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.     

Oxygen transfer in viscous non-Newtonian liquids having yield stress in bubble columns

The oxygen transfer and hydrodynamics in viscous media having a yield stress in bubble columns operated under the slug flow regime were investigated to design an optimum bubble column fermentor for culture media having a yield stress.The gas holdup of escapable bubbles was well estimated by the equation of Nicklin et al. (Trans. Inst. Chem. Eng. 40 (1962) 61), which was modified for the viscous liquid having a yield stress by Terasaka and Tsuge (Chem. Eng. Sci. 58 (2003) 513). The volumetric oxygen transfer coefficient k_La increased with increasing superficial gas velocity and decreasing column diameter under the present conditions. To predict k_La in the non-Newtonian liquids having a yield stress under the operation in slug flow regime, the proposed correlation equation estimated relatively well the experimental k_La.To increase oxygen transfer rate, two types of novel bubble columns were compared with the standard bubble column. The partitioned bubble column presented the better performance than those of the other ones.     

Study of geometry and operational conditions on mixing time, gas hold up, mass transfer, flow regime and biomass production from natural gas in a horizontal tubular loop bioreactor

A horizontal tubular loop bioreactor (HTLB) was used for production of biomass from natural gas. Hydrodynamic characterizations (mixing time and gas hold up) and mass transfer coefficients were considered in the HTLB (L=2.2 m, H=0.4 m and D=0.03 m) as functions of design parameters, i.e., horizontal length to diameter ratio (L/D) and volume of gas-liquid separator (S) as well as operational parameters, i.e., superficial gas and liquid velocities (U_sG, U_sL). In addition, flow regime in different gas and liquid flow rates was investigated. It was observed from experimental results that U_sL has remarkable effects on gas hold up and k_La due to its influence on mixing time. The volumetric mass transfer coefficients for oxygen (k_La_O2) and methane (k_La_CH4) were determined at different geometrical and operational factors. In average, the amount of oxygen consumption for metabolism is approximately 1.4 times higher than that of methane. In bubble flow regime, the HTLB was used for biomass production, too. A gas mixture of 50% methane and 50% oxygen (based on results of dry cell weight, optical density and doubling time) was the best gas mixture inlet for biomass production. The empirical correlations for mixing time, gas hold up and k_La in terms of U_sG, U_sL, L/D and volume of gas-liquid separator were obtained and expressed separately.     

Effects of temperature and pressure gradients on catalyst pellet effectiveness factors—I

The dusty gas model is used to establish the effects of temperature and pressure gradients on catalyst pellet effectiveness factors for reaction systems in which species molecular weights and transport coefficients are indistinguishable and Σν_i = 0. For this class of reactions, the total molar flux of species i is shown to be expressible simply as N_i = ?cD ??_i in terms of the molar concentration, the Bosanguet diffusivity, and the mole fraction gradient. The effects of temperature and pressure gradients are reflected only in variations in molar concentration and diffusivity. Furthermore, the temperature-pressure relationship is shown to be given by the thermal transpiration equation for a pure gas.Typical numerical results are reported for first order reactions in spherical pellets under diffusive conditions ranging from the Knudsen through the bulk diffusion regimes.The variation in diffusion regime is shown to be controlled by an additional parameter α, the Knudsen to bulk diffusion ratio. Comparisons are made with the classical Weisz-Hicks nonisothermal pellet solutions based on N_i = ?D_eff?c_i. For highly exothermic reactions, effectiveness factors are 18% lower in the Knudsen regime and 30% higher in the bulk diffusion regime than are the Weisz—Hicks values. For highly endothermic reactions with a significant diffusion limitation, the effectiveness factors are 30% lower than the Weisz—Hicks values.The classical Damköehler relationship for pellet temperature rise is shown to apply in the Knudsen regime, with the maximum dimensionless center temperature given by (1 + β), where β is the heat of reaction parameter. This temperature is accompanied by a maximum dimensionless center pressure of (1 + β)^{$\text{1}\text{2}$}.In the bulk diffusion regime, the maximum center temperature is shown to be increased by the additional term β²/4. This additional temperature rise accounts for the 42% increased bulk diffusion effectiveness for highly exothermic reactions.     

A new expression for spherical aerosol drag in slip flow regime

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier–Stokes equations were solved and the velocity jump at the gas–particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed. The particle total drag coefficient was also correlated against Re and Kn over the range of gas–particle relative speeds yielding the incompressible slip flow from the Stokesian regime up to the threshold of compressibility. Inclusion of gas slip on the particle surface enhances the accuracy of particle drag force prediction up to 40.9% in the range of 0.01<Kn<0.1 and 0.125<Re<20 compared to the no-slip continuum drag values.     

Two regime transitions to pseudo-homogeneous and heterogeneous bubble flow for various liquid viscosities

The gas hold-up variation and regime transition were investigated with different liquid viscosities ranging from 1.0 mPa s to 31.5 mPa s using a 0.15-m-in-diameter bubble column. In contrast to common observations, the gas hold-up graph with the superficial gas velocity could be categorized into three flow regimes: homogeneous, pseudo-homogeneous and heterogeneous flow regimes. The formation of large bubbles caused a transition from the homogeneous to the pseudo-homogenous flow regime, in which large bubbles rose vertically without oscillatory turbulence. According to the results from the dynamic gas disengagement (DGD) technique, large bubbles began to form at the transition superficial gas velocity to the pseudo-homogeneous flow regime. The transition to a heterogeneous flow regime was initiated by the turbulent movement of large bubbles. The transition superficial velocities to pseudo-homogeneous and heterogeneous flow regimes, u_t1 and u_t2, decreased with increasing liquid viscosity below a critical viscosity and converged to a certain value above that viscosity. However, the correlations from the literatures could not make a reasonable estimation of the transition superficial velocities because they did not consider the possible transition to a pseudo-homogeneous flow regime. Therefore, the two transition points should be predicted separately.     

An analytical model for real gas flow in shale nanopores with non‐circular cross‐section

An analytical model for gas transport in shale media is proposed on the basis of the linear superposition of convective flow and Knudsen diffusion, which is free of tangential momentum accommodation coefficient. The present model takes into the effect of pore shape and real gas, and is successfully validated against experimental data and Lattice–Boltzmann simulation results. Gas flow in noncircular nanopores can be accounted by a dimensionless geometry correction factor. In continuum‐flow regime, pore shape has a relatively minor impact on gas transport capacity; the effect of pore shape on gas transport capacity enhances significantly with increasing rarefaction. Additionally, gas transport capacity is strongly dependent of average pore size and streamline tortuosity. We also show that the present model without using weighted factor can describe the variable contribution of convective flow and Knudsen diffusion to the total flow. As pressure and pore radius decrease, the number of molecule‐wall collisions gradually predominates over the number of intermolecule collisions, and thus Knudsen diffusion contributes more to the total flow. The parameters in the present model can be determined from independent laboratory experiments. We have the confidence that the present model can provide some theoretical support in numerical simulation of shale gas production. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2893–2901, 2016     

Evaluation of hydrogen permselective separation from “synthesis gas” components based on single gas permeability measurements on anodic alumina membranes

Anodic alumina membranes were prepared by anodizing aluminum followed by chemical and hydrothermal treatments. Anodization was performed on both tube surfaces. External anodization was restricted to selected spots leaving an aluminum mechanically strong frame. Nitrogen sorption data analysed with the CPSM method (Corrugated Pore Structure Model) detected a mesopore structure (i.e. D_mean;15–20) and surface areas of 2–20 m²/g. SEM microscopy images revealed a regular pore structure of independent pores with densities of N_pore ~ 5.6 × 10¹⁴ pores/m². Single gas permeances (Π) for X: H₂, CH₄, CO and CO₂ were measured on a Wicke–Kallenbach apparatus at varying mean transmembrane pressure P_m by the “dead-end” method. The observed slight dependence of Π on Ρ_m is indicative of strong Knudsen diffusion and weak viscous flow contributions. By correlating the experimental data with a linear Π vs Ρ_m relationship, Knudsen contribution evaluation was enabled, and found to vary in the range K_C ≈ 0.7–1.0. The Knudsen number criterion for flow regime discrimination is critically discussed and a realistic dual Knudsen number approach is proposed. Experimental permselectivities α_Η2Χ = Π_H2/Π_X (X ≠ H₂) approach by 70–100% their Knudsen selectivity counterparts. Anodic alumina membranes exhibit pore structure and gas permeability characteristics useful in designing integrated gas separation and catalytic membrane reactor systems.     

Vertical slug flow in laminar regime in the liquid and turbulent regime in the bubble wake—Comparison with fully turbulent and fully laminar regimes

An experimental and simulation study on free bubbling vertical slug flow in laminar regime in the main liquid and turbulent regime in the near-wake bubble region is reported. A non-intrusive image analysis technique and a previously developed slug flow simulator (SFS) were used. Two aqueous glycerol solutions (0.012-0.013 and 0.022 Pa s) were studied. A single bubble-to-bubble interaction curve was obtained. Strong interaction was found for bubbles flowing less than 3-4D apart, with slight interaction persisting for longer distances. The shape of the interaction curve bridges those for fully turbulent and fully laminar regimes. The experimental average bubble velocity in undisturbed conditions was shown not to follow the correlation-based predictions for laminar regime in the liquid. Alternative fitting coefficients are proposed. An entrance length of 50-80D (or 90-170D) was obtained for normal inlet slug length distributions centred on 2-5D (or 2-6D), for superficial gas and liquid velocities up to 0.40 and 0.30 m/s, respectively. More contrasting inlet slug length distributions were found not to converge within the length of the column (6.5 m). An overall comparison between the three regimes is presented.     

Residence time distribution and liquid holdup in Kenics KMX static mixer with hydrogenated nitrile butadiene rubber solution and hydrogen gas system

A Kenics^® KMX static mixer that has curved-open blade internal structure was investigated to study its hydrodynamic performance related to residence time distribution and liquid holdup in a gas/liquid system. The static mixer reactor had 24 mixing elements arranged in line along the length of the reactor such that the angle between two neighboring elements is 90°. The length of the reactor was 0.98 m with an internal diameter of 3.8 cm and was operated cocurrently with vertical upflow. The fluids used were hydrogen (gas phase), monochlorobenzene (liquid phase) and hydrogenated nitrile butadiene rubber solution (liquid phase). In all the experiments, the polymer solution was maintained as a continuous phase while hydrogen gas was in the dispersed phase. All experiments were conducted in the laminar flow regime with the liquid side hydraulic Reynolds number in the range of 0.04-0.36 and the gas side hydraulic Reynolds number in the range of 3-18. Different polymer concentrations and different operating conditions with respect to gas/liquid flow rates were used to study the corresponding effects on the hydrodynamic parameters such as Peclet number (Pe) and the liquid holdup (ε_L). Empirical correlations were obtained for the axial dispersion coefficient (D_a) and liquid holdup in liquid system alone and for the gas/liquid system separately. It was observed that the Peclet number decreased with the introduction of gas in to the reactor while in the liquid system alone, an increase in viscosity decreased the Peclet number. The liquid holdup was empirically correlated as a function of the physical properties of the fluids used in addition to the operating flow rates.     

The intensification of gas-liquid flows with a periodic, constricted oscillatory-meso tube

The experimental study of gas dispersion in a vertical periodically, constricted, oscillatory meso-tube (OMT) is herein presented. Water was continuously pumped through the OMT in the laminar flow regime along with an oscillatory flow component superimposed into the net flow in a range of fluid oscillation frequency (f) and centre-to-peak amplitude (x₀) of and 0-3 mm, respectively, in the presence of a very low superficial gas velocity . Bubble images were recorded with a CCD camera and analysed with Visilog^® software. A bimodal distribution of bubble size was in general observed but the bubble size was found strongly dependent on the oscillatory flow mixing conditions imposed into the fluid. A number fraction of micro-bubbles (with an equivalent diameter, D_eq, equal or bellow 0.2 mm) up to 60% was generated with increasing values of x₀ (i.e. 3 mm) and values of f in the range . Furthermore, it is demonstrated that the Sauter mean diameter, D₃₂, and the specific interfacial area, a, can be fined tune by setting both f and x₀ in this studied range. The high number fraction of micro-bubbles was concluded to have a positive impact in enhancing the liquid-side mass transfer coefficient, k_L. Globally, the differences in bubbles sizes were found to play a marginal effect in the global enhancement of the k_La in the meso-tube in comparison with the intensive contact experimented by the bubbles rising in the oscillatory flow. The higher order of magnitude of the k_L values found in this work (up to ) is promising for running numerous industrial gas-liquid flows processes through smaller and better, while aeration of biotransformations can be run more efficiently, as supported by our recent proof-of-concept studies carried out in the platform.     

The effects of diffusion mechanism and void structure on transport rates and tortuosity factors in complex porous structures

Tracer diffusion simulations within random porous structures show that tortuosity factors are independent of diffusion mechanism for all practical void fractions when an equivalent Knudsen diffusivity is correctly defined. Previous studies concluded that tortuosity factors, a geometric property of the void space as defined, increase with increasing Knudsen number, K_n, a measure of the relative number of molecule-surface and intermolecular collisions. The model porous structures in this study consist of random-loose packings of spheres overlapped to achieve a given void fraction and to accurately reflect the void space in practical porous solids. Effective diffusivities were estimated using tracer or flux-based Monte Carlo methods for Knudsen numbers of 10⁻³-10¹⁰; the two methods lead to similar diffusivities for void fractions of 0.06-0.42. Tortuosity factors estimated using the number-averaged distance between collisions, 〈l_p〉, for the characteristic void length scale increased with increasing Knudsen number, even though simulations in infinite cylinders confirmed the accuracy of the Bosanquet equation for all values of K_n. These unexpected changes in a geometric property of the void space become most apparent near the percolation void fraction (∼0.04). For example, the Knudsen tortuosity factor defined in this manner is 1.8 times larger than in the bulk regime for a solid with 0.10 void fraction. Even at high void fractions (∼0.42), the two extreme values of tortuosity factor differ by a factor of ∼1.4. These apparent effects of diffusion mechanism on tortuosities reflect the inaccurate use of number-averaged chord lengths when tracer reflections from random obstacles obey the Knudsen cosine law for diffuse reflection. A corrected length scale, first proposed by Derjaguin, leads to tortuosity factors independent of K_n for void fractions above 0.20; tortuosities differ by only 18% and 4% between Knudsen and bulk regimes even for void fractions of 0.10 and 0.15, respectively. The residual differences at void fractions below 0.10 arise from the increasingly serial nature of the remaining voids. Thus, a long-standing inconsistency between the defined geometric nature of tortuosity factors and their inexplicable dependence on diffusion mechanism is essentially resolved. In practice, these simulations allow the consistent and accurate use of tortuosity factors determined at any value of K_n for all diffusion regimes; they also prescribe, rigorously for void fractions above 0.15 and empirically for lower void fractions, the length scale relevant to diffusion in the Knudsen and transition diffusion regimes.     

Effect of ultrasonic waveforms on gas–liquid mass transfer in microreactors

This study aims to investigate the effect of ultrasonic waveforms on the gas–liquid mass transfer process. For a given load power (P), continuous rectangular wave yielded stronger bubble oscillation and higher mass transfer coefficient (k_La) than continuous triangular and sinusoidal wave. For pulsed ultrasound, the k_La decreased monotonically with decreasing duty ratio (D), resulting in weak enhancement at low D (≤33%). For a given average load power (P_A), concentrating the P for a shorter period resulted in a higher k_La due to stronger cavitation behavior. For a given P_A and D, decreasing the pulse period (T) led to an increase in k_La, which reached a constant high level when the T fell below a critical value. By optimizing the D and T, a k_La equivalent to 92% of that under continuous ultrasound was obtained under pulsed ultrasound at a D of 67%, saving 33% in power consumption.     

The effect of bubble column diameter on gas holdup in fiber suspensions

Three bubble column diameters (D=10.2, 15.2, and 32.1 cm) are employed to study the scale-up effect on gas holdup in air-water and air-water-cellulose fiber (hardwood, softwood, and BCTMP) systems. The effect of column diameter depends on flow regime and fiber mass fraction. When , gas holdup decreases with increasing column diameter for the transitional and heterogeneous flow regime, and column diameter effects are negligible in the homogeneous flow regime. When , gas holdup is only affected by column diameter in the transitional flow regime for an air-water system and low fiber mass fraction suspensions (C?0.25%); column diameter effects disappear at medium fiber mass fractions (e.g., C=0.8%) but are significant at high fiber mass fractions (e.g., C=1.4%).     

The effect of pore necking on Knudsen diffusivity and collision frequency of gas molecules with pore walls

Straight pores whose walls were concave (for “Swiss cheese” type solids), convex (for “cannonball” type), or cylindrical (for capillary type) were simulated by computer. The pores having concave and convex walls were represented as an assemblage of spherical elements since any pore could be described merely by listing the radii and coordinates of the elements. Using a Monte Carlo method, molecular trajectories of gas molecules inside the pores were computed in the Knudsen regime to obtain the diffusivities, collision numbers and collision densities. These parameters were strongly dependent on the pore wall configuration. An equation was presented which enabled the prediction of Knudsen diffusivity from the mean pore size d̄ and (d_n/d_w)² (where d_n and d_w are the diameters of narrow and wide sections inside the pores, respectively). The average number of collisions per molecule J̄ was also correlated quite well with the ratio of geometric diffusion length to mean pore size L₀/d̄ for each type and was in the order capillary type > Swiss cheese type > cannonball type. It was found that the pore of capillary type had the preferred wall configuration among these three types from the view point of diffusivity and collision numbers of molecules. The results obtained here will have application to the design of micro- and macro-pore structures of supported catalysts.     

Effect of the radical scavenger t-butanol on gas-liquid mass transfer

The alcohol t-butanol has been used as a radical scavenger in the studies of ozone reactions in water and has been found to affect the gas-liquid mass transfer rates. An understanding of the effects of t-butanol on mass transfer parameters, including bubble size, gas holdup, mass transfer coefficient and the mass transfer specific surface area, is of key importance to not only improve the knowledge of this particular system but also to gain fundamental understanding about the effects of gas/liquid surface modifiers on the contact between phases and the mass transfer rates. An experimental study has been carried out to investigate the effects of t-butanol concentrations on the physical properties of aqueous solutions, including surface tension and viscosity. It was found that t-butanol reduced both properties-by 4% for surface tension and by a surprising 30% for viscosity. These reductions in the solution physical properties were correlated to enhancement in the mass transfer coefficient, k_L. The hydrodynamic behaviour of the system used in this work was characterised by a homogeneous bubbling regime. It was also found that the gas holdup was significantly enhanced by the addition of t-butanol. An equation to predict the gas holdup from the gas flow rate and t-butanol concentration was proposed to describe the experimental data. Moreover, the addition of t-butanol was found to significantly reduce the size of gas bubbles, leading to enhancement in the volumetric mass transfer coefficient, k_La. Bubble mean diameter was predicted using an equation developed by the Radial Basis Function Neural Network architecture obtained from the literature, and the mass transfer coefficient, k_L, was predicted using an equation based on the surface coverage ratio model. The ratio was found not to depend either on t-butanol concentration or on gas flow rate. A significant increase in the volumetric mass transfer coefficient, k_La, due to an increase in both k_L and a, was obtained following the addition of t-butanol, even at low concentrations.     

Conductivity of some rare earth chlorides in sub and supercritical aqueous solutions

The electrical conductances of 0.001 M NdCl₃, SmCl₃, GdCl₃ and DyCl₃ solutions were measured in the temperature range 373–673 K at pressures up to 37.27 MPa, using a flow type electrical conductance cell. The cell constant was calculated by means of the measured conductance of five solutions of KCl, with concentrations range of 0.0001–0.002 M and the equivalent values calculated from Barthel equation at 298 K and was found to be equal to 0.111 cm⁻¹. By using the measured electrical conductance values, the specific conductance, σ, and the equivalent conductance, Λ, were calculated. The maximum electrical conductance was obtained in the sub critical region at ≈548 K in all cases. At this temperature, the electrical conductance was found to increase with the increase in the ionic radius from Dy to Sm. The electrical conductance of Nd was found to be smallest, which could be attributed to a higher ionic association.     

Temperature influence on transport parameters characteristic of Knudsen and Poiseuille flows

Single gas permeation experiments results using neon, argon, nitrogen and methane are reported. From gas permeation experiments the characteristic parameters of the Knudsen and Poiseuille transport mechanisms were determined by means of an equation derived from the “Dusty-Gas” model. The experiments were performed at different temperatures from 303.15 to 323.15 K, in order to study the temperature influence on those parameters. For PVDF and PCTE membranes the influence of the temperature on K_o and B_o parameters was not significant. Gas influence was also investigated for both types of membrane, a slight tendency of K_o to decrease with increase in molar mass and a very slight tendency of B_o to increase with increase in molar mass, although these trends were not fulfilled by neon gas.     

Multicomponent isothermal diffusion and forced flow of gases in capillaries

Isothermal transport is described of a multicomponent gas mixture in a capillary. The governing equation (eqn 24) derived in the paper accounts for sim and pressure. The equation applies to the transition region between the Knudsen diffusion and the region of continuum and provides also for the slip on equations for the H₂C₂H₂, H₂C₂H₂C₂H₄ and H₂N₂NH₃ mixtures indicates give rise to a pressure gradient representing the driving force for additional transport. Notions of a critical component and diffusion-stoichiometric