UNIVERSITY OF CALGARY Measurement of Liquid-Liquid Diffusion in Solvent-Bitumen Systems by Franklin Aldemar Grimaldos Aguilar A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING CALGARY, ALBERTA November, 2018 © Franklin Aldemar Grimaldos Aguilar 2018 Abstract The objective of this study was to determine the mutual diffusivity for bitumen and maltenes with liquid hydrocarbons at ambient conditions. A new apparatus was designed and commissioned to measure the mass transfer in these systems based on the density profiles established over time in a column of solvent over bitumen. A one dimensional numerical model based on molecular diffusion was developed to determine the mutual diffusivity from the concentration profiles. The model accounted for the dependence of diffusivity on viscosity through a correlation based on the infinite dilution diffusivities of the solvent and the oil. Diffusivities were determined for Athabasca bitumen and maltenes with toluene, n-heptane, and n-pentane at ambient conditions and diffusion times from 3 to 15 days. The model matched the measured concentration profiles to within ±2% for bitumen and ±7% for maltenes. In addition, the effect of asphaltene precipitation of the mass transfer rate was assessed. ii Acknowledgements First, I am so grateful to God because everything that has happened in my life is because of you. God´s time is perfect. I am also so grateful to my family and my girlfriend for their support. I would like to make a special mention to Dr. Harvey Yarranton who is by far the best supervisor I could have had. Doctor, thanks for your guidance and support during this project. None of this would have happened with your help. Thanks for teaching me how to do research. Thanks for being so patient and for helping me to improve my presentation and writing skills. I really admire the person you are, your intelligence, and your commitment to science. I want also to make a special acknowledgement to Florian. Thanks for being such a nice person. Thanks for all your support in the lab, for your guidance and for make us exercise our brain muscle. I am grateful for your advice; I will keep them for life. I also want to say thanks to Elaine for helping me to improve my presentation and writing skills, for helping with some of experiments, and for the candies. They always make us happy. I want also to make a special recognition to Will Richardson. Thanks for being always willing to help and for answering all my questions. I am also grateful to Dr Maini. Thanks for sharing your ideas with me and for your support during this project. Thanks for helping me with the mathematical side of my project. Special thanks to Apostolos Kantzas for providing the CT data used to test my mathematical model. I want to thank Alejandra Plata. You started this journey and you have helped me to go through it. I want to extend this gratitude to Andres and Yulman. This would have not been the same without you two. Finally, I want to say thanks to my friends Javier, Adel, Sandra, John, Daniela, Juan Diego, Nicolay, Anderson, Jairo, Diego, Camila, Laura, John R and Sonia for everything we did together and for being my family in Calgary. iii Dedication A Dios por haberme dado tanto. A mi mama Rubiela y a mi Papa Jesús Martin, por ustedes hago todo. A mi hermano José Daniel, siempre orgulloso de usted. A mi novia Yuli, por todo su amor y apoyo incondicional. A mi abuelo José Aristóbulo, siempre presente en todos mis logros. iv Table of Contents Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iii Table of Contents .................................................................................................................v List of Tables ..................................................................................................................... ix List of Figures and Illustrations ......................................................................................... xi List of Symbols, Abbreviations and Nomenclature ......................................................... xvi CHAPTER ONE: INTRODUCTION ..................................................................................1 1.1 Objectives ................................................................................................................4 1.2 Thesis Structure .........................................................................................................5 CHAPTER TWO: LITERATURE REVIEW ......................................................................7 2.1 Mass Transfer Theory ................................................................................................7 2.1.1 Diffusion Concept .............................................................................................7 2.1.2 Mass Fluxes and Diffusivities ...........................................................................9 2.1.3 Gas-Liquid Systems: Solving the Continuity Equation ...................................11 Initial Conditions ...............................................................................................11 Boundary Conditions .........................................................................................11 Dilute Systems: Infinite Acting Solution ............................................................12 Dilute Systems: Finite Acting Solution ..............................................................12 2.1.4 Liquid-Liquid Systems: Solving the Continuity Equation ..............................13 Initial Conditions ...............................................................................................13 Boundary Conditions .........................................................................................13 Dilute Systems: Infinite Acting Solution ............................................................14 Boltzmann-Transformation Approach: ..............................................................15 Slopes and Intercept Technique: ........................................................................16 2.2 Models for Diffusivity in Liquids ............................................................................17 2.2.1 Theoretical Models ..........................................................................................18 Hydrodynamic Theory .......................................................................................18 Kinetic Theory ....................................................................................................18 Eyring’s Theory .................................................................................................18 2.2.2 Empirical Diffusivity Models at Infinite Dilution. ..........................................19 Wilke-Chang Correlation ..................................................................................19 Hayduk and Minhas Correlation .......................................................................20 Hayduk and Cheng Correlation .........................................................................20 2.2.3 Empirical Diffusivity Correlations for Concentrated Systems. .......................20 Modified Darken Equation ................................................................................21 Vignes Equation .................................................................................................21 Leffler and Cullinan Equation ...........................................................................22 Modified Hayduk and Cheng Equation .............................................................22 2.3 Methods for Measuring Diffusivity of Solvents in Heavy Oil ................................22 2.3.1 Methods for Measuring Diffusivity of Gas into Heavy Oil ............................23 Pressure Decay Method .....................................................................................23 2.3.2 Methods for Measuring Diffusivity of Liquid Solvents in Heavy Oil ............23 Spinning Disk Method ........................................................................................23 v Transpiration Technique ....................................................................................24 Taylor Dispersion Method .................................................................................24 Nuclear Magnetic Resonance ............................................................................24 Light Transmission Absorption ..........................................................................25 X-Ray Tomography ............................................................................................25 Microfluidics: Visible Light Transmission Imaging ..........................................25 2.4 Gas and Liquid Diffusivity in Bitumen ...................................................................26 2.4.1 Data for Liquid Hydrocarbon Diffusivity in Bitumen .....................................26 2.4.2 Modeling of Liquid Hydrocarbon Diffusion in Bitumen ................................28 Constant Diffusivity ...........................................................................................28 Concentration Dependent Diffusivity ................................................................29 CHAPTER