PC-SAFT Equation Research Articles

Role of Characterization in the Accuracy of PC-SAFT Equation of State Modeling of Asphaltenes Phase Behavior

The ability to capture asphaltene precipitation conditions is key to minimize costs associated with production caused by asphaltene depositing and blocking wellbores and pipelines. In this work, mo...

Modelling phase behavior of triglycerides, diglycerides and monoglycerides related to biodiesel transesterification in mixtures of alcohols and CO2 using a polar version of PC-SAFT

Soh et al. [1] showed that one can achieve high conversion (98%) of triglycerides to fatty acid methyl esters at 95 °C when carbon dioxide (CO2) is used as a co-solvent to enhance mixing of the immiscible alcohol and triglyceride. Soh's results demonstrated the benefits of using CO2 as a co-solvent yet did not provide information on the evolution of the phase behavior during the reaction. The PC-SAFT equation of state has been employed to understand and predict the phase behavior of the various biodiesel components versus temperature and pressure in the presence of CO2. In previous work [2] the interaction between alkyl-esters and low molecular weight alcohols, glycerol, and CO2 were investigated. Polar PC-SAFT and the Group Contribution PPC-SAFT EoS were used to model phase equilibria amongst the various multicomponent systems. The same approach is extended here, specifically applied to mixtures containing tri-, di- and monoglycerides plus low molecular weight alcohols and CO2.Data for different types of glycerides are scarce and in general the phase boundary curves in CO2-based mixtures are only weakly dependent on CO2 concentration, creating curves with very high slopes in P-T space that accumulate larger prediction errors compared to the previously investigated alkyl-ester systems. Nonetheless, it was found that one could generate a general correlation for binary interaction coefficient that depends only on carbon chain length and degree of unsaturation for description of triglyceride-CO2 mixtures. Binary interaction parameters as low as 12% were obtained for all glyceride-methanol systems and binary interaction coefficient below 3.5% are sufficient to correctly capture CO2 – glyceride vapor-liquid and liquid-liquid phase equilibria.

(ρ, VE, T) Measurements of the Ternary Mixture (Dibutyl Ether + 1-Heptanol + Heptane) at Temperatures up to 393.15 K and Pressures up to 140 MPa and Modeling Using the Peng–Robinson and PC-SAFT Equations of State

New measurement density data (1360 points) for dibutyl ether (1) + 1-heptanol (2) + heptane (3) were measured at various temperatures, T (298.15–393.15) K, and various pressures, p (0.1–140) MPa, a...

Physical Properties of 7-Methyl-1,5,7-triazabicyclo[4.4.0]dec-5-ene (mTBD)

7-Methyl-1,5,7-triazabicyclo[4.4.0]dec-5-ene (mTBD) has useful catalytic properties and can form an ionic liquid when mixed with an acid. Despite its potential usefulness, no data on its thermodynamic and transport properties are currently available in the literature. Here we present the first reliable public data on the liquid vapor pressure (temperature from 318.23 K to 451.2 K and pressure from 11.1 Pa to 10 000 Pa), liquid compressed density (293.15 K to 473.15 K and 0.092 MPa to 15.788 MPa), liquid isobaric heat capacity (312.48 K to 391.50 K), melting properties, liquid thermal conductivity (299.0 K to 372.9 K), liquid refractive index (293.15 K to 343.15 K), liquid viscosity (290.79 K to 363.00 K), liquid–vapor enthalpy of vaporization (318.23 K to 451.2 K), liquid thermal expansion coefficient (293.15 K to 473.15 K), and liquid isothermal compressibility of mTBD (293.15 K to 473.15). The properties of mTBD were compared with those of other relevant compounds, including 1,5-diazabicyclo(4.3.0)non-5-ene (DBN), 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU), and 1,1,3,3-tetramethylguanidine (TMG). We used the PC-SAFT equation of state to model the thermodynamic properties of mTBD, DBN, DBU, and TMG. The PC-SAFT parameters were optimized using experimental data.

A PC-SAFT model for hydrocarbons IV: Water-hydrocarbon phase behavior including petroleum pseudo-components

This paper is the fourth installment of a series which develops a new generalized treatment of hydrocarbon molecules based on the PC-SAFT equation of state. In this paper, a generalized approach to water/hydrocarbon phase behavior is developed. The model accurately predicts mutual solubilities (partitioning in LLE) of saturates, aromatics and alkenes with water. The generality is a result of incorporating hydrogen bonding interactions between unsaturated bonds and water in a general/scalable way. Further, we extend our PC-SAFT hydrocarbon characterization model EMPETRO to allow for aromatics to receive hydrogen bonds from hydrogen bond donors (water, ethanol, etc.). We demonstrate the model can accurately predict mutual solubilities for hydrocarbons with water when the hydrocarbon is parameterized solely from petroleum variables boiling point, specific gravity and molecular weight.

Characterization and determination of thermodynamic properties of waste cooking oil biodiesel: Experimental, correlation and modeling density over a wide temperature range up to 393.15 and pressure up to 140 MPa

Biodiesel can be described as mono-alkyl esters of long chain fatty acids, derived from a vegetable oil in reactions with alcohols. The physical properties of biodiesel are largely determined by the length of the hydrocarbon chain, the degree of unsaturation, and the effect of molecular packing, while the calculation of the thermodynamic properties of biodiesel is difficult in reason they are high molar weight components and complex structures. The density data (136 points) for waste cooking oil biodiesel at several temperatures between 298.15 K and 393.15 K and pressures up to 140 MPa are reported. The chemical constituents were analyzed by GC/MS, 1HNMR and 13CNMR in order to determine the fatty acid composition of waste cooking oil biodiesel. An Anton Paar vibrating tube densimeter, calibrated with an uncertainty of ±0.7 kg m−3 was used to perform these measurements between 298.15 K and 393.15 K. In this work, the density experimental data of biodiesel were correlated with the Tait equation of state (EoS), an empirical equation widely used for high pressure density correlation. The PC-SAFT equation of state using group contribution methods was employed for the calculation of parameters and prediction of biodiesel densities.The statistical parameters of empirical Tait-correlation are much lower than the experimental uncertainty of the density measurements with the AAD (0.01%), MD (0.04%), Bias (7.1 × 10−4%), and standard deviation, σ (1.5 × 10−4g.cm−3), and from PC-SAFT, density of sample was reasonably well predicted with an average relative deviation 0.083%In addition, the isobaric thermal expansivity and the isothermal compressibility have been derived from the Tait-like equation.

Evaluation of the PR, tc-PR, CPA, PC-SAFT and IAPWS-95 models in the predicting thermodynamic properties of pure water at the supercooled, compressed liquid, saturated liquid-vapor and superheat regions

This study provides a comprehensive understanding of the potential and limitations of the PR, tc-PR, CPA, PC-SAFT and IAPWS-95 equations of state in the prediction of thermodynamic properties of pure water. Using these equations of state (EoS), non-derivative properties, including entropy, enthalpy, internal energy, volume and derivative properties including heat capacity at constant pressure (∂H/∂T)P and constant volume (∂U/∂T)V, isobar expansivity (∂V/∂T)P, isothermal compressibility (∂V/∂P)T and speed of sound were calculated for water. The IAPWS-95 is a specialized formulation for water, which has great performance, but it shows limitation to the temperature and the pressure range where the parameters are fitted. At supercooled and compressed liquid region, the PR, tc-PR, CPA, and PC-SAFT models could not predict the properties well. At saturated liquid-vapor region, all of the equations of state lead to acceptable results for non-derivative properties; however, the CPA and PC-SAFT, as the associating type models, have limitations at the near-critical region. Accordingly, the parameters of these two models must be re-tuned to experimental data covering triple to the critical point. The PR, tc-PR, CPA and PC-SAFT models have a major shortcoming in predicting derivatives properties including (∂P/∂V)T, (∂P/∂T)V, (∂V/∂T)P and (∂V/∂P)T in all regions. Results showed that the tc-PR is a suitable EoS for predicting thermodynamic properties in saturated liquid-vapor and superheated regions. None of the models can predict the thermodynamic properties of pure water at the supercooled and compressed liquid region.

A theoretically modified PC-SAFT equation of state for predicting asphaltene onset pressures at low temperatures

This paper presents a modified perturbed chain-statistical association fluid theory (mod-PC-SAFT EoS) obtained by including into PC-SAFT the second-order dispersion term developed originally by Zhang [Fluid Phase Equilibria, 154 (1999) 1–10] for pure components. This version of PC-SAFT was then used to predict asphaltene onset pressures (AOPs) for nine petroleum reservoir fluids with asphaltene contents, based on saturates-aromatics-resins-asphaltenes (SARA) analyses, varying from 0.80 to 16 wt%. In all modeled cases, this new version predicted less accelerated AOPs at low temperatures than the original PC-SAFT, and then the well-known and widely discussed tendency of PC-SAFT of predicting very high AOPs at these conditions was corrected. The new model also reduced or eliminated the crossover temperatures predicted by PC-SAFT when a reservoir fluid, prone to precipitate asphaltenes, was enriched with CO2.

Observations regarding the first and second order thermodynamic derivative properties of non-polar and light polar fluids by perturbed chain-SAFT equations of state

This paper focuses on the second order derivative properties of some pure components, as the most significant challenges to develop the equations of states. For this reason, PC-SAFT equation of state has been used to predict derivative properties of n-alkanes, such as heat capacities, the speed of sound and Joule-Thomson coefficient in the wide temperature and pressure ranges up to 20 MPa. The performance of this model is evaluated against experimental data so that a good agreement with predicted properties can be observed except near the critical point and in some cases, near the coexistence phases. Furthermore, this study has tried to demonstrate the capability of polar sPC-SAFT equation of state to estimate the saturated pressure, liquid density and the speed of sound for light alcohols. Therefore, the system-dependent parameters of this model have been reassigned. The results have been compared with the available literature data and have shown a very good agreement.

Density of biofuel mixtures (Dibutyl ether + Heptane) at temperatures from (298.15–393.15) K and at pressures up to 140 MPa: Experimental data and PC-SAFT modeling

Density has been reported to binary mixtures (552 points) of dibutyl ether (DBE) + heptane in the composition range (4 compositions; 0.325 ≤ dibutyl ether mole fraction x ≤ 0.85), between 298.15,393.15 K, and for 23 pressures ranging from 0.1 MPa to 140 MPa.These experimental measurements were carried out using an apparatus, comprising a vibrating tube densimeter Anton Paar, calibrated with an uncertainty of about 0.7 kg· m-3.The volumetric behavior and excess molar volume of DBE + heptane were modeled using PC-SAFT equation. The PC-SAFT parameters of DBE and heptane were optimized using experimental density data at atmospheric pressure. The density of the mixture was reasonably well predicted, with a mean relative difference between 0.0009% and 1.99%. Whereas the excess molar volume not satisfactorily predicted.A Tait equation was used to adjust the experimental density data. In addition, from this equation the isobaric thermal expansion and the isothermal compressibility were derived.

Minimum Miscibility Pressure Using the Multiple Mixing-cell Combined with the PC-SAFT Equation of State

The minimum miscibility pressure (MMP) is one of the crucial and substantial parameters in the gas injection projects for enhanced oil recovery (EOR). This parameter indicates the minimum pressure at constant temperature and composition conditions for reaching 100 percent of the oil production recovery which leads to a huge economic income. Therefore, an inaccurate prediction of the MMP may lead to increase the costs of oil production. Among the various methods for prediction of the MMP: slim-tube experiment, slim-tube simulation techniques and their simplified cell-to-cell could be considered as the most accurate methods. Although the experimental methods for calculation the MMP take into account the real crude oil, but they are always expensive; therefore, thermodynamic simulation is a better way for the estimation of this parameter. Indeed, the analytical methods are fast and some of them like multiple mixing-cell method used in this study lead to the reliable results and often show good agreements with the experimental methods. A combination of multiple mixing-cell model proposed by Ahmadi and Johns and pressure-temperature (P-T) flash calculations including the PC-SAFT equation of state (EoS), and the cubic equations of state of Peng-Robinson (PR) and Esmaeilzadeh-Roshanfekr (ER) were used in this work for the prediction of MMP. The results overally prove that the PC-SAFT EoS leads to more accurate results in comparison with the ER and PR equations of state.

THERMODYNAMIC ANALYSIS AND MODELING OF BRAZILIAN CRUDE OIL AND ASPHALTENE SYSTEMS: AN EXPERIMENTAL MEASUREMENT AND A PC-SAFT APPLICATION

ABSTRACT Asphaltenes represent the heaviest fraction of crude oils, being recognized by their tendency to self-associate and precipitate. Asphaltene precipitation and subsequent deposition can cause problems in all stages of production. The objective of this paper is to model Brazilian crude oil and asphaltene systems using the PC-SAFT equation of state. Asphaltenes were extracted from crude oil through the addition of different n-alkanes. The PC-SAFT was capable of accurately predicting liquid density for toluene and asphaltenes and boiling point elevation for crude oil at different concentrations of toluene. Asphaltene precipitation from model oil allowed us to evaluate the influence of binary interaction parameters on modeling results. The influence of precipitant agent (n-hexane and n-heptane) on the asphaltene phase behavior was analyzed, showing that n-hexane was able to precipitate more asphaltenes than n-heptane, as expected. Furthermore, simulated results are in agreement with experimental observations: the average relative errors are 3.75 % and 10.25 % for the weight percentage of precipitated asphaltene using n-hexane and n-heptane as precipitant, respectively.

A PC-SAFT model for hydrocarbons I: Mapping aromatic π-π interactions onto a dipolar free energy

Aromaticity is an important property of many petroleum derived streams. Traditional thermodynamics tools (e.g., cubic equations of state) do not provide any special treatment to these aromatic hydrocarbons. A feature which discriminates aromatics from paraffins is that aromatic rings exhibit anisotropic π-π interactions. Accounting for this key difference between aromatic and non-aromatic hydrocarbons in an equation of state will allow for a level of predictability which is not possible with our current tools. By mapping the anisotropy of π-π attractions onto a dipolar free energy, we develop a simple and powerful treatment of aromatic hydrocarbons within the PC-SAFT equation state. We demonstrate that this approach provides a substantial increase in performance over the standard non-polar treatment of aromatic molecules. The methodology developed is used to develop a generalized hydrocarbon model in instalment II of this series.

Thermodynamic analysis of biodiesel production systems at supercritical conditions

This work reports thermodynamic analysis of systems involved in the biodiesel production using ethanol at supercritical conditions. PC-SAFT equation of state was used from ASPEN Plus simulator for modeling all investigated systems. Binary and ternary phase equilibrium data at high pressure and temperature were used to assess the PC-SAFT capability of predicting the thermodynamic behavior of the complex mixture of interest in this work. The results showed that the PC-SAFT is a reliable tool to represent the phase behavior of mixtures involving ethanol, vegetable oil, fatty acid, ethyl esters of fatty acid and glycerol. Phase behavior of the reaction system was evaluated under specified experimental conditions and considering different reaction conversions. Pressure-temperature diagrams demonstrated that the two-phase region for the reaction mixture decreases as the extension of reaction is increased. The PC-SAFT equation of state was used to estimate the density of the reactant mixture and the effect of this parameter over the residence of the reaction was assessed, where it was clearly demonstrated that the density of the mixture greatly affects the residence time calculation for the reactions of biodiesel production at high pressure conditions.

Modeling phase behavior of Poly(ɛ-caprolactone) solutions at high pressure

Poly(ɛ-caprolactone) (PCL) is a biocompatible and biodegradable polymer and is widely used in controlled drug-delivery applications. For the production of polymeric microspheres loaded with pharmaceutical products, the supercritical fluid technology using carbon dioxide (CO2) is favored because of its non-toxic nature. In this work, the phase behavior of PCL in various supercritical solvents such as CO2, CHClF2, dimethyl ether (DME), 1-butene, and propylene is described by the PC-SAFT model. The effects of the molecular weight of PCL, the type of solvent, pressure, temperature, and the concentration of the cosolvent are investigated. The solubility of PCL in supercritical solvents is accurately described over a wide range of temperatures (from 293.15 to 503 K) and for pressures up to 300 MPa. CO2 shows the poorest solubility, while CHClF2 shows the highest solubility. The predicted cloud-point pressures show an increasing tendency with an increase of the molecular weight of the PCL. The addition of cosolvents, i.e., DME and CHClF2, to the PCL/CO2 solution increases of the dissolving power of the mixed solvent. The results predicted with the PC-SAFT equation of state are in good agreement with the experimental data.

Modeling the phase behavior of refrigerants with ionic liquids using the QC-PC-SAFT equation of state

In this work, the phase behavior of several binary systems, each containing an IL and a refrigerant, was determined using the quasi-chemical PC-SAFT equation of state (QC-PC-SAFT EoS). A total of 578 bubble and dew point data of a number of IL + refrigerant binary systems were used for modeling. For the comparison of the QC-PC-SAFT with other models, the PC-SAFT EoS and the Peng-Robinson EoS with the Wong-Sandler mixing rules using the NRTL activity coefficient model (PR + WS) were used to study the phase behavior of the same systems. It was observed that the QC-PC-SAFT gives the best results, with an average absolute relative deviation (AARD%) of 3.11%, in comparison with the PC-SAFT and the PR + WS models with AARD% values of 6.28% and 6.01%, respectively.

A PC-SAFT model for hydrocarbons II: General model development

This is the second paper in a series which describes the development of a general PC-SAFT hydrocarbon model. In instalment I, a new treatment of aromaticity was included in the PC-SAFT equation of state by mapping aromatic π-π attractions onto a dipolar free energy. In this paper we include this aromatic-polar map into the development of a generalized thermodynamic model for hydrocarbons. The characterization model incorporates heteroatom polarity as well as aromaticity. The minimum level of input to the model is boiling point, molecular weight, and specific gravity. If a specific molecular structure is known, the model formalism accommodates inclusion of various aromatic and heteroatom functional groups. We demonstrate by comparison to pure component properties of defined hydrocarbon molecules that the new approach is of nearly quantitative accuracy. We also demonstrate how the use of the polarity contributions allows for accurate prediction of non-idealities in mixture phase equilibria.

An interfacial statistical associating fluid theory (iSAFT) approach for surface/interfacial tension predictions

Interfacial properties play an important role in many industrial processes and in the design of new materials. A fundamental understanding of interfacial phenomena and predictive tools that predict interfacial properties can greatly facilitate new process/material design. In this work, we propose an extension to the original interfacial Statistical Associating Fluid Theory (iSAFT) by Tripathi and Chapman [1]. This resulting classical Density Functional Theory (DFT) reduces to PC-SAFT equation of state in the bulk limit. It accepts PC-SAFT parameter values as input and predicts interfacial properties. The model is applied to vapor-liquid interfaces and liquid-liquid interfaces of both non-associating and associating fluids and the predicted surface/interfacial tensions agree very well with experimental data.

On the anomalous composition dependence of viscosity and surface tension in refrigerant blends

The Polar PC-SAFT equation of state coupled with DGT and excess entropy scaling was applied to predict the phase, interfacial and transport properties of refrigerant blends. Results show the presence of several thermophysical anomalies in systems under consideration. The literature has always linked aneotropic behavior at the interface (extrema in surface tension) to azeotropic behavior (extrema in vapor pressure) at the bulk. However, a minimum in surface tension as a function of composition was predicted in this work for R-32 + R-1234yf zeotropic mixture. The system also exhibits a significant positive excess volume in comparison to other R-32 binary mixtures. The latter phenomena indicate the presence of excessively weak intermolecular interactions between both species. Furthermore, a minimum in viscosity as a function of composition was predicted for R-32 + R-143a binary mixture. This was attributed to the homogenous distribution of charges found in both symmetrical molecules which leads to molecular repulsion and structure breaking. On contrary, a maximum in viscosity as a function of composition was predicted for R-32 + R-125 binary mixture. This was attributed to strong charge-charge interactions between the highly fluorinated R-125 molecule and R-32. The latter promotes structure making as evidenced by the system's negative excess volume. A maximum in the viscosity was also predicted for R-152a + R-1234ze(E) binary mixture. Aggregate formation is promoted in this system due to the strong charge-charge interaction between the unshielded fluorine atom in R-1234ze(E) and the undisturbed methyl group in R-152a.

Comparison of two modelling approaches for the interfacial tension of binary aqueous mixtures

The present study focuses on the interfacial tension at liquid-liquid phase split of aqueous mixtures, namely water + 1-butanol, water + 1-hexanol and water + hexyl acetate. The interfacial tensions were calculated using the density gradient theory (DGT) coupled with the PC-SAFT equation of state and the incompressible version of DGT in combination with UNIQUAC or the NRTL-model. The application of the incompressible version of DGT in combination with the NRTL-model is a suitable tool for a very accurate correlation of the interfacial tension, including the correct modelling of the occurring maximum as function of temperature for water + 1-alcohol mixture. The prediction of the interfacial tension using DGT based on the influence parameters of the pure-components fails to a large extend. The problem could be solved, if the influence parameters of water were readjusted using binary data. The PC-SAFT allows also the prediction of the density difference between the coexisting phases which enter the spinning drop measurements. The predicted densities are not accurate enough in order to replaces the experiment.