PC-SAFT在烯烃共聚物体系物性计算中的应用进展

综述了PC-SAFT状态方程在计算共聚物性质以及共聚物-溶剂相平衡方面的研究进展,介绍了用PC-SAFT状态方程计算的几种共聚物体系的相平衡以及计算值与实验值的比较情况。结果表明PC-SAFT状态方程可以很好地描述二元共聚物-溶剂体系的相平衡。此外,对于由极性和非极性重复单元构成的共聚物,需要用相互作用参数来校正不同类型重复单元之间的相互作用力。     

基于PR状态方程的二元体系临界性质计算中不同混合规则对比

基于PR状态方程,结合四种不同混合规则,利用Heidemann和Khalil的临界性质计算方法,关联了二十一种不同二元体系的临界温度并预测了其临界压力,其中包括非极性、极性和缔合三类体系.对临界温度的关联结果表明,四种混合规则对所有体系均适用.对临界压力的预测结果表明,四种混合规则中van der及Waals-1 Panagiotopoulos-Reid混合规则对非极性-极性(四偶极)体系的估算精度高,而van der Waals-2和Sadus van der Waals-2混合规则更适用于非极性-非极性体系及极性-极性(四偶极)体系.对于缔合体系,随着组分缔合能力的增强,四种混合规则的预测误差均增大,除含1-丁醇及苯组分的体系外有待于寻找更合适的状态方程及混合规则.     

乙烯淤浆聚合体系组分的物性计算方法

聚合反应体系的物性计算是聚合过程模拟和优化的难点问题之一.针对乙烯淤浆聚合反应体系,采用链扰动统计缔合流体理论(PC-SAFT)状态方程,通过再参数化方法确定了聚合物体系中乙烯、己烷、氮气、氢气、聚乙烯的PC-SAFT模型参数.物性计算结果分别与文献的PC-SAFT模型、统计缔合流体理论(SAFT)状态方程、Sanchez-Lancombe状态方程等方法进行了比较,表明研究所采用的PC-SAFT模型参数计算乙烯淤浆聚合体系物性的计算精度优于文献提供的方法.     

HFO-1336mzz(Z)环保制冷工质的PC-SAFT状态方程研究

以新型环保制冷工质HFO-1336mzz(Z)作为研究对象,采用链扰动统计缔合流体理论(PC-SAFT)状态方程,通过关联文献中的PVT数据,回归得到了HFO-1336mzz(Z)制冷工质的PC-SAFT状态方程参数。在此基础上,使用MATLAB软件编制了工质的PC-SAFT状态方程计算程序,得到了较为全面的HFO-1336mzz(Z)PVT数据。研究结果表明:PC-SAFT方程关联得到的饱和蒸汽压及饱和液体密度与文献值的平均相对偏差分别为0.40%和0.92%;同时,方程预测得到的压力及密度与文献值的平均相对偏差在超临界区分别为0.96%和1.35%,在液相区偏差分别为1.06%和1.67%。     

用改进的重正化群理论计算缔合流体的临界表面性质

针对通常的统计缔合流体(SAFT)状态方程结合全局重正化群理论不能正确预测缔合流体的临界非对称性的问题，提出用微扰链-统计缔合流体(PC-SAFT)方程结合改进的全局重正化群方法描述缔合流体的临界热力学性质。通过改写原始重正化群理论的哈密顿量，以及对自由能的偏导数建立重正化迭代过程，计算包括醇、醋酸、水在内的各种单组分缔合流体的表面张力，以及与表面张力曲率修正密切相关的Tolman长度。结果表明PC-SAFT方程+全局重正化群的方法可以准确预测缔合流体的临界表面性质，所得结果可用于改善经典成核理论对成核速率的预测。     

二元交互参数化PC-SAFT在超临界乙烯配位聚合体系相平衡计算中的应用

超临界烯烃配位聚合技术是近年来国际聚烯烃工业领域中的重要进展之一,超临界体系相平衡计算则是该聚合工艺设计与优化操作的基础。本文以链扰动统计缔合流体理论（PC-SAFT）状态方程描述工业级超临界乙烯配位聚合体系的相平衡,得到了适用于该复杂体系的PC-SAFT二元交互参数。与公开报道的实验数据比较表明,获得的二元交互参数可准确描述该超临界体系在较宽温度、压力范围的相平衡。基于上述二元交互参数,针对2个不同双峰聚乙烯产品牌号,计算了工业装置内多组分的相平衡状态,结果表明,反应器内的[H₂]/[C₂H₄]摩尔比、淤浆密度的计算值与工业数据吻合较好,验证了二元交互参数的适用性。研究结果为进一步的工艺流程模拟与优化奠定了基础。     

乙烯淤浆聚合物体系的相平衡计算

乙烯淤浆聚合反应体系的流程模拟与优化过程中气液相平衡的准确计算影响到聚乙烯生成量和聚乙烯分子量的模拟. 通过再参数化含链扰动统计缔合流体理论(Perturbed-Chain Statistical Associating Fluid Theory, PC-SAFT)状态方程,建立了乙烯淤浆聚合体系物性的计算方法. 以文献数据为基准,利用Polymers Plus软件平台,分别得到了乙烯、氢气、己烷、聚乙烯、氮气纯组分的PC-SAFT方程的模型参数,并在准确确定纯组分模型参数的基础上,得到了乙烯-己烷、氢气-己烷、氮气-己烷、以及聚乙烯-乙烯、聚乙烯-己烷组分二元交互系数. 计算结果表明,采用再参数化PC-SAFT状态方程可以准确计算乙烯淤浆聚合反应体系的纯组分物质性质和两组分之间的相平衡. 同时对工业过程中5个不同牌号聚乙烯的反应器内气液平衡状态进行了模拟计算,氢气与乙烯在气相的摩尔比与工业分析值能很好地吻合,最大误差为7.5%.     

费托合成水相关二元体系热力学模型评价

采用活度系数模型中的Wilson,NRTL,UNIQUAC和UNIFAC模型,对费托合成水中相关的二元体系汽液相平衡数据进行计算,并进一步通过Hayden-O'Connell状态方程对汽相修正,从而得到Wilson-HOC,NRTL-HOC,UNIQUAC-HOC和UNIFAC-HOC模型的计算结果,并对比模型预测的计算结果和实验数据的偏差,对模型进行评价。结果表明:醇-水/醇体系,采用Hayden-O'Connell状态方程校正汽相计算结果后,模型计算结果的准确性得到提高;水-醛/酮体系,计算时不需要对汽相进行修正;水-酸/酯体系,由于水-酸体系是强缔合体系,采用Hayden-O'Connell状态方程修正汽相计算后,计算结果与实验值的偏差明显降低;醇-酸体系,采用Hayden-O'Connell方程修正后,Wilson,NRTL和UNIQUAC计算偏差没有明显降低,但UNIFAC-HOC的计算偏差明显减小,因此在采用UNIFAC模型计算时,应对汽相计算进行修正。     

二元交互参数化PC-SAFT在超临界乙烯配位聚合体系相平衡计算中的应用

超临界烯烃配位聚合技术是近年来国际聚烯烃工业领域中的重要进展之一,超临界体系相平衡计算则是该聚合工艺设计与优化操作的基础。本文以链扰动统计缔合流体理论(PC-SAFT)状态方程描述工业级超临界乙烯配位聚合体系的相平衡,得到了适用于该复杂体系的PC-SAFT二元交互参数。与公开报道的实验数据比较表明,获得的二元交互参数可准确描述该超临界体系在较宽温度、压力范围的相平衡。基于上述二元交互参数,针对2个不同双峰聚乙烯产品牌号,计算了工业装置内多组分的相平衡状态,结果表明,反应器内的[H2]/[C2H4]摩尔比、淤浆密度的计算值与工业数据吻合较好,验证了二元交互参数的适用性。研究结果为进一步的工艺流程模拟与优化奠定了基础。     

C6～C10烷醇的SAFT-VR Mie状态方程参数回归及其热物性研究

统计缔合流体理论(SAFT)状态方程对长链烷醇的热物性研究具有重要意义，而状态方程参数的获取是流体热物性研究的基础。基于SAFT-VR Mie状态方程，采用Levenberg-Marquardt算法并结合相平衡、过冷液相密度和声速性质的参数回归策略，获取C₆～C₁₀烷醇的状态方程模型参数。进一步评估SAFT-VR Mie状态方程对C₆～C₁₀烷醇在宽温度和压力范围内的相平衡和热力学偏导特性的预测性能，并与PC-SAFT状态方程进行比较。结果表明，SAFT-VR Mie对五种烷醇整体具有更优的饱和蒸气压、饱和液相密度、蒸发焓、过冷液相密度、比定压热容和声速预测性能，平均预测偏差分别为0.74%、0.82%、3.02%、0.54%、2.88%和2.31%。同时，SAFTVR Mie具有可靠的外推预测能力，其对高压声速的预测结果与实验数据具有较好的一致性。此外，SAFT-VR Mie对压力-密度导数的不合理描述是造成声速预测偏差的主要原因。改进分子间单体和缔合相互作用能够有效提高比热容的预测精度，为长链烷...     

Prediction of Solubility of Cholesterol in Supercritical Solvents

In this study the solubility of cholesterol was calculated in two supercritical pure solvents (carbon dioxide and ethane) as binary systems, and four supercritical solvent/co-solvent systems as ternary systems (cholesterol/carbon dioxide/methanol, cholesterol/ethane/acetone, cholesterol/ethane/hexane, cholesterol/ethane/propane) in various temperatures by SRK, PR, and SAFT equations of state. Pure molecular parameters of SAFT equation of state were obtained by fitting vapor pressure and liquid density data. Also the molecular parameters of cholesterol were obtained by fitting the solubility data of binary systems in one temperature, then they were used for the same system in other temperatures and for ternary systems with the same solvent. Results show that the SAFT equation of state can predict the trend and amount solubility of cholesterol in supercritical solvents much better than the other equations of state.     

Solving Systems of Fourth-Order Emden–Fowler Type Equations by the Variational Iteration Method

In this paper, we investigate systems of nonlinear fourth-order Emden–Fowler type equations. We employ the variational iteration method (VIM) for solving these systems of equations. The newly developed fourth-order Emden–Fowler equation is characterized by three types, where the shape factor appears three times, twice, and once for the first type, second type, and the third type respectively. We use distinct Lagrange multipliers for these specific types to overcome the singularity at the origin. We solve several numerical examples obtaining a rapidly convergent sequence of approximations. In all examples investigated, we achieved approximations with a high level of accuracy, thus confirming that we can get accurate approximations with few variational iterations.     

Modeling infinite dilution activity coefficients of organic-aqueous systems using a modified regular solution equation and cubic equations-of-state

Expressions derived from the regular solution equation and the generalized cubic equations-of-state (EOS) were employed to model the infinite dilute activity coefficient (γ^∞) of organic-aqueous systems. A database of 119 organic species in aqueous systems, divided into six classes, was gathered for models evaluations. The use of the molar density, the first order molecular connectivity, and the dipole moment appear to be adequate correlating variables for describing the structural dependence of the residual part in the modified regular solution equation (MRS). The Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) were specified and employed in the generalized cubic EOS form. The excess activity coefficient concept was used in the SRK and PR EOS models to account for the deficiency of EOS in dealing with highly non-ideal or polar systems. The abilities of two existing correlation models along with two modified versions of the UNIFAC model were also assessed. The proposed models provide creditable equations for correlating γ^∞ of organic-aqueous systems.     

Error estimation and control for the steady state population balance equation: 1. An a posteriori error estimate

An a posteriori error estimate is derived for the finite element formulation of the nonlinear, integro-differential equations that govern the steady-state behaviour of particulate systems (more commonly known as population balance equations). Since this estimate is derived in terms of calculable parameters it may be used as a means of quantitatively assessing the quality of an obtained numerical solution and additionally it has the potential to be incorporated into adaptive mesh refinement algorithms. Several numerical case studies are investigated and it is demonstrated that the estimate reliably predicts an upper bound of the error in numerically obtained solutions.     

Measurement and Correlation of Liquid—Liquid Equilibrium Data for Ethanol—Water—KF and Ethanol—Water—K2CO3Systems

1 INTRODUCTION Ethanol and water form an azeotropic system[1], and ethanol must be separated through azeotropic distillation. In ethanol-2-propanol-1-butanolwater[2], ethanol-acetone-1-butanolwater[3] and aceto- nitrilewater[4] systems, water was successfully separated out by adding salts. The measurement and correlation of liquidliquid equilibrium data for ethanolwaterKF and ethanolwaterK2CO3 systems with relatively high concentration of KF and K2CO3 at 25oC have not been reported y…     

Transport of organic penetrants through films of cellulose esters in transient regimes: a non-equilibrium thermodynamics analysis

Transport equations are derived in the framework of the rational thermodynamics approach for membrane processes involving a dense (active) polymer layer. The influence of the deformation of the polymer matrix, formation of interacting species, changes in polymer configuration, etc., due to mixing of the penetrant and the polymer can be accounted for in the equations. Studies of permeation fluxes in the transient regime in which the membrane is suddenly put into contact with a solvent can give useful information on the behaviour of polymer-penetrant systems. Experimental results obtained for the transient permeation of alcohols and heptane through different cellulose ester membranes are reported and discussed in the framework of this approach.     

Statistical Analysis of the Gab and Henderson Equations for Sorption Isotherms of Foods

ABSTRACT

GAB and Henderson equations were fitted lo experimenwl sorption isotherms of wheal, apricot and cassava. The statistical significance of equation parameters were tested with joint interval confidence as well as differences between linear regression and non-linear fits. The results showed that two equations (GAB and Henderson) had a good fit (r² > 0.95) with respect to experimental points for linear and non-linear fits. Nevertheless, the GAB equation can predict water activity values grater than one, and this result is a thermodynrmic inconsistency. The statistical analysis showed that some parameters with theoretical basis of the GAB equation had no significance. This important result shows the possibility that theoretical basis of the GAB equation must be revised.     

Prediction of ethane and CO2 solubilities in heavy norma paraffins using generalized-parameter soave and peng-robinson equations of state

A study was made of the abilities of the Soave and Peng-Robinson equations to represent the phase behavior of ethane + n-paraffin and CO₂ + n-paraffin systems. These equations are capable of describing the phase behavior of such systems; however, the level of precision obtained varies with the degree of complexity used in representing the interaction parameters in the mixing rules employed. For ethane/C0₂ with n-paraffins extending from C₃ to n-C₄₄, an uncertainty of about 1 % is obtained for bubble point pressures (or about 0.005 mole fraction for solubilities) when two system-specific interaction parameters per isotherm are used. Simple generalized correlations are presented for the equation-of-state interaction parameters which allow prediction of the bubble point pressures with an expected uncertainty of about 5.7% (0.014 in mole fraction).     

Population balance discretization for growth,attrition, aggregation,breakage and nucleation

This paper presents a new discretization method to solve one-dimensional population balance equations (PBE) for batch and unsteady/steady-state continuous perfectly mixed systems. The numerical technique is valid for any size change mechanism (i.e., growth, aggregation, attrition, breakage and nucleation occurring alone or in combination) and different discretization grids.The developed strategy is based on the moving pivot technique of Kumar and Ramkrishna and the cell-average method of Kumar et al. A novel contribution is proposed to numerically handle the growth and attrition terms, for which a new representation of the number density function within each size class is developed. This method allows describing the number particle fluxes through the class interfaces accurately by preserving two sectional population moments.By comparing the numerical particle size distributions with analytical solutions of one-dimensional PBEs (including different size change mechanisms and particle-size dependent kinetics), the accuracy of the proposed numerical method was proved.     

Mass transfer simulation of biodiesel synthesis in microreactors

A coupled nonlinear mathematical model for the mass transfer of the species involved in the transesterification reaction between soybean oil and methanol in a parallel plates geometry microreactor is presented. The set of partial differential equations that governs the concentration profile of these species were obtained from the general mass balance equation for the case of isothermal flow and steady state with constant physical properties. The velocity profile was obtained from the Navier-Stokes equations assuming fully developed stratified laminar flow for two immiscible Newtonian fluids, with a plane interface between them, based on experimental observation of this flow pattern. The second order kinetic equations for the species were developed assuming homogeneous and reversible chemical reactions and these equations were written as source terms in the main equations. The mathematical model was solved using the hybrid method known as Generalized Integral Transform Technique (GITT). The simulation results were critically compared with those obtained by using the COMSOL multiphysics platform, showing a good agreement between the hybrid and fully numerical simulations. The effects of governing parameters such as residence time, temperature and microreactor dimensions were investigated. It was observed that higher triglycerides conversion rates occurred at higher temperatures and residence times and lower microreactor depths.