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Phase Diagrams

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...

Phase Transitions: Sublimation and Deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...

Phase Transitions: Vaporization and Condensation

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...

Phase Transitions: Melting and Freezing

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

Phase Diagrams of Ternary Systems

Phase Diagrams of Ternary Systems

Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...

Sublimation

Sublimation

Sublimation is the direct transformation of a solid to a gaseous state. For instance, at standard pressure and room temperature, solid carbon dioxide sublimes to gaseous carbon dioxide. The phase diagram depicts the conditions required for sublimation. This process occurs at the solid-gas phase boundary and is not observed above the triple point of the substance. The reverse of sublimation is called deposition, where a gaseous substance condenses directly into a solid. Sublimation and...

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Related Experiment Video

Updated: May 8, 2026

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

A Uniaxial Compression Experiment with CO₂-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

Published on: June 12, 2019

Interpretable modeling to forecast CO₂ solid phase boundaries in cryogenic methane rich systems.

¹College of Computer Sciences and Engineering, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia. e.kariri@psau.edu.sa.

Scientific Reports

|May 6, 2026

Summary

This study developed a data-driven model to predict carbon dioxide frost formation temperatures in natural gas. The CatBoost algorithm accurately forecasts frosting, enhancing safety and efficiency in cryogenic processing.

Keywords:

CO2 frosting CatBoost Machine learning Natural gas Predictive model

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Related Experiment Videos

Last Updated: May 8, 2026

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

A Uniaxial Compression Experiment with CO₂-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

Published on: June 12, 2019

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

Methane Hydrate Crystallization on Sessile Water Droplets

Methane Hydrate Crystallization on Sessile Water Droplets

Published on: May 26, 2021

Area of Science:

Chemical Engineering
Data Science
Thermodynamics

Background:

Unintended solid carbon dioxide formation during natural gas cryogenic processing causes operational hazards and financial losses.
Accurate prediction of frosting temperatures is crucial for safe and efficient natural gas purification.

Purpose of the Study:

To develop a highly accurate, explainable, data-driven framework for forecasting frosting temperatures.
To identify the most robust machine learning algorithm for predicting frost formation based on operating parameters.

Main Methods:

Trained and evaluated ten machine learning algorithms on a dataset of 430 experimental points.
Comprised molar concentrations of methane, carbon dioxide, nitrogen, and ethane.
Utilized SHapley Additive exPlanations (SHAP) for model interpretability.

Main Results:

Tree-based ensemble methods, particularly the CatBoost algorithm, showed superior predictive performance.
CatBoost achieved an R² of 0.9918 and an MRD of 0.55% on the test set.
SHAP analysis identified pressure and CO2 concentration as key drivers, while methane concentration mitigated frost formation.

Conclusions:

The developed CatBoost model offers a novel, transparent, and deployable prognostic tool for chemical engineers.
Bridging machine learning accuracy with thermodynamic interpretability establishes a trustworthy foundation for predictive modeling.
Empowers industrial operators to optimize natural gas purification, reduce energy costs, and ensure process safety.