Chemical and Biomolecular Engineering - Theses
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ItemThermodynamic modelling of liquid–liquid equilibria using the nonrandom two-liquid model and its applications( 2015)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 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.