AN ABSTRACT OF THE THESIS OF Jacob Aaron Jones for the degree of Master of Science in Chemical Engineering presented on September 1, 2010. Title: Deep Desulfurization of Diesel Fuel Using a Single Phase Photochemical Microreactor. Abstract approved: ___________________________________________________________________ Goran N. Jovanovic Alexandre F Yokochi There is an urgent need to lower the concentration of sulfur in diesel fuels. Growing concern over environmental effects caused by burning sulfur-‐containing diesel has led the world to higher standards in fuel refinement. Because of these lower standards, many techniques have been researched to remove sulfur containing compounds or otherwise reduce the sulfur content. Hydrodesulfurization remains the primary method to reduce most light sulfur-‐containing compounds. This process removes sulfides, sulfates, and thiols using high temperature and pressure reactions but is unable to remove aromatics and long chains containing sulfur molecules. Biodesulfurization has also been considered, utilizing microorganisms to target specific sulfur-‐containing compounds to remove the sulfur while leaving the high energy fuel intact. Oxidative reactions have also been considered including photocatalytic oxidation in an attempt to oxidize these aromatic compounds so that they may be removed using a polar solvent. An ultraviolet light assisted oxidative reaction occurring in a microreactor was studied. Dibenzothiophene was used as a model refractory organic compound mixed in Decane as a solvent. Dibenzothiophene undergoes a series of oxidative reactions which produce an intermediate, Dibenzothiophene Sulfoxide, and a final product, Dibenzothiophene Sulfone. This reaction only proceeds in the presence of Tert-‐Butyl Hydroperoxide and ultraviolet light. These reactions are reversible and an equilibrium is established between Dibenzothiophene, Dibenzothiophene Sulfoxide, and Dibenzothiophene Sulfone. The equilibrium is strongly affected by the molar ratios of the reactants. Increasing the molar ratio of Tert-‐Butyl Hydroperoxide to Dibenzothiophene reduces the concentration of Dibenzothiophene in the product stream or causes the reaction to shift its equilibrium towards the products. Equilibrium may not be affected by Temperature. Previous studies have shown that equilibrium concentrations have a temperature dependence. However, under the conditions of this research there was no indication of a temperature dependence. It is possible that because of the molar ratios used the reaction did not proceed appreciably regardless of temperature so the temperature dependence was not apparent. A Taylor dispersion apparatus was assembled to measure infinite dilution diffusion coefficients for Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydroperoxide were measured. Values were close to those calculated using the Wilke-‐Chang equation. These coefficients along with measured absorption coefficients were important in developing an accurate mathematical model. A mathematical model was developed to include convective and diffusive flux, fluid ƚƌĂŶƐƉŽƌƚ͕ĂŶĚƌĞĂĐƚŝŽŶŬŝŶĞƚŝĐƐ͘KD^K>ΡDƵůƚŝƉŚǇƐŝĐƐǁĂƐƵƐĞĚƚŽŶƵŵĞƌŝĐĂůůǇ solve the mathematical model. Experimental data is fitted to the model to determine the reaction rate constants for each of the reversible reactions. The model was compared to previously reported data taken at 22 oC and 40oC using a reactor thickness of 50 um and 100um. The model fit the data very well and can be implemented in predicting concentrations within the reactor. © Copyright by Jacob Aaron Jones September 1, 2010 All Rights Reserved Deep Desulfurization of Diesel Fuel Using a Single Phase Photochemical Microreactor by Jacob Aaron Jones A THESIS submitted to Oregon State University In partial fulfillment of the requirements for the degree of Master of Science Presented September 1, 2010 Commencement June 2011 Master of Science thesis of Jacob Aaron Jones presented on September 1, 2010. Approved: ___________________________________________________________ Co-‐Major Professor, representing Chemical Engineering ___________________________________________________________ Co-‐Major Professor, representing Chemical Engineering ___________________________________________________________ Head of the School of Chemical, Biological, and Environmental Engineering ___________________________________________________________ Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. ___________________________________________________________ Jacob Aaron Jones, Author ACKNOWLEDGEMENTS The author expresses sincere apƉƌĞĐŝĂƚŝŽŶ͙ To my colleagues for all of their help: Jeremy Campbell, Justin Ong, Debbie Gilbuena, Kevin Caple, Reese Garrett and especially Nick AuYeung for being a sounding board and dropping what he was doing to help me out on many occasions. Good luck with all your endeavors and call me if I can ever return the favor. To my shipmates, Lieutenants Chris Martin and Adam Christensen for covering for me so I could go to class and conduct experiments. To my beautiful wife, Tiffany and the many hours she had to pull double duty including having to drive across most of the country so I could finish this. She has ďĞĞŶƐŽŐŽŽĚƚŽŵĞĂŶĚŵǇĐŚŝůĚƌĞŶƚŚĂƚƚŚĞƌĞĐĂŶ͛ƚďĞĞŶŽƵŐŚƚŚĂŶŬƐŐŝǀĞŶ͘ To my kids for being patient with me and understanding that I do love them very much. To my parents for raising me to value education, for teaching me to serve others, and helping me develop strong moral courage and the drive to finish what I start. To God, for inspiring me and providing me the time and resources I needed to complete this project. CONTRIBUTION OF AUTHORS Dr. Yokochi and Dr. Jovanovic assisted me throughout this entire process in designing and conducting the experiments. Eileen Hebert and the work she conducted contributed significantly in inspiring this work. TABLE OF CONTENTS Chapter 1 ʹ Introduction Page Sulfur Content Regulations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘2 Chapter 2 ʹ Literature Review Hydrodesulfurization͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙6 Biodesulfurization͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘7 Oxidative Desulfurization͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘8 Microreactors͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘..10 Numbering Up͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙..10 Goals and Objectives͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙11 Chapter 3-‐ Mathematical Model Chemicals͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘14 Reaction Rate Equations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙13 Thiophene Reactions͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙17 Peroxide Reactions͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙21 Fluid Flow Equations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙23 Mass Transfer Equations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘28 Light Intensity Equations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘33 Chapter 4 ʹ Numerical Model COMSOL Multiphysics͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘36 Developing the Model͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘37 Chapter 5 ʹ Materials and Methods Diffusion Coefficient Determination͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘41 Materials͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘41 Equipment͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘41 TABLE OF CONTENTS (CONTINUED) Methods͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘͘͘͘͘͘͘͘͘͘͘͘.42 Absorption Coefficient Determination͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.45 Materials and Equipment͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘.45 Methods͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘͘45 Rate Constant Determination͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘49 Materials͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘͘49 Equipment͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙49 ǆƉĞƌŝŵĞŶƚĂůDĞƚŚŽĚ͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘54 Analytical Method͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘54 Chapter 6 ʹ Experimental Measurements No UV Light͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘59 Molar Ratios͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘60 Chapter 7 ʹ Results and Discussion Molar Ratios͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙62 Temperature͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘63 Mathematical Model͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙64 Chapter 8 ʹ Conclusion and Recommendation Conclusions͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘70 Recommendations͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘73 LIST OF FIGURES Figure Page 3-‐1 Dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙15 3-‐2 Dibenzothiophene Sulfoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘15 3-‐3 Dibenzothiophene Sulfone͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘15 3-‐4 Tert-‐ƵƚǇů,ǇĚƌŽƉĞƌŽǆŝĚĞ͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙16 3-‐5 T1 reaction, Equations 3-‐1 and 3-‐2͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘16 3-‐6 T2 reaction, Equations 3-‐3 and 3-‐4͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘18 3-‐7 T3 reaction, Equations 3-‐5 and 3-‐6͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘19 3-‐8 T4 reaction, Equations 3-‐7 and 3-‐8͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘19 3-‐9 reaction 1, Equation 3-‐9͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘20 3-‐10 reaction 2, Equation 3-‐10͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘21 4-‐1 side view of reactor͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.37 5-‐1 Taylor Dispersion Setup͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙42 5-‐2 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min͙͙͙͙͙͙͙...43 5-‐3 Absorbance Peak for dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘46 LIST OF FIGURES (CONTINUED) Figure Page 5-‐4 Absorbance Peak for dibenzothiophene sulfoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙46 5-‐5 Absorbance Peak for dibenzothiophene sulfone͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙47 5-‐6 Absorbance Peak for Tert-‐Butyl HyrdoperoxidĞ͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘47 5-‐7 Individual ŽŵƉŽŶĞŶƚƐŽĨƚŚĞDŝĐƌŽƌĞĂĐƚŽƌ͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙50 5-‐8 Solution Delivery System͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘51 5-‐9 Complete Reaction System͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙52 5-‐10 Cooling Fan and Heating Element͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘52 5-‐11 HP 1090 HPLC͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘53 5-‐12 Autosampler loaded with vials͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙55 6-‐1 No UV Light͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘60 6-‐2 Molar Ratio Comparison͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘61 7-‐1 Comparison of Molar Ratios to Previous Data͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙63 7-‐2 Normalized Dibenzothiophene and Dibenzothiophene Sulfoxide Concentrations plotted against residence time͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙66 LIST OF FIGURES (CONTINUED) Figure Page 7-‐3 Normalized Concentration Profile for Dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙67 7-‐4 Normalized Concentration Profile for Tert-‐Butyl Hydroperoxide͙͙͙͙͙͙͙͙͘͘67 7-‐5 Normalized Concentration Profile for Dibenzothiophene Sulfoxide͙͙͙͙͙͙͙68 7-‐6 Normalized Concentration Profile for Dibenzothiophene Sulfone͙͙͙͙͙͙͙͙69 LIST OF TABLES Table Page 4-‐1 Physical Constants for COMSOL model͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙38 4-‐2 Initial Concentrations and Extinction Coefficients͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙39 4-‐3 Reaction Rate Expressions͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘40 5-‐1 Diffusion Coefficient Comparison͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘44 5-‐2 Extinction Coefficients͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘48 5-‐3 Comparison of different wavelengths for correlating Concentration to Absorption͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘ϱϲ LIST OF APPENDICES APPENDIX Page A HPLC Calibration data for Dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͘͘75 B HPLC Calibration data for Dibenzothiophene Sulfoxide͙͙͙͙͙͙͙͙͙͙͘͘78 C HPLC Calibration data for Dibenzothiophene Sulfone͙͙͙͙͙͙͙͙͙͙͙͘͘81 D HPLC Calibration data for Tert-‐Butyl Hydro Peroxide͙͙͙͙͙͙͙͙͙͙͙͙84 E Comparison of experimental data with mathematical model at 22oC with a height of 50 um͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙...86 F Comparison of experimental data with mathematical model at 22oC with a height of 100 um͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.89 G Taylor Dispersion data for determination of diffusion coefficients͙͙͙...92 H Taylor Dispersion restrictions͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.95 LIST of APPENDIX FIGURES Figure Page Figure A-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 255 nanometers͙͙͙͙͙͙͙76 Figure A-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 285 nanometers͙͙͙͙͙͙͙76 Figure A-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 315 nanometers͙͙͙͙͙͙͙77 Figure A-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 325 nanometers͙͙͙͙͙͙͙77 Figure B-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 255 nanometers͙.79 Figure B-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 285 nanometers͙.79 Figure B-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 315 nanometers͙.80 Figure B-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 325 nanometers͙.80 Figure C-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 255 nanometers͙͙.82 Figure C-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 285 nanometers͙͙.82 Figure C-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 315 nanometers͙͙.83 Figure C-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 325 nanometers͙͙.83 Figure D-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Tert Butyl Hydro Peroxide at 240 nanometers͙͙..85 LIST of APPENDIX FIGURES (CONTINUED) Figure Page Figure D-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Tert Butyl Hydro Peroxide at 255 nanometers͙͙..85 Figure E-‐1 Normalized Dibenzothiophene and Dibenzothiophene Sulfone versus residence time (s)͙͙͙͙͙͙͙͙͙͙͙͙.86 Figure E-‐2 Normalized Concentration Profile for Dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙..87 Normalized Concentration Profile for Tert-‐Butyl Hydroperoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙..87 Figure E-‐3 Figure E-‐4 Normalized Concentration Profile for Dibenzothiophene Sulfoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙88 Figure E-‐5 Normalized Concentration Profile for Dibenzothiophene Sulfone͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙88 Figure F-‐1 Normalized Dibenzothiophene and Dibenzothiophene Sulfone versus residence time (s)͙͙͙͙͙͙͙͙͙͙͙͙.89 Figure F-‐2 Normalized Concentration Profile for Dibenzothiophene͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙..90 Normalized Concentration Profile for Tert-‐Butyl Hydroperoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙..90 Figure F-‐3 Figure F-‐4 Normalized Concentration Profile for Dibenzothiophene Sulfoxide͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙91 Figure F-‐5 Normalized Concentration Profile for Dibenzothiophene Sulfone͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙91 Figure G-‐1 Figure G-‐2 Dibenzothiophene Taylor dispersion data at .3 ml/min run 1͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙92 Dibenzothiophene Taylor dispersion data at .3 ml/min run 2͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙93 LIST of APPENDIX FIGURES (CONTINUED) Figure Page Figure G-‐3 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 1͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.93 Figure G-‐4 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 2͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.94 Figure G-‐5 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 3͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙͙.94 LIST OF APPENDIX TABLES Table Page Table A-‐1 Dibenzothiophene absorption data for known concentrations at 255, 285, 315, and 325 nanometers͙75 Table B-‐1 Dibenzothiophene Sulfoxide absorption data for known concentrations at 255, 285, 315, and 325 nanometers͙78 Table C-‐1 Dibenzothiophene Sulfone absorption data for known concentrations at 255, 285, 315, and 325 nanometers͙81 Table D-‐1 Tert Butyl Hydro Peroxide absorption data for known concentrations at 240 and 255 nanometers͙͙͙͙͙͙͙84 Table H-‐1 Taylor Dispersion restrictions͙͙͙͙͙͙͙͙͙..͙͙͙͙͙..95 Deep Desulfurization of Diesel Fuel Using a Single Phase Photochemical Reaction in a Micro-‐Reactor 2 CHAPTER 1 INTRODUCTION SULFUR CONTENT REGULATIONS The world as a whole is moving toward stricter standards for sulfur emissions. There are several reasons for lowering the sulfur content of diesel fuel. The combustion byproducts from sulfur containing fuels are emitted as gases which combine with rain water to form sulfurous and sulfuric acid. These acids are a major source of erosion in cement and stone structures and corrosion in steel structures. These substances have also been linked to higher incidences of asthma, bronchitis, and heart and lung diseases. Sulfates also introduce toxins into soil and water sources. Furthermore, sulfur contributes to particulate matter which leads to smog. (Benson and Clifford, 2010, EPA 2006) Another important reason for reducing sulfur content is because it contaminates advanced emission control systems (Boehman , 2005, Song, 2000, ASTM standard, 2010, Li, 2004). These systems have been designed to further reduce particulate matter and nitrogen oxides. However, as they reduce the amount of sulfur exhausted they become caked causing a degradation of performance, until they become 3 ineffective and need to be replaced entirely. This process becomes expensive and many manufacturers choose less effective systems because of the predicted effects of sulfur pollutants in exhaust gases. If sulfur can be further reduced or eliminated from exhaust gases better emission controls can be implemented (Benson and Clifford 2010). Oil companies extract and refine varying levels of crude oil. It is more economical for companies to begin by refining the crude that has a lower concentration of sulfur before refining crude with higher sulfur content. Over time the oil reserves with lower sulfur concentrations have been depleted, leaving only, the crude oil with the higher sulfur content that must now be used. (Labana, 2005) The Euro IV standard has been in place since 2005 and specifies a 50 parts per million (ppm) maximum for sulfur in diesel fuel for most highway vehicles (Knudsen, 1999). Ultra-‐low Sulfur Diesel (ULSD) containing a maximum of 10 ppm must be available and became the new EURO V standard in 2009. Non-‐highway vehicles will also be expected to conform to the EURO V standard. The next standard, Euro VI is already in place and will be implemented by 2013, further restricting particulate matter and NOx emissions, but not directly impacting sulfur content. 4 Sweden has offered Low Sulfur Diesel meeting the Euro IV standard since 1990. As of 2000 the low sulfur diesel had penetrated 99% of the diesel market. They have also had zero sulfur, low aromatic diesel available since 2003 for use in highly polluted areas or confined spaces (Lloyd and Cackette, 2001). As of 2006 most of the diesel fuel available in the United States meets <15 ppm ULSD standards. All highway diesel fuel will be ULSD by December 2010 (Kilbane, 2006). Non-‐highway vehicles such as locomotives, marine, and off-‐road vehicles have been required to meet the <500 ppm low-‐sulfur diesel standard since 2007 and will also be required to meet the ULSD requirement by 2012 (ASTM standard, 2010). Regulations in Canada are similar to the regulations in the United States (Aviden, 2001, Environment Canada, 2006, Canada Gazette, 2002, 2005, 2006). Many South American countries have adopted a <50 ppm sulfur content standard some as early as 2004 and many are aiming for the <10 ppm ULSD standard over the next 5 years. China and the former Soviet Union have the loosest regulations requiring <2000 ppm sulfur content with a <500 ppm restriction only for certain cities. Hong Kong, Taiwan, Singapore and other Asian countries have also adopted 5 the <50 ppm sulfur content standard. New Zealand and Australia have adopted the new <10 ppm ULSD standard as of January 2009 while the previous limit was 50 ppm (Environment, water and heritage, 2010, New Zealand Legislation, 2010). Many Central and Eastern European countries also conform to the <10 ppm ULSD standard(Wikipedia). This work develops a method for the reduction of sulfur through oxidative desulfurization using a microreactor and ultraviolet light. 6 CHAPTER 2 BACKGROUND HYDRODESULFURIZATION Currently there are several different methods available to reduce sulfur content in diesel fuel. Though many different methods have been tried with varying levels of success, hydrodesulfurization is the most common (Song, 2003). Hydrodesulfurization removes most of the simple sulfur containing compounds such as thiols, thiolates, sulfoxides, and sulfones. Even at elevated temperatures and pressures many of the sulfur-‐containing aromatic compounds and long chains remain while the quality of the fuel is reduced because of the extreme conditions (Shafi and Hutchings, 2000). 7 BIODESULFURIZATION Using microorganisms that specifically target the carbon-‐ sulfur bonds in diesel fuel is another method which has had some success in producing low sulfur fuels. Some microorganisms require sulfur to grow and sustain their biological activity (Soleimani 2007). They typically get their sulfur from enzyme cofactors, amino acids, or proteins. Depending on their metabolic pathways, some of these microorganisms may be able to process the sulfur found in diesel fuels thus reducing the total sulfur content in the fuel. This process, called biodesulfurization, is meant to extract the sulfur content into an easily separable water soluble inorganic phase which produces less greenhouse gases in the process. Furthermore, because each microorganism utilizes a specific pathway the biodesulfurization process targets specific molecules, leaving other high-‐energy sulfur-‐free molecules intact (Soleimani, 2007). These processes are highly dependent on the chemical content of sulfur-‐containing species and are usually time-‐consuming. Castillo utilized a silica gel achieving an 85% conversion of sulfur content in about four hours (Castillo, 2009). Furuya used Mycobacterium Phlei WU-‐F1 to achieve a 100% conversion in 8 hours (Furuya, 2001). Bressler achieved a 60% conversion in 18 hours using a Fungal Laccase (Bressler, 2000) and Lu used a strain of Sphingomonas which took 21 hours to achieve 8 conversion (Lu, 1999). Research has also been conducted using Microbacterium ZD-‐ M2 (Li, 2005) or Rhodococcus (Matsui, 2002) and have achieved a near complete conversion but residence times were 3 or 4 days. Experiments have also shown less desirable pathways that took longer and achieved lower conversion rates such as Grossman which took seven days to achieve 38% conversion (Grossman, 2000), or Labana that required 15 days to achieve 50% reduction of sulfur (Labana, 2005). Research has also shown great possibilities with bacteria that require large volumes of water (Rhee 1998, Yu, 2006). Others have made great progress without excess water and have achieved 61% conversion in about 15 hours (Ryu, 2003). Jia enhanced the conversion rate by irradiating the bacterial strain with lasers (Jia, 2006). These methods become more complicated, time consuming, and expensive making them less likely to be utilized on a larger scale. (pathway, Gray 2003) OXIDATIVE DESULFURIZATION Selective Catalytic and Photocatalytic Oxidative reactions have also been explored in an attempt to find a faster, more efficient and more economical means of removing these heavy sulfurs. It is desirable to separate the aromatic sulfur compounds from those compounds without sulfur. Sulfides are much less polar than the corresponding 9 sulfoxides or sulfones. Therefore, if the sulfides can be oxidized, then they can be removed much more efficiently (Li, 2004). Generally these oxidation reactions are accelerated by a catalyst and sometimes ultraviolet light is used to activate the catalyst. These reactions are known as photocatalytic reactions where an ultraviolet light is used to manipulate a molecule to create active sights where a reaction may take place. Other catalysts used to accelerate the reaction can include metal oxides (Gregory, 1997, Che, 2005). Oxidizing thiophenes using a selective catalyst has produced promising results. Nearly complete conversion can be achieved with much lower residence times compared to biodesulfurization reactions such as the work done by Li which had residence times between 8 and 80 minutes (Li, 2004). Zapata achieved 78% conversion in 20 minutes while experimenting with Pd/Al2O3 and Pd/ZrO2, Mn3O4, Cr2O3 Pd/MgO-‐Al2O3 20 minutes up to 78% conversion (Zapata, 2005). Torres-‐Nieto achieved a 90% conversion using Nickel and Platinum complexes in 5 days (Torres-‐ Nieto, 2007). Horwitz also achieved a 90% conversion in just three hours using Fe-‐ TAML (Horwitz, 2003). Photocatalytic reactions have also been explored with varying degrees of success Matsuzawa reached 37% conversion in ten hours (Matsuzawa, 10 2002) and Vargas claims complete conversion of sulfur containing compounds using TiO2 in 100 minutes (Vargas, 2008). MICROREACTORS Micro-‐reactors have significant advantages over macro-‐scale reactors such as a high surface area to volume ratio and fast, uniform mixing (Zhuang, 2008). Microreactors can be difficult to fabricate because of their size but they can also be specifically designed around a particular process to overcome the large obstacles which hinder macro processes. One example is the use of photoreactions, which are nearly impossible in a macro-‐scale reactor because the light does not penetrate deep enough into the reactor to be used effectively. Another example is when a reaction is thermodynamically limited in a macro-‐process. The same reaction conducted in a micro-‐reactor may not be limited because the high surface area to volume ratio allows for better heat transfer (Freemantle, 2003). This can lead to better selectivity and or higher yields (Zhuang, 2008,Freemantle, 2003). NUMBERING UP One obstacle to implementing microdevices is the complexities associated with mass production or scaling up the process. The complications lie in construction, process 11 control, and reliable operation (Schenk, 2004). There are some that believe this will never be achievable on the scale of industrial production (Worz, 2001). There are two different types of numbering up processes, external numbering up and internal numbering up. External numbering up is achieved by designing a microreactor, duplicating it many times, and then connecting them in parallel (Freemantle, 2008). This can be related to having several flashlights which together produce a brighter light. Internal numbering up is achieved by producing several channels with the same dimensions of the microreactor in a larger device, usually sharing a common input and output. This can be related to having a single bright flashlight using several small light bulbs such as LEDs. It is more difficult and less economical to number up externally rather than internally due to the number of joints, unions, and external piping. External numbering up also produces a higher maintenance cost from increased failure rates of the system due to the extra hardware required. For this reason, internal numbering up is generally more favored (Freemantle, 2008). GOALS and OBJECTIVES The primary goal of this research was to produce a mathematical model useful in predicting the products in the photocatalytic oxidation reaction of Dibenzothiophene 12 in a micro reactor. In order to accomplish this goal several objectives need to be met. These objectives include developing a mathematical model based on: x fluid flow equations x mass transfer equations x reactor kinetics x measuring constants which have a direct impact on solving the model such as diffusion coefficient and absorption coefficients x performing experiments to produce data to compare the model x fitting the model to the data produced. The first objective in developing a mathematical model is a simple matter of applying math, physics, and chemical engineering principles. Although this process may be considered trivial it is important to understand the equations as they apply to this specific case so that they may be applied correctly. It is the objective of this research to use commercial software as a numerical solver to aid in fitting the mathematical model to the data. The commercial software uƐĞĚǁĂƐKD^K>Ρmultiphysics version 4.0. The next objective of measuring diffusion and absorption coefficients is necessary since there are no previously reported coefficients for these circumstances. Diffusion 13 coefficients are generally the same order of magnitude and can be closely predicted using equations, though it is helpful to have more specific constants. Absorption coefficients can vary greatly even among similar compounds and can have a significant impact on reaction rates. Having just one component with a high absorptivity can block the ultraviolet light and stop the reaction. Another objective of collecting data from a physical experiment relates theory to the real world. Without this comparison there is no purpose in developing the theory, having no place to put it into practice. The experimental results need to be unique and reproducible, collected under rigorous lab techniques while using reliable equipment. Fitting the model to the data is a process of fine tuning. Once all of the physical constants are determined and the mathematical model is developed the remaining variables are narrowed down to a reasonable range. From this point the process becomes a trial and error process of adjusting the constants in the model in order to produce data points which match the experimental set. This will produce a model which accurately reflects the experimental conditions which successfully completes the primary goal. 14 CHAPTER 3 MATHEMATICAL MODEL It is common to use Dibenzothiophene as a model sulfur-‐containing aromatic hydrocarbon to study the removal process in diesel fuels (Gates, 1997, Mezcua, 2007). Most of the simple sulfur containing compounds such as sulfides and thiols are easily removed in other processes leaving the refractory organic sulfurs (Soleimani, 2003 , Song, 2003). These aromatic sulfur-‐containing compounds include Benzothiophene, Dibenzothiophene, and other compounds. Dibenzothiophene in Decane or Hexadecane is typically used to simulate sulfur contaminated diesel fuel. Chemicals Figures 3-‐1 through 3-‐4 represent the compounds involved in the reactions studied. Figure 3-‐1 is a sketch of Dibenzothiophene, the model aromatic sulfur-‐containing compound. Figure 3-‐2 represents Dibenzothiophene Sulfoxide, a stable intermediate compound. Figure 3-‐3 shows Dibenzothiophene Sulfone, the oxidized product. Figure 3-‐4 represents Tert-‐Butyl Hydro Peroxide, the photoactivated catalyst. 15 Figure 3-‐1 Dibenzothiophene Figure 3-‐2 Dibenzothiophene Sulfoxide Figure 3-‐3 Dibenzothiophene Sulfone 16 Figure 3-‐4 Tert-‐Butyl Hydro Peroxide The oxidation of Dibenzothiophene (DBT) utilizes hydroxyl radicals produced by the photochemical decomposition of tert-‐butyl hydro peroxide (TBHP). This decomposition is similar to that studied by Hunt and Taube (Hunt 1952). The mechanism is summarized by equations 3-‐1 through 3-‐12 shown below. Hunt and Taube also found that with high light intensity the concentration of radicals was nearly independent of the TBHP concentration. Once the radicals are formed they are highly reactive and can attack molecules that would not normally be reactive. This creates a long list of possible reactions that can take place. These side reactions were considered individually and ultimately eliminated because of steric hindrance in most cases. Another consideration was that when the product streams were analyzed there were not any unexpected products. This indicates that none of these side reactions took place at an appreciable rate. For all equations listed herein, the following conventions are used: TBHP ʹ tert butyl hydroperoxide, DBTS-‐ 17 Dibenzothiophene, DBTSO ʹ Dibenzothiophene Sulfoxide, and DBTSOO ʹ Dibenzothiophene Sulfone. THIOPHENE REACTIONS The mechanism for the oxidation of dibenzothiophene to dibenzothiophene sulfone has been studied and equations 3-‐1 through 3-‐8 represent the generally accepted pathway (reference). Equation 3-‐1 DBTS + ʞOH Equation 3-‐2 d^ʞK, kT1 d^ʞK, kT1r d^нʞK, kT1 kT1r Figure 3-‐5: T1 reaction, Equations 3-‐1 and 3-‐2 18 Equation 3-‐3 d^ʞK,нʞK, kT2 DBTSO + H2O Equation 3-‐4 DBTSO + H2O kT2r d^ʞK,нʞK, kT2 kT2r Figure 3-‐6: T2 reaction, Equations 3-‐3 and 3-‐4 Equation 3-‐5 DBTSO + ʞOH kT3 d^KʞK, Equation 3-‐6 d^KʞK, kT3r d^KнʞK, 19 kT3 kT3r Figure 3-‐7: T3 reaction, Equations 3-‐5 and 3-‐6 Equation 3-‐7 d^KʞK,н ʞOH kT4 DBTSOO + H2O Equation 3-‐8 DBTSOO + H2O kT4r d^KʞK,нʞK, k T4 k T4r Figure 3-‐8: T4 reaction, Equations 3-‐7 and 3-‐8 20 Because the intermediate species for the KT2 and KT4 are unstable and unobservable these four reversible reactions are combined to form the following two reversible reactions. Equation 3-‐9a Equation 3-‐9b d^нϮʞK, k1 DBTSO d^нϮʞK, k1r DBTSO k1 k1r Figure 3-‐9: reaction 1, Equation 3-‐9 Equation 3-‐10a DBTSO нϮʞK, k2 Equation 3-‐10b DBTSOO d^KнϮʞK, k2r DBTSOO 21 k2 k2r Figure 3-‐10: reaction 2, Equation 3-‐10 PEROXIDE REACTIONS The radical formation from ultraviolet light activated Tert-‐Butyl Hydro Peroxide is represented by Equations 3-‐11 and 3-‐12. Equation 3-‐11 TBOOH + light k3 dKͼнʞK, Equation 3-‐12 dKͼнʞK, k3r TBOOH 22 A reaction rate equation may be developed for each of these species based on the reaction rate constants and species present for each of the equations. These reaction rate equations are listed below as equations 3-‐13 through 3-‐18. ௗ Equation 3-‐13 ௗ௧ ሾܶ‫ܲܪܤ‬ሿ ൌ ݇ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ െ ݇ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ ௗ Equation 3-‐14 ௗ௧ ሾܶ‫ ܱܤ‬ȉሿ ൌ ݇ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ െ ݇ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ ௗ Equation 3-‐15 ௗ௧ ሾʞܱ‫ܪ‬ሿ ൌ ݇ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ ൅ ʹ݇ଵ௥ ሾ‫ܱܵܶܤܦ‬ሿ ൅ ʹ݇ଶ௥ ሾ‫ܱܱܵܶܤܦ‬ሿ െ ݇ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ െ ݇ଵ ሾ‫ܵܶܤܦ‬ሿሾʞܱ‫ܪ‬ሿଶ െ݇ଶ ሾ‫ܱܵܶܤܦ‬ሿሾʞܱ‫ܪ‬ሿଶ ୢ Equation 3-‐16 ୢ୲ ሾሿ ൌ ଵ୰ ሾሿ െ ଵ ሾሿሾʞሿଶ 23 ୢ Equation 3-‐17 ୢ୲ ሾሿ ൌ ଵ ሾሿሾʞሿଶ ൅ ଶ ሾሿ െ ଵ୰ ሾሿ െ ଶ୰ ሾሿሾʞሿଶ ୢ Equation 3-‐18 ୢ୲ ሾሿ ൌ ଶ ሾሿሾʞሿଶ െ ଶ୰ ሾሿ FLUID FLOW EQUATION To describe the flow in the system we start with the Navier Stokes equations in the cartesian coordinate system in terms of velocities: డ௩ డ௩ೣ Equation 3-‐19 ߩ ቀ డ௧ೣ ൅ ‫ݒ‬௫ െ డ௫ ൅ ߤ ቂ డ௫ మೣ ൅ Equation 3-‐20 ߩ ቀ డ௧೤ ൅ ‫ݒ‬௫ డ௣ డ௫ డమ௩ ൅ ‫ݒ‬௬ డ௩ೣ డ௬ డ మ ௩ೣ డ௬ మ ൅ ൅ ‫ݒ‬௭ డ మ ௩ೣ డ௭ మ డ௩ೣ డ௭ ቁ ൌ ቃ ൅ ߩ݃௫ డ௩ డ௩೤ డ௫ ൅ ‫ݒ‬௬ డ௩೤ డ௬ ൅ ‫ݒ‬௭ డ௩೤ డ௭ ቁ ൌ ߲ ଶ ‫ݒ‬௬ ߲ ଶ ‫ݒ‬௬ ߲ ଶ ‫ݒ‬௬ ߲‫݌‬ ቉ ൅ ߩ݃௬ െ ൅ߤቈ ଶ ൅ ൅ ߲‫ݕ‬ ߲‫ݔ‬ ߲‫ ݕ‬ଶ ߲‫ ݖ‬ଶ 24 Equation 3-‐21 డ௩ ߩ ቀ డ௧೥ ൅ ‫ݒ‬௫ െ డ௩೥ డ௫ ൅ ‫ݒ‬௬ డ௩೥ డ௬ ൅ ‫ݒ‬௭ డ௩೥ డ௭ ቁ ൌ ߲‫݌‬ ߲ ଶ ‫ݒ‬௭ ߲ ଶ ‫ݒ‬௭ ߲ ଶ ‫ݒ‬௭ ቉ ൅ ߩ݃௭ ൅ߤቈ ଶ ൅ ൅ ߲‫ݖ‬ ߲‫ݔ‬ ߲‫ ݕ‬ଶ ߲‫ ݖ‬ଶ We must make a few assumptions in order to solve these equations for the desired conditions. The first assumption is that the density is constant, or that the fluid flow is incompressible. Secondly, the fluid being modeled is considered a Newtonian fluid and throughout the process the fluid remains at a constant temperature or is isothermal. Next, the fluid flow is assumed to be laminar, unidirectional, flat and horizontal and at steady state. Because the reactor is small, the gravity components of the fluid flow equation are negligible over such a short distance. The effects of the assumptions are summarized by the following equations. ʌсĐŽŶƐƚ vy=0, vz=0, vxтϬ͕ǀx = vx(y) డ௩ డ௩ డ௩ డ௬ೣ ് Ͳ, డ௫ೣ ൌ Ͳ, డ௭ೣ ൌ Ͳ 25 ߲‫ݒ‬௫ ߲‫ݒ‬௬ ߲‫ݒ‬௭ ሼ ǡ ǡ ൌ Ͳሽ ߲‫ݐ߲ ݐ߲ ݐ‬ (gx , gy , gz =0) Therefore the equations simplify as follows: Equation 3-‐22 డ௩ ߩ ቀ డ௧ೣ ൅ ‫ݒ‬௫ డ௩ೣ డ௫ ൅ ‫ݒ‬௬ డమ௩ డ௣ డ௩ೣ డ௬ డ మ ௩ೣ െ డ௫ ൅ ߤ ቂ డ௫ మೣ ൅ డ௬ మ ൅ ൅ ‫ݒ‬௭ డ మ ௩ೣ డ௭ మ డ௩ೣ డ௭ ቁൌ ቃ ൅ ߩ݃௫ Equation 3-‐23 డ௩೤ ߩ ቀ డ௧ ൅ ‫ݒ‬௫ െ డ௣ డ௬ డ௩೤ డ௫ డ మ௩೤ ൅ߤቂ ൅ ‫ݒ‬௬ డ௫ మ ൅ డ௩೤ డ௬ డ మ ௩೤ ൅ డ௬ మ ൅ ‫ݒ‬௭ డ మ ௩೤ డ௭ మ డ௩೤ డ௭ ቁൌ ቃ ൅ ߩ݃௬ Equation 3-‐24 డ௩ ߩ ቀ డ௧೥ ൅ ‫ݒ‬௫ డ௣ డ௩೥ డ௫ డమ௩ ൅ ‫ݒ‬௬ െ డ௭ ൅ ߤ ቂ డ௫ మ೥ ൅ డ௩೥ డ௬ డ మ ௩೥ డ௬ మ ൅ ൅ ‫ݒ‬௭ డ మ ௩೥ డ௭ మ డ௩೥ డ௭ ቁൌ ቃ ൅ ߩ݃௭ 26 We simplify Equations 3-‐22 through 3-‐24 to obtain Equation 3-‐25. It is also apparent డ௣ that డ௬ ൌ Ͳܽ݊݀ డ௣ డ௭ ൌ Ͳ. Equation 3-‐25 డ௣ డ௫ ൌ ߤ డ మ ௩ೣ డ௬ మ డ௣ డ௫ డ௣ ݅‫ ݐ݄ܽݐ݁݉ݑݏݏܽ݊ܽܿ݁ݓ݋ݏݔ݃݊݋݈ܽݐ݊ܽݐݏ݊݋ܿݏ‬డ௫ ൌ ο௉ ௅ , then the expression can then be integrated once to obtain Equation 3-‐26, and integrated again to obtain Equation 3-‐27. Equation 3-‐26 డ௩ ο௉ డ௬ೣ ൌ െ ఓ௅ ‫ ݕ‬൅ ܽ ‫ݒ‬௫ ൌ െ ଶఓ௅ ǇϮ ൅ ܽ‫ ݕ‬൅ ܾ Equation 3-‐27 ο௉ Boundary conditions must be applied for the physical conditions of the reactor and then Equation 3-‐27 can be solved for the constants a and b. The boundary conditions 27 that exist here are that there is continuity at the center of the pipe and that a no slip condition exists along the surfaces of the reactor. These boundary conditions are described by the following equations. Equation 3-‐28 At y = 0 : vx (y) = 0 (no slip)(ref#027) At ‫ ݕ‬ൌ ଶ : డ௬ೣ ൌ Ͳ (continuity at center of pipe) Equation 3-‐29 ு డ௩ Equation 3-‐28 is applied to Equation 3-‐27 to obtain a value for the constant b. Ͳൌെ οܲ ሺϬሻϮ ൅ ܽሺͲሻ ൅ ܾ‫ ܾݎ݋‬ൌ Ͳ ʹߤ‫ܮ‬ Equation 3-‐29 is then applied with b known to Equation 3-‐27 to obtain a value for the constant a. 28 Ͳൌെ οܲ‫ܪ‬ οܲ‫ܪ‬ ൅ ܽ‫ ܽݎ݋‬ൌ ʹߤ‫ܮ‬ ʹߤ‫ܮ‬ Using these constants Equation 3-‐27 is simplified to form Equation 3-‐30. ‫ݒ‬௫ ൌ െ οܲ Ϯ οܲ‫ܪ‬ Ǉ ൅ ‫ ݕ‬ ʹߤ‫ܮ‬ ʹߤ‫ܮ‬ Equation 3-‐30 ο௉ ‫ݒ‬௫ ൌ ଶఓ௅ ‫ݕ‬ሺ‫ ܪ‬െ ‫ݕ‬ሻ MASS TRANSFER EQUATIONS Consider a differential element of fluid with dimensions οǡ οǡ ο. A material balance of this differential element produces the following equations based on each species, denoted as i. Equation 3-‐31 ǣ୧౮ ȁ୶ǡ୲ οο ൅ ୧౯ ȁ୷ǡ୲ οο ൅ ୧౰ ȁ୸ǡ୲ οο 29 Equation 3-‐32 ǣ୧౮ ȁ୶ାο୶ǡ୲ οο ൅ ୧౯ ȁ୷ାο୷ǡ୲ οο ൅ ୧౰ ȁ୸ାο୸ǡ୲ οο Equation 3-‐33 ǣ‫ݎ‬௜ οοο ǣ Equation 3-‐34 େ౟ ȁ౯ǡ౪శο౪ ିେ౟ ȁ౰ǡ౪ ο୲ οοο These equations are combined to form the conservation of mass equation, Equation 3-‐35. Equation 3-‐35 is then simplified to obtain the differential mass conservation equation, Equation 3-‐36. Equation 3-‐35 input -‐ output + generation = accumulation Equation 3-‐36 డ డ డ డ െ డ௫ ݊௜ೣ െ డ௬ ݊௜೤ െ డ௭ ݊௜೥ ൅ ‫ݎ‬௜ ൌ డ௧ ‫ܥ‬௜ 30 Flux equations for each species including diffusive and convective mass transfer terms are then developed for each species in each direction given by Equations 3-‐37 through 3-‐39. Equation 3-‐37 ௗ ୧౮ ൌ െ‫ܦ‬௜ ‫ כ‬ௗ௫ ‫ܥ‬௜ ൅ ‫ݒ‬௫ ‫ܥ‬௜ ୧౯ ൌ െ‫ܦ‬௜ ‫ כ‬ௗ௬ ‫ܥ‬௜ ൅ ‫ݒ‬௬ ‫ܥ‬௜ ୧౰ ൌ െ‫ܦ‬௜ ‫ כ‬ௗ௭ ‫ܥ‬௜ ൅ ‫ݒ‬௭ ‫ܥ‬௜ Equation 3-‐38 ௗ Equation 3-‐39 ௗ Substituting Equations 3-‐37 through 3-‐39 into the differential mass conservation equation, Equation 3-‐36, yields Equation 3-‐40. Rearranging Equation 3-‐40 yields Equation 3-‐41. Using the assumptions above this equation can be further simplified to Equation 3-‐42. 31 Equation 3-‐40 డ ௗ డ ௗ െ డ௫ ቀെ‫ܦ‬௜ ‫ כ‬ௗ௫ ‫ܥ‬௜ ൅ ‫ݒ‬௫ ‫ܥ‬௜ ቁ െ డ௬ ቀെ‫ܦ‬௜ ‫ כ‬ௗ௬ ‫ܥ‬௜ ൅ ‫ݒ‬௬ ‫ܥ‬௜ ቁ െ ߲ ݀ ߲ ൬െ‫ܦ‬௜ ‫ܥ כ‬௜ ൅ ‫ݒ‬௭ ‫ܥ‬௜ ൰ ൅ ‫ݎ‬௜ ൌ ‫ܥ‬௜ ߲‫ݖ‬ ݀‫ݖ‬ ߲‫ݐ‬ Equation 3-‐41 డమ డమ డమ ቀ‫ܦ‬௜ డ௫ మ ‫ܥ‬௜ ൅ ‫ܦ‬௜ డ௬ మ ‫ܥ‬௜ ൅‫ܦ‬௜ డ௭ మ ‫ܥ‬௜ ቁ െ ൬‫ݒ‬௫ ߲ ߲ ߲ ߲ ‫ܥ‬௜ ൅ ‫ݒ‬௬ ‫ܥ‬௜ ൅ ‫ݒ‬௭ ‫ܥ‬௜ ൰ ൅ ‫ݎ‬௜ ൌ ‫ܥ‬௜ ߲‫ݔ‬ ߲‫ݕ‬ ߲‫ݖ‬ ߲‫ݐ‬ Equation 3-‐42 డమ డమ డ ቀ‫ܦ‬௜ డ௫ మ ‫ܥ‬௜ ൅ ‫ܦ‬௜ డ௬ మ ‫ܥ‬௜ ቁ െ ‫ݒ‬௫ డ௫ ‫ܥ‬௜ ൅ ‫ݎ‬௜ ൌ Ͳ Equation 3-‐42 can be applied for each species. This generates the series of equations below, Equations 3-‐43 through 3-‐48. Tert-‐Butyl Hydroperoxide Equation 3-‐43 డమ డమ ‫்ܦ‬஻ு௉ డ௬ మ ‫்ܥ‬஻ு௉ ൅ ‫்ܦ‬஻ு௉ డ௫ మ ‫்ܥ‬஻ு௉ െ 32 ‫ݒ‬௫ ߲ ‫ܥ‬ ൅ ‫ܭ‬ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ െ ‫ܭ‬ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ ൌ Ͳ ߲‫் ݔ‬஻ு௉ Tert-‐Butyl Hydroxyl Radical Equation 3-‐44 డమ డమ డ ‫்ܦ‬஻ைȉ డ௬ మ ‫்ܥ‬஻ைȉ ൅ ‫்ܦ‬஻ைȉ డ௫ మ ‫்ܥ‬஻ைȉ െ ‫ݒ‬௫ డ௫ ‫்ܥ‬஻ைȉ ൅‫ܭ‬ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ െ ‫ܭ‬ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ ൌ Ͳ Hydroxyl Radical Equation 3-‐45 డమ డమ డ ‫ܦ‬ைு‫ כ‬డ௬ మ ‫ܥ‬ைு‫ כ‬൅ ‫ܦ‬ைு‫ כ‬డ௫ మ ‫ܥ‬ைு‫ כ‬െ ‫ݒ‬௫ డ௫ ‫ܥ‬ைு‫ כ‬൅ ݇ଷ ሾܶ‫ܲܪܤ‬ሿሾ݈݄݅݃‫ݐ‬ሿ ൅ ʹ݇ଵ௥ ሾ‫ܱܵܶܤܦ‬ሿ ൅ ʹ݇ଶ௥ ሾ‫ܱܱܵܶܤܦ‬ሿ െ ݇ଷ௥ ሾܶ‫ ܱܤ‬ȉሿሾʞܱ‫ܪ‬ሿ െ ݇ଵ ሾ‫ܵܶܤܦ‬ሿሾʞܱ‫ܪ‬ሿଶ െ ݇ଶ ሾ‫ܱܵܶܤܦ‬ሿሾʉܱ‫ܪ‬ሿଶ ൌ Ͳ Dibenzothiophene Equation 3-‐46 డమ డమ డ ‫ܦ‬஽஻்ௌ డ௬ మ ‫ܥ‬஽஻்ௌ ൅ ‫ܦ‬஽஻்ௌ డ௫ మ ‫ܥ‬஽஻்ௌ െ ‫ݒ‬௫ డ௫ ‫ܥ‬஽஻்ௌ ൅ଵ୰ ሾሿെ ଵ ሾሿሾʞሿଶ ൌ Ͳ 33 Dibenzothiophene Sulfoxide Equation 3-‐47 డమ డమ ‫ܦ‬஽஻்ௌை డ௬ మ ‫ܥ‬஽஻்ௌை ൅ ‫ܦ‬஽஻்ௌை డ௫ మ ‫ܥ‬஽஻்ௌை െ ‫ݒ‬௫ ߲ ‫ܥ‬ ൅ ݇ଵ ሾ‫ܵܶܤܦ‬ሿሾʉܱ‫ܪ‬ሿଶ ൅ ݇ଶ ሾ‫ ܱܱܵܶܤܦ‬ሿȂ ߲‫ ݔ‬஽஻்ௌை ݇ଵ௥ ሾ‫ܱܵܶܤܦ‬ሿ െ ݇ଶ௥ ሾ‫ܱܵܶܤܦ‬ሿሾʉܱ‫ܪ‬ሿଶ ൌ Ͳ Dibenzothiophene Sulfone Equation 3-‐48 ‫ܦ‬஽஻்ௌைை ‫ݒ‬௫ డమ డ௬ మ ‫ܥ‬஽஻்ௌைை ൅ ‫ܦ‬஽஻்ௌைை డమ డ௫ మ ‫ܥ‬஽஻்ௌைை െ ߲ ‫ܥ‬ ൅ ݇ଶ ሾ‫ܱܵܶܤܦ‬ሿሾʉܱ‫ܪ‬ሿଶ െ ݇ଶ௥ ሾ‫ܱܱܵܶܤܦ‬ሿ ൌ Ͳ ߲‫ ݔ‬஽஻்ௌைை LIGHT INTENSITY EQUATIONS Light is important in causing the desired reactions. The intensity of light (I) can be measured using a spectrophotometer which measures the number of photon counts detected per defined integration time or counts per millisecond (ms-‐1). The light at any point in the reactor depends on the light intensity coming in the reactor as well 34 as the concentration and absorbance of all species present between the reactor entrance and the desired location. Thus, it is important to know the extinction coefficients for each reactant and product that may be present. A differential mass balance on the photons of light yields Equation 3-‐50. Simplifying this equation using Equation 3-‐49 results in Equation 3-‐51 with Equation 3-‐49 σே ௜ୀଵ ߝ௜ ‫ܥ‬௜ ൌ ߝ஽஻்ௌ ‫ܥ‬஽஻்ௌ ൅ ߝ஽஻்ௌை ‫ܥ‬஽஻்ௌை ൅ ߝ஽஻்ௌைை ‫ܥ‬஽஻்ௌைை ൅ ߝ்஻ு௉ ‫்ܥ‬஻ு௉ dŚĞĞǆƚŝŶĐƚŝŽŶĐŽĞĨĨŝĐŝĞŶƚƐĂƌĞĐĂůĐƵůĂƚĞĚƵƐŝŶŐĞĞƌ͛Ɛ>Ăǁ, equation 3-‐52, where, A is absorbance, C is concentration (M), L ŝƐůĞŶŐƚŚ;ĐŵͿ͕ĂŶĚɸŝƐĞǆƚŝŶĐƚŝŽŶĐŽĞĨĨŝĐŝĞŶƚ͘ Equation 3-‐50 ‫ܫ‬ȁ௬ ሺܹ݀‫ ݔ‬ሻο‫ ݐ‬െ ‫ܫ‬ȁ௬ାௗ௬ ሺܹ݀‫ ݔ‬ሻο‫ ݐ‬െ ‫ߝܫ‬௜ ሺܹ݀‫ݕ݀ݔ‬ሻ‫ܥ‬௜ ο‫ ݐ‬ൌ Ͳ Equation 3-‐51 ௗூ ௗ௬ ൅ ‫ ܫ‬σே ௜ୀଵ ߝ௜ ‫ܥ‬௜ ൌ Ͳ 35 Equation 3-‐52 ஺ ߝ௜ ൌ ஼ ೔௅ ೔ 36 CHAPTER 4 NUMERICAL MODEL COMSOL MULTIPHYSICS COMSOLΡ Multiphysics is a commercially available numerical modeling tool which may be utilized in many different fields. The simulation environment is easy to learn and allows the user to define the following: geometry, physics, reactions, meshing, and more. With an experienced user specific constants, variables, and equations may be manipulated to reflect almost any given environment. Multiple physics environments are easily coupled implementing computational fluid dynamics (CFD), Particle Transport, Heat Transfer, reaction kinetics or any number of physics environments. Output can be specified as raw data, tables, or plots (1D, 2D, 3D). Plots can be manipulated to show values for specified variables, for a specified geometry, and can include a parametric study to produce results over a range of initial conditions (COMSOL, 2010). 37 DEVELOPING THE MODEL The geometry of the microreactor used for experiments was 2.2 cm long (x direction) by 1 cm wide (z direction) by 50 um tall (y direction) and defined in COMSOL using a scaling factor of 100 in the x direction to allow higher resolution and meshing. Figure 4-‐1 below shows a side view of the reactor. The diffusion coefficients and flow velocity were scaled appropriately. Physical dimensions, velocity, viscosity, and density are defined in Table 4-‐1 below. X Y UV Light DBTS DBTSOO O TBHP DBTS Figure 4-‐1 Side view of reactor 38 VARIABLE VALUE DESCRIPTION L .00022[m] length W .01[m] Width H 5e-‐5[m] height velocity 660e-‐7[liter/min]/H/W Volumetric flowrate rho 726.28[kg/m^3] density vis 9.2e-‐4[Pa*s] viscosity Table 4-‐1 Physical constants for COMSOL model The UV light was tracked as a concentration flowing orthogonally to the bulk flow. Although the UV light is required for the reaction it is not consumed by the reaction in the same sense as typical reactants. It is not consumed by the amount of reactant that it reacts with but rather the amount of reactants or products that it encounters as it passes through the reactor. Therefore the UV light shows up as a reactant in each of the applicable reactor kinetics equations to ensure the reaction does not go forward unless there is sufficient light present even though the reaction rate equation for light itself is entirely different. The reaction rate for light follows the correlation in equation 4-‐1. Equation 4-‐1: ‫ܥ‬ூ ൌ ‫ܥ‬ூ଴ ‫ כ‬σ ߝ௜ ‫ܥ‬௜ 39 Where ‫ܥ‬ூ଴ is the initial concentration of light at the boundary, ߝ௜ is the extinction coefficient for each species present, ‫ܥ‬௜ is the concentration of each species present, and ‫ܥ‬ூ represents the concentration of light at a given point. Initial concentrations and absorption coefficients of individual species are defined in COMSOL according to Table 4-‐2 below. VARIABLE DESCRIPTION CI_0 Initial Light Intensity C0_DBTS Initial concentration of DBTS C0_DBTSO Initial concentration of DBTSO C0_DBTSOO Initial concentration of DBSOO C0_TBOOH Initial concentration of TBOOH C0_OH Initial concentration of OH C0_TBO Initial concentration of TBO eta_DBTS extinction coefficient of DBT eta_DBTSO extinction coefficient of DBTSO eta_DBTSOO extinction coefficient of DBSOO eta_TBOOH extinction coefficient of TBOOH eta_OH extinction coefficient of OH eta_TBO extinction coefficient of TBO Table 4-‐2 Initial Concentrations and Extinction Coefficients Reaction rates are defined by a reaction rate constant and associated species for each reaction. The reaction rate for light is defined as the sum of the extinction coefficients and concentrations for each species present. It is not constant but varies 40 both in the x and y directions based on the concentration of each species between the top of the reactor and the bottom of the reactor. The expressions used in COMSOL to achieve these reaction rates are shown below in Table 4-‐3. The reaction rate constants varied for different conditions so they will be reported later. VARIABLE EXPRESSION (eta_DBTS*C_DBTS+eta_DBTSOO*C_DBTSOO+eta_TBOOH*C_TB kI OOH+eta_OH*C_OH+eta_DBTSO*C_DBTSO+eta_TBO*C_TBO) rI -‐kI*C_light r1 -‐K1*C_DBTS*C_OH*C_OH r1r -‐k1r*C_DBTSO r2 -‐K2*C_DBTSO*C_OH*C_OH r2r -‐k2r*C_DBTSOO r3 -‐K3*C_TBOOH*C_light r3r -‐k3r*C_OH*C_light Ctot C_DBTS+C_DBTSOO+C_DBTSO Table 4-‐3 Reaction rate expressions Normal inflow velocity and an outlet pressure of 0 psig were used to establish a normal fluid flow profile. All reactants with the exception of light were defined as flowing in the positive x direction, while light was defined as flowing in the negative y direction. No slip boundary conditions were assumed along the walls of the reactor. 41 CHAPTER 5 MATERIALS AND METHODS DIFFUSION COEFFICIENT DETERMINATION MATERIALS Dibenzothiophene (purity 98+ % Fluka Chemical Company) , Dibenzothiophene sulfone (purity 97 % ALDRICH Chemical Company), Dibenzothiophene sulfoxide (generated locally), and Tert-‐butyl hydroperoxide (Fluka Chemical Company ~5.5 M in decane) were used to measure diffusion coefficients. Decane (purity 95+ % from Fluka Chemical Company) is used as the solvent. All chemicals were used as received without further purification. EQUIPMENT Diffusion coefficient experiments were set up and conducted using a Taylor Dispersion Apparatus as shown in Figure 5-‐1. A Beckman 112 solvent delivery pump was used to control flow rate at 0.277 (+/-‐ .005) ml/min through a 25 ft (7.62 m) column with inside diameter of 0.02 inch (0.0005 m). ϭϬϬʅ>ƐĂŵƉůĞǀŽůƵŵĞǁĂƐ 42 used for each solution and data was collected by a Gilson model 111b UV Detector and TI board using TracerDAQ. Data Collection UV Detector Capillary Coil Pump Fig 5-‐1 Taylor Dispersion setup METHODS Marquez et all determined the infinite dilution diffusion coefficient for Dibenzothiophene in Tetradecane for the temperature range 313.2 to 473.2 K (Marquez, 2008). This study presents infinite dilution diffusion coefficients for Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydroperoxide in Acetonitrile at 378 K. 43 Taylor correlated the variance of the distribution of elution time to the second moment of the elution time using the Diffusion coefficient as shown in Equation 5-‐1 (Shiraishi, 1998, Rhee 1998, Yu, 2006). The first and second moments can be measured using a refractive index to provide the diffusion coefficient. The data is plotted as in Figure 5-‐2 below and ʏ and ʍ are calculated. The noise preceeding the peak is due to an air bubble. Additional peaks are included in appendix G 0.18 0.16 0.14 absorbance 0.12 0.1 ʍ 0.08 0.06 0.04 0.02 ʏ 0 300.00 350.00 400.00 450.00 500.00 time (s) Figure 5-‐2 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min 44 Equation 5-‐1 ఙమ ఛ௥ మ ௦ మ ൌ ଶସ஽ భమ tŚĞƌĞʏŝƐƚŚĞĨŝƌƐƚŵŽŵĞŶƚŽĨƚŚĞĞůƵƚŝŽŶƚŝŵĞ͕ʍŝƐƚŚĞƐĞĐŽŶĚŵŽŵĞŶƚŽĨƚŚĞ elution time, r is the inside radius of the capillary, and D 12 is the diffusion coefficient. The assumptions used in deriving Equation 5-‐1 require certain restrictions in flow characteristics. These are summarized in Appendix H. The values obtained are similar to those predicted by Wilke-‐Chang as demonstrated in Table 5-‐1 (Jia, 2006, Wilke, 1955). DBTS DBTSO DBTSOO Taylor Dispersion 1.5713E-‐09 1.21039E-‐09 1.26788E-‐09 2.38543E-‐09 (Standard Deviation) 3.9925E-‐11 5.21538E-‐10 6.37802E-‐11 3.87447E-‐10 Wilke -‐ Chang 1.14E-‐09 1.22E-‐09 Table 5-‐1: Diffusion Coefficient comparison (m2/s) TBHP 1.19E-‐09 1.68E-‐09 45 ABSORPTION COEFFICIENT DETERMINATION MATERIALS and EQUIPMENT Dibenzothiophene (purity 98+ % Fluka Chemical Company), Dibenzothiophene Sulfone (purity 97 % ALDRICH Chemical Company), Dibenzothiophene Sulfoxide (generated locally) and Tert-‐butyl Hydroperoxide (Fluka Chemical Company ~5.5 M in decane) were used to measure extinction coefficients. Decane (purity 95+ % from Fluka Chemical Company) is used as the solvent. All chemicals were used as received without further purification. Light absorption was measured using an Avaspec 3648 spectrometer. METHODS Solutions of known concentration were mixed for each species: Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydroperoxide. Solutions were placed in a one cm by one cm cuvette and measured using the spectrophotometer. Each solution was measured three times and a light and dark standard were entered between each species. Absorbance data was 46 collected for Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydro Peroxide shown in Figures 5-‐3 through 5-‐6. Figure 5-‐3: Absorbance peak for DBTS (0.000109 M) 47 Figure 5-‐4: Absorbance peak for DBTSO (0.00005 M) Figure 5-‐5: Absorbance peak for DBTSOO (0.00004 M) Figure 5-‐6: Absorbance peak for TBHP (0.1442 M) 48 Dibenzothiophene at 1.09 * 10-‐4 M and an absorbance of 1.129 gives an absorption coefficient of 10358 M-‐1cm-‐1. Dibenzothiophene Sulfoxide at 1.5 * 10-‐4 M and an absorbance of 1.349 gives an absorption coefficient of 8993 M-‐1cm-‐1. Dibenzothiophene Sulfone at 4 * 10-‐5 M and an absorbance of 0.382 gives an absorption coefficient of 9550 M-‐1cm-‐1. Tert-‐Butyl Hydro Peroxide at 0.1442 M and an absorbance of 1.06 gives an absorption coefficient of 7.350 M-‐1cm-‐1. These are summarized in Table 5-‐2 below. DBTS Concentration (mol/L) Concentration (ppm) 1.09*10-‐4 1.5*10-‐4 DBTSOO TBHP 4.0*10-‐5 0.14422 20 0.3 8.7 13000 absorbance 1.129 1.349 0.382 1.06 absorption coefficient (M-‐1cm-‐1) 10358 8993 9550 7.3498 Table 5-‐2: Absorption coefficients DBTSO 49 RATE CONSTANT DETERMINATION MATERIALS Dibenzothiophene (purity 98+ % Fluka Chemical Company) was used as the model refractory organic solvent. Dibenzothiophene sulfone (purity 97 % ALDRICH Chemical Company) and Dibenzothiophene Sulfoxide (generated locally) were used to obtain standards for calibration curves on the HPLC. Tert-‐butyl Hydro Peroxide solution was obtained from Fluka Chemical Company (~5.5 M in decane) and used as the oxidizing agent and as a standard for a calibration curve. Decane (purity 95+ % from Fluka Chemical Company) is used as the solvent or the simulated fuel. Acetonitrile (HPLC grade, Fischer Scientific) and water (HPLC grade, Mallinckrodt Chemicals) were used as a mobile phase for the HPLC column. All chemicals were used as received without further purification. EQUIPMENT The micro reactor is made up of two stainless steel plates, two silicone gaskets, two fused quartz glass windows, and a 50 um or 100 um Teflon spacer. Quartz plates were obtained from Technical Glass Products (Item # 1.50X1.5X0.125). They were cut 50 to size using a tile saw and holes were drilled using a DremelΡ high speed cutting tool with diamond bits obtained from UKAM Industrial Super hard Tools. Steel plates, gaskets, and spacers were acquired from previous experiments. Figure 5-‐7 shows the individual parts which make up the micro reactor. Figure 5-‐7 Individual components of the micro reactor compared to the size of a penny (Hebert, 2007).. Two programmable syringe pumps manufactured by New Era Pump Systems, Inc. model NE-‐1010 (see Figure 5-‐8 below) were used to deliver feed reactants to the micro-‐reactor. One was dedicated to Dibenzothiophene delivery and the other to 51 Tert-‐Butyl Hydro Peroxide delivery. A mercury lamp, model STER-‐L-‐RAY G12T6L-‐ 52431 from Atlantic Ultraviolet Co. (see Figure 5-‐9 below), with a wave length of 254 nm irradiates reactants inside the micro-‐reactor. A heating element and fan (model 273-‐242) from radio shack (see Figure 5-‐10 below) were used with a temperature controller to maintain a constant temperature during each experiment. Figure 5-‐8: Solution delivery system. 52 Figure 5-‐9: Complete reaction setup Figure 5-‐10 Cooling fan and heating element 53 A HP 1090 High Pressure Liquid Chromatography (HPLC) system was used to analyze the product stream as shown in Figure 5-‐11 below. A C-‐18 column was used with mobile phase consisting of 70% Acetonitrile and 30% Water flowing at a rate of 1 ml/min. The HPLC utilized an autosampler and a UV detector which measured 5 preset wavelengths to detect when a species of interest was passing the detector. These preset wavelengths were set to 240, 255, 285, 315, and 325 nm which correspond to peaks for the expected species as seen in figures 5-‐2 through 5-‐5. Figure 5-‐11 HPΡ 1090 HPLC. 54 EXPERIMENTAL METHOD Solutions of Dibenzothiophene (DBTS) and Decane were loaded into a 30 ml syringe and mounted on one of the syringe pumps. Solutions of Tert-‐Butyl Hydro Peroxide (TBHP) and Decane were loaded into another 30 ml syringe and mounted on the other syringe pump. Each syringe pump delivered its solution at a constant volumetric flow rate. The ultraviolet mercury lamp was suspended 8.5 mm directly above the reactor and oriented parallel to it. Opaque tubing and a tinted polymer shield were used to prevent premature UV exposure while the solution traveled to and from the reactor or while it remained in the syringes. Samples were collected in amber vials and placed in a -‐20 oC freezer to prevent further reaction. Flowrates of 44, 66, 88, 132, 165, 220, 330, 660 ul/min were used which correlate to 30, 20, 15, 10, 8, 6, 4, and 2 second residence times. ANALYTICAL METHOD Samples were transferred to .9ml autosampler vials with septum caps for analyzing. The autosampler was used to inject 10 ul from each vial into the HPLC column at 10 minute intervals as shown in Figure 5-‐12 below. The samples traveled through the C-‐ 18 column (Microsorb, Rainin Instrument)and past the UV detector where they were analyzed for content and then collected in a waste bottle. 55 Figure 5-‐12 Autosampler loaded with vials. Standards of known concentrations of each of the expected reactants and products were run through the HPLC and indicated that all species eluted within 7 minutes at this flow rate and injection volume. The calibration curves for Dibenzothiophene (DBTS), Dibenzothiophene Sulfoxide (DBTS), Dibenzothiophene Sulfone (DBTSOO), and Tert-‐Butyl Hydroperoxide (TBHP) are included in Appendices A-‐D. These curves correlate a given peak area with a known concentration. The equations fitting this data and the R2 values are summarized in Table 5-‐3. 56 Dibenzothiophene Dibenzothiophene Sulfoxide Dibenzothiophene Sulfone Tert-‐Butyl Hydro Peroxide 255 Absorbance 285 315 325/240(TBHP) Equation y = 0.0506x -‐ 23.154 y = 0.1209x -‐ 77.347 y = 0.2873x + 2.1664 y = 0.3339x -‐ 15.883 Fit R² = 0.9984 R² = 0.9962 R² = 0.9992 R² = 0.999 Equation y = 0.0865x -‐ 7.9127 Fit R² = 0.9993 y = 0.121x + 0.665 R² = 0.9989 y = 0.3573x + 0.0521 y = 0.378x + 1.0795 R² = 0.999 R² = 0.9989 y = 0.2255x + 9.5039 y = 0.1632x -‐ 72.466 y = 0.4551x + 28.094 y = 0.4961x + 17.495 Fit R² = 0.9996 R² = 0.997 R² = 0.9996 R² = 0.9995 Equation y = 92.658x -‐ 615.67 Fit R² = 0.9993 Equation y = 66.97x -‐ 607.18 R² = 0.9932 Table 5-‐3 Comparison of different wavelengths for correlating Concentration (ppm) to Absorption (counts/s) Dibenzothiophene was mixed in Acetonitrile at concentrations of : 10777, 7779, 5158, 2578, 505, 262, 214, 113, and 50 ppm mass. Corresponding absorbances from running these concentrations through the HPLC were taken at the preset wavelengths of 255, 285, 315, and 325 nanometers and are shown in Table A-‐1 found in Appendix A. The experimental data measured at 315 nm gives the best correlation between concentration and absorbance with a fit of 0.9992. 57 Dibenzothiophene Sulfoxide was mixed in Acetonitrile at concentrations of: 6678, 5030, 3363, 1690, 839, 396, 202, 101, 51, and 25 ppm mass. Corresponding absorbances from running these concentrations through the HPLC were taken at the preset wavelengths and are shown in Table B-‐1 found in Appendix B. The correlation of data at 255 gives the best correlation with an R 2 value of 0.9993. Dibenzothiophene Sulfone was mixed in Acetonitrile at concentrations of: 8612, 5439, 2703, 1349, 1005, 488, 253, 126, and 62.5 ppm mass. Corresponding absorbances from running these concentrations through the HPLC were taken at the preset wavelengths and are shown in Table C-‐1 found in Appendix C. The correlations at 255 and 315 nanometers both give a fit of 0.9996. Tert-‐butyl Hydro Peroxide was mixed in Acetonitrile at concentrations of : 192636, 95646, 48248, 24749, 11843, 5981, 2995, 1483, 710 and 356 ppm mass. Corresponding absorbances from running these concentrations through the HPLC were taken at the preset wavelengths and are shown in Table D-‐1 found in Appendix D. The data measured at 255 nm gives the best correlation between concentration and absorbance with a fit of 0.9993. 58 Dibenzothiophene eluded at 4.7 minutes, Dibenzothiophene Sulfoxide at 4.2 minutes, Dibenzothiophene Sulfone at 3.3 minutes, and Tert-‐Butyl Hydro Peroxide at 4.8 minutes. Because three of the four species eluded so close together it was desirable to obtain better separation by adjusting the mobile phase. Similar analytical methods used by others use a mobile phase of Acetonitrile and water, Acetonitrile, Tetrahydrofuran, and water, or Methyl Hydroxide and water (Mezcua, 2007). After several attempts of adjusting the mobile phase it was determined that the 70:30 Acetonitrile to water ratio provided the best separation achievable with the C-‐18 column on hand. 59 CHAPTER 6 EXPERIMENTAL MEASUREMENTS All experiments were conducted in accordance with the materials, equipment, and methods described previously in Chapter 5. Results from the HPLC analysis are summarized in Appendix G. Each data set repeated the set of conditions twice to obtain a redundant set of data. Each collection vial was weighed before and after and compared against the expected mass to ensure there were no leaks in the system. Each data set was analyzed by the HPLC in a semi-‐random order and at least three times to verify instrument error. It was discovered during analysis that the sensitivity of the UV detector had changed predictably and the data would need to be adjusted in accordance with this shift. NO UV LIGHT To prove that the UV light is necessary to conduct this reaction an experiment was conducted at 35 oC and 50 oC in the absence of UV light. Known concentrations of Dibenzothiophene and Tert-‐Butyl Hydro Peroxide were pumped through the reactor without any UV light at residence times of 2,4,6,8,10,12, 15, 20, and 30 seconds at a 60 molar ratio of 2:1 TBHP to DBTS. Figure 6-‐1 shows Dibenzothiophene concentration as a function of residence time for 35oC and 50 oC. It indicates that there is no appreciable decrease in Dibenzothiophene concentration. In all cases there was no Dibenzothiophene Sulfone produced and negligible Dibenzothiophene Sulfoxide produced. Normalized DBTS concentration 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0 5 10 15 20 25 30 35 Residence Time Figure 6-‐1 Normalized Dibenzothiophene concentration versus residence time (s) without ultraviolet light at 35 oC (blue diamond), 50 oC (red square) MOLAR RATIOS Experiments were also conducted at 45 oC at molar ratios of 2:1, 4:1, 6:1, 12:1, , and 24:1 TBHP:DBTS with UV light to determine the effects of molar ratio on the reaction. 61 Figure 6-‐2 shows that when the molar ratio of Tert-‐Butyl Hydro Peroxide to Dibenzothiophene was increased the amount of Dibenzothiophene in the product stream was reduced. Normalized DBTS concentration 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0 10 20 30 40 50 60 Molar Ratio TBHP/DBTS Figure 6-‐2 Normalized Dibenzothiophene concentration versus molar ratio at 20 seconds residence time. 4:1, 8:1, 12:1, 48:1 TBHP:DBTS 62 CHAPTER 7 RESULTS and DISCUSSION MOLAR RATIOS Experiments were conducted at the same temperature with different molar ratios of reactants. Adjusting the molar ratio has a significant impact on the extent of reaction. As more Tert-‐Butyl Hydro Peroxide is added more hydroxyl radicals are available for reaction resulting in a higher reaction rate for Dibenzothiophene. The reaction only reaches about 20% conversion after 20 seconds with only a stoichiometric ratio of Tert-‐Butyl Hydro Peroxide, whereas it achieves a 50% conversion rate with a 24:1 TBHP: DBTS ratio. This agrees with previous studies conducted by Eileen Hebert (Hebert, 2007) at a high molar ratio of Tert-‐Butyl Hydro Peroxide to Dibenzothiophene as shown in Figure 7-‐1. 63 Normalized DBTS concentration 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0 100 200 300 400 Molar Ratio Figure 7-‐1, Normalized Dibenzothiophene concentration versus molar ratio of TBHP to DBTS including data presented by Hebert (Hebert, 2007) TEMPERATURE Previous studies have shown a significant change in conversion rate with respect to temperature when comparing reactions at 22 oC and 40 oC using a molar ratio of 425:1 (Hebert, 2007). This study found no correlation between temperature and conversion rate when comparing data collected between 35 oC and 50 oC. These results do not contradict the previous data but rather support the claim that in order for the reaction to proceed at an appreciable rate Tert-‐Butyl Hydro Peroxide needs to be in abundance. Perhaps if the same experiments were conducted at a higher molar ratio a different result would be seen. 64 MATHEMATICAL MODEL The model described in Chapter 4 uses the software package COMSOL Multiphysics 4.0 to obtain a numerical solution for the given set of equations and a given set of experimental conditions. This model was originally generated in COMSOL 3.4a and was later rewritten in COMSOL Multiphysics 4.0 when the software upgrade became available. Model development began with a simple model implementing only a simple one way reaction involving two reactants and one product. Once a solution was obtained under these simple conditions more reactions were added increasing the complexity of the solution. The second model involved adding another reactant which reacted with the first product to form a second product. The third model added reversibility to the reactions. The fourth model added the light component simulating the photoactivation of the oxidizing agent. The fifth model utilized the properties of the actual reactants and products. The sixth model included all known reactions and possible side reactions. From the sixth model revisions were aimed at simplifying the model based on actual kinetic data from experiments. Models one through six were developed in COMSOL 3.4a whereas all models following model six were developed in COMSOL 4.0. 65 General trends in the experimental data were apparent as explained previously. However, a comparison to the experimental standards resulted in confusing results, such as final concentrations higher than initial concentrations of reactants with evidence of products from the reaction. This was most likely a result of equipment malfunction. Throughout the analysis the HPLC machine had several equipment issues with the low pressure pumps, high pressure check valves, and the detector bulb. While measuring the standards of known concentration for each of the species the elution times increased as did the absorption peaks. This also occurred as the experimental results were measured, the samples that were measured towards the end were much higher than those measured at the beginning. In order to make the above comparisons the data was normalized by dividing by the initial concentration and only compared to data gathered within the same time period. In order to compare the model to experimental data, the model was fitted to previously reported data (Hebert, 2007). The previous experimental data (Hebert, 2007) did not account for the Dibenzothiophene Sulfoxide. This brought up the question of whether it was measured with the Dibenzothiophene or the Dibenzothiophene Sulfone. This 66 mathematical model assumed that the Dibenzothiophene Sulfoxide was measured with the Dibenzothiophene Sulfone to be conservative. For comparison the model predictions of these two species were added together. Figure 7-‐2 shows that the model fits the data collected at 40 oC with a 50 um spacer. Additionally surface plots of the developed model show concentration profiles for each of the major species. These are included as Figures 7-‐3 through 7-‐6. The model was effective in matching the data sets at 22 oC with a 50 um spacer and at 22 oC with a 100 um spacer as well. These are shown in Appendices E and F. Normalized Concentration 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Reported DBTS Reported DBTSOO model DBTS Model DBTSO + DBTSOO 0 5 10 15 20 Residence Time (s) 25 30 Figure 7-‐2 Normalized DBTS and DBTSOO concentrations plotted vs Residence Time 67 Figure 7-‐3 Normalized concentration profile for Dibenzothiophene Figure 7-‐4 Normalized concentration profile for Tert-‐Butyl Hydro Peroxide. 68 Though the concentrations of Dibenzothiophene Sulfoxide and Dibenzothiophene Sulfone are added together for comparison purposes it is also helpful to see the individual components. The concentration profile for the intermediate species Dibenzothiophene Sulfoxide is shown in Figure 7-‐5 and the final product Dibenzothiophene Sulfone is shown in Figure 7-‐6. Figure 7-‐5 Normalized concentration profile for Dibenzothiophene sulfoxide. 69 Figure 7-‐6 Normalized concentration profile for Dibenzothiophene sulfone. 70 CHAPTER 8 CONCLUSIONS and RECOMMENDATIONS CONCLUSIONS The primary goal of this research was to develop a mathematical model useful in predicting the products of the photocatalytic oxidation reaction of Dibenzothiophene in a micro reactor. A mathematical model was developed and solved using COMSOL ΡDƵůƚŝƉŚǇƐŝĐƐsoftware which can predict the products of the reaction for various residence times under various conditions. Experiments were conducted using a Taylor Dispersion apparatus to determine the diffusion coefficients for Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydroperoxide, all in Decane as a solvent. These measured values were close to those predicted by the Wilke-‐Chang equation. Absorption coefficients for Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, and Tert-‐Butyl Hydro Peroxide in Decane were also measured using a spectrophotometer. Measuring these coefficients helps to accurately model the reactions. 71 Dibenzothiophene and Tert-‐Butyl Hydro Peroxide in the solvent Decane were irradiated by an ultraviolet light with wavelength of 253 nm through a fused quartz window. Samples were collected and analyzed by HPLC using a mobile phase of Acetonitrile and water through a C-‐18 column with a UV detector. The experimental data collected was only able to show general trends. An increase in molar ratio of Tert-‐Butyl Hydro Peroxide to Dibenzothiophene from 4:1 to 48:1 also increases the reaction rate pushing the equilibrium in the direction of oxidation. This directly impacts the amount of sulfur remaining in the fuel. Increasing the temperature from 35 oC to 50oC does not have a significant impact on the reaction rate when using a stoichiometric molar ratio of Tert-‐Butyl Hydro Peroxide to Dibenzothiophene. The reaction is not sensitive to temperature at a low molar ratio of reactants. The series of oxidation reactions was determined to be reversible with one stable intermediate species, Dibenzothiophene Sulfoxide. Dibenzothiophene Sulfone was used as a reactant both by itself and in a mixture with Tert-‐Butyl Hydro Peroxide at a ratio of 235:1 to determine if Dibenzothiophene Sulfoxide and Dibenzothiophene would be produced. In the absence of ultraviolet light there was no 72 Dibenzothiophene or Dibenzothiophene Sulfoxide in the product stream. However, when reacted with the ultraviolet light a small amount of Dibenzothiophene and Dibenzothiophene Sulfoxide were produced. It is clear that there is an equilibrium between Dibenzothiophene and Dibenzothiophene Sulfoxide and between Dibenzothiophene Sulfoxide and Dibenzothiophene Sulfone. It is also apparent that the first equilibrium between Dibenzothiophene and Dibenzothiophene Sulfoxide is the rate limiting step. The equilibrium concentration of Dibenzothiophene Sulfoxide is very low under the conditions studied. It is possible that at different temperatures or molar ratios the equilibrium may shift in favor of the Sulfoxide. Because of the quality of experimental data collected, the generated mathematical model was compared to previously collected data. The model developed in COMSOL ΡDƵůƚŝƉŚǇƐŝĐƐǁĂƐƐƵĐĐĞƐƐĨƵůůǇfit to previously obtained experimental data. This model includes the species: Dibenzothiophene, Dibenzothiophene Sulfoxide, Dibenzothiophene Sulfone, Tert-‐Butyl Hydroperoxide, Tert Butoxyl Radical, and Hydroxyl Radical. Light is also tracked as a concentration to ensure the additive ĂďƐŽƌƉƚŝŽŶĐŽĞĨĨŝĐŝĞŶƚƐĚŽŶ͛ƚƉƌĞǀĞŶƚƚŚĞƌĞĂĐƚŝŽŶĨƌŽŵƉƌŽĐĞĞĚŝŶŐ͘ŝĨĨƵƐŝǀĞĂŶĚ convective flux for each species is also considered. Adjustable parameters include geometry, physical properties and reaction rate constants. The model may be adjusted for a spacer of 50 um or 100 um or any conceivable thickness and 73 temperature effects may be accounted for in the form of adjusting the physical properties of each species such as density, viscosity, and diffusion coefficients. However, at different temperatures the reaction rate coefficients are expected to favor higher temperatures. RECOMMENDATIONS A photocatalytic oxidation of Dibenzothiophene holds the most promise in reducing the amount of sulfur in diesel fuels with high sulfur content. The reaction can be conducted economically and quickly, with residence times less than one minute. Additional experiments should be done in the temperature range between 22 oC and 60 oC at a high molar ratio of Tert-‐Butyl Hydroperoxide to Dibenzothiophene. This would help determine the temperature dependence of the oxidation reactions. Experiments to determine the best molar ratio of Tert-‐Butyl Hydroperoxide to Dibenzothiophene should also be conducted, at ratios above 100:1 and perhaps as high as 500:1 or higher to see if the equilibrium can be forced more in the direction of the oxidation reactions. These reactions do not seem to be sensitive to temperature so they should be performed after determining the best temperature for the reactions according to the above recommendation. 74 To confirm the assumption that the first oxidation reaction to produce the sulfoxide is the rate limiting step, additional experiments using Dibenzothiophene Sulfoxide as a reactant should be completed. This will reveal how much of the products undergo the oxidation reaction to form the sulfone and how much of the products form the Dibenzothiophene. It would also be beneficial to conduct these experiments at different temperatures to see how the equilibrium changes with temperature. Additionally, results should be analyzed using accurate reproducible techniques such as a HPLC using an appropriate column and mobile phase that can achieve separation between all species. New techniques also hold promise such as the energy dispersive X-‐Ray Fluorescence spectroscopy (ED-‐XRF) developed by Shimadzu (Benson, 2010). 75 APPENDIX A HPLC Calibration data for Dibenzothiophene Standard 1 2 3 4 5 6 Known Concentration (ppm) 2578 505 262 214 113 50 Elution Time (min) 4.745 4.701 4.704 4.743 4.715 4.744 4.7787 1 2 3 4 5 6 2578 505 262 214 113 50 1 2 3 4 5 6 4.973 4.953 4.965 4.956 4.965 4.97 4.9848 2578 505 262 214 113 50 6.317 6.322 6.299 6.235 6.273 6.28 Equation Fit Absorption (counts/s) 285 nm 315 nm 2.17E+04 8971.115 5527.741 1736.228 2996.614 914.44 2475.33 750.097 1319.307 395.889 576.934 172.199 255 nm 5.13E+04 1.09E+04 5786.89 4774.33 2525.678 1102.82 325 nm 7.76E+03 1.61E+03 8.51E+02 7.01E+02 3.71E+02 1.61E+02 5.54E+04 1.15E+04 6015.89 4958.01 2646.09 1143.667 2.34E+04 5789.4 3111.48 2571.91 1382.75 598.615 9.62E+03 1.81E+03 9.46E+02 7.82E+02 4.13E+02 1.81E+02 8.33E+03 1.68E+03 8.86E+02 7.32E+02 3.88E+02 1.70E+02 6.52E+04 1.47E+04 7635.5 6070 3282.1 1337.69 y = 0.0506x -‐ 23.154 2.80E+04 7418.6 3952.1 3148.3 1710.7 703.15 y = 0.1209x -‐ 77.347 1.15E+04 2.31E+03 1.20E+03 9.53E+02 5.10E+02 2.12E+02 y = 0.2873x + 2.1664 9.94E+03 2.14E+03 1.13E+03 8.90E+02 4.80E+02 1.98E+02 y = 0.3339x -‐ 15.883 R² = 0.9984 R² = 0.9962 R² = 0.9992 R² = 0.999 Table A-‐1 Dibenzothiophene absorption data for known concentrations at 255, 285, 315, and 325 nanometers 76 3000 255 2500 2000 y = 0.0506x -‐ 23.154 R² = 0.9984 1500 1000 500 0 0 20000 40000 60000 Figure A-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 255 nanometers. 3000 285 2500 2000 1500 y = 0.1209x -‐ 77.347 R² = 0.9962 1000 500 0 0.00E+00 5.00E+03 1.00E+04 1.50E+04 2.00E+04 2.50E+04 Figure A-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 285 nanometers 77 3000 315 2500 2000 y = 0.2873x + 2.1664 R² = 0.9992 1500 1000 500 0 0.00E+00 2.00E+03 4.00E+03 6.00E+03 8.00E+03 1.00E+04 Figure A-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 315 nanometers 3000 325 2500 2000 y = 0.3339x -‐ 15.883 R² = 0.999 1500 1000 500 0 0.00E+00 2.00E+03 4.00E+03 6.00E+03 8.00E+03 1.00E+04 Figure A-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene at 325 nanometers 78 79 APPENDIX B HPLC Calibration data for Dibenzothiophene Sulfoxide Standard 7 8 9 10 11 12 7 8 9 10 11 12 Known Concentration (ppm) 839 396 202 101 25 839 396 202 101 51 25 Elution Time (min) 4.251 4.183 4.25 4.263 4.188 4.273 4.314 4.226 4.263 4.348 4.134 255 nm 9.77E+03 4.55E+03 2.42E+03 1.33E+03 2.89E+02 Equation 9.84E+03 4.61E+03 2.61E+03 1.35E+03 6.78E+02 3.01E+02 y = 0.0865x -‐ 7.9127 Fit R² = 0.9993 Absorption (counts/s) 285 nm 315 nm 7.07E+03 2390 3.16E+03 1068 1.61E+03 548 8.75E+02 293 1.91E+02 68 6.86E+03 2331 3.14E+03 1069 1.75E+03 602 8.86E+02 301 4.48E+02 151 1.94E+02 68 y = 0.121x y = 0.3573x + 0.665 + 0.0521 R² = 0.9989 R² = 0.999 325 nm 2258 1005 514 278 64 2204 1004 559 282 143 63 y = 0.378x + 1.0795 R² = 0.9989 Table B-‐1 Dibenzothiophene Sulfoxide absorption data for known concentrations at 255, 285, 315, and 325 nanometers 80 900 255 800 700 y = 0.0865x -‐ 7.9127 R² = 0.9993 600 500 400 300 200 100 0 0.00E+00 2.00E+03 4.00E+03 6.00E+03 8.00E+03 1.00E+04 1.20E+04 Figure B-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 255 nanometers. 900 800 285 700 600 y = 0.121x + 0.665 R² = 0.9989 500 400 300 200 100 0 0.0E+00 1.0E+03 2.0E+03 3.0E+03 4.0E+03 5.0E+03 6.0E+03 7.0E+03 8.0E+03 Figure B-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 285 nanometers 81 900 315 800 700 y = 0.3573x + 0.0521 R² = 0.999 600 500 400 300 200 100 0 0 500 1000 1500 2000 2500 3000 Figure B-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 315 nanometers 900 325 800 700 y = 0.378x + 1.0795 R² = 0.9989 600 500 400 300 200 100 0 0 500 1000 1500 2000 2500 Figure B-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfoxide at 325 nanometers 82 83 APPENDIX C HPLC Calibration data for Dibenzothiophene Standard 12 13 14 15 16 17 18 19 20 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 Known Concentration (ppm) 8612 5439 2703 1349 1005 488 253 126 62.5 5439 2703 1349 1005 488 253 126 62.5 8612 5439 2703 1349 1005 488 253 126 62.5 Elution Time (min) 3.291 3.268 3.274 3.276 3.286 3.283 3.297 3.304 3.286 3.285 Equation y = 0.4551x + 28.094 Fit R² = 0.9996 R² = 0.9995 R² = 0.9996 3.455 3.404 3.415 3.455 3.446 3.465 3.451 3.465 3.4445 4.146 4.182 4.157 4.246 4.201 4.196 4.162 4.246 4.157 4.188111 315 nm 1.89E+04 1.18E+04 5.96E+03 2.85E+03 2.12E+03 1.06E+03 5.30E+02 2.65E+02 1.26E+02 1.26E+04 5990.97 3.00E+03 2125.33 1.10E+03 564.66 2.74E+02 133.48 2.43E+04 1.48E+04 7.11E+03 3.75E+03 2.82E+03 1.30E+03 6.98E+02 3.29E+02 1.57E+02 Absorption (counts/s) 325 nm 255 nm 1.71E+04 3.81E+04 1.08E+04 2.36E+04 5.47E+03 1.22E+04 2.62E+03 6.12E+03 1.97E+03 4.41E+03 9.81E+02 2.21E+03 4.99E+02 1.12E+03 2.44E+02 5.95E+02 1.15E+02 2.93E+02 1.14E+04 2.50E+04 5524.25 1.25E+04 2.78E+03 6.22E+03 1986.536 4.44E+03 1.02E+03 2.31E+03 528.06 1.18E+03 2.55E+02 5.85E+02 126.03 2.82E+02 2.24E+04 4.93E+04 1.43E+04 3.09E+04 6.60E+03 1.43E+04 3.48E+03 7.60E+03 2.62E+03 5.71E+03 1.21E+03 2.64E+03 6.54E+02 1.45E+03 3.06E+02 6.89E+02 1.47E+02 3.41E+02 y = 0.4961x y = 0.2255x + 17.495 + 9.5039 285 nm 5.15E+04 3.51E+04 1.78E+04 8867.05 6.67E+03 3.35E+03 1.72E+03 8.58E+02 4.32E+02 3.71E+04 1.86E+04 9.42E+03 6.69E+03 3.49E+03 1.78E+03 8.75E+02 4.36E+02 6.50E+04 4.54E+04 2.22E+04 1.18E+04 8.84E+03 4.03E+03 2.22E+03 1.04E+03 5.24E+02 y = 0.1632x -‐ 72.466 R² = 0.997 Table C-‐1 Dibenzothiophene Sulfone absorption data for known concentrations at 255, 285, 315, and 325 nanometers 84 10000 255 9000 8000 y = 0.2255x + 9.5039 R² = 0.9996 7000 6000 5000 4000 3000 2000 1000 0 0.00E+00 1.00E+04 2.00E+04 3.00E+04 4.00E+04 5.00E+04 Figure C-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 255 nanometers 10000 285 9000 8000 7000 y = 0.1632x -‐ 72.466 R² = 0.997 6000 5000 4000 3000 2000 1000 0 0.0E+00 1.0E+04 2.0E+04 3.0E+04 4.0E+04 5.0E+04 6.0E+04 Figure C-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 285 nanometers 85 10000 315 9000 8000 y = 0.4551x + 28.094 R² = 0.9996 7000 6000 5000 4000 3000 2000 1000 0 0.00E+00 5.00E+03 1.00E+04 1.50E+04 2.00E+04 2.50E+04 Figure C-‐3 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 315 nanometers 10000 325 9000 8000 y = 0.4961x + 17.495 R² = 0.9995 7000 6000 5000 4000 3000 2000 1000 0 0.00E+00 5.00E+03 1.00E+04 1.50E+04 2.00E+04 Figure C-‐4 Plot of Concentration (ppm) against Absorption (counts/s) for Dibenzothiophene Sulfone at 325 nanometers 86 87 APPENDIX D HPLC Calibration data for Tert-‐Butyl Hydro Peroxide Standard 21 22 23 24 25 26 27 28 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 Known Concentration 192636 95646 48248 24749 11843 5981 2994.64 1483.06 192636 95646 48248 24749 11843 5981 2994.64 1483.06 710 356 192636 95646 48248 24749 11843 5981 2994.64 1483.06 Elution Time 5.063 5.074 5.069 5.087 5.102 5.148 5.126 5.11 5.097375 5.163 5.228 5.254 5.284 5.32 5.315 5.306 5.273 5.253 5.261 5.2657 4.813 4.839 4.868 4.854 4.874 4.8496 6.473 6.497 6.538 6.502667 240 255 Absorption 2817.91 1421.26 699.83 391.607 185.354 101.046 64.029 36.374 2734.57 1409.728 729.416 375.439 191.535 114.931 65.16 38.314 35.737 20.031 2964.793 1508.775 710.553 388.333 174.822 101.21 52.343 30.192 y = 66.97x -‐ 607.18 Absorption 2101.507 1049.872 515.125 283.435 133.06 68.221 37.134 18.424 2014.584 1049.723 533.732 274.995 137.646 74.707 39.488 22.099 14.973 2130.583 1031.508 524.4 276.332 127.229 73.978 38.935 21.329 y = 92.658x -‐ 615.67 R² = 0.9932 R² = 0.9993 Equation Fit Table D-‐1 Tert Butyl Hydro Peroxide absorption data for known concentrations at 240 and 255 nanometers 88 250000 240 200000 150000 y = 66.97x -‐ 607.18 R² = 0.9932 100000 50000 0 0 500 1000 1500 2000 2500 3000 3500 Figure D-‐1 Plot of Concentration (ppm) against Absorption (counts/s) for Tert Butyl Hydro Peroxide at 240 nanometers 250000 255 200000 150000 y = 92.658x -‐ 615.67 R² = 0.9993 100000 50000 0 0 500 1000 1500 2000 2500 Figure D-‐2 Plot of Concentration (ppm) against Absorption (counts/s) for Tert Butyl Hydro Peroxide at 255 nanometers 89 APPENDIX E Comparison of experimental data with mathematical model at 22 oC with a height of 50 um. 1 Reported DBTS Normalized Concnetration 0.9 Reported DBTSOO 0.8 Model DBTS 0.7 Model DBTSO + DBTSOO 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 Residence Time (s) 25 30 Figure E-‐1 Normalized Dibenzothiophene and Dibenzothiophene Sulfone versus residence time (s). Mathematical Model plotted with experimental results (Hebert, 2007) 90 Figure E-‐2 Normalized concentration profile for Dibenzothiophene Figure E-‐3 Normalized concentration profile for Tert Butyl Hydro Peroxide 91 Figure E-‐4 Normalized concentration profile for Dibenzothiophene Sulfoxide Figure E-‐5 Normalized concentration profile for Dibenzothiophene Sulfone 92 APPENDIX F Comparison of experimental data with mathematical model at 22 oC with a height of 100 um. Model DBTS Reported DBTS 1 Reported DBTSOO Normalized Concentration 0.9 Model DBTSO + DBTSOO 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 Residence time (s) 20 25 30 Figure F-‐1 Normalized Dibenzothiophene and Dibenzothiophene Sulfone versus residence time (s). Mathematical Model plotted with experimental results (Hebert, 2007) 93 Figure F-‐2 Normalized concentration profile for Dibenzothiophene Figure F-‐3 Normalized concentration profile for Tert Butyl Hydro Peroxide 94 Figure F-‐4 Normalized concentration profile for Dibenzothiophene Sulfoxide Figure F-‐5 Normalized concentration profile for Dibenzothiophene Sulfone 95 96 APPENDIX G Taylor Dispersion data for determination of diffusion coefficients 0.4 0.35 absorbance 0.3 0.25 0.2 0.15 0.1 0.05 0 300 350 400 450 500 time (s) Figure G-‐1 Dibenzothiophene Taylor dispersion data at .3 ml/min run 1 97 0.35 0.3 absorbance 0.25 0.2 0.15 0.1 0.05 0 300 350 400 450 500 time (s) Figure G-‐2 Dibenzothiophene Taylor dispersion data at .3 ml/min run 2 0.05 0.045 0.04 absorbance 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 300.00 350.00 400.00 450.00 500.00 time (s) 98 Figure G-‐3 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 1 0.05 0.045 0.04 absorbance 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 300.00 350.00 400.00 450.00 500.00 time (s) Figure G-‐4 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 2 99 0.18 0.16 0.14 absorbance 0.12 0.1 0.08 0.06 0.04 0.02 0 300.00 350.00 400.00 450.00 500.00 time (s) Figure G-‐5 Dibenzothiophene Sulfoxide Taylor dispersion data at .3 ml/min run 3 APPENDIX H Taylor Dispersion restrictions Flow rate (ml/min) 1 2 Area Velocity Peclet (m^2) (m/s) 2.03E-‐07 0.0710 1.78E+08 2.03E-‐07 0.1441 3.61E+08 axial rest >700L/r check check radial Laminar rest Reynolds flow Dean <.1L2/r2 28.62703 check 0.7213 fail fail 58.11586 check 1.4644 3 2.03E-‐07 0.2127 5.33E+08 check fail .1 2.03E-‐07 0.0071 5.40E+07 check check .3 2.03E-‐07 0.0227 8.68E+08 check check .5 2.03E-‐07 0.0381 1.46E+08 check fail Table H-‐1 Restriction calculations for Taylor Dispersion 85.73747 2.857848 9.182884 15.3948 check check check check 2.1605 0.0720 0.2314 0.3879 secon secon flow Schmidt flow <16 De*Sc^.5 <10 check 414.53 14.687 fail check 414.53 29.819 fail check check check check 414.53 414.53 414.53 414.53 43.988 1.466 4.711 7.898 fail check check check 1. The analysis assumes laminar flow. Reynolds numbers for these experiments were between 3 and 86 which indicates the flow was laminar. 2. Axial molecular diffusion is neglected in the Taylor analysis. The radial concentration differences are assumed to be small. Alizadeh demonstrated analytically that the effect on ɐ2 is less than 0.01 % when the Peclet number (Pe ) =(uL/D12) is larger than 700L/r and smaller than 0.1L2/r2 , where L is the capillary length and u is the fluid velocity. Experimentally obtained values are between 5.4 *10 7 and 8.68*108. Only flowrates of 0.1 and 0.3 ml/min pass the radial restriction (Alizadeh, XXXX). 3. Because the capillary must be coiled additional restrictions must be fulfilled. Secondary flow due to coiling does not have an effect when: Dean numbers (De)=(Re(r/rc).5) is less than 16, rc/r is greater than 20, and De(Sc).5 is less than 10 (Janssen, XXXX). Values of De were found to be less than 3. rc/r = 1574.8. 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