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).     

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.     

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.     

Measurement and correlation of vapor-liquid equilibria of the binary carbon dioxide-chloroform mixture system

Binary vapor liquid equilibrium data of the carbon dioxide+chloroform system were measured at five isotherms from 310.13 K to 333.32 K. A circulating type apparatus with on-line gas chromatography was used in this study. The experimental data were correlated by classical Peng-Robinson equation of state using van der Waals one fluid mixing rules and the multi-fluid nonrandom lattice fluid (MF-NLF) equation of state.     

High pressure phase behavior for the binary mixture of pentafluoropropyl methacrylate and poly(pentafluoropropyl methacrylate) in supercritical carbon dioxide and dimethyl ether

Pressure-composition isotherm is obtained for the carbon dioxide+2,2,3,3,3-pentafluoropropyl methacrylate (PFPMA) using static apparatus with a variable volume view cell at temperature range from 40 °C to 120 °C and pressure up to 130 bar. This system exhibits type-I phase behavior with a continuous mixture-critical curve. The experimental result for carbon dioxide+PFPMA mixture was modeled using the Peng-Robinson (P-R) and multi-fluid nonrandom lattice fluid (MF-NLF) equation of state. Experimental cloud-point data of pressure up 470 bar and temperature to 182 °C were reported for the binary mixture of poly(2,2,3,3,3-pentafluoropropyl methacrylate) [Poly(PFPMA)] in supercritical carbon dioxide and dimethyl ether (DME). The Poly(PFPMA)+carbon dioxide and Poly(PFPMA)+DME systems showed LCST behavior.     

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.     

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.     

A crossover quasi-chemical nonrandom lattice fluid model for pure carbon dioxide and hydrocarbons

Thequasi-chemical nonrandom lattice fluid model is capable of describing thermodynamic properties for complex systems containing associating fluids, polymer, biomolecules and surfactants, but this model fails to reproduce the singular behavior of fluids in the critical region. In this research, we used the quasi-chemical nonrandom lattice fluid model and combined this model with a crossover theory to obtain a crossover quasi-chemical nonrandom lattice fluid model which incorporated the critical scaling laws valid asymptotically close to the critical point and reduced to the original quasi-chemical nonrandom model far from the critical point. The crossover quasi-chemical nonrandom lattice fluid model showed a great improvement in prediction of the volumetric properties and second-order derivative properties near the critical region.     

Rigorous and simplified lattice-hole equations of state for calculating specific volumes of common pure polymers

Specific volumes of common pure polymers such as low- and high-density poly(ethylene), poly(n-butyl methacrylate), poly(styrene), and poly(o-methylstyrene) were calculated by the NLF and the MF-NLF equations of state, which were developed from nonrandom lattice-hole theory. Both models contain only two molecular parameters for a pure r-mer. The NLF model is based on the rigorous approximation of lattice-hole theory and thus it is somewhat complicated in practice. The MF-NLF model is based on the two-fluid approximation of the same lattice-hole theory and thus is relatively more semi-empirical than the NLF, while preserving comparable accuracy. In this work the models were comparatively applied to the calculation of the specific volumes of pure polymers, and the results obtainedto date were presented with emphasis on the practical utility of the models.     

Nonrandom lattice fluid group contribution parameter for vapor-liquid equilibrium of esters and their mixtures

A group contribution version of the nonrandom lattice fluid equation of state (NLF-GC EOS) has been used to predict the vapor-liquid phase equilibria (VLE) of esters and their mixtures. The investigated esters were divided into groups according to the contribution scheme. Two different types of parameters were regressed from experimental datasets. Size parameters were fitted to pure component properties, and the group-group energy interaction parameters were simultaneously fitted to several binary mixture data sets. For systems containing propylene oxide, missing binary VLE data was predicted by using the COSMO-RS method. Parameters obtained by using the COSMO-RS method were later used to successfully predict experimentally measured binary propylene oxide+esters systems. The overall good prediction capability of the NLF-GC EOS could be proven for the investigated 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.     

The rigid adsorbent lattice fluid model for pure and mixed gas adsorption

The ability of macroscopic models to predict correctly multicomponent systems from pure component isotherms alone remains a major challenge in adsorption engineering. A new fundamental thermodynamic model for multicomponent adsorption of molecules of different size in nanoporous materials is derived from a modified lattice fluid model. Expressions for the fugacity coefficients are derived and the resulting equilibrium relationships are shown to be consistent with a type I adsorption isotherm. Expressions are obtained for the saturation capacity, the Henry law constant and the adsorption energy. The model is applied to silicalite and the parameters for the adsorbent are obtained from crystal properties, the adsorption energy of n-alkanes and Henry law constants for six gases. Model predictions for gas adsorption up to 20 bar are shown to be comparable to empirical adsorption isotherm equations. Extension to binary and quaternary systems shows good a priori predictive capability when compared to experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1304–1314, 2019     

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 phase equilibrium for water+carbon dioxide system using nonrandom lattice fluid equation of state

For the geological sequestration of carbon dioxide to prevent global warming, the phase equilibrium data for water and carbon dioxide mixture play an important role in process design and operation. In this work, the nonrandom lattice fluid equation of state with hydrogen bonding (NLF-HB EOS) was applied for the prediction of phase equilibrium of mixtures containing water and carbon dioxide. A new set of pure component parameters for carbon dioxide above critical condition was found and optimum binary interaction parameters were reported to correlate mutual solubility of mixtures. The calculated results were compared with the Peng-Robinson Equation of State with the conventional mixing rule (PR-EOS) and the Wong-Sandler mixing rule (PR-WS-EOS). The calculation results show that NLF-HB EOS can correlate mutual solubility of water+carbon dioxide mixtures with reasonable accuracy within a single theoretical framework.     

A molecular thermodynamic model for binary lattice polymer solutions

A molecular thermodynamic model for binary lattice polymer solutions with concise and accurate expressions for the Helmholtz energy of mixing and other thermodynamic properties is established. Computer simulation results are combined with the statistical mechanics to obtain the expressions. Yan et al.'s model for Ising lattice and the sticky-point model of Cumming, Zhou and Stell are incorporated in the derivation. Besides the nearest neighbor cavity correlation function obtained from the Ising lattice, the long range correlations beyond the close contact pairs are represented by a parameter λ, the linear chain-length dependence of which is obtained by fitting the simulated critical parameters of two systems with chain lengths of 4 and 200. The predicted critical temperatures and critical compositions, spinodals and coexistence curves as well as internal energies of mixing for systems with various chain lengths are in satisfactory agreement in comparison with the computer simulation results and experimental data indicating the superiority of the model over other theories. The model can serve as a basis to develop more efficient models for practical applications.     

Segregation in polydisperse fluidized beds: Validation of a multi-fluid model

In many industrial-scale fluidized-bed reactors, particle mixing and segregation play an important role in determining reactor performance. Detailed information about the particle size distribution (PSD) throughout the bed at different operating conditions is crucial for design and scale up of practical systems. In this work, a multi-fluid model based on the Euler-Euler approach and the direct quadrature method of moments (DQMOM) is used to describe particle segregation, and the model predictions are validated with available experimental and simulation data. For binary mixtures, multi-fluid simulations are compared with digital image analysis experiments for beds of glass beads. By properly defining the solid-solid drag force, the multi-fluid model can reproduce the segregation rate found experimentally for different flow conditions with binary mixtures. Segregation phenomena in gas-solid fluidized beds with a continuous PSD are also investigated. Here, the multi-fluid simulations are compared with discrete particle simulations (DPS). Using the moments of the PSD from DPS, the weights and abscissas used in DQMOM are initialized in the multi-fluid model. The segregation rate and the local moments of the PSD predicted by the multi-fluid model are compared to the DPS results. The dependence of the results on the number of DQMOM nodes is also investigated.     

Measurements and correlation of hydrogen-bonding vapor sorption equilibrium data of binary polymer solutions

Vapor sorption equilibrium data of ten binary polymer/solvent systems were measured using sorption equilibrium cell equipped with a vacuum electromicrobalance. Tested solvents were water, methanol, ethanol and npropanol and polymer solutes were poly(ethylene glycol), poly(propylene glycol), poly(tetramethylene glycol) and poly(ethylene oxide). The measured sorption obtained in the present work, were compared with existing literature data and the degree of reliability of the measured data was discussed. Vapor sorption equilibrium data obtained in the present study were correlated by UNIQUAC model and the multi-fluid non-random lattice fluid hydrogen bonding equation of state (MF-NLF-HB EOS) recently proposed by the present authors.     

Generalization of thermodynamic Langmuir isotherm for mixed-gas adsorption equilibria

This work presents a comprehensive thermodynamic model for both pure component isotherms and mixed-gas adsorption equilibria. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed-gas adsorption equilibria, and it applies an area-based adsorption nonrandom two-liquid activity coefficient model in the activity coefficient calculations for the adsorbate phase. The resulting generalized Langmuir isotherm properly captures both surface loading dependence and adsorbate phase composition dependence for mixed-gas adsorption equilibria. The model is validated with accurate representations of gas adsorption equilibrium data for varieties of unary, binary, and ternary gas systems. The model results are further compared with those calculated from extended Langmuir isotherm and Ideal Adsorbed Solution Theory.     

A molecular thermodynamic model for temperature- and solvent-sensitive hydrogels,application to the swelling behavior of PNIPAm hydrogels in ethanol/water mixtures

The swelling curves of poly-N-isopropylacrylamide (PNIPAm) hydrogels in ethanol/water mixtures were determined. A molecular thermodynamic model for swelling behavior of temperature- and solvent-sensitive hydrogels in solvent mixtures was developed by integrating a modified multiple lattice model developed previously for the mixing term and the Flory's Gaussian chain model for the elastic term. Three energy parameters and one volume parameter are included in this model for gel/solvent mixtures systems. Three of the four parameters can be determined from the swelling behavior of hydrogels in pure solvents. The energy parameter measuring the interaction between the two solvents is adjustable and expressed as a quadratic form of the inverse temperature. The calculated results for the swelling curves of PNIPAm hydrogels in ethanol/water mixtures at different temperatures are in good agreement with the experiments. In addition, the equilibrium concentrations of solvent mixtures inside and outside hydrogels can be predicted by this model, which is important for the application of hydrogels.