Prediction of phase behaviour of gas-containing systems with cubic equations of state

The Soave Redlich-Kwong (S.R.K.) equation of state is used to correlate the phase behaviour of light compounds-containing systems and gas-hydrocarbon systems. Gases considered include H₂, CH₄, N₂, CO₂, CO and SH₂. An extensive literature search was conducted to obtain the binary experimental vapour-liquid equilibrium data which were used to build a predictive procedure of phase behaviour. Average error in bubble pressure predictions for 812 isothermal data sets (4399 experimental points) is 4%. Calculations with systems containing highly polar substances, water and methanol, are included. Good results are obtained when the proposed method is used to predict phase behaviour of some ternary systems typically encountered in petroleum and related industries.     

CO2-C2H6共沸物分离的立方型状态方程选取

汽液平衡热力学模型的准确选取对CO₂-C₂H₆共沸物分离流程的设计和操作分析至关重要。在汽液平衡实验数据的基础上,依据逸度平衡原则,评估vdW、RK、SRK和PR立方型状态方程结合vdW、Margles和CVD混合规则预测CO₂纯物质、CO₂-C₂H₆共沸物和n-C₅H₁₂-CO₂-C₂H₆三元体系汽液平衡的可靠性,采用平均绝对误差的方法进行状态方程的选取。结果表明：SRK状态方程计算CO₂纯物质汽液平衡性质的精度最高;PR状态方程结合Margles混合规则可以准确计算CO₂-C₂H₆共沸体系汽液平衡特性;对于n-C₅H₁₂-CO₂-C₂H₆三元体系,SRK状态方程结合Margles混合规则计算精度明显优于vdW、RK和PR状态方程。通过试差迭代法优化CO₂-C₂H₆共沸体系和n-C₅H₁₂-CO₂-C₂H₆三元体系的二元交互作用参数,状态方程的计算精度得到明显提高。     

Experimental measurement and correlation of phase behavior for the CO2+heptafluorobutyl acrylate and CO2+heptafluorobutyl methacrylate systems at high pressure

Experimental data of high pressure phase behavior from 313.2 to 393.2 K and pressures up to about 14.3 MPa were reported for binary mixture of 2,2,3,3,4,4,4-heptafluorobutyl acrylate (HFBA) and 2,2,3,3,4,4,4-heptafluorobutyl methacrylate (HFBMA) in supercritical carbon dioxide. The high pressure experiment was performed by static method using variable-volume view cell apparatus. The CO₂+HFBA and CO₂+HFBMA systems are correlated with the Peng-Robinson equation of state using a van der Waals one-fluid mixing rule. The CO₂+HFBA and CO₂+HFBMA systems exhibit type-I phase behavior with continuous critical mixture curves.     

Twenty‐one new theoretically based cubic equations of state for athermal hard‐sphere chain pure fluids and mixtures

Eight new hard‐sphere equations of state (EOS's) were obtained from molecular simulation data for the pair correlation function g_HS(σ) vs. packing fraction η and combined with three theoretical schemes to obtain 21 new cubic EOS's for athermal hard‐sphere chains (AHSC's). The eight new hard‐sphere EOS models successfully reproduced isotropic fluid compressibility factor Z_HS and g_HS(σ) vs. η simulation data and predicted metastable liquid Z_HS vs. η and virial coefficients up through B₁₀. Moreover, calculated Z vs. η and reduced second‐virial coefficient vs. chain length m were compared with molecular simulation data for chains up to m = 201 for a set of representative (eight of twenty‐one) chain equations. Z vs. η for three AHSC binary mixtures was also successfully predicted. The results indicate that the new cubic EOS's give a satisfactory representation of simulation data for chain fluids and can be used to develop theoretically based cubic EOS's for “real” fluids including attractive effects. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1677–1690, 2015     

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.     

The controlling quantity in cubic equations of state for phase equilibrium calculations

It has been demonstrated that the vapor—liquid equilibrium values calculated from the modified Martin equation and the Clausius equation are identical to those obtained from a properly modified van der Waals equation of state. The reason for this observation is explained in this work in terms of the role of Ω_a (= aP_c/r²T) at specified state conditions. It is the controlling quantity in VLE calculations when simple van der Waals-type equations of state together with the conventional mixing rules are used. Thus, equations capable of yielding identical values of Ω_a give identical equilibrium values. The evidence and the mathematical proof of the relationship required for defining such a role for Ω_a are presented.     

Modeling the phase behavior of ternary systems ionic liquid + organic + CO2 with a Group Contribution Equation of State

This work presents the results of the use of a Group Contribution Equation of State (GC‐EOS) to model experimental data obtained for ternary systems of the type bmim[BF₄] + organic solute + CO₂ with four different organic compounds, namely acetophenone, 1‐phenylethanol, 4‐isobutylacetophenone, and 1‐(4‐isobutylphenyl)‐ethanol. Our results show that the GC‐EOS is able to qualitatively predict not only L+V→L but also L₁+L₂→L phase transitions. As the two two‐phase boundaries L+V and L₁+L₂ of the experimentally found three‐phase region L₁+L₂+V almost coincide with the saturated vapor pressure curve of pure CO₂, the phase transitions L+V→L₁+L₂+V and L₁+L₂+V→L₁+L₂ have been represented as this vapor‐pressure curve by the model. The average absolute deviations between experimental and predicted values for all phase transitions have been found to be very satisfactory. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

On the modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species

A technique of modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species is considered. Attention is focused on the structure of equation of states with inclusion of non-electrolyte and electrostatic contributions. A hole quasichemical model was applied to illustrate the technique and to show how an EOS can be modified for systems with chemical reactions and electrostatic interactions in the liquid phase. The concentration dependency of the density and dielectric permittivity was taken into account in describing the electrostatic contribution that is required for thermodynamic consistency of the results of modeling. A method of assessing the appropriate relationships for mixtures containing supercritical components is suggested, alongside with the way to estimate the “true” composition of mixtures where ionic species are formed due to chemical reactions. The raised questions are discussed with respect to the following systems: solutions of acid gases in water-alkanolamine mixtures and water-ammonia-carbon dioxide system in a broad interval of temperatures and pressures.     

Mixing rules and excess properties in cubic equations of state

The limitations implied by using conventional quadratic mixing rules for Redlich—Kwong's modified equations of state are studied. A close relation is     

Adsorption behavior and kinetics of CO2 on amine-functionalized hyper-crosslinked polymer

A hyper-crosslinked polymer (XAD-4-pc) was developed by modifying the commercial polystyrene resin (XAD-4) through a Friedel–Crafts reaction, followed by impregnation with polyethyleneimine (PEI) for CO₂ capture. The physicochemical properties of the as-synthesized adsorbents were analyzed by different characterization techniques, and the adsorption behavior of CO₂ on these adsorbents was evaluated in a self-assembled adsorption setup with gas chromatography. Experimental results found that the Brunauer–Emmett–Teller surface area and pore volume of XAD-4-pc were significantly higher than that of XAD-4, which was favorable to the improvement of PEI loading and CO₂ adsorption. The maximum CO₂ uptake for PEI-functionalized XAD-4-pc was 3.24 mmol g⁻¹ at 25 °C. The adsorption isotherm of CO₂ on the adsorbent was well described by the Langmuir equation, and the kinetics data could be accurately described by Avrami model over the entire adsorption range. The diffusion mechanism study showed that the film diffusion and intraparticle diffusion were mainly the rate-limiting steps. Moreover, this adsorbent could be well regenerated at relatively low temperature and exhibited stable regenerability after five adsorption-regeneration cycles, showing its high potential for the capture of CO₂ from flue gases. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48479.     

Friction and multiple scratch behavior of polymer+monomer liquid crystal systems

We have studied in turn: polystyrene (PS), styrene/acrylonitrile (SAN) and Polyamide 6 (PA6), adding each time to the polymer 1, 3, 5, 7 or 10 wt% of 4,4′-dibutylazobenzene (LC1) which is a monomer liquid crystal (MLC). LC1 reduces both static and dynamic friction of PS and SAN against stainless steels or polytetrafluoroethylene (PTFE). By contrast, friction values are lower for pure PA6 than for PA6 modified with various MLCs or with MoS₂.Multiple scratching tests were carried out with a micro scratch tester on every system between 2.5 and 15 N. The presence of LC1 in PS reduces penetration depth and residual depth and increases the viscoelastic recovery. So far PS was the only polymer, which does not show strain hardening in multiple scratching. The present results confirms this, but it also shows that only 1 wt% of LC reduces the brittleness of PS so that strain hardening appears. This effect is maintained at all higher concentrations of LC1 investigated as well. For SAN or PA6, additions of LC1 reduce penetration depth values with respect to pure polymers, but do not have a significant effect on viscoelastic recovery. Scanning electron microscopy (SEM) was used to study the deformation and wear mechanisms, and to relate the data obtained in multiple scratch sliding wear tests. For PS we see in SEM that increasing the LC1 concentration causes a more ductile behavior, with less crack nucleation. For SAN the debris accumulation in sliding wear is mitigated by the presence of the liquid crystalline lubricant. No debris formation is observed in PA6, with or without a lubricant.     

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg2+-Ca2+-Cl- binary and ternary systems

Salt lake brine is a complex salt-water system under natural environment. Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution, the multi-temperature characteristics and predictability are still the goals of model development. In this study, a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements: (1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range; (2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients, the liquid parameters, which associated with Gibbs energy, enthalpy, and heat capacity contribution; and (3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range. Together the activity coefficient model, property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl₂-CaCl₂-H₂O binary and ternary systems, and it shows excellent agreement with the literature data for the ternary and binary systems. The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-ideality system, and the ability to extrapolate the temperature.     

High-pressure phase behavior in polyethylene/n-butane binary and polyethylene/n-butane/CO2 ternary systems

Solubility of polyethylene molecular weight standards (M_w = 2150, 16,400, 108,000, and 420,000 and M_w/M_n = 1.14, 1.16, 1.32, and 2.66, respectively) has been studied in near- and supercritical n-butane and n-butane/CO₂ mixtures at pressures up to 70 MPa. For each polyethylene/solvent system at selected compositions, demixing pressures have been determined using a high-pressure variable-volume view-cell at temperatures up to 200°C. Solutions in pure n-butane are found to display LCST (lower critical solution temperature)-type behavior. The behavior of the solutions in n-butane/CO₂ mixtures are observed to change from the LCST to the UCST (upper critical solution temperature) with increasing CO₂ content in the binary solvent. Sanchez–Lacombe theory has been used to model these systems. The predictions correctly describe the nature of the phase diagrams for both binary and ternary systems and the calculations are in reasonable agreement with experimental data. © 1994 John Wiley & Sons, Inc.     

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).     

An effective characterization procedure for petroleum reservoir fluids using molecular type methods and cubic equations of state

Two eminent molecular type composition methods (paraffins, naphthenes, and aromatics [PNA] and saturates, aromatics, and polynuclear aromatics [SAP]) are employed to construct new characterization procedures for predicting the phase behaviour of petroleum fluids using a modified Peng–Robinson equation of state. The PNA and SAP methods divide a petroleum fraction into (PNA) and (SAP) homologous groups, respectively. Two generalized models are developed to predict the physical properties ($\mathrm{Mw},\mathrm{SG},T_b$) and equation of state (EOS) parameters ($T_c,P_c,\omega$) for both PNA and SAP sub-fractions. Each generalized model covers 18 different correlations in a single mathematical form that enables the model to return 18 outputs for PNA and SAP sub-fraction parameters. A new lumping method is also developed to convert triple PNA or SAP pseudo-components into single characterized fractions. Accordingly, seven different characterization procedures are introduced and compared with one another. The first two procedures are completely constructed based on the proposed models, and the other procedures encompass the models already developed. The results obtained from the simulation of the differential liberation test for 12 diverse reservoir fluids and bubble pressure prediction for 40 oil samples revealed that the first two methods (1 and 2) could enhance the abilities of the traditional characterization procedures for reservoir fluid modelling. The mean value of average absolute relative deviations (AARDs) over a total of 52 oil samples is about 6.5% for the proposed methods and is about 13.2% for the best previously existing methods. Moreover, an efficient workflow is provided for the parameter tuning process, which is notably capable of reducing the level of prediction errors using only three adjustable parameters.     

Prediction of phase equilibrium of CO2/cyclic compound binary mixtures using a rigorous modeling approach

Vapor liquid equilibrium (VLE) data has significant role in designing processes which include vapor and liquid in equilibrium. Since it is impractical to measure equilibrium data at any desired temperature and pressure, particularly near critical region, thermodynamic models based on equation of state (EOS) are usually used for VLE estimating. In recent years due to the development of numerical tools like artificial intelligence methods, VLE prediction has been find new alternatives.In the present study a novel method called Least-Squares Support Vector Machine (LSSVM) used for predicting bubble/dew point pressures of binary mixtures containing carbon dioxide (CO₂) + cyclic compounds as function of reduced temperature of the system, critical pressure, acentric factor of the cyclic compound, and CO₂ composition. A 333 binary equilibrium data points of CO₂ and six cyclic compounds within temperature and pressure ranges of 308.15–473.15 K and 0.5–27.71 MPa were used to develop the model. Results show that the proposed model is able to predict VLE data for binary systems containing supercritical or near-critical CO₂/cyclic compounds with an acceptable average absolute relative deviation percent (AARD%) of 3.9381% and the coefficient of determination (R²) value of 0.9980. For detection of the probable doubtful experimental data, and applicability of the model, the Leverage statistical approach performed on the data sets. This algorithm showed that the proposed LSSVM model is statistically valid for VLE prediction and the whole phase equilibrium data points are in applicability domain of the model.