Two new apparatuses have been developed to measure solid-liquid and liquid-liquid equilibria through a synthetic visual method with the determination of thermal signatures. Both devices have been semi-automated to increase accuracy and improve efficiency of data measurements.
Introduction
Importance of Solid-Liquid and Liquid-Liquid Equilibria
The study of solid-liquid equilibria is essential for the design of separation processes, such as crystallization. Finally, application of solid-liquid equilibrium data is also used for the determination of parameters in thermodynamic models.
Background to Work and Objectives
As a follow-up to this work, measurements of solid-liquid equilibria are made for binary mixtures of carboxylic acids. The focus of the work in this study has been on SLE measurements of carboxylic acids and the most important ones.
Theoretical Review of Solid-Liquid and Liquid-Liquid Equilibria
Criterion for Equilibrium
Liquid-Liquid Equilibrium
- Liquid-Liquid Equilibrium in Binary Systems
- Thermodynamic Description of Binodal Curves
- Thermodynamic Treatment of Liquid-Liquid Equilibrium
Solid-Liquid Equilibrium
- Phase Diagrams
- Thermodynamic Description of Phase Diagrams
- Thermodynamic Description of Solid-Liquid Equilibria
Activity Coefficient Models
- Activity Coefficient Models Used in this Work
- Wilson Model
- NRTL (Non Random Two Liquid Equations)
- The UNIQUAC Model
Review of Experimental Apparati and Methods
Analytical Methods
The analytical method of determining the liquid-liquid equilibrium requires the measurement of the composition of the immiscible phases of the system. The cell had two sample points, one at the top of the cell to sample the lighter phase and one at the bottom of the cell to sample the heavier phase (Figure 3-1).
Synthetic Methods
A schematic diagram of the apparatus by Ochi and co-workers (1993) is given in Figure 3-2 which is an example of an LLE cell for the synthetic method. The video camera is directed to look into the equilibrium cell through the side of the apparatus at a right angle to the He-Ne laser (not shown in Figure 3-3).
Experimental Methods for Measuring Solid-Liquid Equilibrium Data
- Analytical Methods
- Synthetic Method
- Thermal Signatures
- Visual Method
- Apparati requirements for the measurement of SLE and LLE
- Solid-Liquid equilibria apparatus of Jakob et al. (1995)
- Apparatus of Torzo et al. (2007)
- Other SLE and LLE Apparati
Equipment Description and Procedures
Glass Apparatus
- Equipment List
- Equilibrium Cell and Apparatus Assembly
- Temperature Measurement and Data Capture
- Cooling and Heating
The Peltier Solid-Liquid Equilibrium Apparatus
- Equipment List
- The Equilibrium Cell and Apparatus Assembly of the Peltier Setup
- Data Capture
Software – Peltier and Glass Apparati
- Description of Interfaces
Operating Procedures for the Apparati
- Cleaning of the Apparati
- Temperature Sensor Calibrations
- Purity of Chemicals and Sample Preparation
- Experimental Procedure for the Peltier Apparatus (SLE)
- Apparatus Start Up and Operating Procedure
- Analysis of Results
- Shut-Down Procedure
- Experimental Procedure for the Glass Apparatus (SLE)
- Start up Procedure
- Shut-Down Procedure
- Liquid-liquid Equilibria Experimental Procedure Using the Peltier Apparatus
- Analysis of LLE Results
- Experimental (LLE) Procedure Using the Glass Apparatus
Evaluation of Equipment
- Design and Operation of Equipment
- Peltier Apparatus
- Glass Apparatus
Analysis of Results
- Analysis of Solid-Liquid Equilibria Results
- Analysis of LLE Results
Results and Discussion
Systems Measured
The binary test systems for melting points were the cyclohexane + hexadecane system, measured on both apparatuses separately, and the 2-butanol + water system, measured only on the Peltier apparatus, for solid-liquid equilibrium measurements. Since the 2-butanol + water system has a region of immiscibility, liquid-liquid equilibria were also measured to demonstrate the versatility of the apparatus. These measurements constituted new systems whose solid-liquid equilibria had previously been unmeasured and are part of ongoing research into solid-liquid equilibria of carboxylic acid mixtures.
The motivation for measuring these systems stems from the fact that extensive vapor-liquid equilibria work has been done on carboxylic acids (Sewairan, 2001, Clifford, 2004, and Iwarere, 2009), but no investigation has been made of solid-equilibria. of fluids. In addition to phase equilibrium data (VLE and LLE) for separation, solid-liquid equilibria can significantly contribute to obtaining low-temperature parameters for various systems and thus improve thermodynamic predictions made for these systems and systems Similar. Solid-liquid equilibrium data for carboxylic acid mixtures are minimal in the literature with only a few combinations having been measured for C1 to C7 acids (refer to Table.
Temperature Calibrations
The scatter plot for the Peltier Pt-100 (Figure 5-2) shows a less even spread than that of the Glass device. One of the factors that contributed to this was the positioning of the Pt-100s in the calibration bath. The standard probe was a long, straight probe, like the sample Pt-100 for the Glass equipment.
The Pt-100 sample for the Peltier apparatus, however, was L-shaped and shorter compared to the other two probes. However, the shape of the Peltier probe probe may have caused it to shift, causing the tip of the probe to be misaligned with the tip of the standard probe. This would result in larger errors recorded on the Pt-100 Peltier sample compared to the Glass apparatus, despite the fact that both Pt-100s were of the same type and accuracy.
Purity of Chemicals
Test Systems
- Pure Component Melting Points
- The Cyclohexane (1) + Hexadecane (2) System
- The 2-Butanol (1) + Water (2) System
- Liquid-Liquid Equilibrium
The limiting temperature of the Peltier apparatus was 253.15 K and the melting point of octanol 5.23 K above the minimum temperature. The purpose of measuring the melting points in the area of the Peltier apparatus was also to determine the accuracy of the temperature measurements. The absolute mean deviation for the Peltier device compared to the glass was 0.14 K and is in the same range as the literature values.
The mean absolute deviation of the Peltier apparatus from the literature was 0.08 K, which was lower than that of the Glass apparatus, which was 0.12 K. The mean absolute deviations of the melting points (Table 5-5) compared to the literature values were in acceptable limits (area K). A comparison of the experimental data and the data of Ochi with colleagues showed very large discrepancies.
New Systems
- The Heptanoic Acid (1) + Butyric Acid (2) System
- The Heptanoic Acid (1) + Hexanoic Acid (2) System
- Discussion of Results
- Modelling Background
- Modelling Results
In the heptanoic acid + hexanoic acid system, there could have been a possibility of the existence of a peritectic point in the heptanoic acid-rich branch of the phase diagram. The temperature profile of the phase diagram for the heptanoic acid + hexanoic acid system is similar to that of Costa and co-workers for the SLE binary system of capric acid + lauric acid (Figure 5-10). After several experimental measurements, it was found that the value of the parameter can be estimated to be 0.3 (Prausnitz et al. 1999).
The results of modeling the measured data for all systems using local composition models are shown graphically in the following figures. From the values of the activity coefficients calculated using the models, it was clear that the system is almost ideal. Two points located directly in front of the immiscibility zone were found not to fit all models.
Conclusions
Each system was modeled with all three models (Wilson (1964), NRTL (1968) and UNIQUAC (1975)) and it was found that the UNIQUAC model gave the best overall results for the cyclohexane + hexadecane test and the 2-butanol + water test. systems. From these results, different model parameters are made available for each of the systems. Not only were both apparatuses tested by measuring known systems, but based on the reliability of these results, these apparatuses were used to generate new solid-liquid equilibrium data for two binary carboxylic acid mixtures.
The calculated deviations showed that the NRTL model provided the best fit to the results with a mean absolute deviation of 0.61 K for the heptanoic acid + hexanoic acid system and 0.49 K for the heptanoic acid + hexanoic acid system. The measurement of these systems provides phase equilibrium data that can be used to simulate the crystallization process and/or that can be used for design purposes. From the modeling results it can be concluded that the local composition models can be sufficiently applied to the modeling of n-alkyl carboxylic acid mixtures and with these parameters the phase equilibrium of similar systems can be predicted.
Recommendations
For the analysis procedure of data obtained from both apparatus, the data points were found to be too many for analysis. The procedure can be improved by averaging a larger amount of data points (temperature readings) to reduce the volume of data to be analyzed during analysis than the number used (180 data points) used. According to the overview in Table 1-1, these systems are the binary carboxylic acid mixtures yet to be measured for SLE.
The data have thermodynamic significance in the design of separation processes such as crystallization and will contribute to the flexibility and temperature dependence of thermodynamic model parameters. However, for the acid systems, if a peritectic point is suspected or determined, the modeling results can be improved by considering the solid-phase non-idealities. An example is the procedure used for modeling solid-phase non-idealities in fatty acids by Costa et al.
Gibbs Phase Rule
Chemical Potential
Fugacity and Activity
- Fugacity in Phases
- Fugacity in Solution, Excess Properties and Activity Coefficients
Caloric Methods
- Adiabatic Calorimetry
- Differential Scanning Calorimetry (DSC)
- Apparatus by Wahayudi et al. (1989)
- Other Caloric Equipment
- Apparatus by Coutinho et al. (1998)
Synthetic Methods
- Apparatus of Di Nicola et al., (2008)
- Apparatus of Domanska (1996)
- Apparatus of Zhang et al. (1998)
- Apparatus of Schrödle et al. (2003)
- Apparatus of Wachter et al. (2008)
Uncertainties in Test System Measurements
Uncertainties in New System Measurements
Equilibrium cell transparency or some form of visualization technique into the cell is required. The rear sensor was suspended horizontally on the top surface of the sample inside the balance cell.
The numbers refer to features in Figure 4.1 and the letters of the alphabet refer to features shown in Photo 4-1 and Photo 4-2. The equilibrium cell is a cylindrical glass vessel with a height of 200 mm and a diameter of 30 mm. The glass device is transparent and allows visual observation of the sample in the equilibrium cell. A camera is built into the device for visual observation of the sample in the cell.
In this way, by adjusting the power supplied to the Peltier modules, the temperature of the sample can be controlled. In the configuration interface, the software operation is manual or automatic for the Peltier device. It is a rapid melting stage and raises the temperature of the sample to near and below the equilibrium temperature.
Follow steps 1 through 14 of the solid-liquid-equilibrium-equilibrium start-up procedure for the Peltier apparatus. Align the camera to the side of the balance cell so the sample can be viewed.
For the Peltier apparatus, it was observed that the greatest uncertainty in temperature reading recorded was for the measurement of octanol, which has a melting point close to the limiting temperature of the apparatus. The temperatures of the environment during these measurements were unfortunately very high due to the season. Supercooling distorts the identification of the equilibrium temperature and the equilibrium shape of the crystals (Nyvlt, 1977).
The measurement of the melting points within the miscibility gap was difficult due to the presence of two phases in the sample. The number of independently variable intensive properties required to determine the state of the system. The equation describing chemical potential comes from the description of the Gibbs energy (Prausnitz et al., 1999);
The temperature probe used was from the National Institute of Standards and Technology (NIST) and was reported to have an accuracy of better than 0.01 K. The temperature measured by the probe is taken as the sample temperature). The apparatus measured the solid-liquid as well as liquid-liquid balance using the visual method by analyzing the temperature profile.
