Thermodynamics and Machine Learning Based Approaches for Vapor–Liquid–Liquid Phase Equilibria in n-Octane/Water, as a Naphtha–Water Surrogate in Water Blends
Abstract
:1. Introduction
2. Approach Adopted in the Present Study
3. Specific Strategy
n-Octane | Naphtha [21] | |
---|---|---|
Carbon number | 8 | 6–13 |
Molecular weight (g/gmole) | 114.23 | 145 |
Boiling point (°C) | 125.6 | 65–230 |
Density (kg/m3) | 703 | 781 |
Conditions | Ref. | |
---|---|---|
Temperature: 5–25 °C | Mutual solubilities. | [22] |
Temperature: 0–430 °C | Mutual solubilities. Liquid–liquid equilibrium. | [23] |
Temperature: 5–75 °C | Vapor–liquid equilibrium | [24] |
Temperature: 0–568 °C | Vapor–liquid equilibrium | [25] |
Temperature: 25 °C | Mutual solubilities | [26] |
Temperature: 0–25 °C | Mutual solubilities | [27] |
Temperature: 357–387 °C Pressure: 19–23 MPa | Liquid–liquid–vapor equilibrium | [28] |
3.1. Materials
3.2. CREC Vapor Liquid Equilibrium Cell
4. Mathematical Formulation
4.1. Vapor–Liquid–Liquid Equilibrium Using NRTL Model
4.2. Gibbs Energy Analysis from Activity Coefficient Model
5. Results and Discussion
5.1. Issues with Available Models while Evaluating VLLE
- Discrepancies between models when running with two different available software (e.g. HYSYS V9 and Aspen Plus V9).
- Inconsistency of the available thermodynamic model predictions (e.g. Aspen Plus V9) with available experimental data.
5.2. Theoretical Discussion of Model Discrepancy
5.3. Analysis of Experimental Results
- (a)
- Three coexisting liquid–liquid–vapor (VLL) phases with the vapor pressure remaining unchanged, while the initial water composition is varied (horizontal broken line).
- (b)
- Two liquids phases at higher pressures, with every phase involving highly diluted blends,
- (c)
- Two phases, vapor and liquid, with the liquid phase encompassing completely solubilized species.
- (d)
- A mixed vapor phase at low pressures.
6. The Machine Learning Approach
6.1. Classification Methodology
6.2. Classification Models Results
7. Conclusions
- It is shown that reliable models, based on fundamentals principles, are still needed to represent the number of phases, in diluted hydrocarbon in water mixtures at phase equilibria.
- It is proven that a phase stability analysis involving the Gibbs energy of mixing, can be used to explain calculation result discrepancies, in water/n-octane mixtures when using available simulation software.
- It is demonstrated that runs in a CREC VL Cell employing a dynamic technique (1.22 °C/min temperature ramp), can provide the “big data sets” required to accurately determine the fully miscible, partially miscible, and fully immiscible octane/water blend states.
- It is proven that ML models based on the obtained “big data sets” can be proposed for the prediction of the number of phases under the studied conditions, with the KNN model and the weighted SVC model, identified as the ones with best performance.
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbols with Latin letter | |
F | Function |
G | Gibbs Free Energy |
P | Pressure |
R | Universal Gas Constant |
T | Temperature |
x | Molar Fraction of Liquid Phase |
y | Molar Fraction of Vapor Phase |
z | Overall Molar Fraction |
Parameter for accounting local composition variations (NRTL method) | |
Activity coefficient | |
Interaction energy (NRTL method) | |
Dimensionless interaction parameters (NRTL method) | |
Subindex and Superindex | |
identifies component of the solution | |
identifies component of the solution | |
identifies a subgroup | |
L | Liquid |
mix | mixing |
obj | objective |
sat | Saturation |
V | vapor |
I | Phase I |
II | Phase II |
Acronyms | |
ANN | Artificial Neural Networks |
AUC | Area Under Curve |
BIP | Binary Interaction Parameters |
CREC | Chemical Reactors Engineering Center |
EoS | Equation of State |
FN | False Negative |
FNN | Feedforward Neural Networks |
FP | False Positive |
FPR | False Positive Rate |
KNN | K-Nearest Neighbors |
LL | Liquid–Liquid |
LLE | Liquid–Liquid Equilibrium |
ML | Machine Learning |
NRTL | Non-Random Two-Liquid Model |
NRU | Naphtha Recovery Unit |
PC | Personal Computer |
PNN | Probabilistic Neural Networks |
PR-EoS | Peng–Robinson-Equation of State |
ROC | Receiver Operating Characteristic |
RVM | Relevance Vector Machines |
SVM | Support Vector Machine |
SVC | Support Vector Classification |
TN | True Negative |
TP | True Positive |
TPR | Three Phase Region |
UNIQUAC | Universal Quasichemical model |
USB | Universal Serial Bus |
VL | Vapor–Liquid |
VL Cell | Vapor–Liquid Cell |
VLE | Vapor-Liquid Equilibrium |
VLL | Vapor–Liquid–Liquid |
VLLE | Vapor–Liquid–Liquid Equilibrium |
Appendix A
Appendix A.1. Brief Description of Classification Models
Appendix A.1.1. Logistic Regression
Appendix A.1.2. Decision Tree Classifier
Appendix A.1.3. K-Nearest Neighbors (KNN)
Appendix A.1.4. Support Vector Machine (SVM)
Appendix A.2. Additional Figures
Appendix A.3. The CREC VL Cell and Its Instrumentation
Name | Volume |
---|---|
Thermofluid | 2.4 L |
CREC-VL-Cell | 275 mL |
Sample analyzed | 100 to 140 mL |
Instrument | Parameter | Data Range | Uncertainty (±) [10,11] |
---|---|---|---|
OMEGATM Transducer PX409-50GUSBH Series | Pressure | 0–345 kPa5 Hz frequency | ±0.28 kPa |
OMEGATM USB TC-08 Unit | Temperature data acquisition rate | 10 Hz frequency | 1% |
OMEGATM PID Controller | Temperature increase rate in the Cell | 4 to 20 mA | ±0.5 °C |
Thermocouple:OMEGATM type k | Temperature | −200 to 1250 °C | ±2.2 °C |
VELP® DLS Digital Overhead Stirrer | Torque Maximum | 40 Ncm | N/A |
Mixing speed | 50 to 2000 rpm |
Operation | Set Value |
---|---|
Impeller Mixing Speed | 1080 rpm |
Heating Rate | 1.22 °C/min |
Temperature Range | 30 to 120 °C |
Run Time | 90 min |
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Model | Boiling Point Difference | Dew Point Difference |
---|---|---|
Peng Robinson | Min: 5.67% Mean: 7.98% Max: 11.58% | Min: 1.78% Mean: 3.91% Max: 6.83% |
NRTL | Min: 92.88% Mean: 99.95% Max: 104.66% | Min: 34.12% Mean: 49.96% Max: 66.45% |
UNIQUAC | Min: 83.20% Mean: 86.28% Max: 90.39% | Min: 37.86% Mean: 62.98% Max: 48.89% |
70 °C | 100 °C | |||
---|---|---|---|---|
BIP reference | Water in Hydrocarbon phase (x1I) | n-Octane in Aqueous phase (x2II) | Water in Hydrocarbon phase (x1I) | n-Octane in Aqueous phase (x2II) |
Klauck et al. (2006) [6,29] | 3.32245 × 10−3 | 9.1571 × 10−7 | 9.56125 × 10−3 | 9.3652 × 10−7 |
Aspen Plus (Python) | 7.50095 × 10−3 | 8.1543 × 10−6 | 2.644388 × 10−2 | 2.1395 × 10−5 |
HYSYS (estimated BIP) | 8.9570 × 10−6 | 0.02069 | 1.3065 × 10−5 | 0.05936 |
HYSYS (zero) (* one single phase) | −6.1590 × 10−10 | 1 | −6.1590 × 10−10 | 1 |
Model # | Type | Hyper-Parameters | Class Weight Option |
---|---|---|---|
1 | Logistic Regression | penalty: 12, tol: 0.0001, C: 1.0, fit_intercept: True, intercept_scaling: 1 | Yes |
2 | Decision Tree Classifier | criterion: entropy, splitter: best, max_depth: 3, min_samples_split: 2, min_samples_leaf: 1 | Yes |
3 | K-Neighbors Classifier | n_neighbors: 5, weights: uniform, algorithm: auto, leaf_size: 30, p: 2, metric: Minkowski | No |
4 | Support Vector Classifier (SVC) | C:1.0, kernel: rbf, degree: 3, gamma: scale, shrinking: True, probability: True, tol = 0.001 | Yes |
Logistic Regression | |||
Precision | Recall | F1 score | |
3-Phases | 0.92 | 0.93 | 0.94 |
2-Phases | 0.78 | 0.83 | 0.80 |
Decision Tree Classifier | |||
Precision | Recall | F1 score | |
3-Phases | 1.00 | 0.90 | 0.95 |
2-Phases | 0.75 | 0.99 | 0.85 |
K-Neighbors Classifier (KNN) | |||
Precision | Recall | F1 score | |
3-Phases | 1.00 | 0.97 | 0.98 |
2-Phases | 0.91 | 1.00 | 0.95 |
SVC | |||
Precision | Recall | F1 score | |
3-Phases | 1.00 | 0.93 | 0.96 |
2-Phases | 0.80 | 0.99 | 0.88 |
Logistic Regression (penalized) | |||
Precision | Recall | F1 score | |
3-Phases | 0.92 | 1 | 0.96 |
2-Phases | 1 | 0.72 | 0.84 |
Decision Tree Classifier (penalized) | |||
Precision | Recall | F1 score | |
3-Phases | 0.95 | 1.00 | 0.97 |
2-Phases | 1.00 | 0.82 | 0.90 |
K-Neighbors Classifier (KNN) | |||
Precision | Recall | F1 score | |
3-Phases | 1.00 | 0.99 | 0.99 |
2-Phases | 0.97 | 0.98 | 0.98 |
SVC (penalized) | |||
Precision | Recall | F1 score | |
3-Phases | 0.98 | 1 | 0.99 |
2-Phases | 1 | 0.94 | 0.97 |
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Lopez-Zamora, S.; Kong, J.; Escobedo, S.; Lasa, H.d. Thermodynamics and Machine Learning Based Approaches for Vapor–Liquid–Liquid Phase Equilibria in n-Octane/Water, as a Naphtha–Water Surrogate in Water Blends. Processes 2021, 9, 413. https://doi.org/10.3390/pr9030413
Lopez-Zamora S, Kong J, Escobedo S, Lasa Hd. Thermodynamics and Machine Learning Based Approaches for Vapor–Liquid–Liquid Phase Equilibria in n-Octane/Water, as a Naphtha–Water Surrogate in Water Blends. Processes. 2021; 9(3):413. https://doi.org/10.3390/pr9030413
Chicago/Turabian StyleLopez-Zamora, Sandra, Jeonghoon Kong, Salvador Escobedo, and Hugo de Lasa. 2021. "Thermodynamics and Machine Learning Based Approaches for Vapor–Liquid–Liquid Phase Equilibria in n-Octane/Water, as a Naphtha–Water Surrogate in Water Blends" Processes 9, no. 3: 413. https://doi.org/10.3390/pr9030413