Prediction of phase equilibrium of CO2/cyclic compound binary mixtures using a rigorous modeling approach

Vapor liquid equilibrium (VLE) data has significant role in designing processes which include vapor and liquid in equilibrium. Since it is impractical to measure equilibrium data at any desired temperature and pressure, particularly near critical region, thermodynamic models based on equation of state (EOS) are usually used for VLE estimating. In recent years due to the development of numerical tools like artificial intelligence methods, VLE prediction has been find new alternatives.In the present study a novel method called Least-Squares Support Vector Machine (LSSVM) used for predicting bubble/dew point pressures of binary mixtures containing carbon dioxide (CO₂) + cyclic compounds as function of reduced temperature of the system, critical pressure, acentric factor of the cyclic compound, and CO₂ composition. A 333 binary equilibrium data points of CO₂ and six cyclic compounds within temperature and pressure ranges of 308.15–473.15 K and 0.5–27.71 MPa were used to develop the model. Results show that the proposed model is able to predict VLE data for binary systems containing supercritical or near-critical CO₂/cyclic compounds with an acceptable average absolute relative deviation percent (AARD%) of 3.9381% and the coefficient of determination (R²) value of 0.9980. For detection of the probable doubtful experimental data, and applicability of the model, the Leverage statistical approach performed on the data sets. This algorithm showed that the proposed LSSVM model is statistically valid for VLE prediction and the whole phase equilibrium data points are in applicability domain of the model.     

Phase equilibria of palm oil,palm kernel oil,and oleic acid + supercritical carbon dioxide and modeling using Peng–Robinson EOS

Vapor–liquid equilibria of the binary supercritical carbon dioxide (scCO₂) + oleic acid, scCO₂ + palm oil, and scCO₂ + palm kernel oil were measured at a wide range of temperatures from 333.2 to 373.2 K and pressures from 8.5 to 35 MPa in a circulation-type phase equilibrium apparatus. The samples from liquid and vapor phases were analyzed using UV–vis spectrometer and a liquid hold-up equipment. The phase equilibrium data were correlated with Peng–Robinson Equation of State (PR-EOS) using Wong–Sandler mixing rule and optimum values of binary interaction parameters were determined. The relative deviation between experimental data and predicted data was in the range of 6.9–8.7%, suggesting that the PR-EOS with Wong–Sandler mixing rule is capable of predicting the vapor–liquid equilibria of oleic acid + scCO₂, palm oil + scCO₂, and palm kernel oil + scCO₂.     

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.     

High-pressure phase equilibria of systems carbon dioxide + n-eicosane and propane + n-eicosane

In this work we investigated the phase equilibrium behavior of the binary asymmetric systems propane (C3) + n-eicosane (C20) and carbon dioxide (CO₂) + n-eicosane (C20). We used a variable-volume view cell for obtaining fluid–fluid equilibrium (FFE), solid–fluid equilibrium (SFE) and solid–fluid–fluid equilibrium (SFFE) experimental data. We modeled the phase equilibria of both systems using the Peng–Robinson Equation of State for describing the fluid phases and an expression for the fugacity of pure solid n-eicosane with parameters fit to reproduce the pure n-eicosane melting line. We performed the phase equilibrium calculations by implementing path-following methods for tracking entire solid–fluid (SF) and solid–fluid–fluid (SFF) equilibrium curves for binary asymmetric mixtures. This made it possible to obtain complete isoplethic lines or complete three-phase equilibrium lines in single runs. Although the model is relatively simple, it is able to grasp the complex observed behavior for the systems studied here.     

Study of competitive adsorption of malachite green and sunset yellow dyes on cadmium hydroxide nanowires loaded on activated carbon

Cadmium hydroxide nanowires loaded on activated carbon (Cd(OH)₂-NW-AC) was applied for removal of malachite green (MG) and sunset yellow (SY) in single and binary component systems. This novel material was characterized and identified by different techniques such as Brunauer, Emmett and Teller (BET), scanning electron microscopy (SEM), X-ray diffraction (XRD) analysis. Unique properties such as high surface area (>1271 m² g⁻¹) and low pore size (<35 Å) and average particle size lower than 50 Å in addition to high reactive atom and presence of various functional groups make it possible for efficient removal of these two dyes. In the single component system in this study, maximum adsorption capacity of 80.6 for SY and 19.0 mg g⁻¹ for MG at 25 °C was reported. The Langmuir model had very well fit with the experimental data (R² > 0.996). A better agreement between the adsorption equilibrium data and mono-component Langmuir isotherm model was found. The kinetics of adsorption for single and binary mixture solutions at different initial dye concentrations were evaluated by the nonlinear first-order and second-order models. The second-order kinetic model had very well fit with the dynamical adsorption behavior of a single dye for lower and higher initial dye concentrations. SY and MG without spectra overlapping were chosen and analyzed with high accuracy in binary solutions. The effect of multi-solute systems on the adsorption capacity was investigated. The isotherm constants for SY and MG were also calculated in binary component systems at concentrations within moderate ranges, the Langmuir isotherm model satisfactorily predicted multi-component adsorption equilibrium data. The competitive adsorption favored the SY in the A mixture solution (both SY and MG concentration at 10 mg L⁻¹) and B mixture solution (25 mg L⁻¹ of SY and 10 mg L⁻¹ of MG). Also, in both cases, kinetic data was fairly described by two-step diffusion model. An endothermic and spontaneous nature for the adsorption of the dyes studied were shown from thermodynamic parameters in single and binary component systems.     

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.     

Liquid–liquid equilibria and thermo physical properties for 1-methyl-2-pyrrolidinone + heterocyclic nitrogen compounds + hexadecane systems at 298.15 K

Liquid–liquid equilibrium data for {1-methyl-2-pyrrolidinone (NMP) + heterocyclic nitrogen compounds + hexadecane} systems were analytically determined at 298.15 K and atmospheric pressure using stirred and thermo-regulated cell. The experimental data were modeled with the NRTL and UNIQUAC equations. Besides, the Bachman–Brown correlation was used to ascertain the reliability of the experimental data. Additionally, excess molar volumes (V^E) and deviations in the molar refractivity (ΔR) data at 298.15 K were determined for the {NMP + heterocyclic nitrogen compounds} binary systems using a digital vibrating-tube densimeter and a precision digital refractometer. The V^E and ΔR data were modeled with the Redlich–Kister equation.     

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.     

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.     

Thermodynamic calculations of t to m martenstic transformation of ZrO2–CaO binary system

The phase transformation of different polymorphs in zirconia is very important for the processing and mechanical properties of zirconia ceramics. This paper adopts thermodynamic model which is suitable for ceramic system to calculate the Gibbs free energy change of tetragonal and monoclinic phases in ZrO₂–CaO binary system. The difference of the Gibbs free energy between tetragonal and monoclinic phases in ZrO₂–CaO as a function of composition and temperature, namely t → m phase transformation driving force, is thermodynamically calculated from the binary systems. Furthermore, in 8.0 mol% CaO–ZrO₂, the equilibrium temperature between tetragonal and monoclinic phases, T₀, was obtained as 1270.3 K, and martensitic transformation starting temperature (M_s) for t → m transformation of this ceramic with a mean grain size of 2.0 mm was calculated as 805.9 K, which is good agreement with experiment one of 793 K with 12.9 K residual.     

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.     

High pressure phase behavior of methanol + ethylene: Experimental measurements and CPA modeling

High pressure–temperature isopleths were obtained, experimentally, for the binary system of methanol + ethylene within a temperature and pressure range of 293–373 K and 38–119 bar, respectively. The experimental results were modeled using the Cubic-Plus-Association (CPA), Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state. The ability of the CPA model to predict the phase behavior of methanol + ethylene is much better than the SRK and PR models. However, even though the p–T diagrams indicate that the CPA equation of state correlates well with the experimental results, by increasing ethylene concentrations, the errors of CPA increase due to the solvation that occurs in methanol + ethylene systems. In this work, the effect of solvation is also investigated. Results show that deviations from experimental data are less for CPA with solvation than for the CPA without solvation. Correlations are presented for the binary interaction (k_ij) and the association volume (β^A_iB_j) parameters to model the phase behavior of methanol + ethylene, as both of these parameters were indicated to be temperature-dependent.     

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.     

Prediction of chloride binding isotherms of cementitious materials by analytical model or numerical inverse analysis

In this paper, various methods of prediction of chloride-binding isotherms (CBIs) of cementitious materials at equilibrium and in saturated conditions are proposed. The first group of methods consists in numerical inverse analysis of an experimental total-chloride-concentration profile. In this group, a first method requires as input data the effective-chloride-diffusion coefficient (D_Cl ?), while a second method predicts D_Cl ?. Once D_Cl ? and the CBI are assessed, profiles after other exposure times can be predicted. The second group of methods is an analytical model based on the composition of the material, which includes physical and chemical components. The “numerical” and “analytical” CBIs respectively obtained, as well as D_Cl ? and the profiles predicted, have been compared to experimental data for various mixtures (with and without SCM) and ages. The excellent agreement observed between predicted and experimental results, as well as between “analytical” and “numerical” CBIs, demonstrates the reliability and accuracy of the proposed methods.     

Optimized and functionalized paper sludge activated with potassium fluoride for single and binary adsorption of reactive dyes

The yield and adsorption uptake of optimized paper sludge activated carbon (PSAC) prepared using potassium fluoride as alternative chemical activation agent was investigated. The PSAC was functionalized with ethylenediamine (FPSAC) and both adsorbents were used for single and binary adsorption of Reactive orange 16 (RO16) and Reactive blue 19 (RB19). Effect of pH on the adsorption process, equilibrium, kinetics, isotherm and thermodynamic studies were carried out. Optimum PSAC preparation parameters were: activation temperature, X₁ = 810 °C; activation time, X₂ = 105 min; and impregnation ratio, X₃ = 0.95 which gave adsorption uptake of 178 and 158 mg/g for RO16 and RB19, respectively.     

Lead zirconium titanate thin films prepared by thermal annealing of multilayer structures composed of PbO,ZrO2 and TiO2

Lead zirconium titanate [Pb(Zr_xTi_1?x)O₃ or PZT] thin films were prepared by the thermal annealing of multilayer films composed of binary oxide layers of PbO, ZrO₂ and TiO₂. The binary oxides were deposited by metal organic chemical vapor deposition. An interdiffusion reaction for perovskite PZT thin films was initiated at approximately 550 °C and nearly completed at 750 °C for 1 h under O₂ annealing atmosphere. The composition of Pb/Zr/Ti in perovskite PZT could be controlled by the thickness ratio of PbO/ZrO₂/TiO₂ where the contribution of each binary oxide at the same thickness was 1:0.55:0.94. The electrical properties of PZT (Zr/Ti = 40/60, 300 nm) prepared on a Pt-coated substrate included a dielectric constant ?_r of 475, a coercive field E_c of 320 kV/cm, and remnant polarization P_r of 11 μC/cm² at an applied voltage of 18 V.     

High pressure phase behavior and density of the carbon dioxide + 1-methylimidazole binary system

The phase behavior of the carbon dioxide + 1-methylimidazole binary system has been investigated in a high-pressure variable-volume view cell using an analytical method. Phase equilibrium data for the system carbon dioxide + 1-methylimidazole was measured at 293.15, 309.75 and 323.15 K. The pressure under investigation was between 2.83 and 14.16 MPa. There coexisted three phases (LLV) of the binary system, which were found in a temperature range of 297.85–313.95 K. The densities of the binary mixture at phase transition points were also measured. The experimental data were correlated well by the Peng–Robinson equation of state with two binary parameters. According to the experimental results, the phase behavior of the binary system might be classified to Type-IV or Type-V according to the classification of six principal types of binary phase diagrams.     

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.     

Crystal and geometry-optimized structure,Hirshfeld surface analysis and spectroscopic studies of tetrachlorocuprate and nitrate salts of 1-(2-fluorophenyl)piperazine cations, (C10H15FN2)[CuCl4] (I) and (C10H14FN2)[NO3] (II)

Two new organic-inorganic hybrid materials, 1-(2-fluorophenyl)piperazine-1,4-diium tetrachlorocuprate, (C₁₀H₁₅FN₂)[CuCl₄] (I) and 1-(2-fluorophenyl)piperazin-4-ium nitrate, (C₁₀H₁₄FN₂)[NO₃] (II), have been synthesized by an acid/base reaction at room temperature in the presence of 1-(2-fluorophenyl)piperazine as an organic-structure directing agent and their structures were determined by single crystal X-ray diffraction. Compound (I), (C₁₀H₁₅FN₂)[CuCl₄], crystallizes in the monoclinic system and P2₁/c space group with a = 7.5253 (2), b = 20.6070 (7), c = 9.7281 (3) Å, β = 103.6730 (17)°, V = 1465.82 (8) Å³ with Z = 4. Full-matrix least-squares refinement converged at R = 0.037 and wR(F²) = 0.088. Compound (II), (C₁₀H₁₄FN₂)[NO₃], belongs to the monoclinic system, space group P2₁/c with the following parameters: a = 10.8034 (2), b = 7.5775 (1), c = 14.4670 (3) Å, β = 111.761 (2)°, V = 1099.91 (4) ų and Z = 4. The structure was refined to R = 0.044, wR(F²) = 0.136.In the structures of (I) and (II), the anionic and cationic entities are interconnected by means of set of hydrogen bonding contacts forming three-dimensional networks. Intermolecular interactions were investigated by Hirshfeld surfaces and the contacts of the four different chloride atoms were notably compared. The results of the optimized molecular structure are presented and compared with the experimental one. The Molecular Electrostatic Potential (MEP) maps and the HOMO and LUMO energy gap of both compounds were computed. The vibrational absorption bands were identified by infrared spectroscopy. Theory (DFT) calculations of normal mode frequencies are compared with experimental ones.