Perturbed-chain Statistical Associating Fluid Theory Research Articles

Effect of Composition, Temperature, and Pressure on the Viscosities and Densities of Three Diesel Fuels

In this work, a rolling-ball viscometer/densimeter is used to measure high-pressure, high-temperature (HPHT) density and viscosity data from 298.2 to 532.6 K and pressures up to 300.0 MPa for three different diesel fuels. The densities and viscosities have combined expanded uncertainties of 0.6 and 2.5%, respectively, with a coverage factor, k = 2. Two of the diesels contain either a larger paraffinic or a larger aromatic content relative to the others and are standard engine test fuels. The third is an ultralow sulfur diesel that resembles an unfinished commercial diesel. Detailed compositional information is also reported for each diesel that provides a basis for interpreting the impact of composition on density and viscosity at high pressures. Both density and viscosity data are correlated to Tait-type equations with uncertainties of 0.6 and 4.0%, respectively. The Tait equations provide a facile means to compare observed differences in the density–pressure and viscosity–pressure profiles of the three different diesels. Density data are modeled with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) with pure component parameters calculated representing diesel as a single, pseudo-component only requiring average molecular weight (Mave) and hydrogen-to-carbon ratio (RH/C) as inputs. Viscosity data are modeled reasonably well using entropy scaling coupled with the PC-SAFT EoS and information on the diesel Mave and RH/C. The HPHT viscosity data are also modeled reasonably well with free volume theory with model parameters correlated to Mave and RH/C.

Experimental setup with automatic control. High pressure VLE data of binary systems 2–Butanol with n–Heptane and 2,2,4–Trimethylpentane at both 1.5 MPa and 2.0 MPa

The isobaric vapor–liquid equilibrium for the binary mixtures of 2–Butanol + n–Heptane and 2–Butanol + 2,2,4–Trimethylpentane at 1.5 MPa and 2.0 MPa were obtained experimentally using a stainless steel ebulliometer. The experimental data have been verified thermodynamically. The data were fitted by using a polinomial zetas equation to perform the data reduction. The ϕ–ϕ approach was applied using the Perturbed Chain–Statistical Associating Fluid Theory and the Peng–Robinson–Stryjek–Vera equation of state using both quadratic and Wong–Sandler mixing rules. It has been verified that composition of the azeotropic points in both mixtures is modified by increasing the pressure. The trend of the azeotropic data was studied using bibliographic data from each mixture.

Experimental pressure versus temperature isochoric – isoplethic curves for n-pentane – dimethyl ether, n-pentane – dimethyl ether – polybutadiene and n-pentane – dimethyl ether – polybutadiene– hydrogen at high pressures

Loci of isochoric - isoplethic experimental phase equilibrium data, were determined for the binary mixture dimethyl ether (DME) + n-pentane (C5); the ternary mixture: DME + C5 + polybutadiene (PB); and the quaternary mixture DME + C5 + PB + hydrogen (H2). Binary experiments were performed at varying overall density (ρ) and varying quantity of C5. Ternary experiments were performed at varying ρ and varying relative quantities of each light solvent. In the case of quaternary mixtures, the mass fraction of polymer was kept constant, and the amount of H2 and ρ were varied. The experimental data obtained for binary and ternary mixtures were correlated using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS).

Experimental High-Temperature, High-Pressure Density Measurement and Perturbed-Chain Statistical Associating Fluid Theory Modeling of Dimethyl Sulfoxide, Isoamyl Acetate, and Benzyl Alcohol

Experimental high-temperature, high-pressure (HTHP) density of three solvents including dimethyl sulfoxide, benzyl alcohol, and isoamyl acetate was measured at temperatures of 293.15–473.15 K and pressures up to 35–37.5 MPa. The density was measured with an Anton Paar density meter (DMA HP) at 20 K and 2.5 MPa intervals. The calibration fluids were water and benzene. The combined expanded uncertainty of density taking into account the device specification and the impurities of the materials was 1 kg·m–3 (0.95 level of confidence). The experimental density data were correlated with the Tait and new modified Tait equations. The thermal expansion coefficient (αp) and isothermal compressibility (κT) were calculated with the new modified Tait equations. Moreover, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state was used to model the density data at HTHP. In most cases, the PC-SAFT parameters are obtained from saturated vapor pressure and liquid phase density; however, these ...

Modeling Binary Mixtures of Water + Light Hydrocarbon Using the Perturbed-Chain Statistical Associating Fluid Theory with Induced Association: Improvement in Describing All Equilibrium Phases

Hydrophobic effects, including low mutual solubilities, are well-documented between water and hydrocarbons. However, as deduced from quantum chemical calculations and molecular simulations, an attractive interaction as a result of electrostatic interactions and induction by water on hydrocarbon molecules exists and must be included to adequately model water–hydrocarbon systems. As shown in this work, the inclusion of these interactions allows for the perturbed-chain statistical associating fluid theory equation of state (EOS) to perform well in all equilibrium phases. Without these corrections, the EOS usually performs well only for the phase used for parametrization. Because the EOS will also be used in near-freezing water temperatures, the parameters of water are carefully derived to be able to reproduce the density anomaly of water and behavior when extrapolated to the supercooled region. The improvements and calculations will be useful for the assessment of the occurrences of potentially habitable wat...

High-Pressure Density of Bis(1-alkyl-3-methylimidazolium) Tetraisothiocyanatocobaltate Ionic Liquids: Experimental and PC-SAFT with Volume-Shift Modeling

Tetraisothiocyanatocobaltate-based ionic liquids (ILs) have shown interesting thermophysical properties, mainly surprisingly low melting points and moderate viscosity. In addition, they have been tested to separate aromatics from aliphatics because of the high molar relation between cyano groups per molecule, with highlighted results. In this work, high-pressure density data (ρpT) were measured for bis(1-alkyl-3-methylimidazolium) tetraisothiocyanatocobaltate ILs ([CnC1im]2[Co(NCS)4]) (n = 1, 2) over wide ranges of temperature (283–363 K) and pressure (0.1–95 MPa). The new ρpT data and derivative properties, namely, the isothermal compressibility and isobaric expansivity, were successfully modeled with perturbed-chain statistical association fluid theory (PC-SAFT) and using the so-called volume shift, allowing us to propose a new molecular model and parameters for these solvents. The proposed model for tetraisothiocyanatocobaltate-based ILs is shown to be robust enough to model the phase equilibria of thi...

Guide to efficient solution of PC-SAFT classical Density Functional Theory in various Coordinate Systems using fast Fourier and similar Transforms

Classical density functional theory (DFT) is a powerful tool for studying solvation or problems where resolution of interfacial domains or interfacial properties among phases (or thin films) is required. Many interesting problems necessitate multi-dimensional modeling, which calls for robust and efficient algorithmic implementations of the Helmholtz energy functionals. A possible approach for achieving efficient numerical solutions is using the convolution theorem of the Fourier transform. This study is meant to facilitate research and application of DFT methods, by providing a detailed guide on solving DFT problems in multi-dimensional domains. Methods for efficiently solving the convolution integrals in Fourier space are presented for Cartesian, cylindrical, and spherical coordinates. For cylindrical and spherical coordinate systems, rotational and spherical symmetry is exploited, respectively. To enable easy implementation, our approach is based on fast Fourier, fast Hankel, fast sine and cosine transforms on equidistant grids, all of which can be applied using off-the-shelf algorithms. Subtle details for implementing algorithms in cylindrical and spherical coordinate systems are emphasized. The work covers functionals based on weighted densities exemplarily. Functionals according to fundamental measure theory (FMT) as well as a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state are worked out in detail (and given as Supporting Information).

Surrogate Modeling of Fugacity Coefficients Using Adaptive Sampling

Complex thermodynamic models such as the perturbed chain statistical associating fluid theory (PC-SAFT) model describe the phase equilibria in a chemical process in a very precise way; however, because of their implicit and complex nature, the application of such models in process simulation and optimization can lead to a high computational effort, which may prevent the direct application of such models in process simulation and optimization. In this contribution, we replace the iterative calculation of the fugacity coefficient using PC-SAFT with explicit surrogate models that are trained using a novel adaptive sampling method.

Thermophysical properties of 1-Hexyl-3-methylimidazolium nitrate and 2-alkanol; measurement and modeling

For binary systems containing 1-Hexyl-3-methylimidazolium nitrate ([Hmim][NO3]) ionic liquid and a homolog series of 2-alkanols, new data of density and viscosity at different temperatures and atmospheric pressure have been reported. Temperature range is 293.15–323.15 K, and the considered alcohols are 2-propanol, 2-butanol, and 2-pentanol. Regarding these data, values of thermal expansion coefficient, α excess thermal expansion coefficient, αE excess molar volume, VmE and deviation in viscosity, Δη were calculated. Both excess molar volumes and viscosity deviations are negative over the whole concentration range. The magnitude and type of interactions were interpreted versus the temperature and increase of carbon atom of alcohols. Findings show that strong interactions in the mixtures occur relative to the pure state, and intermolecular forces are weaker in the long-chain alcohols. For correlation and prediction of systems density, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was applied and results obtained from this theory are consistent with experimental data. Outcome densities from this theory were implemented for free volume theory to correlate the binary viscosities. Results are satisfactory with the maximum of 1.75% deviation from experimental viscosities. The whole data reported for binary systems are novel, and so far no reports have been investigated in scientific papers.

Complex multicomponent real-fluid thermodynamic model for high-pressure Diesel fuel injection

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) has been coupled with Vapor-Liquid Equilibrium (VLE) calculations in a density-based solver of the Navier-Stokes equations to perform multicomponent two-phase simulations of Diesel injections at high-pressure conditions. This molecular-based EoS requires three empirically determined but well-known parameters to model the properties of a specific component, and thus, there is no need for extensive model calibration, as is typically the case when the NIST (REFPROP) library is utilised. PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures for which the NIST (REFPROP) library supports only limited component combinations. Moreover, complex hydrocarbon mixtures can be modelled as a single pseudo-component knowing its number averaged molecular weight (MW) and hydrogen-to-carbon (HN/CN) ratio. Published molecular dynamic simulations have been utilised to demonstrate that the developed algorithm properly captures the VLE interface at high-pressure conditions. Several advection test cases and shock tube problems were performed to validate the numerical framework using analytical and exact solutions. Additionally, two-dimensional simulations of n-dodecane and Diesel injections into nitrogen are included to demonstrate the multidimensional, multispecies and multiphase capability of the numerical framework.

Structure and thermodynamics of aqueous urea solutions from ambient to kilobar pressures: From thermodynamic modeling, experiments, and first principles simulations to an accurate force field description

Molecular simulations based on classical force fields are a powerful method for shedding light on the complex behavior of biomolecules in solution. When cosolutes are present in addition to water and biomolecules, subtle balances of weak intermolecular forces have to be accounted for. This imposes high demands on the quality of the underlying force fields, and therefore force field development for small cosolutes is still an active field. Here, we present the development of a new urea force field from studies of urea solutions at ambient and elevated hydrostatic pressures based on a combination of experimental and theoretical approaches. Experimental densities and solvation shell properties from ab initio molecular dynamics simulations at ambient conditions served as the target properties for the force field optimization. Since urea is present in many marine life forms, elevated hydrostatic pressure was rigorously addressed: densities at high pressure were measured by vibrating tube densitometry up to 500 bar and by X-ray absorption up to 5 kbar. Densities were determined by the perturbed-chain statistical associating fluid theory equation of state. Solvation properties were determined by embedded cluster integral equation theory and ab initio molecular dynamics. Our new force field is able to capture the properties of urea solutions at high pressures without further high-pressure adaption, unlike trimethylamine-N-oxide, for which a high-pressure adaption is necessary.

High-Pressure Soybean Oil Biodiesel Density: Experimental Measurements, Correlation by Tait Equation, and Perturbed Chain SAFT (PC-SAFT) Modeling

Biodiesel can easily become the crucial solution for environmental problems. The high production rate of soybean oil has been the subject of several research works to transform it into biodiesel. K...

Modeling H2S solubility in aqueous N-methyldiethanolamine solution using a new ePC_SAFT-MB equation of state

Perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), mean spherical approximation (MSA) term and Born term are combined and proposed as a new electrolyte equation of state (ePC_SAFT-MB EoS) to model the solubility of H2S in aqueous N-methyldiethanolamine (MDEA) solutions in a wide range of temperature, pressure, MDEA concentration, and H2S loading. In order to find the best association schemes (2B, 3B and 4C) for H2O, MDEA and H2S in PC-SAFT EoS, different association schemes are considered for each one of the components in the wide range of temperature and pure parameters are determined. The binary interaction parameters (BIP) for H2O + H2S and MDEA + H2O binary systems are adjusted in the VLE calculation for different association schemes. The best result with minimum average absolute relative deviation percent (AAD%) of 2.21 and 2.72 are obtained with considering the 4C, 4C and 3B association schemes for MDEA, water and H2S, respectively. By using the obtained BIPs, 277 data points of the bubble pressure for H2O + MDEA + H2S system are predicted by PC-SAFT EoS with the AAD% of 25.5. To improve the accuracy of PC-SAFT EoS, the Born and MSA terms are added to PC-SAFT EoS. The BIPs between the ion-ion and molecules-ions are adjusted by the bubble pressure calculation algorithm using 277 experimental data points. Very good results with the AAD% of 18.6 are obtained by adjusting the binary parameters (MDEAH+−MDEA,MDEAH+−H2O,MDEAH+–H2S and MDEAH+−HS−) in H2O + MDEA + H2S ternary system. Finally, to investigate the predictive ability of the proposed ePC_SAFT-MB EoS, it is employed to model the selected 44 solubility data points of H2O + MDEA + H2S system without further adjustment for model parameters. The value of AADs% is obtained about 30.0 for the H2 S partial pressure, which shows the predictive ability of the proposed model.

Prediction of Adsorption Isotherms and Selectivities: Comparison between Classical Density Functional Theory Based on the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Ideal Adsorbed Solution Theory.

This study gives an assessment of the predictive capability of classical density functional theory (DFT) for adsorption processes of pure substances and mixtures of spherical and nonspherical molecular species. A Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to calculate isotherms and selectivities of multicomponent adsorption. In order to unambiguously assess the accuracy of the DFT model, we conduct molecular simulations. Monte Carlo (MC) simulations are performed in the grand canonical ensemble using the transition matrix. Two types of systems are studied: a model system, where fluid-fluid and solid-fluid interactions are defined as (single-site) Lennard-Jones interactions, and a more realistic methane-n-butane mixture in a graphite-like pore. Differences between a slit-shaped and a cylindrical pore geometry are examined for the model system. Adsorption isotherms and selectivities obtained from DFT calculations and MC simulations are found in very good agreement, particularly at high pressures. Capillary condensation observed along adsorption isotherms containing n-butane was accurately predicted, both, in equilibrium pressure and in density-increase. Comparisons with results from the ideal adsorbed solution theory are presented, confirming powerful predictions of the DFT approach.

Predicting the Phase Behavior of Alcohols, Aromatic Alcohols, and Their Mixtures Using the Modified Group-Contribution Perturbed-Chain Statistical Associating Fluid Theory

The modified group-contribution perturbed-chain statistical associating fluid theory (PC-SAFT) has been extended to model the phase equilibria of alcohols, branched alcohols, aromatic alcohols, and...

Thermodynamic properties of CO2 + SO2 + CH4 mixtures over wide ranges of temperature and pressure. Evaluation of CO2/SO2 co-capture in presence of CH4 for CCS

In this work, density, vapor-liquid equilibrium and speed of sound measurements of the mixtures [CO2 + 4.72 mol% SO2 + 1.85 mol% CH4] and [CO2 + 0.09 mol% SO2 + 1.54 mol% CH4] were performed over the temperature range 263–373 K and at pressures of up to 30 MPa for density and up to 190 MPa for speed of sound. For the speed of sound measurements, the mixtures were doped with ≅0.8 mol% CH3OH. We compared our results to the values calculated using an extended version of the equation of state for combustion gases (EOS-CG) that includes binary models for the CO2 + SO2 and CO2 + CH4 subsystems, and a perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, validating both equations in this way. From our experimental results, we evaluated the impact of the simultaneous presence of SO2 and CH4 as impurities in anthropogenic CO2 on selected parameters for carbon capture and storage technology. With the understanding that chemical effects have not been considered, we concluded that the presence of 4.72 mol% SO2 compensates for the negative effect of 1.85 mol% CH4 on most of the studied parameters, resulting in a favorable fluid for carbon, capture and storage, contrary to the mixture with 0.09 mol% SO2 and 1.54 mol% CH4.

Density variations of TMAO solutions in the kilobar range: Experiments, PC-SAFT predictions, and molecular dynamics simulations

We present measurements, molecular dynamics (MD) simulations, and predictions using Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) of the density of aqueous solutions in a pressure range from 1 bar to 5000 bar, a pressure regime that is highly relevant for both biochemical applications and the fundamental understanding of solvation. The accurate determination of density data of pressurized solutions remains challenging. We determined relative density changes from the variations in X-ray absorption through the sample and developed a new water parameter set for PC-SAFT modeling that is appropriate for high pressure conditions in the kilobar regime. As a showcase, we studied trimethylamine N-oxide (TMAO) solutions and demonstrated that their compressibility decreases with the TMAO content. This result is linked to the stabilizing effect of TMAO on the local H-bond network of water. Experiments and calculations, which represent two independent methods, are in very good agreement and are in accordance with results of force field molecular dynamics simulations of the same systems.

Evaluation of PC-SAFT on the Saturation Pressure Prediction of Different Mixture System at High Temperatures and Pressures

Perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) has been used to predict saturation pressure of five different mixing systems which are n-alkane mixture, CH4-CO2-H2O mixture, CO2-dimethyl carbonate (DMC), C3H8-pentafluoroethane (PFE) and methanol-methyl propionate (MTP) under high temperatures and pressures conditions. The data for those five types of mixing systems are cited from previous research. For the n-alkane mixture, PC-SAFT prediction is compared with experimental data. The mixture composition is 30%-70% CH4-C6H14, 50%-50% CH4-C6H14 and 70%-30% CH4-C6H14, respectively. The average absolute relative deviation (AARD) for each mixture is 1.51%, 2.68% and 4.87%. As for 20%-80% CO2-H2O and 4%-16%-80% CH4-CO2-H2O mixture, the AARD is 1.27% and 4.14%, respectively. The AARDs of PC-SAFT prediction on different CO2-DMC mixture are 0.78%, 0.72% and 0.91%, and the overall AARDs between PC-SAFT prediction and experimental data for C3H8-PFE and methanol-MTP mixtures are 6.76% and 5.5%, respectively. Compared with Peng-Robinson (PR) EOS used in original work, PC-SAFT EOS successfully predict the bubble point pressure for common substances used in chemical industry.

Theoretical and experimental study of physicochemical behavior of binary mixtures: SAFT and PC-SAFT models

The type and magnitude of interactions between diisobutyl ketone (DIBK) and a homologous series of 2-alkanols (2-propanol up to 2-pentanol) are studied in this paper using density and viscosity data. Studies have been carried out in a wide range of temperature (293.15 K to 323.15 K), atmospheric pressure, and in the entire range of composition. The calculated excess molar volumes of the above-mentioned systems are positive, and the viscosity deviations are negative. For the correlation of the density values of binary systems, the statistical association fluid theory (SAFT) and perturbed chain statistical association fluid theory (PC-SAFT) have been used, and the output of two models are compared by average absolute deviation. The results show that the PC-SAFT model is more efficient. Densities and viscosities reported for binary systems along with applied models are all novels, and so far no reports have been investigated in the scientific papers. PC-SAFT and SAFT models were applied to model the densities of binary mixtures containing Diisobutyl ketone and 2-alkanol at various temperatures. Results show that models provide satisfactory outcomes and PC-SAFT model produces better results.

Modeling of Gas Solubility in Hydrocarbons Using the Perturbed-Chain Statistical Associating Fluid Theory Equation of State

Fitted functions that correlate binary interaction parameters (BIP) for the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) with the carbon number of n-alkane...