Multiphase Equilibria Modeling with GCA-EoS. Part I: Carbon Dioxide with the Homologous Series of Alkanes up to 36 Carbons (original) (raw)
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The Journal of Supercritical Fluids, 2010
Both the equation of state (EOS) and the quadratic mixing rules proposed by van der Waals towards the end of the XIX century were enormous contributions to the understanding and modeling of fluids phase behavior. They set the basis for a consistent and useful representation of phase equilibria for a great diversity of mixtures. Nevertheless, the models for representing phase equilibria and physico-chemical properties of asymmetric systems may require more flexible mixing rules than the classical quadratic van der Waals (vdW) mixing rules or their equivalent (with regard to the number of available interaction parameters) in modern equations of state. In particular, the phase equilibria of binary mixtures containing CO 2 and heavy n-alkanes have been studied by an important number of authors and using different types of models, achieving only partially accurate results and realizing the difficulties that these systems showing type III phase behavior (from C14 on) present for predicting or even correlating their phase equilibrium data in wide ranges of temperature and pressure. Cubic mixing rules (CMRs), implemented as a natural extension of the classical quadratic mixing rules, constitute the simplest alternative among different flexible approaches. In addition, they have the advantage of allowing correlation of multicomponent data by fitting ternary interaction parameters, while leaving invariant the description of the constituent binary systems. In this work, and after having detected the need for temperature-dependent interaction parameters in a previous study, we implemented an automated parameterization procedure based on characteristic key-points for binary systems showing type III phase behavior. Using the RK-PR EoS coupled to CMRs we present the parameters obtained and results showing for the first time a quite successful complete description of asymmetric CO 2 + n-alkane binary systems, with n-alkane carbon number from 14 to 22.
Chemical Engineering Science, 2001
In the present study we present the ÿnal development of the Global Phase Diagram-based semi-predictive approach (GPDA), which requires only 2-3 key data points of one homologue to predict the complete phase behavior of the whole homologues series. The ability of GPDA to predict phase equilibria in CO2-heavy n-alkanes is compared with the equations of state LCVM and PSRK. It is demonstrated that both LCVM and PSRK are more correlative rather than predictive because their parameters are evaluated by the local ÿt of a considerable amount of VLE experimental data. In addition, these models fail to predict accurately the VLE of systems, which have not been considered in the evaluation of their parameters. They are also particularly inaccurate in predicting LLE and critical lines. In contrast, GPDA is reliable in the entire temperature range and for all types of phase equilibria. It yields an accurate prediction of the global phase behavior in the homologues series and their critical lines. Moreover, increasing asymmetry does not a ect the reliability of GPDA; it predicts very accurately even the data of the heaviest homologues of the series. ?
Industrial & Engineering Chemistry Research, 2012
The phase equilibria of binary CO 2 + n-alkane mixtures have been studied by an important number of authors, both experimentally and using different types of thermodynamic models. Modeling studies of the phase behavior of such highly nonideal systems have generally achieved only partially accurate results in the correlation of phase equilibrium data when considering wide ranges of temperature, pressure, and n-alkane molecular weight. In this study, a predictive correlation for the phase behavior of CO 2 + n-alkane systems, based on a three-parameter cubic equation of state (EOS), that is, the RK-PR EOS, coupled to cubic mixing rules (CMRs), is developed and tested. CMRs have been shown to be capable of an accurate correlation of the phase equilibria asymmetric CO 2 + n-alkane binary systems, in wide ranges of temperature and pressure, when using system-specific interaction parameters. For developing the predictive correlation a critical review of published experimental data for the series was carried out, covering a total of about 100 references. An important degree of inaccuracy or scatter is often found when comparing data sets from different laboratories, specially for the more asymmetric systems (CO 2 + a long chain n-alkane). Tables of references covering CO 2 + n-alkane systems from C1 to C36 are presented for different types of experimental data, including critical end points (CEPs), critical points, liquid−liquid−vapor (LLV) equilibrium, and isobaric (Txy), isothermal (Pxy), and isoplethic (PT) two-phase equilibrium data sets. Examples of disagreement between different sets of data are presented and discussed. In some cases, a decision concerning the identification of the set that should be regarded as the most reliable, can be based on the experimental method employed, on the purity of the n-alkane, and on the observation of other data for conditions, and/or systems in the series, which are close to those of the data set under scrutiny. Nevertheless, the availability of such information is not enough, in other cases, to assess the quality of a given data set, where we have either different data sets in disagreement or a unique set, for which we are in doubt about its accuracy. In such situation, a predictive correlation for the whole series of binary systems is helpful to make a decision on the possible level of reliability of a given phase equilibrium data set. The present study is useful both to make decisions on conflicts between contradictory phase equilibrium data sets and to predict the phase equilibria of binary systems that have no experimental information available in the literature.
2012
This work deals with estimation of temperature dependent binary interaction parameters (kij) for binary systems containing CO2 using the Soave-Redlich-Kwong equation of state with a group contribution method. In this paper six groups, namely CH3, CH2, CH, CH4 (methane), C2H6 (ethane), and CO2 (carbon dioxide) are defined and their relevant values of group interaction parameters are optimized. Using this method, it is possible to estimate the kij of any mixture containing carbon dioxide and hydrocarbons at any temperature along the coexistence curve. The results obtained in this study are, in most cases, accurate.
Journal of Supercritical Fluids - J SUPERCRIT FLUID, 2011
Knowledge regarding the high pressure phase behavior of CO2 mixtures is of primary importance for designing, operating and optimizing many industrial processes, such as supercritical fluid extraction for pharmaceutical, food and biodiesel industries and oil recovery enhancement through CO2 flooding.In the present work, it is investigated how the CPA EoS (Cubic-Plus-Association equation of state) can be used for an adequate description of the VLE of an extensive series of CO2 binary systems containing n-alkanes, n-alcohols, esters and n-acids, in a broad range of temperatures and pressures. These families constitute a series of non-self associating, associating and cross-associating components whose potential associative interactions with CO2 are evaluated here.A detailed investigation regarding the differing behavior of CO2 depending on the nature of the second component and how the CPA EoS can best describe them is presented here, namely explicitly considering the CO2 association a...
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Fluid phase equilibria, 1993
A generalized form of the Peng-Robinson equation of state is used to calculate two and three phase equilibria in systems containing dense C02 in contact with both well defined hydrocarbons and with reservoir oils. The thermodynamic model combines completely generalized interaction parameters and critical property correlations with a tnmcated form of a gamma distribution model for describing the hexane plus fraction of a reservoir oil in a semi-continuous manner. Predictions of phase behaviour in well defined systems are used to demonstrate the accuracy of the method and are compared to regressed fits of the data. Characterization of the C~ fraction of the reservoir oil requires specification of the nature of the oil (p+a~a~ffinic, olefinic, naphthenic, or aromatic), the average molecular weight of the C6 fraction, and a single parameter describing the skew of the gamma distribution model. Sensitivity of phase behaviour predictions to the above parameters is found to be reasonably limited and surprisingly good fits of the data are obtained over a wide range of parameter values.
The Journal of Supercritical Fluids, 2017
Six predictive approaches based on the Peng-Robinson (PR) equation of state (EOS), conductor-like screening model segment activity coefficient (COSMO-SAC), and mixing rules were applied to model solid-liquid-gas equilibrium for 21 binary mixtures of CO2 and an organic compound. The accuracy of these approaches in predicting equilibrium temperatures at given pressures (635 experimental data with T = 220~413.97 K and P = 0.05~48.35 MPa), liquid phase compositions, and liquid molar volumes was examined and compared to provide an overview on their performance. The recently developed PR+COSMO-SAC EOS was found to be most accurate, with deviations of 6.25 K in temperature, 0.071 in liquid mole fraction, and 21% in liquid molar volume. The performance of these models can be very different for the solid containing different functional groups. Nevertheless, the PR+COSMO-SAC EOS could provide useful a priori predictions with only input of experimental heat of fusion and melting temperature of the solid.
Journal of Chemical and Petroleum Engineering, 2020
The accurate description of the phase equilibria of CO2 and n-Alkane multicomponent mixtures over a wide range of temperature, pressure, and n-Alkane molecular weight, requires models that are both consistent and mathematically flexible for such highly non-ideal systems. In this study, a predictive correlation was proposed for the vapor-liquid equilibrium data (VLE) of CO2 and n-Alkane ternary systems, based on the Peng-Robinson equation of state (PR EOS), coupled with cubic mixing rules (CMRs). The ternary interaction parameters (TIP) correlation is developed using binary VLE data and tested for CO2 + n-Alkane + n-Alkane ternary systems. For this purpose, binary VLE data of CO2 + n-Alkane and n-Alkane + n-Alkane systems for n-Alkane from C3 to C24, covering a total of about 70 references, used to correlate TIP in the ranges of 0.5-31 MPa and 230-663 K. Two temperature-dependent TIP correlations, based on acentric factor ratio, have been tuned with more than 2000 data points of the CO2 + n-Alkane and the n-Alkane + n-Alkane binary systems with AARD of 3.13% and 6.71%, respectively. The generalized predictive correlation was proposed based on the proper three-body interaction contributions and successfully tested for VLE data of the CO2 + n-Alkane + n-Alkane ternary systems.
Fluid Phase Equilibria, 2018
This paper deals with the modeling of the phase behavior of CO 2 in water, methanol, ethanol and acetone. The phase equilibria of pure substances and binary mixtures are correlated using different equations of state: PC-SAFT, PCP-SAFT, CPA and GEOS. The adjustable specific coefficients of pure fluids are determined by regression of vapor pressure and saturated liquid and vapor densities data. For binary mixtures, the binary cross-interaction parameters are deduced by regression of the vapor-liquid equilibrium data for wide ranges of temperature and pressure. The obtained results show that the GEOS equation of state appears to be the most adequate in the modeling and prediction of the isothermal vaporliquid phase behavior in the vicinity of the critical region. Moreover, the GEOS model is most adequate in the prediction of the three-phase liquid-liquid-vapor equilibria of CO 2 /water system at temperatures around and below the critical temperature of CO 2 and a formation of a second rich-CO 2 liquid phase. In addition, the dew curves of the water/CO 2 system were most accurately predicted by the GEOS model. The isothermal-isobaric vapor-liquid equilibria of CO 2 /methanol/water and CO 2 /ethanol/water were predicted and the comparison with the literature data demonstrated some advantages to the GEOS equation of state.
Fluid Phase Equilibria, 2010
This study evaluates the accuracy of estimating data in the series of systems carbon dioxide (1)-fatty acids (2) by two cubic equations of state, namely the EOS of Peng and Robinson in its original form and the recently proposed cubic EOS. The classical mixing rules are implemented in entirely predictive manner, i.e. without binary adjustable parameters. It is demonstrated that both models may yield reliable predictions of the data. However the EOS of Peng and Robinson fails in predicting the topology of phase behavior of the heavy homologues. The second cubic EOS predicts the Global Phase Behavior in the homologous series under consideration satisfactorily accurate, which in particular means qualitatively correct estimation of the liquid-liquid equilibria. The recently proposed EOS has no significant advantage over the EOS of Peng and Robinson in predicting the vapour-liquid equilibria data under consideration.