New numerical model for solubility of light alkanes in triethylene glycol

A new numerical model, which covers the full range of dehydration-plant operating conditions and wide range of experimental data results, estimates the amount of CH₄, C₂H₆ and C₃H₈ absorbed per volume of triethylene glycol (TEG) circulated vs. the partial pressure of light alkanes and the absorber temperature. This article shows that the proposed numerical approach is more accurate than routine equation of states in predicting the solubility of light hydrocarbons in TEG. This article also provides comparisons between the results of the proposed model with experimental data and an equation of state results.     

A study on the predictive capability of the SAFT-VR equation of state for solubility of solids in supercritical CO2

In this study, a version of the SAFT-VR equation of state based on the Yukawa potential is used for modeling the solubility of diverse organic compounds, mostly drugs, in supercritical carbon dioxide. Prior to any calculations, the SAFT parameters of pure CO₂ were obtained by correlating the vapor–liquid equilibrium data within the range of 220–300 K. The validity of these parameters was examined by applying them in prediction of the compressibility factor and density in wide temperature and pressure ranges. Due to dependence of the rest of the calculations on the sublimation pressure and lack of its experimental values for most of the solids, it was estimated through two main approaches: application of a group contribution method prior to correlating the solubility data, and calculating it in relation with temperature while correlating the solubility data. For each compound, the first isothermal set of the available experimental data was used for correlation and the rest were predicted. Adopting the same procedure for three empirical models and comparing the resulting deviation percents validated the superiority and high capability of this equation of state in correlating and particularly predicting the solubility in supercritical region. The predicted densities were also in very good agreement with the available experimental values.     

Study of the correctness of the solubility parameters obtained from indirect methods by molecular dynamics simulation

Conformational energies of models of polyethylene (PE), isotactic-polypropylene (i-PP), atactic-polypropylene (a-PP) and polyisobutylene (PIB) with different chain lengths in their unperturbed liquid state (E_l), unperturbed isolated state (E_iu) and perturbed isolated state (E_ip) at 190 °C were computed using molecular dynamics simulation. The computed E_l, E_iu and E_ip were then used to calculate the solubility parameters of the polymers (δ). Our results indicate that there exists a cutoff chain length (∼20 backbone carbons) above which the differences between the solubility parameters (Δδ) computed based on (E_iu−E_l) and (E_ip−E_l), respectively, become significant. In addition, it was found that the higher the degree of shrinkage of the polymer in vacuum is, the larger the Δδ is. Since PE and PIB exhibited considerable shrinkage in vacuum, their Δδ are much higher than those of the PPs. It seems that, at 190 °C, vacuum acts more or less like a Θ solvent for both types of polypropylenes but a bad solvent for PE and PIB. Our results also suggest that the characteristic ratio of the polymer has little effect on Δδ and that it was the long range attractive interactions between the monomers distant along the backbone contour of the same molecule that led to the formation of fairly compact globule in the cases of PE and PIB. Since δ of the high molecular weight models computed from (E_iu−E_l) agree with experiment better than those from (E_ip−E_l), it implies that δ obtained from indirect measurements correspond to a hypothetical vaporization process where the conformations of polymer coils do not undergo significant changes. In other words, δ of a polymer that is determined by the currently available indirect methods may deviates significantly from their ‘true’ value if the polymer exhibits a high degree of swelling or shrinkage in vacuum at the temperature of the experiment.     

A method for determination of thermodynamics and solubility parameters of polymers in dilute solutions from critical volume fractions

An equation using the critical volume fraction and segment number of polymer was proposed for the partial molar entropy change of a polymer for mixing in dilute solution. The partial molar enthalpy change of polymer for mixing was determined from the thermodynamic equilibrium property of two polymer phases at the critical temperature. The solubility or cohesion parameter of a polymer fraction at the critical temperature was calculated by using the partial molar enthalpy change and repeat unit volume of the polymer. The solubility parameter of high molar mass polymer at the theta temperature was determined by extrapolating solubility parameter values of the polymer fractions to high molar mass by using the solubility parameter-segment number relation of polymer fraction. This relation gives good straight line. The solubility parameter of the polymer at the theta temperature and the exchange energy parameter for polymer-solvent pair were obtained directly from the intercept and the slope of this line, respectively. These equations were applied to the critical point data of polystyrene (PS) in methylcyclohexane (MCH) and in cyclohexane (CH) solutions. The results obtained in this study coincide with the literature values for the solubility parameter of PS and exchange energy parameter for PS in CH solution. It was also found that the partial molar entropy change of a polymer for mixing at theta temperatures has about a constant value.     

Stability of crystal forms of syndiotactic polystyrene correlated with their formation in different media having different solubility parameters

The formation of crystal forms of syndiotactic polystyrene having different stability was investigated in different media having different solubility parameters with the help of wide-angle X-ray diffraction, Fourier-transform infrared spectroscopy and differential scanning calorimetry. The starting sample was the γ form of syndiotactic polystyrene, and the solubility parameter of the media was adjusted by changing the temperature, pressure, cosolvent of supercritical carbon dioxide. With increasing solubility parameter, the stability of the resultant crystal forms was increased in the order from γ through α″ and β′ to β″ form.     

氯含量30%和40%氯化聚丙烯三维溶度参数的差别

溶度参数是判断高聚物能否溶解于某种溶剂中的标准,本文介绍了三维溶度参数的优越性,采用穷举法优化并计算了氯含量30%和40%氯化聚丙烯的三维溶度参数,并对比了两者溶度参数的差别。     

A new approach to select solvents and operating conditions for supercritical antisolvent precipitation processes by using solubility parameter and group contribution methods

A new approach is proposed to select operating temperature and pressure for supercritical antisolvent particle precipitation based on solubility parameter calculated by group contribution methods and using only the critical properties of the solvent. Solubility parameters are also used to choose the most suitable organic solvent for a given application. Supercritical antisolvent precipitation operating conditions of 36 systems are investigated including 8 organic solvents (methanol, ethanol, acetone, DMSO, DCM, chloroform, NMP and acetic acid) and 6 solid solutes (atenolol, tartaric acid, flunisolide, paracetamol, amoxicillin and cholesterol) in the temperature and pressure ranges of 25⿿85 °C and 50⿿250 bar. The results show a good agreement between the experimental and calculated data for these systems. Although particle precipitation depends on several parameters such as mass-transfer rates and hydrodynamics, the focus of this work is on the role of thermodynamics to indicate the preliminary conditions for a successful antisolvent precipitation process. Validation and results of this new approach suggest that it can be a useful tool for a qualitative and completely predictive evaluation of supercritical antisolvent particle precipitation in a cheaper way than carrying out experimental runs.     

Correlation of solute solubility in supercritical carbon dioxide using a new empirical equation

A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SCCO₂). The new empirical model has four parameters per each solute that can be obtained by correlation of the experimental solubility data. The input variables of the equation are pressure, temperature and density of pure SCCO₂. The new equation is applied for correlation of solubility of 24 compounds in SCCO₂ at wide range of temperatures and pressures. The overall percent of absolute average relative deviation (%AARD) of the new equation for correlation of the experimental data is 6.54%. Comparison of the results of the present model with a three-parameter and a four-parameter empirical model demonstrates good accuracy of the new empirical model.     

Empirical determination of equation of state for zero internal pressure in rare gas solids and semi-crystalline polymers

An equation of state for zero internal pressure in rare gas solids and semi-crystalline polymers has been determined based on the empirical functions of thermal pressure coefficient γ_V with respect to volume at constant pressure. The experimental data of PVT over wide range of temperature and pressure published by Anderson and Swenson and Syassen and Holzapfel for rare gas solids and Olabisi and Simha and Zoller for semi-crystalline polymers are used to evaluate γ_V. The function of γ_V with respect to volume determined at constant pressure is given by where V₀ is the volume at 0 K, A, ? and c are constants. The function of internal pressure P_i = γ_VT − P with respect to temperature at constant pressure is determined by converting the function of γ_V(V) to a function of temperature γ_V(T). An empirical equation of state for zero internal pressure determined by pressure P^∗, volume V^∗ and temperature T^∗ at which P_i = 0 is expressed by P^∗V^∗/RT^∗=C^∗−D^∗V^∗ for rare gas and semi-crystalline polymer where C^∗ and D^∗ are constants. The practical meaning of the equation of state for P_i = 0 in the semi-crystalline polymers has been discussed.     

Estimation of equation of state parameters for 1,1,1,2-tetrafluoroethane in a modified benedict-webb-rubin equation

Thermodynamic properties of refrigerants are of great importance in the design and simulation of heat pumps and refrigeration units. The parameter values in the modified Benedict-Webb-Rubin equation of state proposed by Lee and Kesler (1975) have been determined for HFC 134a with the Error-in-Variables Model. The types of data used for the parameter estimation have been: pressure-volume-temperature data for subcooled and superheated conditions, vapour pressures, saturated vapour and liquid volumes, isobaric arid isochoric heat capacities and second virial coefficients. Calculations carried out with the equation of state according to Lee and Kesler, with the parameters here proposed, agree well with experimental data for the fluid.     

A method of predicting effective solvent extraction parameters for recycling of used lubricating oils

Solvent extraction technique is one of the cheapest and most efficient processes experienced in recycling of used lubricating oils. In this paper, the performance of three extracting solvents (2-propanol, 1-butanol, and methyl-ethyl-ketone (MEK) in recycling used oil was evaluated experimentally. The effect of the most critical parameters (type of solvent, solvent to oil ratio, and extraction temperature) was investigated. The results show that MEK achieved the best performance with the lowest percent oil losses, followed by 2-propanol and 1-butanol, and as the extraction temperature increases the percent oil losses decreases. The anti-solvency energy (E_s), which originates from the solubility parameters difference between the solvent and oil was related to the solvent to oil ratio. It was found that the critical clarifying ratio predicted from such relations for the three solvents reasonably agrees with that measured experimentally. Relations between E_s and solvent to oil ratio give a proper guideline for preliminary evaluation of the extracting solvent. It also can be used to predict the optimum solvent:oil ratio and extraction temperature based on the solvent ability to dissolve the base oil in used motor oil.     

采用Hansen溶解度参数进行环氧固化体系的匹配

实验测定了25～80℃时3种环氧树脂、3种改性树脂和3种固化剂在77种溶剂中的溶解情况,并经计算得到了相应的Hansen溶解球参数。利用树脂-改性树脂、树脂-固化剂、树脂-改性树脂-固化剂的Hansen溶解球的重叠率,可进行共溶剂的选择及防腐防污自分层涂料的树脂匹配和溶剂配方的选择;对于无溶剂的固化体系则由测得的溶解度参数计算Flory-Huggins相互作用参数χ₁₂,进而计算其相平衡曲线或直接由χ₁₂数值判断其相容性。根据实验结果,可以筛选得到符合制备自分层涂层要求的环氧树脂-改性树脂-固化剂匹配体系,并通过适当的混合溶剂配方,使得涂层中的树脂能有足够的时间进行扩散、分层,最终得到防腐防污性能最佳的效果。     

Modification of a thermodynamic model and an equation of state for accurate calculation of asphaltene precipitation phase behavior

In this study, DPTG (Dashtizadeh-Pazuki-Taghikhani-Ghotbi) equation of state has been modified for calculation of phase behavior of fluids and solubility parameter. The accuracy of the modified EOS has been proved by estimation of the properties of some hydrocarbons such as densities of methane and condensate gases, vaporization enthalpy, sublimation pressure, compressibility factor and comparison of the obtained results with the results of the present equations of state such as NJ (Nasrifar-Jalali), ZMJL (Zhi-Meiren-Jun-Lee) and PR (Peng-Robinson). Then, the Flory-Huggins model has been modified and asphaltene precipitation phase behavior at different ratios of solvents in the crude oil has been predicted by the modified EOS and the developed Flory-Huggins model. Comparison of the obtained results with the experimental data of asphaltene precipitation and the calculated ones by the main Flory-Huggins model shows the accuracy of the developed model.     

状态方程外推法测算碳酸二甲酯的密度

提出了利用液体状态方程测定不同温度、压强下碳酸二甲酯密度的外推法.首先实验测量出3种不同温度(283.15,313.15,343.15 K)下碳酸二甲酯的各10组压强和密度数据,然后运用Goharshadi等提出的密度方程对这些数据进行线性拟合,最后利用拟合出的方程参数外推计算了其他多种温度(278.15-353.15...     

A new four-parameter cubic equation of state for fluids

A simple cubic equation of state of the van der Waals type has been developed and successfully applied to both nonpolar and polar fluids. It contains four parameters and only one parameter is temperature-dependent. The parameters have been determined by using reliable data of vapour pressure and saturated liquid volume, and correlated in terms of critical properties and acentric factor. The P-V-T relationships, vapour pressures, volumes, and enthalpies of vapourization were calculated for a variety of substances. Comparison of the calculated results with experimental data and with results obtained from other equations shows that the proposed equation is a superior one in overall performance.     

Calculation of pure saturation properties using cubic equations of state

A robust algorithm is outlined for the solution of the classical non-linear isofugacity problem by using equations of state (EOS). The procedure suggested is free of numerical pitfalls from the triple point to the critical point. The combination of differential stability (spinodal curve) and zero pressure reference concepts yields an automatic initialization of the calculations inside a region of convergence where the EOS can always predict pure compound vapor pressures at a given temperature.     

A four parameter cubic equation of state with temperature dependent covolume parameter

A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.     

应用马丁─侯状态方程计算含氨气体混合物的物性参数

本文将马丁—侯状态方程用于计算气体混合物的恒压热容、粘度和导热系数．含氨气体混合物的恒压热容为理想气体混合物热容与真实气体混合物剩余热容之和，根据剩余粘度法计算粘度，剩余导热系数法计算导热系数．三种压力，不同温度条件下气体混合物恒压热容、粘度和导热系数的计算结果表明：计算值与实验值相吻合．并分别拟合了合成氨生产三种工艺含氨气体混合物恒压热容、粘度、导热系数的计算式。     

Some properties of the GHC equation of state

The composition functionality of the mixture energy parameter, a_M, used in the Gibbs-Helmholtz Constrained (GHC) equation of state is studied. An analysis is presented that shows that a_M for liquid mixtures is approximately quadratic in composition. All non-quadratic behavior is due solely to ln(T_cM) in the GHC up-scaling equation. If a mean value approximation of this term is used, then a_M^L is quadratic, but non-symmetric, in composition. For vapors, non-quadratic behavior is coupled to the molar volume of the mixture through the term β_M = (V_M + b_M)/V_M. It is shown that the difference between β_M and some average _βM is very small and a_M^V is quadratic in composition. Sensitivity analyses of a_M and resulting molar density to these approximations are also presented. Finally, the non-symmetric composition functionality of a_M is discussed along with GHC predictions of mixture second virial coefficients. Numerical examples are presented to support all claims.     

Comparison of different solubility equations for modeling in cooling crystallization

In this paper we evaluate the sensitivity of using different solubility models on cooling crystallization. Specifically, the cooling crystallization of acetaminophen in ethanol is investigated. Empirical, correlative thermodynamic (namely van Laar, Wilson, and NRTL) and predictive thermodynamic (namely MOSCED, NRTL-SAC, and UNIFAC) models are considered. Equilibrium solubility model prediction determines the predicted supersaturation profile. The different solubility equations are used within a population balance model for prediction of crystal size properties. Incorrect prediction of the supersaturation profile results in incorrect prediction of crystal size distribution. The NRTL model was found to be more accurate at predicting equilibrium solubility and consequently crystal size. After the solubility sensitivity is evaluated, two methods are proposed to make the crystallization model more robust against solubility model errors.