Use of artificial neural networks for prediction of phase equilibria in the binary system containing carbon dioxide

Present work investigated the potential of artificial neural network (ANN) model to correlate the bubble and dew points pressures of binary systems containing carbon dioxide (CO₂) and hydrocarbon systems as functions of reduced temperature of non-CO₂ compounds, critical pressure, acentric factor of non-CO₂ compounds and CO₂ composition. In this regards, five binary systems at the temperature and pressure ranges of 263.15–393.15 K at 0.18–12.06 MPa were used to examine the feasibility of cascade-forward back-propagation ANN model. In this regard, the collected experimental data were divided in to two different subsets namely training and testing subsets. The training subset was selected in a way that covers all the ranges of the experimental data and operating conditions. Then, the accuracy of the proposed ANN model was evaluated through a test data set not used in the training stage. The optimal configuration of the proposed model was obtained based on the error analysis including minimum average absolute relative deviation percent (AARD %) and the appropriate (close to one) correlation coefficient (R²) of test data set. The obtained results show that the optimum neural network architecture was able to predict the phase envelope of binary system containing CO₂ with an acceptable level of accuracy of AARD % of 2.66 and R² of 0.9950 within their experimental uncertainty. In addition, comparisons were done between the Peng–Robinson (PR) equation of state (EOS) and ANN model for three different binary systems including CO₂ + 1-hexene, CO₂ + n-Hexane, and CO₂ + n-butane. Results show that developed optimal ANN model is more accurate compared to the PR EOS.     

High-pressure phase equilibrium measurements and thermodynamic modeling for the systems involving CO2, ethyl esters (oleate,stearate, palmitate) and acetone

The aim of this work was to study the phase behavior of systems involving carbon dioxide (CO₂), fatty acid ethyl esters (ethyl oleate, ethyl stearate and ethyl palmitate) and acetone at high pressures. The phase behavior involving these components is an important step regarding the design and optimization of industrial processes based on supercritical conditions, such as biodiesel production and fatty esters fractionation involving supercritical and/or pressurized solvents. In addition, supercritical CO₂ can offer an interesting alternative for glycerol separation in water-free biodiesel purification processes. The binary systems investigated in this work were CO₂ + ethyl oleate, and CO₂ + ethyl stearate and these were compared with the CO₂ + ethyl palmitate system. The ternary CO₂ + ethyl palmitate + acetone was also investigated at two different ethyl palmitate to acetone molar ratios of (1:1) and (1:3). The static synthetic method using a variable-volume view cell was employed to obtain the experimental data in the temperature range of 303.15–353.15 K. Vapor–liquid (VL), liquid–liquid (LL) and vapor–liquid–liquid (VLL) phase transitions were observed in these systems. In the binary systems, the solubility increased with the presence of unsaturation and decreased with the number of carbon atoms in the fatty ester chain. Addition of acetone as well as ethanol eliminated the liquid–liquid immiscibility and reduced the pressure transitions, therefore increasing the solubility of the ester in supercritical CO₂. The experimental data sets for the binary and ternary systems were successfully modeled using the Peng–Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and Wong-Sandler (PR-WS) mixing rule. Both models showed good performance in the phase equilibrium correlations and in predictions for the binary and ternary systems.     

Experimental measurement and modelling with Aspen Plus® of the phase behaviour of supercritical CO2 + (n-dodecane + 1-decanol + 3,7-dimethyl-1-octanol)

Experimental phase equilibrium data for the systems CO₂ + n-dodecane, CO₂ + 1-decanol and CO₂ + 3,7-dimethyl-1-octanol were used to determine values for binary interaction parameters for use in the RK-ASPEN thermodynamic model in Aspen Plus^®. Bubble and dew point data of the mixtures CO₂ + (n-dodecane + 1-decanol), CO₂ + (n-dodecane + 3,7-dimethyl-1-octanol), CO₂ + (1-decanol + 3,7-dimethyl-1-octanol) and CO₂ + (n-dodecane + 1-decanol + 3,7-dimethyl-1-octanol) were measured experimentally in a static synthetic view cell, and compared to the data predicted by the RK-ASPEN model. The model predicted the phase equilibrium data reasonably well in the low solute concentration region; significant deviation of model predictions from experimental data occurred in the mixture critical and high solute concentration regions due to the exclusion of solute–solute interaction parameters in the model. Distribution coefficients and separation factors were determined for the multi-component mixture and separation of the alkane from the alcohol mixture with a supercritical fluid extraction process was found to be possible.     

Near-infrared spectroscopic solubility measurement for thermodynamic analysis of melting point depressions of biphenyl and naphthalene under high-pressure CO2

Melting temperatures of organic solids are often depressed by high-pressure CO₂ due to a dissolution of CO₂ in the molten organic compounds. For thermodynamic analysis of the melting point depression, solubilities of CO₂ in molten biphenyl and naphthalene were measured by near-infrared spectroscopy at various temperatures and pressures up to 20 MPa. Molarity of the organic component was determined from the 3ν_CH absorption band, and that of CO₂ from the 2ν₁ + ν₃ band. Mole fraction of CO₂ in the liquid phase was found to be an increasing function of the pressure up to 0.6 at 20 MPa and a weakly decreasing function of the temperature. The solubility data were used for modeling of the mixtures by the Peng–Robinson equation of state with a binary interaction parameter k₁₂. Calculation of the solid–liquid–gas phase equilibrium for the model fluid qualitatively described a large decrease in the melting temperature with increasing pressure up to 10 MPa followed by a small change at higher pressures. The melting point change was interpreted by the two competing effects: hydrostatic pressure effect increases the melting point by ca. 8 °C at 20 MPa, whereas CO₂ solubility effect reduces it by ca. 30 °C. Decomposition of the solubility effect into ideal and non-ideal mixing parts revealed that the non-ideality increases the melting point by more than 10 °C.     

CO2 absorption capacity using aqueous potassium carbonate with 2-methylpiperazine and piperazine

Various amines as a promoter have been added to the K₂CO₃ solution in order to improve the performance of the CO₂ absorption process. Piperazine (PZ) and 2-methylpiperazine (2-MPZ), cyclic diamines were used as promoters in this study. The equilibrium partial pressure of CO₂ $(P_{{\text{CO}}_2}^1)$ and pressure changes were measured at 313, 333 and 353 K condition of flue gas using VLE (vapor–liquid equilibrium) equipment. The results show that 2-MPZ possesses the ability to promote CO₂ absorption capacity. The K₂CO₃/2-MPZ solution had an equilibrium partial pressure of CO₂ that was lower than that of the MEA solution at 333 K.     

The pH of CO2-saturated water at temperatures between 308 K and 423 K at pressures up to 15 MPa

We report pH measurements for CO₂-saturated water in the pressure range from (0.28 to 15.3) MPa and temperatures from (308.3 to 423.2) K. Commercially available pH and Ag/AgCl electrodes were used together with a high pressure equilibrium vessel operating under conditions of precisely controlled temperature and pressure. The results of the study indicate that pH decreases along an isotherm in proportion to −log₁₀(x), where x is the mole fraction of dissolved CO₂ in H₂O. The expanded uncertainty of the pH measurements is 0.06 pH units with a coverage factor of 2. The reported results are in good agreement with the literature in pressure ranges up to 16 MPa at temperatures below 343 K. An empirical equation has been developed to represent the present results with an expanded uncertainty of 0.05 pH units. We also compare our results with a chemical equilibrium model and find agreement to within 0.1 pH unit.     

Mathematical modelling of phase equilibria for supercritical CO2 and polyethylene glycol of various molecular weights

The Sanchez–Lacombe equation of state and the Statistical Associating Fluid Theory were applied for modelling the phase equilibrium for the polyethylene glycol–CO₂ systems. The Aspen Plus software was used and polyethylene glycol with various molecular weights was investigated. The results were compared with previously obtained experimental values for solubility. The phase equilibrium was calculated at a temperature of 343 K, in the pressure range of 10–30 MPa and for polyethylene glycol molecular weights from 1000 to 100,000 g/mol. The binary interaction parameters for the models were optimized in order to obtain the best fit between the estimated and the experimental gas solubility data. The results suggest that both models are reliable in describing the phase equilibrium of the polyethylene glycol–CO₂ systems at the proposed conditions. Moreover, the molecular weight of the polymer affects the behaviour of the system, as observed from the variation of solubility values and of binary interaction coefficients.     

Phase equilibria of allyl sulfide + carbon dioxide binary mixtures: Experimental data and thermodynamic modeling

This contribution reports new experimental data on vapor–liquid equilibrium of the binary system diallyl sulfide + carbon dioxide, at temperatures between 275 and 370 K and pressures up to 12 MPa. These data are of interest to study the extraction of Allium oils from garlic and onion, using near-critical CO₂. The experimental data were modeled with a group-contribution equation of state. A (CH₂S) functional group has been defined to represent alkyl and allyl sulfides. Pure group and binary interaction parameters for this new functional group have been determined. Good correlation and prediction of phase equilibrium conditions were obtained.     

Bubble point pressures and densities of hexamethyldisiloxane–carbon dioxide binary mixture using a constant volume view cell

The phase behavior of hexamethyldisiloxane (HMDS)–carbon dioxide (CO₂) binary mixture was investigated using a constant volume view cell. The accuracy of the measurement technique was inspected against the bubble point pressure data in the literature for ethanol (C₂H₅OH)–carbon dioxide (CO₂) binary mixture. The bubble point pressures for C₂H₅OH–CO₂ agreed well with the literature values. The bubble point pressures of HMDS–CO₂ binary mixture were determined at five different temperatures (T = 298.2 K, 308.2 K, 313.2 K, 323.2 K, 333.2 K) and at various compositions. The bubble point pressures increased with increasing temperature and CO₂ mole fraction in the binary mixture. The phase behavior of the binary mixture was modeled using the Peng–Robinson Stryjek–Vera equation of state (PRSVEoS). The binary interaction parameters were regressed from experimental bubble point pressures at each temperature and were found to exhibit a linear dependency on temperature. The HMDS–CO₂ binary mixture was also found to exhibit Type II phase behavior. Additionally, P–T–ρ measurements for the same binary system were conducted and excess molar volumes were calculated.     

Modeling of precipitation of ultra-fine particles by pressure reduction over CO2-expanded liquids

A mathematical model has been developed to describe the process of precipitation of ultrafine particles by pressure reduction over gas (CO₂)-expanded liquids. A rapid pressure reduction over a CO₂-expanded organic solution, from 30–70 to 1 bar at 303 K decreases the solution temperature by 30–80 K in a very short span of time (0.5–1.5 min), which generates a rapid, high, and uniform supersaturation of the dissolved solute in the solution and facilitates precipitation of ultrafine particles. The model developed in this work estimates the supersaturation attained, nucleation and growth rates obtained during the pressure reduction over CO₂-expanded organic solutions, and the particle size distribution of the precipitated particles. Cholesterol has been chosen as a model solute to be precipitated, and acetone has been chosen as a solvent. A new method has been developed for prediction of equilibrium solubility of solute which is affected by a decrease in CO₂ mole fraction as well as a simultaneous decrease in solution temperature during pressure reduction. This method combines the semi-empirical approach of using the partial molar volume fraction of solvent in a CO₂-solvent binary mixture and solid–liquid equilibrium data for a solute–solvent system. Size distributions of the precipitated particles have been calculated assuming primary nucleation (homogeneous as well as heterogeneous nucleation) and diffusion-limited growth kinetics. The predicted mean average particle sizes are then compared with the size of cholesterol particles precipitated by pressure reduction of a CO₂-expanded acetone solution of cholesterol. The particle sizes predicted assuming heterogeneous nucleation are found to be closer to the experimentally observed particle sizes, indicating that the heterogeneous nucleation could be the main mechanism of nucleation, which could occur at the gas–liquid interface of the CO₂ bubbling out of CO₂-expanded solution during pressure reduction.     

High-pressure phase equilibria for the binary system carbon dioxide + dibenzofuran

The experimental solubility of dibenzofuran in near-critical and supercritical carbon dioxide and the solid–liquid–vapor (SLV) equilibrium line for the CO₂ + dibenzofuran system are reported. The built in-house static view cell apparatus used in these measurements is described. The solubility of naphthalene in supercritical CO₂ and the CO₂ + naphthalene SLV line are also determined in order to assess the reliability and accuracy of the measurement technique. The solubility of dibenzofuran in carbon dioxide is determined at 301.3, 309.0, 319.2, 328.7 and 338.2 K in the 6–30 MPa pressure range. Solubility data are correlated using the Chrastil model and the Peng–Robinson equation of state. This equation is also used to predict the CO₂ + dibenzofuran SLV line. Results show the feasibility of using supercritical CO₂ to extract dibenzofuran.     

Phase behavior of 1,3,5-tri-tert-butylbenzene–carbon dioxide binary system

1,3,5-tri-tert-butylbenzene (TTBB) is solid at ambient conditions, and has substantial solubility in liquid and supercritical carbon dioxide. We present the phase behavior of TTBB–CO₂ binary system at temperatures between 298 and 328 K and at pressures up to 20 MPa. Phase diagrams showing the liquid–vapor, solid–liquid and solid–vapor equilibrium envelopes are constructed by pressure–volume–temperature measurements in a variable-volume sapphire cell. TTBB is highly soluble in CO₂ over a wide range of compositions. Single-phase states are achieved at moderate pressures, even with very high TTBB concentrations. For example, at 328 K, a binary system containing TTBB at a concentration of 95% by weight forms a single-phase above 2.04 MPa. TTBB exhibits a significant melting-point depression in the presence of CO₂, 45 K at 3.11 MPa, where the normal melting point of 343 K is reduced to 298 K. With its high solubility in carbon dioxide, TTBB has potential uses as a binder or template in materials forming processes using dense carbon dioxide.     

Viscosity and rheological behavior of carbon dioxide-expanded fish oil fatty acid ethyl esters: Measurement using a rotational viscometer and modeling

The viscosity of fish oil fatty acid ethyl esters (FAEE) in equilibrium with CO₂ was determined at 40, 55, and 70 °C and pressures ranging from 0.1 to about 12 MPa using a rotational rheometer equipped with a high pressure cell. Viscosity of CO₂-expanded (CX) FAEE decreased due to the dissolution of CO₂ with pressure, which was temperature dependent. The viscosity of CX FAEE was correlated using a new empirical model utilizing saturation pressure and temperature with temperature-dependent parameters, which allows interpolation of viscosity data for any pressure and temperature within the envelope of this study. As well, viscosity was modeled using available data for CO₂ solubility in FAEE at specific temperatures of this study utilizing simpler models with only one parameter, such as the Grunberg and Nissan model. The rheological data suggest shear thickening behavior of CX FAEE at elevated pressures. The limitations of the rotational rheometer for measuring CX liquids at viscosities below 1 mPa s are discussed. Understanding of viscosity and rheological behavior of CX FAEE is essential for equipment and process design involving such lipids.     

Phase equilibrium of the CO2/glycerol system: Experimental data by in situ FT-IR spectroscopy and thermodynamic modeling

Phase equilibrium experimental data for the CO₂/glycerol system are reported in this paper. The measurements were performed using an in situ FT-IR method for temperatures ranging from 40 °C to 200 °C and pressures up to 35.0 MPa, allowing determination of the mutual solubility of both compounds. Concerning the CO₂ rich phase, it was observed that the glycerol solubility in CO₂ was extremely low (in the range of 10⁻⁵ in mole fraction) in the pressure and temperature domains investigated here. Conversely, the glycerol rich phase dissolved CO₂ at mole fractions up to 0.13. Negligible swelling of the glycerol rich phase has been observed. Modeling of the phase equilibrium has been performed using the Peng–Robinson equation of state (PR EoS) with classical van der Waals one fluid and EoS/G^E based mixing rules (PSRK and MHV2). Satisfactory agreement was observed between modeling results and experimental measurements when PSRK mixing rules are used in combination with UNIQUAC model, although UNIFAC predictive approach gives unsatisfactory representation of experimental behavior.     

Phase equilibria for the 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in supercritical CO2 at various temperatures and pressures up to 20 MPa

The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems at 313.2, 333.2, 353.2, 373.2 and 393.2 K as well as pressures up to 20.59 MPa have been investigated using variable-volume high pressure view cell by static-type. The solubility curve of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems increases as the temperature increases at a constant pressure. The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems exhibit type-I phase behavior. The experimental results for the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems correlate with the Peng–Robinson equation of state using a van der Waals one-fluid mixing rule including two adjustable parameters. The critical properties of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate are predicted with the Joback–Lyderson group contribution and Lee–Kesler method.     

Density and viscosity of the binary polyethylene glycol/CO2 systems

Density of CO₂ saturated solutions of polyethylene glycols (PEGs) of different molecular weight was measured in pressure range from 8.0 MPa up to 47.7 MPa at a temperature of 343 K by a volumetric method. To validate the method density of pure CO₂ was measured at different pressures and a temperature of 293 K. The results were compared to the literature data and the accuracy was better than 2%. The density was between 1.17 g/mL for PEG 1000/CO₂ at 14.5 MPa and 1.78 g/mL for the system PEG 4000/CO₂ at 35 MPa. Further, the data were compared to results, obtained by a gravimetric method using magnetic suspension balance (MSB).Viscosity of CO₂ saturated solutions of polyethylene glycols (PEGs) of different molecular weight at different pressures and at a temperature of 343 K was measured using a high pressure view cell. Also a temperature impact on the viscosity of pure PEGs was observed at ambient pressure. After saturating PEG 1500 with 10 MPa of CO₂ pressure its viscosity decreases from 76.6 mPa s to 2.24 mPa s at 333 K. Further addition of CO₂ and increasing the pressure results in even lower viscosity and the highest viscosity reduction was reached at the highest pressure; at 35 MPa viscosity of the system PEG 1500/CO₂ is only 0.665 mPa s.     

High pressure densities of carbon dioxide + dipentaerythritol hexaheptanoate: New experimental setup and volumetric behavior

To perform an appropriate selection of the lubricants in air conditioned systems working with carbon dioxide as refrigerant, the thermodynamic behavior of the CO₂ + lubricant systems must be well known. In this work we present a new setup to prepare compressed gas–liquid mixtures and to determine the high pressure density by using an automated densimeter HPM and two syringe pumps. To analyze the reliability of the procedure proposed, we have determined the densities and mixing volumes of four CO₂ + n-decane mixtures. We have found a good agreement with previous literature data. In addition new density values are reported for the binary system CO₂ + dipentaerythritol hexaheptanoate (DiPEC7) at several temperatures and pressures from 10 MPa to 120 MPa.     

Phase equilibria of (CO2 + H2O + NaCl) and (CO2 + H2O + KCl): Measurements and modeling

We report experimental measurements of the phase behavior of (CO₂ + H₂O + NaCl) and (CO₂ + H₂O + KCl) at temperatures from 323.15 K to 423.15 K, pressure up to 18.0 MPa, and molalities of 2.5 and 4.0 mol kg⁻¹. The present study was made using an analytical apparatus and is the first in which coexisting vapor- and liquid-phase composition data are provided. The new measurements are compared with the available literature data for the solubility of CO₂ in brines, many of which were measured with the synthetic method. Some literature data show large deviations from our results.The asymmetric (γ–φ) approach is used to model the phase behavior of the two systems, with the Peng–Robinson equation of state to describe the vapor phase, and the electrolyte NRTL solution model to describe the liquid phase. The model describes the mixtures in a way that preserves from our previous work on (CO₂ + H₂O) the values of the Henry's law constant and the partial molar volume of CO₂ at infinite dilution Hou et al. [22]. The activity coefficients of CO₂ in the aqueous phase are provided. Additionally, the correlation of Duan et al. [14] for the solubility of CO₂ in brines is tested against our liquid-phase data.     

High pressure phase behavior of poly[isopropyl acrylate] and poly[isopropyl methacrylate] in supercritical fluid (SCF) solvent and SCF solvent + cosolvent mixtures

Cloud-point data are reported for poly(isopropyl acrylate) [P(IPA)] in CO₂, propane, propylene, butane, 1-butene, and dimethyl ether (DME) and for poly(isopropyl methacrylate) [P(IPMA)] in CO₂. P(IPA) + alkene cloud-point curves are ∼100 °C lower than the P(IPA) + alkane curves, which are close to the P(IPA) + CO₂ curve located at temperatures greater than 130 °C and pressures of 2500 bar. P(IPA) dissolves in pure DME at conditions as mild as 50 °C and 200 bar. Since IPA and IPMA monomers are used as cosolvents with CO₂, binary IPA + CO₂ and IPMA + CO₂ data are reported to complement the ternary cloud-point data. Both monomer + CO₂ mixtures exhibit type-I behavior and both are adequately modeled with the Peng–Robinson equation of state. IPMA is a more effective cosolvent than IPA. The polymer + CO₂ + monomer phase behavior suggests that it is viable to polymerize IPA or IPMA in CO₂ at moderate operating conditions.     

Phase equlibiria and diffusivity of dense gases in various polyethylenes

The aim of this work was to investigate the properties of polyethylenes (PE) of various densities (low-density and high-density) under pressure of CO₂ and propane. The phase equilibria of PE of different density in presence of CO₂ and in presence of propane in dependence of pressure and temperature were investigated. The phase transitions of PE at atmospheric pressure were determined by differential scanning calorimetry (DSC). Furthermore, phase transitions of polymers under pressure of gases were measured by using an optical high pressure cell. Measurements of phase transition were performed in range of pressure of 1–90 MPa. The results show that melting points of LDPE decreased in presence of CO₂ and in presence of propane. For high-density polyethylene (HDPE) the melting point decrease was observed only in presence of propane, while in presence of CO₂ melting point increases with increasing pressure. The melting points of LDPE and HDPE decrease in average for 10–20 K in presence of propane, while in presence of CO₂ the melting point decrease for both LDPE was lower (5–10 K). Solubility and diffusivity of supercritical CO₂ in two low-density polyethylenes (LDPE) and in high-density polyethylene (HDPE) were measured at temperature 373 K and pressures up to 30 MPa using a magnetic suspension balance (MSB). The solubility data were used for estimating the binary diffusion coefficients. The solubilities increased with increasing density. The diffusion coefficient shows strong CO₂ density and CO₂ solubility dependence. Diffusion coefficient starts to decrease with increasing density and solubility of CO₂.