Hydrogen Sulfide Solubility in Weak Electrolyte Solutions

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<p> Thermodynamic Modeling of Hydrogen Sulfide Solubility in Weak Electrolyte Solutions Master Thesis The Technical University of Denmark Date of delivery: 31st of January 2008 Asger Lindholdt (s021870) Supervisor: Kaj Thomsen Problem formulation I Problem formulation The title of the projects is: Thermodynamic Modeling of H2S in Weak Electrolyte Solutions. The project consists of a theoretical and practical part where the systems H2S, H2S-H2O, H2S-H2O-NH3 and H2S-H2O-CO2 are treated. Theoretical part The theoretical part consists of a literature study with focuses on vapor-liquid equilibrium (VLE) and gas hydrate formation for the treated systems. General gas hydrate theory and thermodynamic modeling of gas hydrate formation described by Munck (1988) with emphasis on hydrogen sulfide is described. The Extended UNIQUAC model is described. Phase diagrams are described with emphasis on the H2S and H2S-H2O systems. Practical part The practical part consists of estimating parameters for hydrogen sulfide in the gas hydrate model and estimating parameters for hydrogen sulfide species in the Extended UNIQUAC for the systems H2S, H2S-H2O, H2S-H2O-NH3. Time schedule and content of status reports The project starts the 3rd of September 2007 and is to be handed in the 31st of January 2008. Through out the period of the project three status reports are to be handed in. Status report 1 The date of delivery is the 12th of October. A literature survey is carried out with focuses on the H2S and H2S-H2O systems. A general description of gas hydrates, modeling of gas hydrate formation and VLE for the H2S and H2S-H2O systems are described. The Extended UNIQUAC model and the article Computations of the formation of gas hydrates by Munck (1988) are described. Status report 2 The date of delivery is the 16th of November. The parameter estimation in the gas hydrate model and the Extended UNIQUAC is estimated for H2S and HS- by using experimental data from the systems H2S and H2S-H2O. The Langmuir constants in the Problem formulation II gas hydrate model are estimated for H2S and for the Extended UNIQUAC model the volume, surface and interaction parameters are estimated for the H2S species. Status report 3 The date of delivery is the 15th of January. The parameter estimation in the Extended UNIQUAC model is carried out for the H2S species in the systems H2S-H2O-NH3 and H2S-H2O-CO2. Preface III Preface This thesis of 30 ECTS points is submitted as partial fulfillment of the requirements for the Masters degree at the Technical University of Denmark. The work was carried out at the Department of Chemical Engineering, from September 2007 to January 2008 under the supervision of Associate Professor Kaj Thomsen. This thesis deals with thermodynamic modeling and a standard graduate course in thermodynamics should be sufficient to easily understand the major contents of the report. The different chapters can be read independently, but in most cases the best understanding is obtained when the previous chapters have been read. In this work the references used are presented by their last name and year of publication. The complete reference is then found in the list of references, which is at the end of the thesis. I thank my supervisor for guidance as well as all the time he used to discuss matters concerning my project. I would also like to thank Post Doc. Philip L. Fosbl for helping me with the thesis and my friend Kristian E. Nrgaard for assisting in the proof reading process. Lyngby, January, 2008 Asger Lindholdt Abstract IV Abstract The Extended UNIQUAC model and the SRK EoS were successfully applied to the systems H2S, H2S-H2O, H2S-H2O-gas hydrates, and H2S-H2O-NH3. Extended UNIQUAC parameters for H2S and HS- were successfully estimated in the systems H2S, H2S-H2O, H2S-H2O-NH3. Langmuir constants in the gas hydrate model presented by Munck (1988) were estimated for H2S. The gas hydrate model, the Extended UNIQUAC model and the SRK EoS were applied and successfully correlate the experimental data points found in the literature for the system H2S-H2O where gas hydrates are present. A major review of the open literature for the systems H2S, H2S-H2O (with and without gas hydrates), H2S-H2O-NH3, and H2S-H2O-CO2 were carried out. The review includes collection of a large amount of experimental data and a presentation of the most important VLE models. A presentation of the differences between the gas hydrate model presented by Munck (1988) and other authors in the open literature are presented. Nomenclature V Nomenclature Notation Symbol Explanation Unit A Avogadros number mol-1 A Debye-Hckel parameter kg1/2 mol1/2 A, B Langmuir parameters K b Constant kg mol-1 C Chemically independent number of components - C Langmuir adsorption constant - Cp Heat capacity difference CP Pure component critical point - d Density kg m-3 f Fugacity Pa 1f , 2f Functions in Pitzers equation - F Degrees of freedom - F Faradays constant C mol-1 H Hydrate - H Enthalpy difference J I Ionic strength mol kg water-1 I Ice - K Three-phase critical end point - LA Aqueous liquid - LS H2S-rich liquid m Molality mol kg water-1 M Molecular weight Mol kg-1 n Number of moles mol P Pressure Pa P Number of phases - Q Quadruple point - R Universal gas constant -1 -1J mol K S Solid - T Temperature K TP Pure component triple point V Molar volume of water (ice or liquid) m3 mol-1 V Volume difference m3 Y Probability of a filled cavity - Nomenclature VI Z Coordination number - Greek letters Symbol Explanation Unit ( ) ( ) 0 1, Binary interaction parameters in Pitzers equation - r Relative permittivity - 0 Vacuum permittivity C2 J-1 m-1 Mathematical constant - Standard deviation - Ternary interaction parameters Chemical potential J Number of cavities - Activity coefficient - Subscripts Symbol Explanation A Aqueous Liquid C Combinatorial i Type of cavity K Component L Large cavity m molar 0 Reference temperature 273.15 K R Residual S Small cavity S Sulfide rich liquid w Water Superscripts Symbol Explanation Non-hydrate phase Hypothetical empty lattice H Hydrate , , i j k Component , , i j k 0 Pure ice or liquid water 0 Reference temperature 298.15 K Infinite solution * Rational, unsymmetrical Nomenclature VII Abbreviation EoS Equation of state LLE Liquid-liquid-equilibrium LM Levenberg-Marquardt NM Nelder-Mead NP Number of experimental data points PR Peng-Robinson SLE Solid-liquid-equilibrium SLVE Solid-liquid-vapor-equilibrium SRK Soave-Redlich-Kvong VLE Vapor-liquid-equilibrium Summary VIII Summary This thesis deals with thermodynamic modeling of hydrogen sulfide systems containing the weak electrolyte solutions CO2 and NH3. The Extended UNIQUAC model is used to describe the excess Gibbs energy in these systems. The Extended UNIQUAC parameters are estimated for H2S and HS- in the systems H2S, H2S-H2O, H2S-CO2-H2O, H2S-NH3-H2O. Langmuir gas hydrate parameters for the model presented by Munck (1988) were estimated for H2S in the system H2S-H2O. Chapter 1: Introduction to aqueous electrolytes and the importance of thermodynamic models containing H2S and weak electrolytes are presented. Chapter 2: Thermodynamic concepts pertinent to thesis including the chemical potential, activity coefficients and the Extended UNIQUAC model are described. Chapter 3: General gas hydrate theory including structures, characteristics of guest molecules, H2S gas hydrates and thermodynamic models for gas hydrates are presented. Chapter 4: Phase diagrams for the systems H2S and H2S-H2O and Gibbs phase rule are presented. Chapter 5: Different thermodynamic VLE models from the literature used to describe weak electrolytes systems containing H2S is described. Chapter 6: Calculations of approximate concentrations of H2S species in the H2S-H2O system are presented. Chapter 7: The principal method used to estimate the Extended UNIQUAC parameters including description of the objective functions, the Levenberg-Marquardt and the Nelder-Mead algorithms are presented Chapter 8: Estimated Extended UNIQUAC parameters for H2S species for the systems H2S and H2S-H2O are presented Chapter 9: Estimated Langmuir gas constants for H2S for the H2S-H2O system are presented. Chapter 10: The Extended UNIQUAC parameters estimated for the H2S-NH3-H2O system are presented. It is argued that the very scarce experimental data points for the system H2S-CO2-H2O are wrong. Summary IX Chapter 11: Is the conclusion, summarizing the results of the project. Chapter 12: Future work related to the project, which is relevant to investigate is presented. Table of Contents X Table of Contents Problem formulation............................................................................................................ I Theoretical part ............................................................................................................ I Practical part ................................................................................................................ I Time schedule and content of status reports ................................................................ I Status report 1 .............................................................................................................. I Status report 2 .............................................................................................................. I Status report 3 .............................................................................................................II Preface............................................................................................................................... III Abstract ............................................................................................................................. IV Nomenclature..................................................................................................................... V Notation.......................................................................................................................... V Greek letters .................................................................................................................. VI Subscripts...................................................................................................................... VI Superscripts................................................................................................................... VI Abbreviation ................................................................................................................ VII Summary.........................................................................................................................VIII Table of Contents............................................................................................................... X 1 Introduction................................................................................................................. 1 2 Thermodynamic model ............................................................................................... 2 2.1 Chemical potential and activity coefficients....................................................... 2 2.1.1 Chemical potential ...................................................................................... 2 2.1.2 Excess chemical potentials and activity coefficients.................................. 3 2.2 The Extended UNIQUAC model........................................................................ 4 3 Gas hydrates................................................................................................................ 9 3.1 General gas hydrate theory ................................................................................. 9 3.1.1 Structure.................................................................................................... 10 3.1.2 Characteristics of Guest Molecules .......................................................... 12 3.2 Hydrogen Sulfide.............................................................................................. 13 3.3 Thermodynamic model for gas hydrates........................................................... 13 4 Phase diagrams.......................................................................................................... 22 4.1 Phase rule.......................................................................................................... 22 4.2 The H2S system................................................................................................. 23 4.3 The H2S-H2O system........................................................................................ 24 4.3.2 Summary of the three-phase loci .............................................................. 33 5 H2S-H2O-weak electrolyte systems .......................................................................... 35 5.1 Solid-liquid-vapor equilibrium......................................................................... 35 5.1.1 The H2S-NH3-H2O system........................................................................ 37 5.1.2 The H2S-CO2-H2O System....................................................................... 38 5.1.3 Vapor-liquid equilibrium models.............................................................. 39 5.1.4 Vapor-liquid equilibrium model by Edwards ........................................... 40 6 Concentration calculations for the H2S-H2O system................................................ 43 7 Parameter estimation and data description ............................................................... 46 7.1 Minimization..................................................................................................... 46 7.1.1 Levenberg-Marquardt Algorithm.............................................................. 47 Table of Contents XI 7.1.2 Nelder-Mead Algorithm............................................................................ 47 7.2 Confidence limit for estimated parameters ....................................................... 47 7.3 Collection and review of data ........................................................................... 48 8 H2S and HS- parameter estimation..............</p>