1 2.70 u 318 6.2 2.29 u 318 9.3 2.01 u 318 12.4 1.67 it 3 0 7 Table G.7 Diffusivity of N 2 0 in MEA+MDEA+H 2 0 T C M E A C M D E A 1 0 9 x D N 2 O (m2/s) Reference (K) (wt%) (wt%) 303 12.5 12.5 1.31 This work 313 12.5 12.5 1.71 u 323 12.5 12.5 2.12 a 303 24.0 6.0 1.49 Li and Lai (1995) 303 18.0 12.0 1.40 u 303 12.0 18.0 1.34 u 303 6.0 24.0 1.24 u 308 24.0 6.0 1.67 u 308 18.0 12.0 1.55 u 308 12.0 18.0 1.46 u 308 6.0 24.0 1.35 u 313 24.0 6.0 1.81 u 313 18.0 12.0 1.68 u 313 12.0 18.0 1.57 u 313 6.0 24.0 1.47 u 303 1.5 28.5 1.14 Hagewiesche et al. 303 3.0 27.0 1.27 (1995) 303 4.5 25.5 1.39 u 303 2.0 38.0 0.84 u 303 4.0 36.0 0.91 tf 303 6.0 34.0 0.97 a 313 1.5 28.5 1.27 u 313 3.0 27.0 1.35 u 313 4.5 25.5 1.45 u 313 2.0 38.0 1.16 u 313 4.0 36.0 1.21 u 313 6.0 34.0 1.29 u 323 1.5 • 28.5 1.49 u 323 3.0 27.0 1.56 u 323 4.5 25.5 1.66 u 323 2.0 38.0 1.31 u 323 4.0 36.0 1.39 u 323 6.0 34.0 1.47 u 308 Table G.8 Diffusivity of N 2 0 in MEA+AMP+H 2 0 T CMEA C A M P 1 0 9 x D N z O (m2/s) Reference (K) (wt%) (wt%) 303 12.5 12.5 1.27 This work 313 12.5 12.5 1.57 u 323 12.5 12.5 2.12 u 303 24.0 6.0 1.51 Li and Lai (1995) 303 18.0 12.0 1.42 u 303 12.0 18.0 1.32 a 303 6.0 24.0 1.21 u 308 24.0 6.0 1.63 tt 308 18.0 12.0 1.57 a 308 12.0 18.0 1.46 u 308 6.0 24.0 1.35 u 313 24.0 6.0 1.80 u 313 18.0 12.0 1.73 u 313 12.0 18.0 1.60 tt 313 6.0 24.0 1.49 u 309 Table G.9 Diffusivity of N 2 0 in DEA+MDEA+H 2 0 T CDEA CMDEA 1 0 9 x D N 2 O (m2/s) Reference (K) (wt%) (wt%) 303 12.5 12.5 1.26 This work 313 12.5 12.5 1.66 u 323 12.5 12.5 1.93 u 303 24.0 6.0 1.15 Li and Lee (1996) 303 18.0 12.0 1.14 u 303 12.0 18.0 1.12 u 303 6.0 24.0 1.11 u 308 24.0 6.0 1.30 i f 308 18.0 12.0 1.27 tf 308 12.0 18.0 1.25 u 308 6.0 24.0 1.22 tf 313 24.0 6.0 1.45 i f 313 18.0 12.0 1.41 tf 313 12.0 18.0 1.38 u 313 6.0 24.0 1.34 tt 293 2.1 47.9 0.28 Rinker et al. (1995b) 313 2.1 47.9 0.42 u 333 2.1 47.9 0.82 t i 353 2.1 47.9 1.30 t i 293 9.0 41.0 0.28 ft 313 9.0 41.0 0.42 u 333 9.0 41.0 0.92 u 353 9.0 41.0 1.10 t i 293 15.3 34.7 0.30 t i 313 15.3 34.7 0.47 ft 333 15.3 34.7 0.77 t i 353 15.3 34.7 1.06 f i 293 18.5 31.5 0.24 u 313 18.5 31.5 0.45 t i 333 18.5 31.5 0.97 t i 353 18.5 31.5 1.03 tf 310 Table G.10 Diffusivity of N 2 0 in DEA+AMP+H 2 0 T CDEA C A M P 1 0 9 x D N a O (m2/s) Reference (K) (wt%) (wt%) 303 12.5 12.5 1.11 This work 313 12.5 12.5 1.41 u 323 12.5 12.5 1.99 u 303 24.0 6.0 1.15 Li and Lee (1996) 303 18.0 12.0 1.12 u 303 12.0 18.0 1.11 u 303 6.0 24.0 1.08 u 308 24.0 6.0 1.30 u 308 18.0 12.0 1.27 u 308 12.0 18.0 1.24 u 308 6.0 24.0 1.20 u 313 24.0 6.0 1.46 u 313 18.0 12.0 1.43 u 313 12.0 18.0 1.39 u 313 6.0 24.0 1.54 u Table G.11: Constants in eq. (G.7) for interaction parameter B i 2 (this work) System B i 2 No. of data A A D % + ai a 2 M EA+M D EA+ H 2 0 • -5.8800 x 10\"6 1.8453 x 10\"3 33 6.6 MEA+AMP+H 2 0 -8.7465 x 10\"6 2.7373 x 10\"3 15 3.7 DEA+MDEA+H 2 0 1.5371 x10 \" 6 -4.3411 x 10\"4 31 17.7 DEA+AMP+H 2 0 1.4169 x10 \" 6 -3.0807 x l O \" 4 15 4.2 + A A D % = average absolute percent deviation 311 + 0 s Q 3 O CO ° 1 CM CO CN l< CO CN CO CO E 00 i f f X x CD X X t - n o i n i o m T - CO O) oo oq cn T - ; CT) cd cvi p 8> S S O O O O uo co CM - CM W co CM CO | T -tf T f o o o o X X X o CD O ^ CM O X LO CO CD N- LO CO CD CD CO CO CO LO LO O O O O T — T — T — T — X X X X CD CD CO OO O LO LO O [•>-CM 00 CO co s •^t CM CD T — | t o i o c o c o b b b o T — T — T — T — X X X X CO LO CM CD CD CO LO CO LO O CO CO O o o T N o CN CJ J - CN x i i x < < LU 0-UJ LU Q ^ 2 Q S < APPENDIX H EQUILIBRIUM CONSTANTS The equilibrium constants required to calculates the absorption and desorption rates from the model presented in Chapter 4 were calculated as a function of temperature from the correlations given below. H.1 Water Dissociation Constant The water dissociation constant (K 9) as defined by reaction (4.9) was calculated from the correlation reported by Olofsson and Hepler (1975) for the temperature range 293-573 K: log 1 0 (K 9 ) = 8909.483 - 1 4 2 ^ 1 3 ' 6 -4229.195log 1 0 (T) + 9.7384T-0.0129638T 2 + 1 . 1 5 0 6 8 x 1 0 - 5 T 3 - 4 . 6 0 2 x 1 0 \" 9 T 4 (H.1) H.2 Rate Constant for Bicarbonate Formation Reaction The forward rate constant for bicarbonate formation (k7) as defined by reaction (4.7), was calculated from the correlation reported by Pinsent et al. (1956) and corrected for ionic strength by Astarita et al. (1983) for the temperature range of 273-313 K: 313 Iog 1 0(k 7) = 13 .635-2895 T + 0.08 Ic (H.2) where, Ic is the ionic strength given by 1 n ^ i=1 H.3 Equilibrium Constant for Bicarbonate Formation Reaction The data for K 7 K 9 were reported by read (1975) for the temperature range of 298-523 K and were correlated according to the following equation: 5652 1 log 1 0 ( K 7 K 9 ) = 115.36 - ^ - 41.882 log 1 0 (T) + 0.0029116T (H.3) H.4 Equilibrium Constant for COf Formation Reaction Equilibrium constant for reaction (4.8), K 8 , was obtained from the correlation given by Edward et al. (1978) for the temperature range of 273-498 K: H.5 MEA Protonation Constant MEA protonation constant (K 1 5) as defined by reaction (4.15) was calculated from the correlation of Bates and Pinching (1951) for the temperature range of 273-323 K: log 1 0 ( K 8 K g ) = 95 .5739-5399.0187 T -35.4819 log 1 0(T) (H.4) l o g 1 0 ( K 1 5 K 9 ) = -0 .3869-2677.91 T -0.0004277T (H.5) 314 H.6 DEA Protonation Constant DEA protonation constant (K 2 i ) as defined by reaction (4.21) was calculated from the correlation of Bower et al. (1962) for the temperature range of 273-323 K: log™ ( K 2 i K 9 ) = -4-0302 _ 1 8 3 ° - 1 5 +0.0043261T (H.6) H.7 MDEA Protonation Constant The MDEA protonation constant (K23) as defined by reaction (4.23) was calculated from the correlation developed using the data of Little et al. (1990) in the temperature range 293-333 K: 3684 5 l o g 1 0 ( K 2 3 K 9 ) = 3 7 . 9 5 6 - ^ ? ^ - 1 3 . 8 3 3 l o g 1 0 ( T ) (H.7) H.8 AMP Protonation Constant The A M P protonation constant (KeKg) as defined by equation (4.6) was obtained from the correlation developed using the data of Littel et al. (1990b) in the temperature range of 293-333 K: 2629 9 log 1 0 ( K 6 K 9 ) = - 0 . 3 9 1 4 7 - - 0.19958 log 1 0 (T) (H.8) 315 H.9 MEA Carbamate Stability Constant MEA carbamate reversion constant (Ku) as defined by reaction (4.14) was calculated from the correlation reported by Kent and Eisenberg (1976) for the temperature range of 298-413 K: log 1 0 (1 / K 1 4 ) = -2.8451 + 1 3 3 6 8 - 0.01964log 1 0(T) (H.9) where T is in Kelvin. Note that in the original correlation the temperature was in Rankin. To be consistent with other correlations we converted this into Kelvin. H.10 DEA Carbamate Stability Constant DEA carbamate reversion constant (K2o) as defined by reaction (4.20) was calculated from the correlation reported by Aroua et al. (1997) for the temperature range of 303-331 K: 1781 l og 1 0 (1 /K 2 0 ) = -5.12 + - ^ (H.10) H.11 AMP Carbamate Stability Constant A M P carbamate reversion constant (K 5) as defined by reaction (4.5) was calculated using the correlation developed from the data of Xu et al. (1992) for the temperature range of 313-373 K: 6914 6 log 1 0 (1/ K 5 ) = -120.86 + + 38.991 log 1 0 (T) (H.11) 316 H.11 Combined Equilibrium Constants The rate expressions for zwitterion mechanisms (e.g. eqs. 4.31-4.33) involve several combined equilibrium constants such as K