PHASE EQUILIBRIUM MEASUREMENTS AND MODELING OF SELECTED ASYMMETRIC TERNARY MIXTURES By Khalid Farouk Omar Bachelor of Science Texas A&M University College Station, TX 1989 Master of Chemical Engineering University of Houston - University Park Houston, TX 1993 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial :fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2002 PHASE EQUILIBRIUM MEASUREMENTS AND MODELING OF SELECTED ASYMMETRIC TERNARY MIXTURES Thesis Approved: 11 PREFACE The current state of the art indicates that a cubic equation-of-state (CEOS) model capable of precisely representing the vapor-liquid equilibrium (VLE) properties of asymmetric binary mixtures and providing reliable generalized predictions for such ' mixtures is predicated on: (a) a modified covolume that accounts for molecular size asymmetry, (b) mixing rules reflective of the local-composition mixing,. and (c) a determination that the model is able to describe asymmetric multi-component mixtures based on pair-wise interactions. Accordingly, the specific objectives of the study were to: (a) evaluate the efficacy of the existing one-fluid and excess free energy mixing rules in representing the selected binary and ternary asymmetric mixtures, (b) develop improved excess Gibbs/Helmholtz energy mixing rules, ( c) modify the CEOS covolume . utilizing the combinatorial contribution to excess free energy formulation, ( d) design and construct a mercury-free, high-pressure experimental apparatus to facilitate accurate solubility measurements for systematically selected ternary asymmetric systems, and ( e) evaluate the correlative and predictive abilities of the new thermodynamic model developed in this work in comparison with recent literature models advanced by Boukovalas, et al. (1994) and Orbey and Sandler (1997). A new, constant-volume, synthetic-type, mercury-free, high-pressure experimental apparatus was designed and constructed based on a new experimental iii technique. Solubility measurements for asymmetric ternary mixtures of(a) hydrogen and carbon dioxide in eicosane, octacosane, and hexatricontane were determined at 323.15, 344.26, 373.15 and 473.15 K and pressures to 15.3 MPa; and (b) ethane and carbon dioxide in eicosane, octacosane, and hexatriconatne were determined at 323.15, 344.26, 3 73 .15 and 4 73 .15 K and pressures to 14.17 MP a. Internal and external consistency tests validate the viability of the newly-acquired ternary solubility nieasurements, which exhibit experimental uncertainties within 0.002 in mole fraction. The efficacy of the one-fluid mixing theory in handling binary and ternary asymmetric mixture was evaluated. For the ternary asymmetric mixtures ethane/carbon dioxide/n-paraffin, the Peng-Robinson (PR) equation of state (BOS) with one-fluid mixing rules was capable of predicting ternary mixture bubble point pressures with the same accuracy as it represents the constituent binaries when two temperature-independent parameters were used per binary. In comparison, for the hydrogen/carbon dioxide/n­ paraffin, the predictive ability of PR BOS with one-fluid mixing rules is as good as its representation of its binaries when one or two temperature-independent parameters were used. Moreover, in the context of one-fluid mixing rules, molecular pair-wise interactions are effective in describing the asymmetric ternary mixtures considered in this study. The present effort to improve the mixing rules for asymmetric mixtures based on a sound theoretical approach has been effective. A new semi-theoretical mixing rule was developed for the Peng-Robinson BOS covolume, which accounts effectively for molecular size asymmetry in mixture phase behavior. In general, the new excess Helmholtz energy mixing rule yields predictions with average absolute deviation of about iv 4. 7 % for the systems studied. These results are comparable to those of Orbey and Sandler (1997) and better than those of Boukovalas et al. (1994). Moreover, the new mixing rules produce excellent results for the challenging hydrogen/n-paraffin binaries. Comparable results were obtained for the excess Gibbs/Helmholtz based models using group contribution method in comparison to predictive model based on the one­ fluid mixing rules. Further, for the excess Gibbs/Helmholtz free energy models, functional group pair-wise interactions are effective in describing the asymmetric ternary mixtures considered in this study. I would like to express my grateful appreciation to my adviser Dr. K. A. M. Gasem. His continuous support, constructive guidance, knowledge, and experience have helped greatly in the completion of this study. I would like to extend any thanks and appreciation to my co-advisor Dr. R. L. Robinson, Jr. for his valuable suggestions and encouragement provided during this study. Also, I extend my thanks to the committee members Dr. J. Wagner and Dr. J. N. Veenstra for their time and efforts in reviewing this work. I like to express my thanks to my wife, Azza, and our sons and daughter, Amr, Ahmad and Salma, for their patience and understanding throughout this process. Finally, I dedicate this dissertation to the memory of my father, Dr. Farouk Omar, whose inspiration, encouragement, moral and financial support made my ambitions throughout the years a reality. Funding provided by the endowed R. N. Maddox Professorship 1s greatly appreciated. V TABLE OF CONTENTS Chapter Page ' I. INTRODUCTION .................................................................... 1 Objectives.............................................................................. 5 Organization. 8 II. BACKGROUND AND LITERATURE REVIEW ............................... 9 Vapor-Liquid Equilibrium Framework.............................................. 10 Mixing Rules. .. .. 10 The Importance of the Covolume Constant;................... 18 The Importance of using Ternary Mixtures in Evaluating EOS Models.............................................................................. 21 Non-Random Solution Model....................................................... 22 Group Contribution Concept....................................................... 24 Combinatorial and Free Volume Contributions to Excess Free Energy ......... .'..................................................................... 28 III. EXPERIMENTAL METHODS AND APPARATUS............................ 36 Review of Experimental Methods.................................................. 37 A New Experimental Technique................................................... 40 New Experimental Apparatus...................................................... 42 IV. EXPERIMENTALPROCEDURE ........................................ ,.......... 50 Pressure Testing . ... .. ......... 50 Pressure Calibration . .. .. .. .. 51 Temperature Calibration............................................................ 54 Volume Calibration................................................................. 55 Solvent Preparation.................................................................. 55 Solute Preparation . .. .. 60 vi Chapter Page Planning for an Experiment ....................................................... 62 Solute and Solvent Injection ....................................................... 65 Determination of Thermodynamic Properties .................................. 72 Apparatus Clean up and Drying ................................................. 76 V EXPERIMENTALDATAANALYSIS .......................... ,.................. 82 Error Analysis........................................................................ 82 Consistency Testing of Experimental Data ............... : . .. ... 87 Instrumental Consistency Testing ................ ,.................................. 88 Internal Consistency Testing . .. .... 88 External Consistency Testing...................................................... 95 VI EXPERIMENTAL RESULTS AND DISCUSSIONS............................ 104 High-Pressure Solubility of Ethane and Carbon Dioxide in Eicosane, Octacosane, and Hexatricontane. ... .. .. .. .. .. ...... .. .. ..... 109 High-Pressure Solubility of Hydrogen and Carbon Dioxide in Eicosane, Octacosane, and Hexatricontane.. .. .. .. .. .. ... .. ... .. ..... 120 Summary.............................................................................. 130 VII. NEW MIXING RULES BASED ON EXCESS HELMHOLTZ FREE ENERGY-1. EVALUATION WITH BINARY MIXTURES .................. 131 Model Development................................................................. 131 Evaluation of Excess Free Energy Combinatorial Expressions............... 135 Database Used...................................................................... 142 Model Evaluations and Comparisons............................................. 142 Results and Discussions............................................................ 150 Summary... 176 VIII NEW MIXING RULE BASED ON EXCESS HELMHOLTZ FREE ENERGY - 2. EVALUATION WITH TERNARY MIXTURES....... 177 Model Development..................................... 178 Database Used ...... :. .. .. .. 178 Results and Discussions............................................................ 178 Summary.............................................................................. 183 vu Chapter Page IX CONCLUSIONS AND RECOMMENDATIONS ................................ 185 Conclusions.......................................................................... 185 Recommendations..................................................................