Visualization of High-Dimensional Liquid−Liquid Equilibrium Phase Diagrams

Abstract

Liquid−liquid extraction is usually used along with other separation processes for the recovery of pure components. It is desirable that the liquid−liquid equilibrium (LLE) phase behavior, which is the thermodynamic basis for liquid−liquid extraction, be represented in a phase diagram. This is because the visualization of process limitations has a crucial role in the construction of feasible separation schemes for achieving the overall separation objective. However, because most applications involve multicomponent mixtures, visualization of the LLE phase diagram in its entirety becomes difficult or even impossible. Therefore, a visualization approach to represent high-dimensional LLE phase diagrams based on projections and cuts to reduce dimensionality is proposed. In such an approach, the liquid−liquid immiscibility regions are represented as a collection of projected tie lines. By superimposing the resulting diagram with any other map of process boundaries in composition space, such as a solid−liquid equilibrium phase diagram, one can clearly observe the possible use of liquid−liquid extraction in crossing the boundaries, an option that is not apparent when only numerical data are presented. Two common separation scenarios are used to demonstrate the applicability and advantages of this approach, particularly in illustrating the close interactions of liquid−liquid extraction with distillation and crystallization.

Liquid–Liquid Equilibria of Quaternary Systems Composed of 1,3-Propanediol, Short-Chain Alcohol, Water, and Salt

“…To represent the phase compositions from the three-dimensional tetrahedron in two dimensions, different projections are available . The method devised by Cruickshank et al is based on projections which are parallel to two axes of the quaternary tetrahedron and lead to square diagrams.…”

“…To represent the phase compositions from the threedimensional tetrahedron in two dimensions, different projections are available. 37 The method devised by Cruickshank et al 38 is based on projections which are parallel to two axes of the quaternary tetrahedron and lead to square diagrams. The experimental results for 1,3-propanediol contents of 0 wt % 1,3-propanediol and 20 wt % 1,3-propanediol in the system K 2 HPO 4 + water + ethanol + 1,3-propanediol are shown in Figure 3 using Cruickshank projections.…”

Synthesis of Supercritical Crystallization Processes

“…The discussion on phase behavior is not exhaustive in order to maintain focus on process design. In reality, the phase behavior can be more complex, such as the presence of liquid−liquid phase split. , While thermodynamics provides a good starting point for designing supercritical crystallization processes by identifying the feasible range of operating conditions, kinetic and mass transfer effects also need to be considered . For example, controlling supersaturation level during crystallization, such as by adjusting the rate of depressurization, is often the key to obtaining the desired particle size and morphology.…”

Experimental determination of solid‐liquid‐liquid equilibrium phase diagrams

“…Because of the high dimensionality, it is impossible to visualize the phase diagram in its entirety. To analyze the phase behavior of such a system, appropriate cuts and projections should be taken to reduce the dimensionality 10. One option is to combine two components as a single pseudo‐component, which produces a three‐dimensional, polythermal constant‐composition cut.…”