Saturated Liquid Molar Volumes Research Articles

Adopting a Residual‐Energy‐Based Approach to Calculate the Solubility Parameters of n‐Alkanes

AbstractTwo different paths were followed to calculate the solubility parameters (SP) of 133 alkanes. The first approach calculates SP from the points of view of internal pressure and residual energy, whereby Soave‐Redlich‐Kwong and Peng‐Robinson equations of state (EOSs) are employed with and without the volume‐shift correction. In the second approach, the cohesive energy concept is used and the saturation pressure and saturated liquid molar volume are separately computed by different models and coupled to one another. The results indicated that Approach 1 predicts SP with an error of 2.24 %, which is in the same order as that of Approach 2 but slightly better. The performance of Approach 1 was assessed by estimating the SP values of 33 substances from various families and comparing the results to an EOS‐based study.

An improvement on Martin–Hou equation of state for more precise prediction in the liquid region

AbstractA modified Martin–Hou (M–H) equation of state (EOS) for the accurate representation of thermodynamic property data of some pure substances in liquid phase is presented in this work. The improvement is achieved by substituting a new parameter η into the original M–H EOS. Eighteen pure substances are chosen to construct the dependency relationship of η on reduced temperature Tr and acentric factor ω. Furthermore, to verify the effectiveness and improvement of the modified M–H EOS, the calculated values of the saturated vapor and liquid molar volumes are compared with the literature data in the reduced temperature ranging from approximately 0.6 to 1.0. The results show that the modified M–H EOS perform a good prediction in gaseous phase for pure substances with the average absolute deviation (AAD) generally less than 1%, and more precise liquid molar volume values can be obtained with the modified equation. In liquid phase, the AAD of the modified M–H EOS is 3.71%, which is much lower than 6.16% of the original M–H EOS.

Improved Prediction of Saturated and Single-Phase Liquid Densities of Water through Volume-Translated SRK EOS

The existing equation of states (EOSs) cannot well reconcile the calculation accuracy and the computational cost for reproducing liquid volumes of water. In this study, we propose a series of improved volume translated Soave-Redlich-Kwong (VT-SRK) EOSs to achieve more accurate volumetric calculation for water with little additional computational cost. The overall average absolute percentage deviation of the saturated liquid molar volume for water yielded by the proposed 4-parameter VT-SRK EOS is 0.26; this calculation error is much lower than the counterpart provided by our previously proposed 3-parameter VT-SRK EOS (1.24) and close to the uncertainty in the pseudo-experimental data reported by NIST (0.1%). After adopting the translated distance function, the proposed 5-parameter VT-SRK EOS provides a more accurate determination for the single-phase liquid volume of water over a wide temperature/pressure range and leads to the crossover of pressure-volume isotherms only at extremely high pressures. The proposed 4-parameter VT-SRK EOS also helps to improve the volumetric prediction for carbon dioxide, while the proposed 5-parameter VT-SRK EOS performs well in improving the density prediction for associating fluids. Moreover, we extend the proposed 5-parameter VT-SRK EOS to mixtures through conventional mixing rules, finding that the VT-SRK EOS provides reliable volume predictions for the aqueous solutions examined in this study.

An improved volume-translated SRK EOS dedicated to more accurate determination of saturated and single-phase liquid densities

Volume translation (VT) has been widely utilized to improve the liquid density (or volume) prediction by cubic equation of state (CEOS). Previous VT-models do not fully exploit the potential of distance function and there is still a room for improving the prediction accuracy of saturated and single-phase liquid densities by CEOS. In this study, we propose an improved volume translated Soave-Redlich-Kwong (VT-SRK) EOS to achieve more accurate volumetric calculations for various pure substances. The overall average absolute percentage deviations of the saturated and single-phase liquid molar volumes yielded by this VT-SRK EOS for 56 compounds are 0.61 and 0.84, respectively; these two errors are obviously lower than the counterparts provided by Abudour et al.'s VT-Peng-Robinson EOS (2012). A fairly good generalization of the fluid-dependent VT parameters can be achieved for hydrocarbons. Moreover, we extend the proposed VT-SRK EOS to mixtures through conventional mixing rules, finding that the proposed VT-SRK EOS provides reliable volume predictions for the hydrocarbon mixtures examined in this study.

Vapour pressure and vaporisation enthalpy for two key apple odorants, ethyl butyrate and ethyl hexanoate, at pressures from (15 to 105) kPa

Vapour pressure complementary data for two key apple aroma esters, ethyl butyrate and ethyl hexanoate, two compounds with high relevance to the food industry, were measure with a dynamic recirculation apparatus. For pressures from (15 to 105) kPa the temperatures experimentally assessed were from (340.1 to 395.2) K for ethyl butyrate, and from (378.4 to 440.9) K for ethyl hexanoate. Results of the vapour pressures were correlated using Antoine’s, extended Antoine’s and Wagner’s equations. Relative root mean square deviations were lower than 0.38% and 0.94% for ethyl butyrate and ethyl hexanoate, respectively. Experimental data of dibutoxymethane showed reasonable consistency with the information available in the literature. The vaporisation enthalpies were evaluated using the Clapeyron equation, together with the Virial equation of state to estimate the vapour compressibility factor, as well a correlation for saturated liquid molar volume. The results for both esters were comparable with data from the literature.

Phase equilibria modeling of polar systems with Cubic-Plus-Polar (CPP) equation of state

In this study, an equation of state (EoS), Cubic-Plus-Polar (CPP), has been constructed to model phase equilibria of polar and practical systems in a wide range of temperatures and pressures. In the proposed model, Soave-Redlich-Kwong (SRK) EoS takes into account dispersive forces while a set of polar terms was employed to account for dipolar and quadrupolar interactions. By applying these terms, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions were directly taken into consideration. The CPP EoS with four pure-compound parameters could accurately correlate both vapor pressure and saturated liquid molar volume of studied pure compounds (water, methanol, ethanol, propanol, 2-propanol, 2-butanol, acetone, N-methyl-2-pyrrolidone (NMP), CO2, and H2S). By utilizing two temperature-dependent binary interaction parameters (BIPs), the phase equilibria of binary mixtures including water-CO2, water-H2S, CO2–H2S, methanol-CO2, ethanol-CO2, propanol-CO2, acetone-CO2, water-acetone, ethanol-acetone, water-NMP, 2-propanol-NMP, and 2-butanol-NMP were satisfactorily calculated by the model. Moreover, the proposed model is sufficiently efficient which is capable of representing minimum water mole fraction in the nonaqueous phase of water-CO2 and water-H2S mixtures. Additionally, the CPP EoS accurately predicted the saturated and single phase mixtures densities of water-CO2 mixture. Finally, the solubility values of CO2 and H2S mixtures in water were reasonably predicted by the model.

Application of an equation of state incorporating association to alcohols up to decanol

The accurate prediction of fluid phase equilibria is essential to the design of any process in chemical industry. Most of the simulators used to model multiphase multicomponent phase equilibria use traditional cubic equations of state, like Peng-Robinson and Soave-Redlich-Kwong. However, self-associating substances, such as alcohols, are not precisely modeled with these equations of state. Different approaches have been proposed to overcome this limitation. In this work, we use the technique that separates the compressibility factor in two parts, a physical and a chemical one, and we compare the results with the Peng-Robinson equation of state and the Cubic Plus Association equation of state against experimental data for alcohols up to decanol.The parameters are estimated adjusting the proposed EOS results to two independent data set measurements, saturation pressures and saturated liquid molar volumes of the pure components, through multi-objective optimization. The results present excellent agreement for all alcohols modeled.

Thermodynamic properties and vapor–liquid equilibria of associating fluids, Peng–Robinson equation of state coupled with shield-sticky model

Combining Peng–Robinson (PR) equation of state (EOS) with Liu et al.’s association contribution derived from shield-sticky model (SSM), a new cubic-plus-association (CPA) EOS is proposed to describe the thermodynamic properties of pure associating fluids and their mixtures. The CPA-SSM EOS contains five molecular parameters (a0, c1, b, ω and δɛ/k) for the pure associating fluids, while for non-associating fluids it reduces to PR EOS with three molecular parameters (a0, c1, b). The molecular parameters are obtained by fitting the saturated pressures and/or liquid molar volumes at wide temperature ranges. The overall average absolute deviations (AADs) of 58 pure associating fluids and 20 non-associating fluids are 0.74% and 0.54% for saturated vapor pressure, 2.00% and 1.85% for liquid molar volumes respectively. The enthalpies of vaporization for 13 pure associating fluids are well predicted by using these molecular parameters. The molecular parameter b for homologous substances shows a good linear relationship with respect to their corresponding molecular weights. Using one temperature-independent binary adjustable parameter kij, satisfactory results of vapor–liquid equilibria (VLE) for both self- and cross-associating systems are obtained. The overall AADs of the equilibrium temperatures, pressures and vapor phase mole fractions are 1.46K, 1.26kPa and 0.0197 respectively for 25 self-associating systems, and 0.75K, 0.50kPa and 0.0155 respectively for 29 cross-associating systems. Other caloric properties such as the excess molar enthalpies of mixing are also successfully computed. The CPA-SSM EOS proposed has been proved to have comparable accuracy as other models but with much simpler form.

Equation of state for square-well chain molecules with variable range, extension to associating fluids

The equation of state developed in our previous work for square-well chain molecules with variable range (SWCF-VR EOS) was further extended to associating fluids. The association contribution is directly calculated by Liu et al.’s association equation which was proposed based on the sticky-shield method. For the real pure associating fluids, the SWCF-VR EOS has six temperature-independent model parameters obtained by fitting the saturated pressures and/or liquid molar volumes. The results are satisfactory with the overall average absolute deviations (AADs) of 0.76% and 0.75% for saturated vapor pressures and liquid molar volumes of 78 pure fluids in wide temperature ranges. The heat of vaporization for 17 associating fluids were well predicted using these molecular parameters. The good relations between the molecular parameters and the molecular weights were observed. By using a simple mixing rule with only one adjustable binary interaction parameter k ij for the cross well depth ɛ ij , the SWCF-VR EOS can satisfactorily reproduce the vapor–liquid equilibria (VLE) of binary mixtures at reduced and elevated pressures containing self- and cross-associating interaction. Furthermore, the VLE for ternary mixtures can be successfully predicted by using the obtained binary interaction parameters.

Application of M 4 cubic equation of state for refrigerants

In this work, M 4 cubic equation of state (EOS) (proposed by Mohsen-Nia et al., 2003) is applied to calculate the saturated properties of refrigerants. A wide range of different types of refrigerants (CFCs, HCFCs, HFCS, etc.) is examined by calculating their saturated pressures, saturated liquid and vapor molar volumes. The comparison between the VLE calculation results and the experimental data, shows that the agreement of this EOS is better than two frequently-used (SRK and PR) EOSs for 42 refrigerants and some of their mixtures.

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO 2. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO 2) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter ( k ij ) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.

Equation of state for square-well chain molecules with variable range. I: Application for pure substances

An equation of state (EOS) for square-well chain molecules with variable range developed on the basis of statistical mechanics for chemical association in our previous work is employed for the calculations of pVT properties and vapor–liquid equilibria (VLE) of pure non-associating fluids. The molecular parameters for 73 normal substances and 46 polymers are obtained from saturated vapor pressure and liquid molar volume data for normal fluids or pVT data for polymers. Linear relations are found for the molecular parameters of normal fluids with their molecular weight of homologous compounds. This indicates that the model parameters of homologous series, subsequently pVT and VLE, can be predicted when experimental data are not available. The predicted saturated vapor pressures and/or liquid volumes are satisfactory through the generalized model parameters. The calculated VLE and pVT for normal fluids and polymers by this EOS are compared with those from other engineering models, respectively.

Modeling of critical lines and regions for binary and ternary mixtures using non-cubic and cubic equations of state

In this work, two non-cubic equations of state, Perturbed Chain Statistical Association Fluid Theory (PC-SAFT) and Simplified Perturbed Hard Chain Theory (SPHCT) were used to predict critical lines and regions for several binary and ternary systems, by fitting one binary interaction parameter ( κ ij ) for each binary system. Results were compared with experimental critical data, which included inorganic gases, hydrocarbons (light and heavy paraffins, non-saturated olefins and aromatics), alcohols, carbon monoxide and carbon dioxide. These experimental data covered wide ranges of temperatures and pressures which are commonly used in industry. For comparison, the data were also modeled using two cubic equations of state: the well-known Peng–Robinson equation (PR) and the Patel–Teja–Valderrama equation (PTV). PC-SAFT and SPHCT pure-component parameters were obtained by regression, adjusting pure-component data such as vapor pressure and saturated liquid molar volume (taken from DIPPR 1.2.0). Excellent results were obtained with the PC-SAFT EoS, while the SPHCT, PR and PTV EoS did not have a good performance. The Heidemann and Khalil algorithm, with two nested single-variable iteration loops (an internal loop for volume and an external loop for temperature), was used for locating a single liquid–liquid or vapor–liquid critical point.

THE MODIFIED PGR EQUATION OF STATE: PURE-FLUID PREDICTIONS

ABSTRACT The Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to enhance the flexibility of the model, and a new expression was developed for the temperature dependence of the attractive term in this segment-segment interaction model. The predictive capability of the modified PGR EOS for vapor pressure and saturated liquid and vapor densities was evaluated for selected normal paraffins, normal alkenes, cyclo-paraffins, light aromatics, argon, carbon dioxide, and water. The generalized EOS constants and substance-specific characteristic parameters in the modified PGR EOS were obtained from pure component vapor pressures and saturated liquid and vapor molar volumes. The calculated phase properties were compared with those of the Peng-Robinson (PR), the simplified-perturbed-hard-chain theory (SPHCT), and the original PGR equations. Generally, the performance of the proposed EOS (%AAD of 1.3, 2.8, and 3.7 for vapor pressure, saturated liquid, and vapor densities, respectively) was better than the SPHCT and original PGR equations in predicting the pure fluid properties.

Modeling the thermodynamic behavior of poly(lactide-co-glycolide) + supercritical fluid mixtures with equations of state

In this work, the thermodynamic behavior of binary systems composed by one commercial biodegradable copolymer [poly( d, l-lactide-co-glycolide)] and supercritical fluids, SCF, (dimethyl ether, carbon dioxide, chlorodifluoromethane and trifluoromethane) was studied. The perturbed chain-SAFT (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS) were used to model the fluid–liquid equilibrium (FLE) for these binary systems, by fitting one temperature-dependent binary interaction parameter. For comparison, the same data were also modeled by using the traditional Peng–Robinson (PR) cubic EoS. The three PC-SAFT and SL pure-component parameters and two PR pure-component parameters were regressed by fitting pure-component data (liquid pressure–volume–temperature, PVT, data for copolymer and saturated liquid vapor pressure and molar volume for SCF). Liquid PVT data of PLAG copolymers were estimated by using a group contribution method, taken from literature. The estimation of pure-component and binary interaction parameters was performed by using the modified maximum likelihood method with an objective function that includes the cloud point pressure. An excellent agreement was obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS were less satisfactory.

Modeling the phase behavior of commercial biodegradable polymers and copolymer in supercritical fluids

Biodegradable polymers have received much attention as materials for reducing environmental problems caused by conventional plastic wastes. In this work, the thermodynamic behavior of binary and ternary systems composed by commercial biodegradable polymers and high-pressure fluids [poly( d, l-lactide) + dimethyl ether, poly( d, l-lactide) + carbon dioxide, poly( d, l-lactide) + chlorodifluoromethane, poly( d, l-lactide) + difluoromethane, poly( d, l-lactide) + trifluoromethane, poly( d, l-lactide) + 1,1,1,2-tetrafluoroethane, poly(butylene succinate) + carbon dioxide and poly( d, l-lactide) + dimethyl ether + carbon dioxide] and binary systems formed by commercial biodegradable copolymers and supercritical fluids [poly(butylene succinate-co-butylene adipate) + carbon dioxide] were studied. The Perturbed Chain-SAFT (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic EoS were used to model the liquid–fluid equilibrium (LFE) for these binary systems, by fitting one temperature-dependent binary interaction parameter. For comparison, the same data were also modeled by using the traditional Peng–Robinson (PR) cubic EoS. The three pure-component parameters of PC-SAFT and SL EoS and two pure-component of PR EoS were regressed by fitting pure-component data (liquid pressure–volume–temperature data for polymers and copolymer and vapor pressure and saturated liquid molar volume for fluids). The estimation of pure-component and binary interaction parameters was performed by using the modified maximum likelihood method with an objective function that includes the cloud point pressure. An excellent agreement was obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS was less satisfactory.

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.

Extension of EOS non‐iterative methods to density calculations: Correlation of saturated molar volumes and heats of vaporization

AbstractSoave's direct calculation procedures for the vapor pressure of pure compounds with cubic equations of state (EOSs), have been extended to the calculation of phase densities at saturation for Peng‐Robinson (PR) type EOSs. These universal relations have been used to propose EOS‐based correlation methods for the pure compound saturated liquid and vapor molar volumes, at temperatures higher than the normal boiling point. The methods yield satisfactory results independently of the molecular nature of the chemical under consideration. The results for phase densities are used to correct the heats of vaporization predicted by the ZVPR‐EOS. Complete relative error information is provided for calculated heats of vaporization and correlated vapor and liquid phase molar volumes for more than one hundred compounds of industrial interest.

Chlorofluorohydrocarbon—alcohol mixtures: bubble pressures and saturated liquid molar volumes (experimental data and modeling)

A static apparatus, described elsewhere, fitted with a variable volume cell was used to obtain new data. Results are given at two temperatures for the 1,1,2-trichlorotrifluoroethane (C 2F 3Cl 3)—ethanol and 1,2-dichlorotetrafluoroethane (C 2F 4Cl 2)—ethanol binary systems and four temperatures for the 1,2-dichlorotetrafluoroethane—trifluoroethanol and monochlorodifluoromethane (CHF 2Cl)—trifluoroethanol binary systems. Solubility data are well represented with nonclassical mixing rules and temperature-dependent binary interaction parameters for all the cubic equations of state used. However, the Trebble—Bishnoi—Salim equation of state yields the best simultaneous representation of saturated liquid molar volumes

Bubble pressures and saturated liquid molar volumes of binary and ternary mixtures of chlorofluorocarbons and hydrochlorofluorocarbons

Laugier, S., Richon, D. and Renon, H., 1994. Bubble pressures and saturated liquid molar volumes of binary and ternary mixtures of chlorofluorocarbons and hydrochlorofluorocarbons. Fluid Phase Equilibria 93; 297-316. The aim of this paper is to present new data for refrigerant mixtures. Bubble pressures and saturated liquid molar volumes were measured at several temperatures for the following binary systems; chlorodifluoroethane-trichlorotrifluoroethane (R142b-R113) trifluoromethane-chlorodifluoromethane (R23–R22), trifluoromethane-dichlorotetrafluoroethane (R23-R114): and the ternary system; trifluoromethane-dichlorotetrafluoroethane-trichlorotrifluoroethane (R23-R114-R113) using a variable volume cell and static isothermal equilibrium method. Data modeling was performed using several cubic equations of state with the present data. The best performance to represent simultaneously vapor pressures and saturated liquid molar volumes of either binary or ternary mixtures was achieved by either the regular or the generalized Trebble-Bishnoï-Salim equation of state (1991).