Modelling of microporous diffusion of n-paraffins in zeolite 5A

Sorptive liquid-phase diffusion of two n-paraffins, C₁₀H₂₂ and C₁₁H₂₄, dissolved in isooctane, onto micropore of 5A zeolite was studied to assess multicomponent diffusion and competitive effects. Diffusion coefficients for adsorbing components are determined from experimental batch reactor data. The experimental data indicate that diffusion through the microporous zeolite crystals is the primary diffusional resistance. A mathematical model of the rate of adsorption of a solute from a liquid by micropore adsorbent in a batch system was developed. The equation describing the mass transport by diffusion in a micropore adsorbent has been solved in order to obtain theoretical uptake curves for systems when the adsorption equilibrium isotherm is the favourable and nonlinear one. A computer simulation of the microporous diffusion is performed by use of the ISIM-Interactive Simulation Language. The effect of main term and cross-term coefficients of micropore diffusion for the system considered is investigated.     

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.     

Interaction model for the critical pressures of aliphatic hydrocarbon mixtures

An interaction model is proposed for the prediction of the critical pressures of multicomponent aliphatic hydrocarbon mixtures which may include methane. This model utilizeg a series consisting of terms of increasing order which has been truncated beyond the fifth interaction term. After a number of algebraic manipulations, the excess critical pressure for these multicomponent mixtures has been represented as follows The nonmethane interaction coefficients A_ij, B_ij, C_ij and β_ijk and the methane interaction coefficients A_1j, B_1j, C_1j, D_1j and β_1jk have been expressed as functions of the critical pressure parameter, π_ij. The resulting relationships permit the evaluation of these interaction coefficients for a multicomponent system and from its composition, the critical pressure of the mixture is calculated. The critical pressures of several binary and multicomponent aliphatic hydrocarbon mixtures have been calculated and have been compared with experimental values. For 99 binary methane-free mixtures representing 11 systems, the average deviation is 3.23%. For 46 binary mixtures representing six methane systems, the average deviation becomes 4.41 %. For 36 multicomponent aliphatic hydrocarbon mixtures containing from three to six components, the average deviation is found to be 3.18%.     

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.     

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.     

Absorption of a multicomponenet gaseous mixtures in the presence of instantaneous surface reaction

The rate of absorption from a multicomponent gaseous mixture into a flowing stream in the presence of instantaneous surface reaction is investigated. This is effected by using the generalized Fick's Law for multicomponent diffusion and also by applying the approximate approach based on the assumption that the concentrations of the reactive species are small. Constant properties are assumed for the mixture which are taken at a reference state. As an example, the absorption of C0₂-H₂S and C0₂-H₂ from air are considered. The results show that when the binary diffusion coefficients of the species in the inert gas are greatly different, the error introduced in calculations based on the “Low Concentration” approach is quite appreciable.     

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.     

On the determination of kinetic characteristics of lithium intercalation into carbon

The diffusional processes proceeding in the intercalation electrode on applying a potential step are theoretically treated. The theory of chronovoltammetry is shown to require the necessary account of the contribution of the surface solid-state film to the overall diffusion resistance of the electrode. For the case of small deviations from equilibrium, analytical solutions of the diffusion problem have been obtained. Ignoring the retarding contribution of the surface film is shown to bring about an error into the diffusion coefficient of lithium in its alloys and intercalates. The theory has been experimentally verified with Li_xC₆ electrodes of various compositions made of pyrocarbon films on a nickel backing as examples. The diffusion coefficients are 10⁻¹¹-10⁻⁹ cm² s⁻¹, depending on composition.     

Some features of isothermal multicomponent mass transfer in the convective instability of gas mixture

Isothermal multicomponent diffusion in the H₂ + Ar–N₂ and CH₄ + Ar–N₂ three-component gas mixtures has been experimentally studied at various pressures and certain concentrations of components in binary mixtures. It has been shown that, in systems where diffusion coefficients differ significantly from each other, convective instability occurs with increasing pressure, which significantly intensifies multicomponent mass transfer. The parameters of transition diffusion mixing to convective can be defined in the framework of stability theory. The comparison carried out between experimental and calculated data shows satisfactory agreement between them.     

Catalyst effectiveness in low-temperature water—gas shift reaction

A procedure has been developed for a priori prediction of intraparticle diffusion effects in low temperature water—gas shift reaction. Use is made of transport characteristics of the Cu/ZnO/A1₂O₃ pelleted catalyst determined independently by combination of diffusion and permeation results obtained under nonreactive conditions. The porous medium is described by the mean transport pore model and diffusional behaviour of the multicomponent reaction mixture by a modified Stefan-Maxwell equation. Using data from kinetic region obtained at 200°C, it was possible to predict the performance of a bench-scale reactor packed with pelleted catalyst at 200°C and 220°C satisfactorily.     

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.     

Knudsen diffusion of various gases through a barium sulphate packed bed

The diffusion coefficients, D_k, of helium, krypton, carbon dioxide and air through a packed bed of barium sulphate calculated from the Knudsen diffusion flow equation were found to be a cumulative parameter obtained from the contribution of the diffusion coefficient through the voids of the packed bed, D_v, and the diffusion coefficient through the pores, D_p, within barium sulphate.The surface area of compacted and uncompacted material obtained from low temperature gas adsorption and the Brunauer, Emmett and Teller equation (BET), together with the void sizes and pore sizes in compacted material obtained by Barrett, Joyner and Halenda (B.J.H.) isotherm analysis, when compared with the surface area values obtained by Knudsen diffusion and permeametry, indicated that the coefficients D_v and D_p evaluate the void and pore areas in compacted barium sulphate, respectively.     

The permeability of gases through reacting solutions: the carbon dioxide—bicarbonate membrane system

The transport of a gas across a stationary liquid film containing reactive species is investigated for the purpose of determining gas permeabilities or mass transfer coefficients in reacting solutions. Under limiting conditions when the reaction time constant far exceeds the diffusional time constant, the flux of the transported gas follows Fick's law of diffusion. Analytical series solution for the contribution of the chemical reaction to the transport process is obtained using the technique of perturbation analysis; criteria for the validity of various terms in the series solution are presented. The permeability of carbon dioxide in water and in 1N NaHCO₃?Na₂CO₃ solution is estimated. It is shown that a high degree of accuracy in the data is necessary for obtaining separate estimates of diffusivity and solubility by this technique.     

Solvent effects on mutual diffusion in concentrated polystyrene solutions

In a previous paper, mutual diffusion coefficients for concentrated solutions of a monodisperse polystyrene in 14 solvents were reported. In this paper, these data are reinterpreted in terms of new thermodynamic data for these solvents. These new results permit evaluation of the activity derivative, ? In a₁/? In v₁, and therefore enable calculation of the diffusional friction coefficient from the mutual diffusion coefficient. The friction coefficient was found to be directly proportional to solvent viscosity to within the experimental errors involved in the combined transport and thermodynamic measurements. The molecular implications of this result are discussed.     

EFFECTS OF GLYCEROL ON THE DRYING OF GELATIN AND SUGAR SOLUTIONS

ABSTRACT

The water diffusion coefficients D of gelatin, sucrose arid maltodextrin solutions were determined from the isothermal drying (desorption) rates as a function of water content u ( 0.1 < u < 1.0 ) and temperature (303, 323K) for various glycerol contents ( W_G = 0 – 0.43 kg-glycerol/kg-total solid). When W_G was above 0.2, D increased especially at low water contents (u < 0.25). The desorption isotherms were measured for the same systems. The equilibrium water content at a given water activity A_w decreased with an increase in W_G when A_w < 0.5. This indicates that adding glycerol weakens the water-solute interaction especially at low water contents. Glycerol also softened gelatin films and resulted in loss possibilities of surface cracks during drying.     

Diffusion and sorption for carbon dioxide in Kapton at extremely low pressure

Pressure-dependent solubility and diffusion coefficients for carbon dioxide in glassy polymers have been well described using the “dual sorption and transport model.” However, the plastisization effect by high-pressure carbon dioxide seems to promote the pressure dependence of the sorption and transport coefficients. To avoid the relaxation process by the plastization which is superimposed on the diffusion process, the diffusion and sorption of carbon dioxide were measured at extremely low pressure (below 1 cmHg). Linear isotherms observed for CO₂ sorption into Kapton were interpreted in terms of the dual model equation at extremely low pressure. From the permeation curve of the Kapton/CO₂ system, the diffusion and permeation coefficients were obtained according to the usual manner, and both coefficients were independent of pressure. Sorption and transport parameters were obtained from sorption isotherms and average values of the permeation coefficients. The parameters thus obtained were substituted in an approximated dual sorption and transport equations at extremely low pressure and the pressure independence of the diffusion and permeation coefficients were sufficiently reproduced. It is a good technique to experiment at such extremely low pressure when the validity of the dual model is evaluated. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 1013–1017, 1998     

Diffusion coefficients of l-menthone and l-carvone in mixtures of carbon dioxide and ethanol

The molecular diffusion coefficients of l-menthone and l-carvone in supercritical carbon dioxide (SCCO₂) and carbon dioxide containing 5 and 10 mol% ethanol as a modifier were measured by the Taylor-Aris chromatographic peak broadening (CPB) method over the ranges of temperature from 308.15 to 338.15 K and pressure from 15 to 30 MPa. It was found that the correlation relationships between diffusion coefficients and the temperature, pressure, viscosity, and density, such as the linear correlation between the D₁₂ and ρ, and between the D₁₂ and T/η, which were valid in binary systems, were also suitable for ternary systems of carbon dioxide containing modifier. The diffusion coefficients in modified SCCO₂ decreased with increasing the ethanol mole fraction due to the chemical association between the two solutes and ethanol. Of several models used to predict experimental data in pure carbon dioxide, the two models of Funazukuri-Ishiwata-Wakao and He-Yu-1998 were the best with the AAD less than 3.2%. Furthermore, the models of modified Wilke-Chang, Scheibel, Reddy-Doraiswamy, Lusis-Ratcliff, Hayduck-Minhas, Tyn-Calus, and Lai-Tan overestimated the diffusion coefficient in ethanol modified SCCO₂ with the AAD values increaseing with the percentage of ethanol, which were probably due to the increase of the volume of solvaton sphere as a true diffusion unit with the percentage of ethanol. Moreover, the free volume model of Dymond is good for predicting the experimental data in pure carbon dioxide and ethanol modified SCCO₂ with the AAD values range from 3.21 to 1.90%.     

Binary interaction coefficients of the Redlich—Kwong equation of state

A direct relationship between the binary interaction coefficients, k_ij and c_ij proposed by Chueh and Prausnitz, and Zudkevitch, for modifying the original mixing rules of the Redlich—Kwong equation of state is presented. Values of k_ij are evaluated by means of two methods for binary vapor—liquid equilibrium data for five systems at a total of thirty-two isothermal conditions. The calculated results from k_ij value obtained by minimizing Σ|ΔP| values are preferable to those obtained by minimizing Σ|Δy| values. The effect of temperature on k_ij for the systems investigated is shown and discussed.     

Relaxation characteristics of poly(vinylidene fluoride) and ethylene-chlorotrifluoroethylene in the transient uptake of aromatic solvents

Poly(vinylidene fluoride) (PVDF) and ethylene-chlorotrifluoroethylene (ECTFE) exhibited non-Fickian diffusion behaviors in the transient uptake of aromatic solvents. The diffusional exponents at the final stage of uptake exhibited asymptotic values ranging from 0.9–1.0 for the sigmoidal sorption of PVDF and 1.2–2.0 for the drastic accelerating sorption of ECTFE. The asymptotic diffusional exponent decreased with rising temperature. PVDF film exhibited a linear increase in both machine and transverse directions with fractional uptake, whereas ECTFE film increased linearly in the transverse direction and exponentially in the machine direction. A rate-type viscoelastic [Camera-Roda and Sarti, 1990] model was applied to reproduce the anomalous sorption of fluoropolymer-solvent systems. The fitted Deborah numbers ranged from 0.2–0.3 for PVDF, and 2–5 for ECTFE. The diffusivity ratio, D _eq /D _o ,of PVDF-solvent system was fitted as tenth order of magnitude lower than that of ECTFE-solvent system. The fraction of initial surface concentration, S_o, was fitted in the range of 0.6–0.8 for both ECTFE and PVDF. It is plausible to assume that diffusion coupled with comparable structural relaxation has the asymptotic diffusional exponents that are strongly dependent on accelerating curvature, and total sorption is contributed by relaxation-induced viscoelastic volume change along with concentration-driven Fickian diffusion.