Application of Chebyshev polynomials to predict phase behavior of fluids containing asphaltene and associating components using SAFT equation of state

In this work, a thermodynamic model based on statistical association fluid theory (SAFT) is developed to predict the phase behavior of mixtures containing asphaltene contents. The SAFT equation of state is a good candidate for closing that gap between statistical mechanic models and the classical models dominated by cubic equation of state. A robust, fast and accurate computational algorithm based on Chebyshev polynomial approximation is developed to calculate the density and hence fugacity using SAFT equation of state in order to perform phase equilibrium calculations. Application of Chebyshev polynomials to approximate pressure-density function leads to an interpolation error of degree 10⁻¹³. Application of the proposed algorithm to calculate density of binary systems composed of ethanol and toluene shows an average relative deviation of 0.143% in the temperature range 283.15-353.15 K and for pressures up to 45 MPa. The proposed model is developed to predict the precipitation behavior of petroleum fluids containing asphaltene. The effect of pressure, temperature and solvent concentration on the amount of asphaltene precipitation is investigated. A good agreement with an AAD of 2.593% is observed between experimental and predicted amount of asphaltene precipitate. The model is also tested to investigate the effect of temperature and solvent concentration on asphaltene onset pressures (upper and lower). Again, an excellent agreement is observed between experimental and predicted values of the asphaltene onset pressure at different temperatures and solvent concentrations with an average 0.705% relative error. The accuracy of the proposed model is compared with WinProp software using Peng-Robinson equation of state with average 53.132% and 8.657% relative errors for the amount of asphaltene precipitate and onset pressure, respectively.     

A practical equation of state for non‐spherical and asymmetric systems for application at high pressures. Part 1: Development of the pure component model

A practical, mathematically and computationally simple, equation of state (EOS) has been developed to accurately describe pure component phase behaviour of spherical and chain‐like molecules. The EOS consists of a newly developed hard sphere model and a perturbation term based on the Barker and Henderson approach using the Chen and Kreglewski intermolecular potential model and a double constrained summation as a mathematical expression thereof. The perturbed hard chain theory (PHCT) approach is used to extend the EOS to non‐spherical molecules. The EOS compares well with other more complex models such as the simplified perturbed hard chain theory (SPHCT) and statistically associating fluid theory (SAFT) models and will be extended to describe mixtures in Part 2 of this series. © 2011 Canadian Society for Chemical Engineering     

超临界CO2二元系统相平衡的数值模拟

应用微扰理论,借助微扰状态方程,对超临界CO2 系统相平衡进行了模拟。编制了求解程序,介绍了状态方程中各参数的确定方法和程序模块的设计思想。针对超临界CO2 /非极性体系、超临界CO2 /极性体系,在不同温度、压力条件下的气液相平衡进行了计算,将计算结果与实验结果进行了比较,结果表明:微扰状态方程适合模拟超高压下的CO2 二元体系的相平衡。     

Mutual solubility study for 94.2:5.8 of ethanol to octane with supercritical carbon dioxide solvent

Solubility data of a mixture containing 94.2% ethanol and 5.8% octane was measured in carbon dioxide solvent using a high-pressure type phase equilibrium apparatus at pressures up to 103.5 bar and at temperature of 75 °C. The results showed that considerable separation was not achieved in this ethanol and octane ratio. However, the experimental data were then compared with the theoretical data which were obtained from two models which are regular solution theory and Redlich-Kwong equation of state. Regular solution theory is employed to each phase by applying activity coefficient expressions. Redlich-Kwong equation of state is employed to the vapor phase and then with applying fugacity coefficient, liquid phase data is obtained. The regular solution theory as a novel model approach has been found to be encouraging for the prediction of phase equilibria solubilities. It concluded that the regular solution theory model could predict two phases equilibrium data better than Redlich-Kwong equation of state.     

A modification of Wong-Sandler mixing rule for the prediction of vapor-liquid equilibria in binary asymmetric systems

Systems consisting of light components and heavy hydrocarbons are highly asymmetric and industrially important. Design and control of facilities for separation and purification of such mixtures require vapor-liquid equilibrium data. Coupling of the cubic equation of state (EOS) with excess Gibbs energy models (EOS/G ^ex models) failed to represent the vapor-liquid equilibria (VLE) of such systems accurately. The main purpose of this work is to present a modification of Wong-Sandler mixing rule with using the composition dependent binary interaction parameter. Vaporliquid equilibria for 30 binary systems are calculated using the SRK equation of state with proposed model and Wong-Sandler mixing rule. Calculated pressures and mole fractions of vapor phase are compared with experimental data. The average absolute percentage deviation indicates that error involved in the application of modified Wong-Sandler model is less than Wong-Sandler model in most cases.     

A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).     

Application of peng-Robinson equation to high-pressure aqueous systems containing gases and sodium chloride

A novel approach is proposed for modeling vapor-liquid equilibria in systems containing aqueous NaCl and supercritical gases. The Peng-Robinson equation of state is used for all species, with the salt treated as a hypothetical liquid component. To correctly model the highly non-ideal liquid solution, a two-fluid model is used for the mixing rules in the equation of state. Effective pure-component parameters are reported for NaCl as well as binary interaction parameters for all possible binaries. Representation of high-pressure phase equilibria data show good agreement with experimental data. The principal advantage of this approach is the ability to treat high pressure systems containing non-volatile salts, while maintaining the simplicity of a cubic equation of state.     

含临界点的统计缔合流体理论研究(Ⅰ)非极性流体

从适合于临界点的计算出发 ,对统计缔合流体理论方程进行改进 :(1)对链状分子的每个链节考虑其非球形度 ;(2 )提出必须考虑链节成链时对色散作用的影响 .建立了扩展的统计缔合流体理论状态方程 ,对于正构烷烃和异构烷烃的计算表明 ,该方程计算温度范围大 ,从低温区到临界区 ,特别是在临界点附近精度有明显提高 ,临界点的计算值和实验值基本符合 .扩展了理论状态方程的适用性 ,可望用于各种含临界区域流体体系的热力学计算     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

超临界二氧化碳和醇类体系的相平衡计算

应用Peng-Robinson(P-R)状态方程对超临界CO2系统进行了相平衡模拟。对超临界CO2和醇类二元系统进行了汽液相平衡计算,结果表明,P-R状态方程模拟高压下CO2系统的相平衡具有较高的精度。     

Algorithm for fluid phase equilibria calculations by means of a multiconstant equation of state

Some methods for correlating multicomponent vapor-liquid equilibria by using an equation of state are examined. A simplified Morbidelli-Carrà algorit is proposed as the best tool for an eight parameter equation previously reported in Chem. Engng Sci. The possibility of reducing the empirical para of this equation from eight to five and the binary interaction parameters from three to two is also discussed. Both these models have been applied to s binary and ternary mixtures of polar and apolar compounds in a wide range of pressure and temperature. The proposed method also correlates systems exhi miscibility gaps or containing quantal gases.     

Improvement of the Van Der Waals equation of state

The Van Der Waals equation of state has been modified in order to improve its accuracy. The introduction of a temperature dependence of the attraction term allows reproducing accurately pure-compound vapour pressures. The modification of the mixing rules, with the infinite-pressure excess-free-energy term expressed by a NRTL-like model, allows reproducing accurately phase equilibria of polar and apolar systems. Finally, the introduction of a volume correction improves markedly the calculated liquid densities, without changing the phase-equilibrium conditions. The improved equation is accurate enough to be applied for design purposes.     

Biomass conversions in subcritical and supercritical water: driving force, phase equilibria, and thermodynamic analysis

Two biomass conversion processes have been studied: hydrothermal upgrading (HTU) under subcritical water conditions; supercritical water gasification (SCWG) in supercritical water. For the design of the two biomass conversion processes, the following contributions of thermodynamics have been presented: phase behavior and phase equilibria in the reactor and separators; indication of the favourable operation conditions and the trends in product distribution for the conversion reactions; construction of heat exchange network and exergy analysis. A wide variety of fluids have been dealt with, from small molecules to large molecules, including non-polar and polar substances. The statistical association fluids theory (SAFT) equation of state has been applied to calculate the mass distribution in different phases and to estimate the entropy and enthalpy values for different mass streams.     

SRK方程α的改进及其在汽-液相平衡预测中的应用

Based on results of saturated vapor pressures of pure substances calculated by SRK equation of state,the factor α in attractive pressure term was modified. Vapor-liquid equilibria of mixtures were calculated by original and modified SRK equation of state combined with MHV1 mixing rule and UNIFAC model, respectively. For 1447 saturated pressure points of 37 substance including alkanes; organics containing chlorine, fluorine, and oxygen; inorganic gases and water, the original SRK equation of state predicted pressure with an average deviation of 2.521% and modified one 1.673%. Binary vapor-liquid equilibria of alcohols containing mixtures and water containing mixtures also indicated that the SRK equation of state with the modified α had a better precision than that with the original one.     

SRK方程α的改进及其在汽-液相平衡预测中的应用

Based on results of saturated vapor pressures of pure substances calculated by SRK equation of state, the factor a in attractive pressure term was modified. Vapor-liquid equilibria of mixtures were calculated by original and modified SRK equation of state combined with MHV1 mixing rule and UNIFAC model, respectively. For 1447 saturated pressure points of 37 substance including alkanes; organics containing chlorine, fluorine, and oxygen; inorganic gases and water, the original SRK equation of state predicted pressure with an average deviation of 2.521% and modified one 1.673%. Binary vapor-liquid equilibria of alcohols containing mixtures and water containing mixtures also indicated that the SRK equation of state with the modified a had a better precision than that with the original one.     

Evaluation of SAFT and PC-SAFT models for the description of homo- and co-polymer solution phase equilibria

Statistical associating fluid theory (SAFT) and perturbed-chain SAFT (PC-SAFT) are used to model the phase behavior of polymer-solvent mixtures over a wide temperature and pressure range. Homopolymers (polyolefins) as well as co-polymers are examined. Calculations were performed using various recently proposed robust algorithms for polydisperse polymers. Various polymer properties that affect substantially the phase behavior, such as molecular weight, polydispersity, and macromolecular architecture, were considered. For most of the systems examined, PC-SAFT correlation is marginally closer to experimental data than SAFT. Nevertheless, there are a number of mixtures where SAFT is the preferred model.     

煤炭直接液化体系高温高压气液相平衡研究进展及模型选择

笔者从气液相平衡基础理论展开并综述了高温高压相平衡计算研究进展，介绍了状态方程法、混合模型法、超额Gibbs自由能-状态方程模型法，并重点介绍了超额Gibbs自由能-状态方程模型法的思路及应用特点。针对煤炭直接液化物系高温、高压、强不对称、强极性、完全非理想体系等特点，与结合传统混合规则的状态方程法及混合模型法相比较，采用超额Gibbs自由能-状态方程模型法能够在更大范围内准确计算和预测煤液化气液相平衡。