Solid Vapor Equilibrium Research Articles

Solid–Vapor Equilibria under Desolvation of Solid Solutions. Topological Isomorphism with Phase Diagrams of Polymorphic Solid Solutions

Solid–Vapor Equilibria under Desolvation of Solid Solutions. Topological Isomorphism with Phase Diagrams of Polymorphic Solid Solutions

A novel numerical simulation approach for cryogenic CO2 frosting in binary mixture gas by integrating desublimation and gas-solid phase equilibrium models

Cryogenic CO2 separation from natural gas is a promising technology due to its environmental benefits and smaller spatial requirement. Nonetheless, the dynamics of CO2 desublimation and subsequent frost layer formation under cryogenic conditions for natural gas pre-treatment remain largely unexplored. Addressing this gap, this paper presents a novel numerical simulation approach by integrating desublimation phase change model and vapor-solid phase equilibrium model to investigate CO2 frost layer formation on the cold wall, revealing that both the cold wall temperature and the initial CO2 concentration significantly influence the thickness of the CO2 frost layer. Moreover, the study finds that the density of frost layer intensifies over time, with the highest density observed near the cold surface. Furthermore, increasing the cold wall temperature and the flow rate not only increases the average density of the CO2 frost layer but also affects the outlet CO2 concentration. To adhere to specific outlet CO2 concentration targets and desublimation duration, it is critical to adjust the cold wall temperature and the inlet flow velocity dynamically. Therefore, cryogenic CO2 removal methods, by reducing the spatial requirements of CO2 pre-treatment units, offer a practical and efficient solution for small-scale natural gas liquefaction plants. This approach not only facilitates operational efficiency but also contributes to the broader effort of mitigating greenhouse gas emissions, aligning with environmental sustainability objectives.

Cryogenic carbon capture design through [formula omitted] anti-sublimation for a gas turbine exhaust: Environmental, economic, energy, and exergy analysis

To achieve a net zero-emission society, current industries must transition to become less carbon-intensive while fulfilling the rising power demand. In this study, we present a novel multigeneration system that produces power, cooling, and solid carbon dioxide by applying cryogenic carbon capture to a gas turbine flue gas. The energy recovery concept is efficiently employed to avoid energy and exergy losses in the system. The system is simulated in Aspen Plus with the mathematical models of the exergy streams and solid-vapor equilibrium written in Matlab. The performance of the plant is assessed based on energy, exergy, economic, and environmental evaluations. Thermodynamic analysis indicates that 1.2 MJ of electricity is required to capture 1 kg of CO2 from the gas turbine exhaust gas (which is lower compared to conventional systems) with 100 % CO2 purity. The net generated power, energy efficiency, exergy efficiency, m˙CO2,captured, and m˙CO2,emitted for the proposed system are 179.4 MW, 41.2 %, 59.3 %, 500,000 tons annually, and 255,000 tons a year, respectively. Sensitivity analysis shows that reducing the flue gas temperature positively impacts the CO2 content in the flue gas while having a negative effect on energy and exergy efficiency. The economic investigation shows that the system is economically profitable.

Thermodynamic assessment of two-step nucleation occurrence in supercritical fluid

For the crystallization of an API in supercritical CO2, a two – step nucleation mechanism involves the apparition of metastable liquid droplets in the vapour phase composed of the API dissolved in the CO2, before crystallization. To find out the pressure and temperature conditions such a two – step mechanism could be observed, we studied the stability / metastability / instability for {(S)-Naproxen + CO2} and {(RS)-Ibuprofen + CO2} vapour binary mixtures. Thermodynamic computations proposed in the paper, have shown that a mixture of API and CO2 at elevated pressures can be unstable and/or metastable with respect to a liquid-vapour equilibrium and at the same time with respect to a solid-vapour equilibrium. Depending on the degree of supersaturation, such a mixture can potentially first decompose via spinodal decomposition into coexisting liquid and vapour phases, which turn due to nucleation and growth theory to a solid-fluid equilibrium.

Crystallization risk of aromatic compounds in LNG production. Part II: The solubility of p-xylene in methane-rich mixtures down to cryogenic temperatures

New measurements of solubility of solid p-xylene in solvents methane and (90%mol/mol)methane + (10%mol/mol)ethane have been carried out using a cryogenic apparatus and adopting a static-analytic method for temperatures from 273 K down to 128 K at nominal pressures of 3 and 6 MPa. Measured solid-liquid and solid-vapor equilibria have been compared to literature values of solubility of solid p-xylene in methane-rich phases and to modeling results obtained by coupling a cubic equation of state and a model for the solid phase. Results confirm the conclusions reported in our previous study of this system that evidenced of a non-monotonic variation of the solubility of p-xylene with temperature when crossing the critical region of the solvent and that binary interaction parameters regressed on vapor-liquid equilibrium can be used for predicting the solubility at cryogenic conditions.

A review on the solid–liquid–vapor phase equilibria of acid gases in methane

AbstractIn spite of the increasing levels of greenhouse gases in the atmosphere, and their impact on the environment, the demand for natural/biogas will increase significantly in the coming few decades. To cover this demand, the global energy industry is continuously exploiting sour gas reserves located around the world. Nonetheless, sour gas has to be sweetened before the practical utilization of natural or biogas. The cryogenic separation technologies have emerged as a new technology to separate carbon dioxide (CO2) and hydrogen sulfide (H2S gases) from natural/biogas. The cryogenic separation produces less harmful gases, and can be less expensive to operate and maintain in comparison to the conventional technologies. To design cryogenic separation equipment, vapor–liquid equilibrium (VLE), solid–liquid equilibrium (SLE), solid–vapor equilibrium (SVE), and solid–liquid–vapor equilibrium (SLVE) data for the corresponding binary systems (of CH4‐CO2, CH4‐H2S, and H2S‐CO2) and ternary system (of CH4‐H2S‐CO2) are required. The main target of this article is to review the SLVE data for the acid gases (CO2 and H2S) in methane (CH4) as the main constituent of natural/biogas. It will address SLVE data for the binary systems of CH4‐CO2, CH4‐H2S and H2S‐CO2 as well as the ternary system of CH4‐H2S‐CO2. It will not only address the available laboratory data, but it will also discuss, compare and evaluate the different models used to correlate/predict these data. © 2022 Society of Chemical Industry and John Wiley & Sons, Ltd.

Experimental investigation of the effect of nitrogen on the phase equilibrium behavior of the CH4–CO2 mixture at low temperature for natural and biogas purification

New fluid-fluid and solid-fluid(-fluid) equilibrium measurements at 4 MPa for the N 2 + CH 4 + CO 2 system have been carried out using a static-analytic method in order to investigate the effect of nitrogen on the phase equilibrium behavior of the methane + carbon dioxide mixture at temperatures between 170 K and 210 K. With respect to equilibria involving solid carbon dioxide, the addition of nitrogen to the mixture reduces the solubility of carbon dioxide in the fluid phase, widens the temperature region of existence of the solid-vapor equilibrium, and spreads the temperature range of existence of the solid-liquid-vapor equilibrium. The comparison between measured values and values calculated by means of the Peng-Robinson Equation of State as implemented in Aspen HYSYS® shows that tabulated binary interaction parameters (regressed with respect to fluid-fluid equilibria) are not always suitable when applied to the calculation of low temperature equilibria.

Simultaneous Multiphase Flash and Stability Analysis Calculations Including Solid CO2 for CO2–CH4, CO2–CH4–N2, and CO2–CH4–N2–O2 Mixtures

This work deals with solid–vapor equilibria and solid–liquid–vapor equilibria of carbon dioxide in mixtures of interest for natural gas purification and biogas upgrading. Experimental data available in the literature are reviewed and an algorithm for solving an isobaric–isothermal flash coupled to a phase stability analysis is presented, which does not require a-priori knowledge of the number and type of phases existing at equilibrium. The good agreement between calculation results, also performed with a tool that makes use of Gibbs free energy minimization, and experimental data suggests that the proposed approach can be used for determining suitable operating conditions for processes aimed at separating CO2 out of a gas by freezing it. This work points out that more experimental studies should be performed on phase equilibria in the presence of solid CO2 for multicomponent mixtures containing species other than methane (e.g., nitrogen and oxygen), which are representative of gaseous streams from which CO2 needs to be removed, such as natural gas, biogas, and flue gas from power plants. Such data are important for a proper calibration of thermodynamic models that must be selected for reliable process simulations.

Vapor–liquid equilibrium pressure of ethanolamine hydrochloride, and vapor–solid equilibrium pressure of methylamine, pyridine, and trimethylamine hydrochlorides by thermogravimetric method

In this work, vapor–liquid and vapor–solid equilibrium pressure and enthalpies of amine hydrochlorides were determined using a thermogravimetric method. Ferrocene was used as the reference compound to determine the calibration constant k. Then, ammonium bromide, ammonium chloride and benzoic acid were used for testing the k-ferrocene. Experimental vapor–solid equilibrium pressure of methylamine hydrochloride obtained in this study showed good agreement with recent literature data. For the other substances investigated, ethanolamine hydrochloride, pyridine hydrochloride, and trimethylamine hydrochloride, no reliable equilibrium data is available in the open literature. Among these substances, ethanolamine hydrochloride was found to be the less volatile, followed by methylamine, trimethylamine, and pyridine hydrochloride. Regarding the equilibrium enthalpies found in this work, all salts have shown a similar value. This can be explained by the similar reaction (dissociation) that takes place for these substances.

Estimating a Stoichiometric Solid’s Gibbs Free Energy Model by Means of a Constrained Evolutionary Strategy

Modeling of thermodynamic properties, like heat capacities for stoichiometric solids, includes the treatment of different sources of data which may be inconsistent and diverse. In this work, an approach based on the covariance matrix adaptation evolution strategy (CMA-ES) is proposed and described as an alternative method for data treatment and fitting with the support of data source dependent weight factors and physical constraints. This is applied to a Gibb’s Free Energy stoichiometric model for different magnesium sulfate hydrates by means of the NASA9 polynomial. Its behavior is proved by: (i) The comparison of the model to other standard methods for different heat capacity data, yielding a more plausible curve at high temperature ranges; (ii) the comparison of the fitted heat capacity values of MgSO4·7H2O against DSC measurements, resulting in a mean relative error of a 0.7% and a normalized root mean square deviation of 1.1%; and (iii) comparing the Van’t Hoff and proposed Stoichiometric model vapor-solid equilibrium curves to different literature data for MgSO4·7H2O, MgSO4·6H2O, and MgSO4·1H2O, resulting in similar equilibrium values, especially for MgSO4·7H2O and MgSO4·6H2O. The results show good agreement with the employed data and confirm this method as a viable alternative for fitting complex physically constrained data sets, while being a potential approach for automatic data fitting of substance data.

Solid-fluid equilibrium measurements of benzene in methane and implications for freeze-out at LNG conditions

Information about the solubility of benzene in light hydrocarbons is particularly important for the prediction of freeze-out risk in LNG production. Engineering models developed to predict this risk need to be tested against high quality experimental data covering a range of conditions to assess their validity. A visual high pressure sapphire cell, housed in a specialized cryogenic environmental chamber, was employed to measure the melting temperature of methane + benzene binary systems at temperatures from 120 K, pressures up to 22 MPa, and benzene concentrations ranging from 120 to 1012 parts per million (ppm) by mole. The results obtained were compared with literature data and the predictions of the thermodynamic model implemented in the software package ThermoFAST. These comparisons reveal that the literature data are in fact consistent with each other, and with the measurements and predictions made in this work, within their experimental scatter. ThermoFAST was able to represent the melting temperatures obtained for benzene concentrations of 1012 and 199 ppm with r.m.s deviations of 0.7 and 3.4 K, respectively. At 120 ppm and 6.3 MPa, the measured solid-liquid equilibrium (SLE) temperature deviated from the ThermoFAST prediction by less than 2 K. However, at the higher temperature conditions representative of solid vapour equilibrium (SVE), the data measured for mixtures with concentrations at 199 and 750 ppm benzene deviated from the model predictions by up to 5 K.

Prediction of carbon dioxide frost point for natural gas and LNG model systems

Many applications dealing with carbon dioxide are limited because of carbon dioxide frosting. Therefore, it has been important to accurately predict the temperature where carbon dioxide solidifies. In this work, using solid – vapor (SV) equilibria, the frost points of binary and ternary model systems resembling natural gases – that are, methane + carbon dioxide, nitrogen + methane + carbon dioxide and methane + ethane + carbon dioxide are predicted by the predictive Peng-Robinson 1978 (PPR78), Redlich-Kwong-Soave (RKS), Nasrifar-Bolland (NB) equations of state and a solid fugacity relation. The equations of state are used to describe the vapor phase in SV equilibria. Accordingly, the equations of state are coupled with a group-contribution temperature-dependent binary interaction parameter that was previously developed from vapor – liquid (VL) equilibria. The solid fugacity relation was developed in this work for describing solid carbon dioxide. The solid fugacity relation expands around the triple point temperature of carbon dioxide. It is explicit in temperature and pressure and needs triple point temperature and sublimation enthalpy of carbon dioxide as input parameters. The model is fully predictive and does not require any adjustable parameter. When the NB equation of state with the solid fugacity relation was applied to natural gas model systems (NGMS), the agreement with experiments was found satisfactory. The NGMS contained 0.1%–54.2% carbon dioxide, temperature and pressure ranged from 140 K to 216 K and 100 kPa–3500 kPa, respectively. The effects of nitrogen and ethane on the frost point were also evaluated and the model accuracy was found adequate. Average absolute deviation (AAD) in predicting 291 experimental frost points for binary and ternary mixtures containing carbon dioxide was found to be 1.58 K.

Enhanced solubility of siloxy-modified polyhedral oligomeric silsesquioxanes in supercritical carbon dioxide

Alkyl siloxy functionalization increases the solubility of polyhedral oligomeric silsesquioxanes (POSS) in supercritical carbon dioxide over an order of magnitude compared to its counterpart with fluoroalkyl groups. The studied component, octatrimethylsiloxy POSS also exhibits higher solubility than other previously studied POSS types with various alkyl and methacryl groups. The octatrimethylsiloxy POSS-CO2 solid-vapor equilibrium curves have been constructed at temperatures between 308 and 328 K by measuring cloud points. The highest measured solubility of octatrimethylsiloxy POSS was 0.176 wt. fr., corresponding to 0.0083 mol fr., at 13.36 MPa, 328 K, and CO2 density of 0.59 g/cm3. The solubility versus CO2 density isotherms fall on a master curve up to about 2 × 10−3 mol fraction, while at higher concentrations, higher solubility was attained with increasing temperature. The experimental data were correlated using various semi-empirical density-based models which provided satisfactory correlations.

Identification and Quantification of CO2 Solidification in Cryogenic CO2 Capture from Natural Gas

The composition of natural gas strongly depends on the geological conditions and depth of the gas well. Presently, CO2 content in the discovered natural gas reservoirs is up to 90%. Prior to customer use, the amount of CO2 needs to be reduced. Cryogenic CO2 capture is one of the emerging technology for CO2 capture from natural gas. Comprehensive knowledge of vapor-liquid, vapor-solid, and solid-liquid equilibria for the gaseous mixture is required for designing cryogenic separation processes for CO2 capture from its gaseous mixtures. No thermodynamic phase data is available for the highest CO2 content N.G mixture. The present work is an effort to generate the thermodynamic data for CO2 capture at low temperatures. CO2 solid phase identification and quantification need to be studied for the CO2-CH4 binary mixture. In this work, four samples of natural gas having CO2 content 40%, 60%, 75% and 90% were selected for simulation through Aspen HYSYS. Pressure-temperature data and temperature-composition data for the binary mixtures were predicted using PR EoS for CO2 phase identification and quantification respectively. Simulation for temperature- composition phase envelope was carried out at different pressures i.e. 10, 20, 30, and 40 bar. The operating region selected from the P-T phase envelop was from 1 to 40 bars. From the temperature composition graphs, it was concluded that temperature for the maximum CO2 capture in S-V region at 10, 20, 30, and 40 bar is -95, -90, -75, and -70 °C respectively.

Grand Canonical Investigation of the Quasi Liquid Layer of Ice: Is It Liquid?

In this study, the solid-vapor equilibrium and the quasi liquid layer (QLL) of ice Ih exposing the basal and primary prismatic faces were explored by means of grand canonical molecular dynamics simulations with the monatomic mW potential. For this model, the solid-vapor equilibrium was found to follow the Clausius-Clapeyron relation in the range examined, from 250 to 270 K, with a Δ Hsub of 50 kJ/mol in excellent agreement with the experimental value. The phase diagram of the mW model was constructed for the low pressure region around the triple point. The analysis of the crystallization dynamics during condensation and evaporation revealed that, for the basal face, both processes are highly activated, and in particular cubic ice is formed during condensation, producing stacking-disordered ice. The basal and primary prismatic surfaces of ice Ih were investigated at different temperatures and at their corresponding equilibrium vapor pressures. Our results show that the region known as QLL can be interpreted as the outermost layers of the solid where a partial melting takes place. Solid islands in the nanometer length scale are surrounded by interconnected liquid areas, generating a bidimensional nanophase segregation that spans throughout the entire width of the outermost layer even at 250 K. Two approaches were adopted to quantify the QLL and discussed in light of their ability to reflect this nanophase segregation phenomena. Our results in the μVT ensemble were compared with NPT and NVT simulations for two system sizes. No significant differences were found between the results as a consequence of model system size or of the working ensemble. Nevertheless, certain advantages of performing μVT simulations in order to reproduce the experimental situation are highlighted. On the one hand, the QLL thickness measured out of equilibrium might be affected because of crystallization being slower than condensation. On the other, preliminary simulations of AFM indentation experiments show that the tip can induce capillary condensation over the ice surface, enlarging the apparent QLL.

Algorithms for the calculation of psychrometric properties from multi-fluid Helmholtz-energy-explicit models

Psychrometric properties of humid air are widely used in the analysis and modeling of thermal systems. In this work, we present a method for obtaining these properties from the multi-fluid mixture formulation of the GERG mixture model. This mixture model was originally developed to model the thermodynamics of natural gas mixtures, and more recently has been extended to model thermodynamic properties relevant for carbon capture and storage. The primary advantage of this formulation is that the dry air composition is not fixed, and can be adjusted to suit the application, for instance for combustion flue gases, for air in submarines, for Martian atmospheres, etc. Furthermore, this multi-fluid framework employs the highest accuracy pure-fluid equations of state in the literature.We present algorithms that can be used to calculate the quantity of water in the saturated vapor in vapor-liquid and solid-vapor equilibria, and other properties that arise out of these equilibria calculations, such as relative humidity and humidity ratio. We also present algorithms for converting other common sets of independent variables (e.g., wet-bulb temperatures), to the natural variables of the mixture model.Comprehensive discussion of the developed algorithms is provided, as well as sample code in the C++ language.

Modeling natural gas-carbon dioxide system for solid-liquid-vapor phase behavior

With the shale gas boom, natural gas has become one of the main energy sources in the United States. But in the cryogenic processes of this natural gas, the formation of solid carbon dioxide remains a concern because it can cause the blockage of equipment. Accurately modeling the rich phase behavior of carbon dioxide in methane is helpful for optimizing the industrial processes, especially where experimental data are lacking at the operation conditions. In this work, the Perturbed Chain-SAFT (PC-SAFT) equation of state is applied to model the phase behavior of hydrocarbon (i.e., methane, ethane, butane) + carbon dioxide systems over a wide range of temperatures and pressures. It is observed that the PC-SAFT equation of state can accurately predict the vapor-liquid equilibria (VLE), solid-vapor equilibria (SVE), and solid-liquid equilibria (SLE) of hydrocarbon + carbon dioxide systems using a single set of temperature and pressure independent binary interaction parameters. In the end, the effect of addition of ethane and butane on SLE of methane + carbon dioxide is also investigated which has applications in reducing the carbon dioxide solidification conditions.

Application of Highly Accurate Phase-Equilibrium Models for CO2 Freezing Prediction of Natural Gas System

It is of great engineering significance to find an accurate model to predict CO2 freezing and avoid plugging in the light hydrocarbon separation process of natural gas. Research starts from CO2 freezing in simple CH4–CO2 binary systems. By use of a traditional model based on the Antoine equation, the calculated freezing temperature in liquid–solid equilibrium (LSE) is not as accurate as that in vapor–solid equilibrium (VSE). Then a new thermodynamic method of reference state of hypothetical fluid is used to replace LSE model based on the Antoine equation to calculate solid CO2 fugacity. The improved phase-equilibrium model based on GERG-2008 is proved to be the most accurate one to calculate CO2 freezing temperature, in which the Antoine equation is used in VSE model while reference state method is used in LSE model. Compared with experimental data, the calculated results also show a higher accuracy in complex natural gas system. Besides, the improved phase-equilibrium model is applied in the actual light...

Performance enhancement using multiple cryogenic desublimation based pipeline network during dehydration and carbon capture from natural gas

Cryogenic carbon capture from natural gas at high pressures requires accurate process synthesis and determination of process parameters due to the presence of solid–vapor and vapor–liquid–solid equilibria. At high pressures, the higher liquid formation not only causes operational problems, but also induces hydrocarbon losses in cryogenic packed beds. The present study proposes a novel multiple cryogenic desublimation based pipeline network with its sections at different cryogenic pressures and temperature profiles to enhance the separation. The experimental study explores the simultaneous separation of water and carbon dioxide from ternary feed gas mixture (CH4–CO2–H2O) by using multiple counter current cryogenic desublimation beds.A novel simulation strategy using multiple equilibrium temperature (MET) concept is also introduced for simulation studies. Simulation studies were subsequently conducted for both atmospheric and high cryogenic bed pressures and compared with experimental measurements. The effect of ambient humidity on dehydration was also investigated experimentally and it was observed that the humidity has significant effects on dehydration due to back diffusion. The effect of some important parameters like bed length, feed gas pressures, bed temperatures, feed flow rates and feed gas pressures for separation were investigated. Experimental investigation was also conducted to quantify liquid formation and vapor–solid equilibrium at high pressures. The experimental results of desublimation based cryogenic pipeline network showed promising potential for industrial exploitation.

Application of Peng-Robinson Equation of State for Calculating Solid-Vapor and Solid-Liquid Equilibrium of CH4-CO2 System

In this study, the performances of Peng-Robinson Equation of State combined with the classical mixing ruleswere evaluated to calculate solid-vapor equilibrium (SVE) and solid-liquid equilibrium (SLE) of CH4-CO2system. The evaluation was performed by comparing the calculated values with the literature data. In thecalculation of SVE, the new binary interaction parameter values (kij) of CH4-CO2 mixtures were proposed in thiswork based on the experimental data. The proposed kij obtained in this work might increase the accuracy ofPeng-Robinson Equation of State by reducing average absolute deviation in the temperatures between calculatedvalues and literature data from (2.18% to 0.26%), (0.88% to 0.70%) and (0.61% to 0.44%) at CO2 compositionof 1%, 1.91% and 2.93%, respectively. Significant improvement was found at CO2 composition of 1%. In thecalculation of SLE, new parameters were not proposed since the calculation using the existing (literature) kijgives good results with an average absolute deviation of 0.5%.