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Predicting Thermodynamic Properties of R1234yf/R152a Mixtures Using Machine Learning and PRSV Equation of state

This study demonstrates that machine learning models, particularly Gradient Boosting for compressibility factor and SVR-RBF for density, outperform or match the accuracy of the PRSV and Tait equations of state in predicting the thermodynamic properties of R1234yf/R152a refrigerant mixtures based on experimental PVTx data.

Original authors: Sadegh Sahraei, Fatemeh Karami, Mohammad Mahdi Tafarroj

Published 2026-09-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sadegh Sahraei, Fatemeh Karami, Mohammad Mahdi Tafarroj

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The world of refrigeration is undergoing a quiet but urgent transformation. For decades, the cooling systems in our cars, homes, and supermarkets relied on chemicals called hydrofluorocarbons. While these substances were safe for the ozone layer, they turned out to be potent drivers of global warming. In response, international agreements have pushed for a phase-down of these older gases, creating a race to find replacements that are gentle on the climate. The new candidates are often single chemicals or carefully balanced mixtures, designed to cool efficiently without trapping excessive heat in the atmosphere. However, designing a system that uses these new fluids requires knowing exactly how they behave under different conditions. Engineers need to predict how much a gas will squish when squeezed, or how heavy a liquid will become when cooled. These properties change in complex ways depending on temperature, pressure, and the exact mix of chemicals, making accurate prediction a difficult but essential task for building reliable, eco-friendly cooling systems.

In a recent study, researchers set out to solve this prediction puzzle for a specific, promising mixture: a blend of two refrigerants known as R1234yf and R152a. This combination is attractive because it balances low environmental impact with good performance, and in some cases, the mix can even reduce flammability risks compared to its individual components. To understand how this mixture behaves, the team gathered 145 specific data points from previous experiments. These points covered a range of temperatures from just above freezing to a warm summer day, and pressures that span from moderate to quite high. The goal was to see if modern computer programs, known as machine learning, could learn from this data to predict two critical properties: the compressibility factor, which tells us how much the gas deviates from ideal behavior, and the density, which is simply how heavy the fluid is for a given volume.

The researchers pitted four different types of machine learning algorithms against each other and against traditional physics-based formulas. The machine learning models included methods that build decision trees, others that find patterns by looking at the closest neighbors in the data, and sophisticated techniques that map complex curves. They also tested a classic thermodynamic formula called the PRSV equation, which has been used for decades to describe how gases and liquids behave, along with a simpler empirical formula known as the Tait equation. The team fed the computer models the temperature, pressure, and the exact amount of one chemical in the mix, then asked them to guess the compressibility and density. They then compared these guesses to the actual experimental numbers to see which method was the most accurate.

The results revealed a clear split in how well the different approaches worked, depending on which property was being predicted. When it came to the compressibility factor, the machine learning models proved to be the superior tools. One specific algorithm, which works by building a series of models that correct the mistakes of the previous ones, achieved the highest accuracy. It captured the subtle, non-linear twists and turns of the data far better than the traditional physics formulas. The best traditional formula, even when tweaked to account for how temperature changes the interaction between the two chemicals, still fell short. The traditional approach relies on simplified rules to describe how molecules interact, and in this case, those rules were not complex enough to fully capture the behavior of the mixture. The machine learning model, by contrast, learned the patterns directly from the data without needing those simplified rules, allowing it to navigate the complex landscape of the gas behavior with greater precision.

The story was quite different when the researchers looked at density. For this property, the playing field leveled out significantly. The machine learning models still performed well, with one method achieving near-perfect accuracy, but the traditional physics-based formulas were almost as good. The classic PRSV equation, when adjusted with a specific mathematical relationship for temperature, matched the data with remarkable closeness, and the simpler Tait equation also came very near. This suggests that density behaves in a more straightforward, predictable way than the compressibility factor. It follows a smoother path that both the complex computer models and the established physical laws can describe with high confidence. The fact that a simple, decades-old formula could compete with modern artificial intelligence on this specific task highlights that not every thermodynamic property requires a black-box computer solution; sometimes, the fundamental laws of physics are sufficient.

Throughout the study, the researchers also examined which factors mattered most. They found that pressure was the dominant force driving changes in both density and compressibility. As pressure increased, the fluid became significantly denser and its compressibility changed in a predictable way. Temperature played a secondary role, and the exact ratio of the two chemicals in the mix had a surprisingly small direct effect on the linear trends, though the machine learning models were able to pick up on the subtle, non-linear ways composition influenced the results. This focus on pressure aligns with basic physical intuition: squeezing a fluid makes it heavier and changes how it behaves, while the specific blend of chemicals matters less than the force applied to it.

The study concludes that for designing systems using this specific refrigerant blend, machine learning offers a distinct advantage when predicting the complex behavior of the gas, particularly the compressibility factor. However, for predicting density, engineers can rely on either advanced computer models or well-established physical equations with equal success. The work does not suggest that one method is universally better than the other; rather, it shows that the best tool depends on the specific property being measured. By demonstrating that data-driven methods can outperform traditional formulas for certain complex behaviors, the research provides a new pathway for engineers to design more efficient and environmentally friendly cooling systems, ensuring they can harness the full potential of these new, low-impact refrigerants.

Technical Summary: Predicting Thermodynamic Properties of R1234yf/R152a Mixtures Using Machine Learning and PRSV Equation of State

Problem Statement
The global phase-down of high-GWP hydrofluorocarbons (HFCs) has necessitated the adoption of eco-friendly refrigerants, specifically binary mixtures such as R1234yf/R152a. While these mixtures offer low Global Warming Potential (GWP) and acceptable safety profiles, their thermodynamic behavior involves complex, non-linear interactions between temperature, pressure, and composition. Accurate prediction of the compressibility factor ( $Z$ ) and density ( $\rho$ ) is critical for the design and optimization of refrigeration systems. Traditional modeling approaches, such as cubic equations of state (EoS), often struggle to capture subtle non-linear trends, particularly in the near-critical region, and may require computationally intensive fitting of complex coefficients. Conversely, while machine learning (ML) has shown promise in other domains, its comparative efficacy against classical thermodynamic models for this specific refrigerant mixture requires systematic evaluation.

Methodology
The study utilized a dataset of 145 experimental PVTx points for R1234yf/R152a mixtures, covering mass fractions of R1234yf from 0.60 to 0.90 and temperatures between 288.15 K and 328.15 K. The input features were temperature ( $T$ ), pressure ( $P$ ), and mass fraction ( $w$ ), with the target variables being the compressibility factor and density.

The research employed a dual-approach methodology:

Machine Learning Models: Four regression algorithms were trained and optimized using 5-fold cross-validation and grid search for hyperparameter tuning:
- Gradient Boosting (GB)
- Random Forest (RF)
- Support Vector Regression with RBF kernel (SVR-RBF)
- K-Nearest Neighbors (KNN)
Thermodynamic Models:
- PRSV Equation of State: The Peng-Robinson-Stryjek-Vera (PRSV) EoS was applied using van der Waals mixing rules. To enhance accuracy, the binary interaction parameter ( $k_{ij}$ ) was optimized using various temperature-dependent formulations (constant, linear, quadratic, exponential, and power-law).
- Tait Equation: An empirical correlation was used specifically for density prediction, optimized via the Levenberg-Marquardt algorithm.

Performance was evaluated using the coefficient of determination ( $R^2$ ), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).

Key Contributions and Results
The study provides a comparative analysis of data-driven and physics-based approaches for predicting the thermodynamic properties of R1234yf/R152a mixtures.

Compressibility Factor ( $Z$ ) Prediction:
- Machine Learning Superiority: Ensemble ML models outperformed classical equations of state. Gradient Boosting achieved the highest accuracy ( $R^2 = 0.8493$ , RMSE = 0.0207). SVR-RBF and Random Forest followed closely with $R^2$ values of 0.8389 and 0.8348, respectively.
- Limitations of PRSV: The PRSV equation, even with an optimized quadratic temperature-dependent $k_{ij}$ , yielded a lower $R^2$ of 0.7429. The constant $k_{ij}$ model performed the poorest ( $R^2 = 0.7080$ ). The authors attribute this gap to the inability of cubic EoS with simplified mixing rules to fully capture the complex non-ideal behavior of polar refrigerant mixtures.
- Feature Importance: Permutation analysis confirmed that pressure is the dominant driver for $Z$ predictions, aligning with Pearson correlation analysis ( $r = -0.864$ ).
Density ( $\rho$ ) Prediction:
- High Accuracy Across Methods: Unlike $Z$ , density prediction yielded near-perfect results across both ML and thermodynamic approaches. SVR-RBF achieved the highest accuracy ( $R^2 = 0.9996$ , RMSE = 0.2727).
- Competitive Thermodynamic Models: The PRSV equation with an exponential $k_{ij}$ formulation achieved $R^2 = 0.9971$ , closely followed by the Tait equation ( $R^2 = 0.9954$ ).
- Model Behavior: The authors note that ensemble ML models (GB and RF) underperformed relative to SVR and thermodynamic models for density ( $R^2 \approx 0.97$ and $0.95$), suggesting that the predominantly linear nature of density variations in this range is better captured by simpler functional forms or kernel methods than by complex tree-based ensembles.

Significance and Claims
The paper claims that the study demonstrates a clear divergence in modeling requirements based on the target property:

Non-linear Complexity: For the compressibility factor, which exhibits sharp non-linear variations, ensemble machine learning models (specifically Gradient Boosting) significantly outperform classical cubic equations of state.
Linear Predictability: For density, which follows a more linear and physically predictable relationship with state variables, both data-driven (SVR) and thermodynamic (PRSV, Tait) approaches yield near-identical, high-accuracy results.
Optimization of Classical Models: The study confirms that incorporating temperature-dependent binary interaction parameters ( $k_{ij}$ ) into the PRSV equation improves predictive capability (by approximately 5% for $Z$ ), though it does not bridge the performance gap with ML for non-linear properties.

The authors conclude that while machine learning offers superior accuracy for complex non-linear properties like the compressibility factor, classical thermodynamic methods remain highly competitive and computationally efficient for predicting density in this specific refrigerant mixture. The work supports the extension of data-driven approaches to binary refrigerant mixtures while validating the continued utility of optimized equations of state for specific thermodynamic properties.

Technical Summary: Predicting Thermodynamic Properties of R1234yf/R152a Mixtures Using Machine Learning and PRSV Equation of State

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