Thermodynamic Modelling of Liquid–liquid Equilibria Using the Nonrandom Two-Liquid Model and Its Applications Zheng Li Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy August 2015 Department of Chemical and Biomolecular Engineering The University of Melbourne The way ahead is long and adventurous, I shall keep on exploring. 路漫漫其修远兮，吾将上下而求索。 — Yuan Qu (屈原) Abstract Solvent extraction is a separation technique widely used in a variety of industrial applications. The basis of separation by this technique is the distribution of a solute between two immiscible solvents, which fundamentally is a phenomenon of thermodynamic phase equilibrium. As a result, the thermodynamic modelling of liquid–liquid equilibria (LLE) is a significant problem of solvent extraction. In general, there are two approaches to calculate phase equilibrium: minimizing the Gibbs free energy combined with the Tangent Plane Distance (TPD) criterion for stability test and solving the isoactivity equations. Compared with the first approach, the second is easier, however, it strongly depends on initial estimation and may lead to erroneous results which correspond to maxima, local minima and saddle points of the Gibbs free energy. Therefore, the primary aim of this thesis is to understand the solution structure of the isoactivity equations of LLE and develop a procedure to determine the correct, physically realistic solution. This thesis has three parts: firstly, understanding the isoactivity equations of LLE using the nonrandom two-liquid (NRTL) model, the most popular thermodynamic model; secondly, regression of NRTL parameters using particle swarm optimization (PSO) and insights into the model’s capabilities in correlating LLE data; thirdly, application of the symmetric eNRTL model and the developed PSO method to the modelling of phenol extraction. The solution structure of the isoactivity equations for ternary and quaternary LLE systems using the NRTL model under two types of mass balance constraints were investigated. The first constraint specifies the concentration of components (one component in a ternary system and two components in a quaternary system) in one phase. In this case, the three isoactivity equations of a ternary LLE system were presented in a three dimensional space as three surfaces with their intersection lines extracted. Three types of solutions were revealed, namely exact solutions, symmetric solutions and approximate solutions. These analyses were called Solution Structure Categorization (SSC). Results yielded by SSC further led to development of a procedure to identify the correct solution of LLE for ternary and quaternary systems. The second constraint specifies the total amount of each component in a system. In this case, the SSC method was again applied and it was found that all solutions of I isoactivity equations can be categorized into two types when converted into mole fractions: one correct solution and a number of symmetric solutions representing a homogeneous phase. A procedure based on solving isoactivity equations to determine the correct solution was also proposed, which was shown to be simple and effective for a number of ternary and quaternary LLE systems from a wide range of literature sources. The new procedure is recommended to be used as a parallel procedure to minimization of Gibbs free energy combined with stability test by the TPD criterion. The NRTL model has binary interaction parameters and non-randomness parameters that need to be regressed before the model can be used. The particle swarm optimization (PSO) method was successfully used to regress the NRTL parameters from liquid–liquid equilibria (LLE) data and the resulting parameters showed smaller root-mean square deviations (RMSD) compared with literature values. Analysis of the results revealed that multiple groups of parameters with sufficiently small RMSDs can be found for the same set of LLE data. The activities calculated using these parameters and their corresponding predicted mole fractions can be far beyond the reasonable range of activity, demonstrating that the NRTL model does not always represent the intrinsic activities of components with these parameters. Finally, extraction of phenol by toluene in the presence of sodium hydroxide was investigated with varying pH and varying concentration of sodium hydroxide to mimic extraction of alkaloids as acidity constant of phenol is close to that of many alkaloids, for example morphine. The phase equilibrium was modelled by the symmetric eNRTL model using the developed PSO method and the correlation agreed well with the experimental results. II Declaration This is to certify that: (i) the thesis comprises only my original work towards the PhD except where indicated in the Preface, (ii) due acknowledgement has been made in the text to all other material used, (iii) the thesis is fewer than 100 000 words in length, exclusive of tables, maps, bibliographies and appendices. Zheng Li August 2015 III Preface Results in Sections 2.2 and 2.3 have been published, or are waiting for publication, in the following forms: Li, Z.; Mumford, K. A.; Shang, Y.; Smith, K. H.; Chen, J.; Wang, Y.; Stevens, G. W., Analysis of the nonrandom two-liquid model for prediction of liquid– liquid equilibria. J. Chem. Eng. Data 2014, 59, (8), 2485-2489. Li, Z.; Mumford, K. A.; Smith, K. H.; Chen, J.; Wang, Y.; Stevens, G. W., Reply to “Comments on ‘Analysis of the nonrandom two-liquid model for prediction of liquid–liquid equilibria’”. J. Chem. Eng. Data 2015, 60, (5), 1530-1531. Li, Z.; Mumford, K. A.; Smith, K. H.; Chen, J.; Wang, Y.; Stevens, G. W., Solution structure of isoactivity equations using the nonrandom two-liquid model for liquid–liquid equilibrium calculations. In preparation. Results in Sections 3.2, 3.3 and 3.4 have been included in the following journal paper: Li, Z.; Smith, K.H.; Mumford, K.A.; Wang, Y.; Stevens, G.W., Regression of NRTL parameters from ternary liquid–liquid equilibria using particle swarm optimization and discussions. Fluid Phase Equilibria 2015, 398, 36-45. Results in Sections 4.2, 4.3 and 4.4 have been presented in the following journal paper and refereed conference proceedings: Li, Z.; Mumford, K. A.; Shang, Y.; Smith, K. H.; Chen, J.; Wang, Y.; Stevens, G. W., Extraction of phenol by toluene in the presence of sodium hydroxide. Sep. Sci. Technol 2014, 49, (18), 2913-2920. Li, Z.; Mumford, K. A.; Smith, K. H.; Stevens, G. W., Experimental and model study on the extraction of phenol by toluene. The 20th international solvent extraction conference. Wurzburg, Germany, September 2014. IV Acknowledgement Gratitude fills my heart when I am able to summarize my work and write this thesis. I was lucky to have the opportunity to meet many awesome people from all walks of life during my PhD study, without their support and help I would not have gone through the PhD journey. I would like to sincerely thank them for their support, encouragement and friendship. First and foremost, I would like to express my sincere acknowledgement to Prof. Geoffrey Stevens for recruiting and supervising me for my PhD study. Since receiving the very first email of mine for enquiring a potential PhD position, he has been patiently and thoughtfully supporting my study and associated affairs. His continuous support and encouragement is the source of power pushing me forward. Dr. Kathryn Smith and Dr. Kathryn Mumford started to help me as my co-supervisors when my project was changed to be thermodynamic modelling, which was a hard decision to make. They devoted lots of time to discuss with me and provided me with constructive suggestions. Their expertise and generous help made my new project went much smoother. For this, I owe them big. Equal thanks go to Dr. Jilska Perera who co-supervised me for study on kinetics of solvent extraction in the first year, during which I was trained for a series of experimental techniques and critical thinking. These skills were very useful in my following studies. I would like to thank Mr. Justin Fox in the engineering workshop and Mr. Leslie Gamel from workshop of physics for constructing experimental equipments. Mr. David Danaci is thanked for his generous help in the trouble shooting of leakage. Thanks to Mr. Edward Nagul and Ms. Kezia Kezia for kind help in developing HPLC methods. Mr. Indrawan Indrawan and Ms. Alita Aguiar are thanked for their patient training for instrument utilization and assistance in apparatus setup. I am also grateful for Mr. Di Che and Dr. Guang Wen for their help in debugging MATLAB programs. Co-authors of my papers, including Prof. Jian Chen at Tsinghua University, Mr. Yidan Shang at the RMIT University and Dr. Yong Wang who shares the same office V with me, are acknowledged for their valuable contributions. Prof. Sandra Kentish is sincerely thanked for her precious and detailed comments on my work regarding a membrane model, despite this work is not included in the thesis. Acknowledgement also goes to Prof. Ray Dagastine for supervising me working as a demonstrator, which was a pleasant experience. I would also like to thank Prof. Hans-Jörg Bart for allowing me to visit his lab at Technische Universität Kaiserslautern. Ms. Hanin Jildeh, Mr. Felix Gebauer and their colleagues in the lab warmly welcomed me. I feel grateful for their hospitality. I had the opportunity to visit Profs. Wei Qin and Jichu Yang at Tsinghua University. Their work in recovery of salt brine resources inspired me deeply. I also had a chance to discuss some potential future research projects with Profs. Weiyang Fei and Yujun Wang from the same university. I would like to sincerely thank these professors for their precious time. Friendships with many awesome people, including Dr. Davide Ciceri, Dr. Judy Lee, Dr. William Lum, Dr. Apple Koh, Dr. Jiwei Cui, Dr. Qiang Fu, Dr. Alex Duan, Dr. Zhou Zhang, Mr. Lachlan Mason, Dr.