Predicting NRTL parameters for binary hydrocarbon mixtures for calculating liquid—vapor equilibriums of multicomponent systems

The parameters of the NRTL method are fitted, for binary hydrocarbon systems, on the activity coefficients calculated by the Flory—Hildebrand method with binary coefficients l_ij of deviation from the geometric mean assumption for cohesive energy densities (NRTL-FH parameters). For aromatic saturated hydrocarbon mixtures, the l_ij coefficients are correlated to the products δ_iδ_j of solubility parameters. The predicted NRTL-FH parameters are used in calculations of bubble pressures and vapor phase compositions of binary hydrocarbon mixtures and of ternary mixtures with at least two hydrocarbon components. The NRTH-FH method is compared to the Chao—Seader and the zero l_ij-Flory-Hildebrand methods for many hydrocarbon systems, and gives the best results among these three predictive methods. The introduction of the non zero l_ij coefficients is an improvement in regards to the case with zero l_ij coefficients, particularly for the cycloparaffin-aromatic hydrocarbon mixtures. The NRTL-FH method is also compared to the NRTL-EXP method (parameters fitted on experimental data), and results obtained with the two methods are satisfactory for binary and ternary mixtures.     

Excess enthalpy data for the ternary system methane—ethylene—carbon dioxide by flow calorimetry

Excess enthalpy data for the ternary system methane – ethylene – carbon dioxide was obtained utilizing an isothermal flow calorimeter. The measurements were made at three temperatures: 293.15, 305.15 and 313.15 K and pressures of 1.114, 1.520 and 3.445 MPa (11, 15 and 34 atm). The determination of excess enthalpies for the binary systems methane—ethylene, ethylene—carbon dioxide and methane—carbon dioxide has been reported in three preceeding articles, respectively: Gagné et al., 1985; Ba et al., 1979 and Barry et al., 1982a. The binary interaction coefficients k_ij obtained for these systems have been utilized as initial values for the optimization procedure leading to the k_ij for the ternary system. For the case of the ternary system studied in this investigation, two types of binary interaction coefficients k_ij have been determined from experimental data: k_ij independent of temperature and pressure and k_ij adjusted as function of temperature and pressure. Experimental data were compared with the predictions from Benedict—Webb—Rubin and Redlich—Kwong equations of state. In both cases, the coefficients k_ij dependent on temperature and pressure led to better prediction of excess enthalpies.     

Onsager coefficients for binary mixture diffusion in nanopores

This paper presents a critical appraisal of current estimation methods for the Onsager coefficients L₁₁, L₂₂, and L₁₂ for binary mixture diffusion inside nanopores using pure component diffusivity data inputs. The appraisal is based on extensive sets of molecular dynamics (MD) simulation data on L_ij for a variety of mixtures in zeolites (MFI, AFI, TON, FAU, CHA, DDR, MOR, and LTA), carbon nanotubes (CNTs: armchair and zig-zag configurations), titanosilicates (ETS-4), and metal-organic frameworks (IRMOF-1, CuBTC). The success of the L_ij predictions is crucially dependent on the estimates of the degree of correlations in molecular jumps for different guest-host combinations; these correlations are captured in Maxwell-Stefan approach by the exchange coefficients ?_ij. Three limiting scenarios for correlation effects have been distinguished; for each of these scenarios appropriate expressions for the L_ij are presented. For CNTs, correlation effects are dominant and the interaction factor, defined by , is close to unity. For cage-type zeolites such as LTA, CHA, and DDR with narrow windows separating cages, correlation effects are often, but not always, negligibly small and the assumption of uncoupled diffusion, i.e., α₁₂=0, is a reasonable approximation provided the occupancies are not too high. In other cases such as zeolites with one-dimensional channel structures (AFI, TON), intersecting channels (MFI), cage-type zeolite with large windows (FAU), ETS-4, CuBTC, and in IRMOF-1, it is essential to have a reliable estimation of the ?_ij; MD simulations underline the wide variety of factors that influence the ?_ij.We also highlight two situations where estimations of the L_ij fail completely; in both cases the failure is caused due to segregated adsorption. In adsorption of CO₂-bearing mixtures in LTA and DDR zeolites, CO₂ is preferentially lodged at the narrow window regions and this hinders the diffusion of partner molecules between cages. The second situation arises in MOR zeolite that has one-dimensional channels connected to side pockets. Some molecules such as methane, get preferentially lodged in the side pockets and do not freely participate in the molecular thoroughfare. Current phenomenological models do not cater for segregation effects on mixture diffusion.     

Phase behaviour of CO2 -bitumen fractions

The phase behaviour of Cold Lake bitumen and its five fractions (or “cuts”) saturated with carbon dioxide is examined. The two lightest fractions (bp < 510°C) were clear liquids, whereas the third and fourth fractions were dark and viscous, i.e. much like the whole bitumen. The fifth fraction was a glass-like solid, with a softening temperature of approximately 100°C. The vapour-liquid equilibrium (VLE) data for the bitumen and bitumen fractions saturated with CO₂ were collected at temperatures from 25 to 150°C and pressures up to 10 MPa. Experiments were also performed at conditions under which pure CO₂ exists as a liquid. The VLE and LLE data were correlated with the Peng-Robinson equation of state by modeling each bitumen fraction as one pseudocomponent whose critical properties and acentric factor were estimated from correlations available in the literature. The CO₂-solubility and density data were used to develop generalized correlations for the critical pressure and the binary interaction parameter (k_ij) in terms of molar mass and critical temperature. The model was subsequently used to predict the solubility of CO₂ in the whole bitumen which was represented as a 5-component mixture. A correlation for Cut i-Cut j binary interaction parameter (k_ij) was developed in terms of temperature and the difference in hydrocarbon molar masses. The average deviation in the predicted and experimental CO₂-solubility in the whole Cold Lake bitumen was less than 7%.     

Validating the Darken Relation for Diffusivities in Fluid Mixtures of Varying Densities by Use of MD Simulations

Molecular Dynamics (MD) simulations have been carried out to determine the self‐diffusivities, D_i,self, of the pure hydrocarbons methane (C1), ethane (C2), propane (C3), and n‐hexane (nC6) at various fluid densities. The MD simulations are in reasonable agreement with published experimental data. The influence of fluid density on both D_i,self and the Maxwell‐Stefan (M‐S) diffusivities, ?_ij, in binary C1‐C2, C1‐C3, C2‐C3, and C1‐nC6 mixtures was also investigated. The MD simulations show that the M‐S diffusivities in binary fluid mixtures can be estimated with good accuracy using the Darken relation.     

Correlation of K-factors for mixtures of hydrogen and heavy hydrocarbons

K-factors for hydrogen-heavy hydrocarbon mixtures are becoming increasingly important in new industrial applications, particularly in coal liquefaction. When equations of state such as Soave's are used to fit hydrogen-heavy hydrocarbon binary data, unrealistic binary interaction parameters k_ij are required because equilibrium ratios are not sensitive to k_ij for highly asymmetric binary systems containing a highly supercritical component.Reliable representation of experimental results can be obtained by modifying the composition dependence of the covolume parameter b for the mixture. The modification introduces a binary parameter E_Hj which has a physically reasonable size. Upon adjusting E_Hj to fit the binary data (setting k_ij = 0), good results are obtained for seven hydrogen-heavy hydrocarbon binaries.     

Measurement of enthalpies of mixing in gaseous phase for the binary system carbon dioxide – hydrogen sulphide by an isothermal flow calorimeter

Enthalpies of mixing for the binary system carbon dioxide – hydrogen sulphide were measured by means of an isothermal flow calorimeter at temperatures of 293.15. 305.15 and 313.15 K. For the first isotherm, excess enthalpy measurements were made at pressures of 0.507, 1.013 and 1.419 MPa. For the last two isotherms, these measurements were performed at pressures of 0.507, 1.013 and 1.520 MPa. The experimental data were treated by the same techniques described for the systems previously studied (Barry et al., 1982a, 1982b, 1982c). Two types of binary interaction coefficients k_ij have been utilized for the prediction of experimental data from equations of state: coefficients k_ij independent of temperature and pressure, and k_ij's adjusted as function of temperature and pressure. A better prediction of the excess enthalpy experimental data was obtained from the latter series of binary interaction coefficients.     

Modeling the phase equilibria of asymmetric hydrocarbon mixtures using molecular simulation and equations of state

Monte Carlo simulation (MC) is combined with equations of state (EoS) to develop a methodology for the calculation of the vapor–liquid equilibrium (VLE) of multicomponent hydrocarbon mixtures with high asymmetry. MC simulations are used for the calculation of the VLE of binary methane mixtures with long n-alkanes, for a wide range of temperatures and pressures, to obtain sufficient VLE data for the consistent fitting of binary interaction parameters (BIPs) for the EoS. The Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) EoS are considered. The ability of each EoS to correlate the VLE data is assessed and the selected ones are used to predict the VLE of multicomponent gas condensate mixtures. MC simulations proved to be very accurate in predicting the VLE in all conditions and mixtures considered. The BIPs regressed from the simulation dataset lead to equally accurate modeling results for multicomponent mixtures, compared to those regressed from experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 792–803, 2019     

Modified response surface methodology (MRSM) for phase equilibrium-application

Attempts are being made to predict multicomponent azeotropic mixtures from the physical property of pure component and compositions of the constituting binary combination pairs. A modified response surface methodology (MRSM) model has been proposed which correlates boiling temperatures of binary, ternary and quaternary mixtures directly with the compositions of vapor and liquid phases. The generalized MRSM-2 models for liquid and vapor phases are proposed as follows: (for liquid phase) (for vapor phase) These models require normal boiling point of the pure components, T, and group-group parameters A_ij B_ij & C_ij which can be estimated by the group-group concepts of the constituent components. Therefore, this methodology is applied for the system of three and four components by the computer simulation. No experimental data is required for seeking of composition and temperature of the multicomponent azeotropic mixtures. By means of this methodology, MRSM, it is possible to depict an isothermal line map, temperature contours of the individual phase of the constituting ternaries for each quaternary system. Furthermore, it is possible to predict the azeotropic behaviors, maximum, minimum, saddle or any other type of azeotropic mixtures by examining the graphic contours obtained by computer graphics in the triangular coordinate for ternary and tetrahedron for quaternary. The proposed methodology (MRSM model) has been tested and compared successfully with previously reported azeotropic data in various journals for several ternary and quaternary multicomponent systems. Two azeotropic mixtures are newly found for each of two different quaternary tetrahedrons. The composition, temperature and type of the newly found azeotropes are reported.     

An empirical method for calculating vapor-liquid critical points of multicomponent mixtures

The critical temperatures and critical pressures of binary mixtures involving nitrogen, carbon dioxide, hydrogen sulfide, and paraffinic hydrocarbons ranging from methane through n-heptane as calculated from the Peng—Robinson equation of state have been correlated using a modified compositional function of the Wilson equation in conjunction with the pseudo-critical properties. The resulting parameters have been used to predict the critical properties of sixty-one multicomponent systems. The empirically calculated critical temperatures and critical pressures deviate from the rigorously calculated values by an average of less than 1 K and 100 kPa, respectively.     

Untersuchung des binären Diffusionskoeffizienten in Argon/Neon‐Gemischen mittels einer Loschmidt‐Zelle kombiniert mit holografischer Interferometrie

Binary diffusion coefficients D_ij were determined for mixtures of argon and neon over the entire composition range using a Loschmidt cell at 293.15 – 333.15 K and 1 – 10 bar. Before the measurements, the different pure gases were added into the two half‐cells of the Loschmidt cell. After connecting both half‐cells, the change in partial molar density, or rather in the refractive index has been detected simultaneously as a function of position and time within each half‐cell using holographic interferometry. The binary diffusion coefficients obtained for the upper half‐cell show systematic deviations from literature data. In contrast, the data measured in the lower half‐cell are in excellent agreement with literature. Within the measurement uncertainty, the product of the molar density of the mixture and D_ij is not affected by the pressure.     

Evaluation of the ratio of the evaporation energy to the activation energy for estimating the thermodiffusion coefficient

Thermodiffusion has an important role in displacements of hydrocarbon reservoir. The ratio of the evaporation energy to the activation energy of viscous flow in pure limits, τ_pure,k, is of a great importance in estimating the thermodiffusion coefficient for non‐associating fluid mixtures. Several methods may be used to estimate τ_pure,k which causes different values for thermodiffusion coefficients. A fixed value for τ_pure,k was considered to predict the thermodiffusion coefficient. In this paper, Abbasi et al.'s [J. Non‐Equilib. Thermodyn. 2010;35:1–14] model and Shukla and Firoozabadi's model have been applied to predict thermodiffusion coefficients for linear chain hydrocarbon binary mixtures. The results show a very good performance of the simple approach in respect to the previous models in estimating thermodiffusion coefficients. © 2011 Canadian Society for Chemical Engineering     

A fractal-like kinetics equation to calculate landfill methane production

Landfill appears as a convenient choice to get rid of municipal solid waste while providing energy, due to methane generated through anaerobic fermentation. However, without capture and treatment landfill gas is considered an important source of atmospheric methane. The control and use of this gas require knowledge of both, current yield and long-term accumulative production. These values are usually calculated with mathematical expressions that consider 100% of conversion, and homogeneous chemical reactivity inside the fill. Nevertheless, fermentation in landfills is erratic and spatially heterogeneous. This work introduces a fractal-like chemical kinetics equation to calculate methane generation rate from landfill, Q_CH4 (m³/year), in the way: where fermentable wastes are partitioned in readily, moderately and slowly biodegradable categories, L₀ is the potential of methane yield of refuse (m³/tonne under standard conditions), d_s is the solid-phase fracton dimension, k_i is the reaction kinetics constant of waste category i (year⁻¹), and t_j is the time from the year of burying j (year), C_ij⁰ (kg/tonne) and M_ij (kg) are the initial concentration and the mass of waste category i landfilled in year j, respectively. The idea behind this equation is that methane production kinetics is limited by the diffusion of hydrolyzed substrate into a heterogeneous solid-phase towards discrete areas, where methanogenesis occurs. A virtual study for a hypothetical case is developed. The predictions from this fractal approach are contrasted with those coming from two equations broadly used in the industrial work. The fractal-like kinetics equation represents better the heterogeneous nature of the fermentation in landfills.     

Density, ultrasonic velocity, viscosity and their excess parameters of the binary mixtures of N,N-dimethylaniline+1-alkanols (C3-C5), +2-alkanols (C3-C4), +2-methyl-1-propanol, +2-methyl-2-propanol at 303.15K

The density, ultrasonic velocity of sound and viscosity of binary mixtures of N,N-dimethyl aniline (N,NDMA) with 1-propanol, +2-propanol, +1-butanol, +2-butanol, +1-pentanol, +2-methyl-1-propanol, +2-methyl-2-propanol were measured at 303.15 K. These experimental data have been used to calculate excess volume V ^E , excess ultrasonic speeds u ^E , excess intermolecular free length L _f ^E , excess acoustic impedance Z ^E , excess isentropic compressibility κ _s ^E , deviation in viscosity Δη and excess Gibbs free energy of activation of viscous flow (G* ^E ). The values of L _f ^E and κ _s ^E are negative over the wide range of composition for all the binary mixtures, while the values of Z ^E are positive. These results have been used to discuss the nature of interaction between unlike molecules in terms of hydrogen bonding, dipole-dipole interaction, proton-acceptor interaction and dispersive forces. The viscosity data have been correlated using three equations: Grunberg and Nissan, Katti & Chaudhri and Hind et al. The excess/deviations were fitted by a Redlich-Kister equation and the results were analyzed in terms of specific interactions present in these mixtures.     

Equilibre entre vapeur et liquide pour le système azote-argon-methane

A forced recirculation apparatus has been used to measure the vapor-liquid equilibrium compositions for the nitrogen-argon-methane system at 123.4d'K. A modified Redlich-Kwong equation of state with the incorporation of binary interaction constants k_ij and temperature-dependent characteristic constants Ω_a and Ω_b have been successfully employed to represent the data. Equilibrium ratios obtained from the equation of state are compared with the experimental values. The average absolute deviations are 1.62%, 1.67% and 7.57% for the components nitrogen, argon and methane respectively.     

Programmed polymer light-scattering data

An ALGOL computer program has been devised to manipulate light-scattering data from the Brice-Phoenix photometer. The input consist of experimental values of the galvanometer deflections and filter factors used for each concentration c and angle of measurement θ. These are transformed to the appropriate variables in the fundamental equation including the particle scattering factor, viz: c/Qθ = (W/K^*)M?_w^?1[1 + (16/3) × π²n₁²λ〈S²〉 sin² (θ/2)] + (W/K^*)2A₂c + (W/K^*)3A₃c² in which Qθ is a corrected from of the Rayleigh ratio and (W/K^*) is a composite constant term for the instrument and polymer–solvent system. By writing X?_ij for the variable c/Q_θ at θ_i and c_j, a function X is found by least squares to fit X?_ij, thus X = l + m sin (θ/2) + nc_j + bc_j². The equations arising from minimizing Σ_i^K=1 Σ_j^L=1 (X_ij ? X?_ij)² are solved by the computer to yield the best-fitting coefficients l, m, n, and b. These can then be related simply to the molecular weight, root-mean-square radius of gyration, second and third virial coefficients, respectively. The final portion of the program is designed to check the fit of these coefficients. It yields a table of the differences between all experimental c/Qθ values and the coressponding ones obtained by inserting the derived l, m, n, and b into the fundamental equation. The procedure has been tested satisfactorily by using a well-standardized sample of polystyrene in toluene at 30°C. and a wavelength of 436 mμ.     

On the solubility parameter of polar polymers

The binary cluster integral, β, was computed from intrinsic viscosity data. Subtracting from β the polar contribution, β_e, calculated from YRCR theory,⁹ the nonpolar interaction parameter, β_n, was found. The calculations were performed for poly(vinylacetate) and poly(methyl methacrylate), each in 16 solvents. The correlation between β_n and the solvent solubility parameter, δ₁, was found to be similar to that reported^8,17 for solutions of natural rubber, cis-polybutadiene and for poly(vinyl chloride). This correlation can be crudely approximated by the formula where E and F are functions of the ill-defined symmetry of the solvent molecule and δ_m is the δ₁ value for the local maximum of the function. At δ₁ = constant, the more spherical is the molecule, the higher is the β_n value. It was shown that for most cases separation of the solvent into two classes (linear and nonlinear) is sufficient. This β_n behavior finds support in the Funk and Prausnitz⁶ report on aromatic–saturated hydrocarbon mixtures and in the theoretical calculations of Huggins.^21,22     

Viscometric and FTIR studies of molecular interactions in 2-propanol+hydrocarbons mixtures at 298.15 and 308.15 K

The deviation in viscosity was coupled with respective excess molar volume data to study the molecular interaction in binary mixtures with one associated component. This approach was applied to the experimentally measured viscosity and excess molar volume data of the 2-propanol+hydrocarbons at 298.15 K and 308.15 K. It was suggested that depolymerization power of aromatic hydrocarbon toward 2-propanol as well as strength of intermolecular interactions (electron-donor-acceptor type) between monomer of 2-propanol and aromatics depend on π-electron density of the aromatic hydrocarbon. These interactions were further confirmed by FTIR spectroscopy. The viscosity of these binary mixtures was best predicted by Gruenberg-Nissan correlation among the four correlations applied.     

Ternary and constituent binary excess molar enthalpies of {1,2-dichloropropane + 2-pentanol + 3-pentanol} at T=298.15K

Excess molar enthalpies for the ternary system of {1,2-dichloropropane (1,2-DCP)+2-pentanol+3-pentanol} and their constituent binary mixtures {1,2-DCP+2-pentanol}, {1,2-DCP+3-pentanol}, and {2-pentanol+3-pentanol} have been measured over the whole range of composition using an isothermal micro-calorimeter with flow-mixing cell at T=298.15 K and atmospheric pressure. The experimental excess molar enthalpies of all the binaries and ternary mixture, including three pseudo-binary mixtures, are positive (endothermic effect) throughout the mole fraction range, except for the binary mixture {2-pentanol+3-pentanol} in which shows a small negative values over the entire composition range. The experimental binary H _{m, ij} ^E data were fitted to Redlich-Kister equation, and the Cibulka and the Morris equations were employed to correlate the ternary H _{m, 123} ^E data. Several empirical equations for predicting ternary excess enthalpies from constituent binary mixing data have been also examined and compared. The experimental results have been qualitatively discussed in terms of molecular interactions.     

Modified van der waals equation for the dense gaseous and liquid regions from PVT data for methane

PVT measurements available in the literature for methane in the gaseous and liquid regions were used with the van der Waals equation of state, to obtain values of the internal pressure parameter, a, where the covolume parameter was taken as b = v_c/3. The conditions covered temperatures from 114.53°K (T_R = 0.599) to 611°K (T_R = 3.20) and pressures up to 3000 atm (P_R = 65.50). A dimensionless relationship was developed for the dependence of the parameter a on density and temperature for the gaseous and liquid regions. Density values for methane were calculated from the resulting equation and were compared with the corresponding experimental values to produce an average deviation of 0.26% (791 points). This relationship also enabled the accurate prediction of density values for substances having similar critical compressibility factors as methane (z_c = 0.289). For neon and ammonia, this relationship was found to have a limited applicability.