A crossover multi-fluid nonrandom lattice fluid model for pure hydrocarbons and carbon dioxide near to and far from the critical region

The multi-fluid nonrandom lattice fluid model with the local composition concept is capable of describing thermodynamic properties for complex systems, but this model cannot represent the singular behavior of fluids near the critical region. In this research, the multi-fluid nonrandom lattice fluid model for pure fluids is combined with a crossover theory to obtain a crossover multi-fluid nonrandom lattice fluid model which incorporates the critical scaling laws valid asymptotically close to the critical point and reduces to the original classical multi-fluid nonrandom model far from the critical point. The crossover multi-fluid nonrandom lattice fluid model shows a great improvement in prediction of the thermodynamic properties of pure compounds near the critical region.     

A crossover random lattice fluid model for hydrocarbons and carbon dioxide

A random lattice fluid model with finite coordination number is a versatile molecular-based lattice fluid equation of state, but this model fails to reproduce the non-analytical, singular behavior of fluids in the critical region. In this work, a method of obtaining the classical critical properties is presented in the random lattice fluid model. This model is combined with the crossover theory to obtain the crossover random lattice fluid model and to calculate the thermodynamic properties of hydrocarbons and carbon dioxide. This crossover random lattice fluid model presents much better agreement with experimental data near to and far from the critical region than the classical random lattice fluid model.     

Solubility of hinokitiol in supercritical fluids; measurement and correlation

Supercritical fluid technology has been an alternative for purification and separation of biological compounds in cosmetic, food, and pharmaceutical products. Solubility information of biological compounds in supercritical fluids is essential for choosing a supercritical fluid processes. The equilibrium solubility of hinokitiol was measured in supercritical carbon dioxide and ethane with a static method in the pressure range from 8 to 40MPa and at temperatures equal to 313.2, 323.2 and 333.2 K. The experimental data were correlated well by Peng-Robinson equation of state and quasi-chemical nonrandom lattice fluid model.     

An empirical near-critical correction for a quasi-chemical nonrandom lattice fluid

This paper proposes a simple empirical correction to improve the near-critical volumetric behavior of a classical equation of state (EOS) which overpredicts the critical point. The focus is on the alternative representation of long-range density fluctuation, an effect neglected in classical EOS, in terms of molecular clustering. To formulate the molecular clustering of interest, the Veytsman statistics is extended and fluctuation parameter is explicitly obtained as a solution to the quadratic equation. The proposed contribution was combined with a quasi-chemical nonrandom lattice fluid (QLF), which overpredicts the critical point. The combined model was found to require three clustering parameters besides three classical parameters and tested against vapor-liquid equilibrium data consisting of 43 nonpolar and polar components. The calculation results showed that the combined model satisfactorily represents the flattened part of the critical isotherm curve for methane as well as the top of the coexistence curve for the tested components.     

Modified Guggenheim-Huggins-Miller combinatorial factor and its application to lattice fluid equation of state

The Guggenheim-Huggins-Miller (GHM) combinatorial factor is modified by introducing a factor in the pair probability of a hole-hole pair. The proposed contribution is combined with the expanded quasi-chemical contribution and tested against saturated vapor pressure and liquid density. The proposed model correlates experimental saturated liquid density better than a quasi-chemical nonrandom lattice fluid (QLF) model based on original GHM combinatorial factor. The optimized parameters show a quite different behavior compared with that of the QLF model and the relationships between the parameters of two models are discussed. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.     

Prediction of nonrandom mixing in lattice model with multi-references

A new lattice theory is proposed to describe nonrandom mixing behavior based on recently developed lattice model theory by Aranovich and Donohue. The present theory assumes multi-references in order to take into account interference effects on non-random mixing among pairs. The number of references was obtained from Monte Carlo simulations for monomer+hole mixtures. Monte Carlo simulation for hole [0]+monomer [1]+monomer [2] mixture shows that this theory is more accurate than Guggenheim’s quasi-chemical theory or the Aranovich-Donohue model in a wide range of temperatures and densities. Especially, even under the stringent condition of zero interaction energy parameter ε₁₂=0, the present theory predicts well the extent of nonrandom mixing. For dimer fluid the non-randomness is calculated using the surface fraction. Here three references was used as in the case of monomer fluid with chain connectivity constraints. Comparison of the theory with Monte Carlo simulation results for dimer+hole system shows a good agreement.     

Calculation of complex phase equilibria in the critical region of fluid mixture based on multi-fluid lattice equation of state

Quantitative correlation of critical loci and multiphase behaviors has received considerable attention because the increased industrial importance of processes operating within the high-pressure region such as supercritical fluid extraction. However, in the critical region, classical thermodynamic models such as equations of state (EOS) frequently fail to correlate phase equilibrium properties. Recently, the present authors proposed a new lattice-hole EOS based on the multi-fluid approximation of the nonrandom lattice theory. The model requires only two molecular parameters reflecting size and interaction energy for a pure fluid and one additional interaction parameters for a binary mixture. In this work, the reliable applicability of the EOS was demonstrated to various phase equilibria of complex mixtures in the critical region. Demonstration of the EOS was made to calculate multiphase behaviors such as solid-liquidvapor (SLV) equilibria and critical loci of binary complex mixtures at high pressure. For P-T, P-x, and T-ρ phase diagrams tested, the model agrees well with experimental data. This paper was presented at the 8th APCChE (Asia Pacific Conferation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

An analytical equation of state for water and alkanols

An analytical equation of state extended from statistical associating fluid theory (SAFT) is modified to describe the thermodynamic properties of fluids with high polarity such as water and alkanols up to the region close to the critical point. Five terms are used in the equation of state: the term for hard convex body, the term for dispersion energy, the term for the chain formation of hard convex body, the term for the change of the dispersion energy because of chain formation, and the term for dipole-dipole interaction. This equation of state is still called SAFT-CP (across critical points). Six fluids water, methanol, ethanol, 1-propanol, 1-butanol and 1-pentanol are used as examples. The new equation of state reproduces saturated pressures and densities in vapor-liquid equilibrium, critical properties (as temperature, pressure and density), and densities in the one-phase region with rational accuracies. The comparison of the calculated critical exponent β with the experimental one for methanol shows the improvement up to the region only with 20 K difference of temperature to the critical point. The result coincides with the estimation of the critical region on the basis of Ginzburg number and also with the available opinion that crossover methods and renormalization theories are necessary in the near-critical region.     

EOS状态下基于多相流有规栅格理论的水-碳氢化合物两相体系的临界轨迹关系

Quantitative representation of complicated behavior of fluid mixtures in the critical region by any of equation-of-state theories remains as a difficults thermodynamic topics to date.In the present work,a computational efforts were made for representing various types of critical loci of binary water with hydrocarbon systems showing Type Ⅱ and Type Ⅲ phase behavior by an elementary equation of state[called multi-fluid nonrandom lattice fluid EOS(MF-NLF EOS)]based on the lattice statistical mechanical theory.The model EOS requires two molecular parameters which representing molecular size and interaction energy for a pure component and single adjustable interaction energy parameter for binary mixtures.Critical temperature and pressure data were used to obtain molecular size parameter and vapor pressure data were used to obtain interaction energy parameter.The MF-NLF EOS model adapted in the present study correlated quantitatively well the critical loci of various binary water with hydrocarbon systems.     

Gas and Liquid Transfer in Narrow Pores

A microhydrodynamic approach is formulated to describe the molecular flows in micro- and mesoporous systems, including the region of capillary phenomena, where one needs a single set of equations characterizing the flows of both dense gases and liquids. The set of equations of the transfer of dense fluids in narrow pores is closed by using the simplest molecular model, specifically, the lattice gas model, which describes the behavior of fluids over wide ranges of concentrations (from the gas to the liquid state) and temperatures, including the critical region. This model takes into account the volume of molecules and the intermolecular interactions in a quasi-chemical approximation, which retains short-range order correlations. The model reflects the strong anisotropy of the molecular distributions along a normal to the pore wall (because of the adsorption forces) and along the pore axis if there is capillary condensation. The derived set of equations is a set of finite-difference equations in increments of coordinates (instead of derivatives). The dissipative coefficients have a nonlocal anisotropic character. The equations of the transfer in near-wall cells and the prospects of the microhydrodynamic approach are discussed.     

A multi-fluid nonrandom lattice fluid model: General derivation and application to pure fluids

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 is presented. The multi-fluid nonrandom lattice fluid (MF-NLF) model with the local composition concept was capable of describing properties for complex systems. However, the MF-NLF model has strong temperature dependence of energy parameters and segment numbers of pure systems; thus empirical correlations as functions of temperature were represented for reliable and convenient use in engineering practices. The MF-NLF model without temperature dependence of pure parameters could not predict thermodynamic properties accurately. It was found that the present model with three parameters describes quantitatively the vapor pressure and the saturated density for the pure fluid.     

Crossover Equation of State for Selected Hydrocarbons (C4–C7)

The organic Rankine cycle (ORC) has attracted attention for waste heat recovery and renewable energy systems. An accurate prediction for thermodynamic properties of working fluids is of great importance for cycle performance evaluations and system design. Particularly, hydrocarbons are promising for their good performance and low global warming potentials. Moreover, the thermal efficiency of the ORC is higher when the evaporation temperature is closer to the critical temperature, which makes the properties in the critical region rather important. Recent research has shown that using mixture as working fluid can achieve better temperature matches. Therefore, an equation of state (EoS) that can be extended to mixture calculations is more attractive. Specific EoS for selected hydrocarbons is precise, but very complex. Cubic EoSs, such as widely used Peng–Robinson EoS and Soave–Redlich–Kwong (SRK) EoS, fail to accurately predict liquid densities over wide pressure ranges or pressure–density–temperature (pρT) properties in the near-critical region. This work combines the volume translation approach and the crossover method to provide better prediction for thermodynamic properties in the critical region and in regions far from the critical point. A crossover volume translation SRK EoS is developed and used for n-butane, i-butane, n-pentane, i-pentane, n-hexane, i-hexane and n-heptane. The volume translation term is set as a constant to ensure the accuracy of the saturated liquid density at low reduced temperatures. Then, the crossover method is introduced into the volume translation EoS to improve the predictions of thermodynamic properties in the critical region. Six crossover parameters are used, which are constants or functions of acentric factor and critical parameters. Therefore, none of the parameters in the crossover volume translation SRK EoS is adjustable, which makes the crossover EoS totally predictive and easily extend to mixtures. Comparisons show that the crossover EoS is in much better agreement with experimental data than the original SRK EoS.     

A multi-fluid nonrandom lattice fluid model for mixtures containing nonionic surfactants

Surfactant systems show highly non-ideal phase behavior because of the inter-association and intra-association hydrogen bond. We present a lattice fluid equation of state that combines the multi-fluid nonrandom lattice fluid model with modified Veytsman statistics for intra+inter molecular association to calculate phase behavior for mixture containing surfactant systems. The literatureresults fitted to this model show good accordance for mixtures containing nonionic surfactant systems. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.     

A semi-empirical molecular clustering based lattice model near to and far from the critical region

A semi-empirical molecular clustering based lattice fluid model is presented to improve the classical lattice model for volumetric properties in the critical region. This model is based on the two assumptions: (1) the Helmholtz energy is individually divided into classical and long-range density fluctuation contribution; (2) all molecules form cluster near the critical region due to long-range density fluctuation. To formulate such molecular clustering, we extended the Veytsman statistics originally developed for the cluster due to hydrogen bonding. The probability function in the statistics is modified to represent the characteristics of long-range density fluctuation vanishing far from critical region. The proposed fluctuation contribution was incorporated into the Sanchez–Lacombe model and the combined model with 6 adjustable parameters has been tested against experimental VLE data for polar and non-polar components. The combined model is found to good agreements with experimental vapor pressure, saturated density and supercritical PVT data.     

A general relation for identifying the liquid like and vapour like regions of supercritical fluids

Supercritical fluids exhibit liquid like behaviour close to a reduced pressure and reduced temperature of 1.0. The density of a supercritical fluid in this region is similar to that of liquids. Many practical applications use the sharp change from liquid like properties to vapour like properties for a variety of uses. There is no correlation in the literature that gives the general locus of the region that separates vapour like and liquid like regions of super critical fluids. In this article, we present a generalized correlation based on the acentric factor, and calculations obtained using NIST REFPROP.     

超临界流体p-V-T方程的研究

木文对目前常用的RK、RKS、PR及CS-vdW等状态方程进行了考察,验算了它们对二氧化碳、乙烯、丙烷等十种体系在超临界区、特别在临界点附近区域的适用性.计算结果表明,在上述区域内计算偏差都较大.作者从统计热力学的角度提出了一个“m-RKS”方程:P=RT/(V-b(T))—a(T)/V[V+b(T)],用该方程进行计算,结果与文献报道的实测值之间的偏差大大低于上述常用的诸方程.     

A simple three-parameter equation of state with critical compressibility-factor correlation

A three-parameter equation of state is proposed for fluids whose critical compressibility factor is not greater than 0.275. The equation is third order in volume and its constants are evaluated from the critical temperature and pressure as well as from the premultipliers that are interrelated and dependent on the reduced limiting volume of the fluid. The premultipliers have been evaluated from a single compressibility-factor correlation extrinsically. The proposed equation is as easy to handle mathematically as the Redlich-Kwong equation and yields analytical expressions for various fluid properties. The results show, however, that it represents the properties of normal and polar fluids much more accurately, particularly in the saturated vapor and the liquid region.     

COMPARISON OF A PAIR OF THREE PARAMETER EQUATIONS OF STATE

The lattice fluid (LF) equation of state derived by Sanchez and Lacombe from a lattice model is compared to the empirical Peng-Robinson (PR) equation for normal alkane fluids ranging from methane to heptadecane in molecular weight. With respect to vapor pressure predictions, the equations are both good. The LF equation is superior, especially for higher molecular weight fluids, to the Peng-Robinson equation in predicting saturated liquid densities. For carbon numbers less than 6, the PR equation predicts heats of vaporization more accurately, whereas for carbon numbers greater than 9 the LF equation is more accurate than the PR one for temperatures lower than about 95% of critical.