A model for gas transport in microfractures of shale and tight gas reservoirs

A model for gas transport in microfractures of shale and tight gas reservoirs is established. Slip flow and Knudsen diffusion are coupled together to describe general gas transport mechanisms, which include continuous flow, slip flow, transitional flow, and Knudsen diffusion. The ratios of the intermolecular collision frequency and the molecule‐wall collision frequency to the total collision frequency are defined as the weight coefficients of slip flow and Knudsen diffusion, respectively. The model is validated by molecular simulation results. The results show that: (1) the model can reasonably describe the process of the mass transform of different gas transport mechanisms; (2) fracture geometry significantly impacts gas transport. Under the same fracture aperture, the higher the aspect ratio is, the stronger the gas transport capacity, and this phenomenon is more pronounced in the cases with higher gas pressure and larger fracture aperture. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2079–2088, 2015     

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     

Valeric acid extraction with tri‐n‐butyl phosphate impregnated in a macroporous resin: II. Studies in fixed bed columns

Extraction and back‐extraction of valeric acid in a fixed bed packed with Amberlite XAD‐4 resin impregnated with tri‐n‐butyl phosphate were experimentally studied at 25 °C. The effects of the feed flow rate, acid concentration in the feed solution and extractant concentration in the impregnated resin on the breakthrough curves, were investigated. The bed saturation capacity was larger under the conditions of higher extractant concentration in the resin phase and higher acid concentration in the feed solution. A dynamic model that considers intraparticle diffusion and external liquid film diffusion as limiting steps in mass transfer rates was successfully applied. The intraparticle effective diffusivities (10^?9 dm² s^?1) were from one to three orders of magnitude lower than the diffusivities in the external liquid film (10^?8–10^?6 dm² s^?1). A fast and complete back‐extraction of valeric acid from the saturated bed was carried out with sodium hydroxide solutions. The operational life of the impregnated resin was also studied. Copyright © 2005 Society of Chemical Industry     

Steady‐state behavior of liquid fuel hydrazine decomposition in packed bed

A general theoretical model is presented to analyze the steady‐state decomposition process of liquid monopropellants in packed beds for thruster systems. Additionally, an experiment studying the decomposition of liquid hydrazine in a packed bed is used to validate this model. The liquid droplet evaporation rate is determined through calculating the gas‐liquid mass transfer for the mixture temperatures lower than the liquid propellant boiling point and solving the gas‐liquid or liquid‐solid heat transfer equations at the temperature exceeding the boiling point. The process of liquid propellant decomposition in packed beds are simulated based on the Naive–Stokes equation for the mixture model integrated with the developed liquid evaporation rate, in which both the heterogeneous catalytic reaction coupled with the diffusion of reactants in the pore of catalyst, and the homogenous decomposition reactions are considered. The calculated results for the axial distribution of the temperature are in good agreement with the experimental data. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1064–1080, 2015     

Automated measurements of gas‐liquid mass transfer in micropacked bed reactors

Gas‐liquid mass transfer in micropacked bed reactors is characterized with an automated platform integrated with in‐line Fourier transform infrared spectroscopy. This setup enables screening of a multidimensional parameter space underlying absorption with chemical reaction. Volumetric gas‐liquid mass‐transfer coefficients (k_La) are determined for the model reaction of CO₂ absorption in a methyl diethanolamine/water solution. Parametric studies are conducted varying gas and liquid superficial velocities, packed bed dimensions and packing particle sizes. The results show that k_La values are in the range of 0.12～0.39 s^?1, which is about one‐to‐two orders of magnitude larger than those of conventional trickle beds. An empirical correlation predicts k_La in micropacked bed reactors in good agreement with experimental data. © 2017 American Institute of Chemical Engineers AIChE J, 64: 564–570, 2018     

Sublimation as a function of diffusion

Purification of large organic molecules in a tubular sublimator occurs by a combination of laminar flow, Knudsen diffusion, and volume diffusion. For laminar flow, the amount purified per area per driving force varies with pd², where p is pressure and d is tube diameter. For Knudsen diffusion, it varies with d and is not a function of pressure. For volume diffusion, it is constant, consistent with experiment. This volume diffusion mechanism may offer an alternative explanation to slip flow for dilute gas transport of both organic semiconductors and common low molecular weight gases. © 2015 American Institute of Chemical Engineers AIChE J, 62: 861–867, 2016     

Hydrodynamics in a pilot‐scale cocurrent trickle‐bed reactor at low gas velocities

Hydrodynamic data obtained from laboratory‐scale trickle‐beds often fail to accurately represent industrial‐scale systems with high packing aspect ratios and column‐to‐particle diameter ratios. In this study, pressure drop, liquid holdup, and flow regime transition were investigated in a pilot‐scale trickle‐bed column of 33 cm ID and 2.45 m bed height packed with 1.6 mm × 8.4 ± 1.4 mm cylindrical extrudates for air‐water mass superficial velocities of 0.0023 – 0.094 kg/m²s and 4.5 – 45 kg/m²s, respectively, at atmospheric pressure. Significant deviation was observed from pressure drop and liquid holdup correlations at low liquid flows rates, corresponding to gravity‐driven flow limit. Likewise, liquid saturation is overestimated by correlations at high liquid flow rates, owing to significantly reduced wall effects. Lastly, trickle‐to‐dispersed bubble flow and trickle‐to‐pulsing flow regime transitions are reported using a combination of visual observations and analysis of the magnitude of local pressure fluctuations within the column. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2560–2569, 2018     

Multicomponent mass diffusion in porous pellets: Effects of flux models on the pellet level and impacts on the reactor level. Application to methanol synthesis

A heterogeneous model has been derived for a fixed packed‐bed reactor producing methanol. Several closures for the intra‐particle mass diffusion fluxes; Maxwell–Stefan, Wilke, dusty gas and Wilke–Bosanquet, have been compared on the level of the catalyst pellet and the impacts of the different particle flux closures on the reactor performance are investigated. A preparatory study of the transport phenomena on the pellet level is recommended prior to any large‐scale reactor simulation to determine what are the rate determining transport mechanisms. Hence, if Knudsen diffusion is apparent on the level of the pellet, a combined bulk and Knudsen diffusion model should naturally be used in the reactor simulations as well, because Knudsen diffusion can influence significantly on the reactor conversion. Minor differences are observed between the diffusion flux models on both pellet and reactor level. Hence, for the reactor operation conditions applied in this study, the Wilke model is a good approximation to the rigorous Maxwell–Stefan model, and similarly, the Wilke–Bosanquet model is an appropriate model to use in replacement for the dusty gas model. Moreover, variable pressure and viscous flow can be neglected in the pellet model, as the effect of these contributions are not visible at neither pellet or reactor level. © 2011 Canadian Society for Chemical Engineering     

Three‐dimensional simulations of gas‐liquid cocurrent downflow in vertical,inclined, and oscillating packed beds

The hydrodynamic behavior of gas‐liquid downflow in vertical, inclined, and oscillating packed beds related to offshore floating applications was analyzed by means of three‐dimensional unsteady‐state two‐fluid simulations. Angular oscillations of the column between two angled symmetrical positions and between vertical and inclined position were considered while bed non‐uniformity was described using radial porosity distributions. For vertical and slightly inclined columns, two‐phase flow was concentrated in the core area of the bed. However, the two‐phase flow was predicted to deviate significantly from axial symmetry at higher inclinations with prominent liquid accumulation in the bottommost reactor cross‐sectional area. Oscillating packed beds unveiled complex reverse secondary flows radially and circumferentially resulting in oscillatory patterns of liquid holdup and pressure drop whose amplitude and propagation frequency were affected by column inclination angle and travel time between vertical and angled positions. © 2015 American Institute of Chemical Engineers AIChE J, 62: 916–927, 2016     

Nitrification by immobilized cells in a micro‐ecological life support system using packed‐bed bioreactors: an engineering study

The nitrifying component of a micro‐ecological life support system alternative (MELISSA) based on microorganisms and higher plants was studied. The MELISSA system consists of an interconnected loop of bioreactors to allow the recycling of the organic wastes generated in a closed environment. Conversion of ammonia into nitrates in such a system was improved by selection of microorganisms, immobilization techniques, reactor type and operation conditions. An axenic mixed culture of Nitrosomonas europaea and Nitrobacter winogradskyi, immobilized by surface attachment on polystyrene beads, was used for nitrification in packed‐bed reactors at both bench and pilot scale. Hydrodynamics, mass transfer and nitrification capacity of the reactors were analysed. Mixing and mass transfer rate were enhanced by recirculation of the liquid phase and aeration flow‐rate, achieving a liquid flow distribution close to a well‐mixed tank and without oxygen limitation for standard operational conditions of the nitrifying unit. Ammonium conversion ranged from 95 to 100% when the oxygen concentration was maintained above 80% of saturation. The maximum surface removal rates were measured as 1.91 gN‐NH₄⁺ m^?2 day^?1 at pilot scale and 1.77 gN‐NH₄⁺ m^?2 day^?1 at bench scale. Successful scale‐up of a packed‐bed bioreactor has been carried out. Good stability and reproducibility were observed for more than 400 days. Copyright © 2004 Society of Chemical Industry     

DUSTY-GAS PARAMETERS OF ACTIVATED CARBON ABSORBENT PARTICLES

Industrial gas phase adsorption processes often operate in the transition region of transport and the currently employed effective pore diffusion models cannot describe accurately the mass fluxes in this transport regime. The dusty-gas model provides appropriate constitutive equations for the mass fluxes in the transition region of transport, and it is expected to replace in the future the models currently used to describe mass transfer in porous adsorbent particles. In order to use the dusty-gas model estimates of the viscous, Knudsen diffusion, and molecular diffusion permeability constants of the adsorbent must be known.

Gas flow and Wicke-Kallenback experiments were performed and from the experimental data and the dusty-gas expressions, the viscous, Knudsen diffusion, and molecular diffusion permeability constants of activated carbon adsorbent particles were, for the first time, calculated     

Theoretical investigation of a water‐gas‐shift catalytic membrane for diesel reformate purification

The novel application of a catalytic water‐gas‐shift membrane reactor for selective removal of CO from H₂‐rich reformate mixtures for achieving gas purification solely via manipulation of reaction and diffusion phenomena, assuming Knudsen diffusion regime and the absence of hydrogen permselective materials, is described. An isothermal, two‐dimensional model is developed to describe a tube‐and‐shell membrane reactor supplied with a typical reformate mixture (9% CO, 3% CO₂, 28% H₂, and 15% H₂O) to the retentate volume and steam supplied to the permeate volume such that the overall H₂O:CO ratio within the system is 9:1. Simulations indicate that apparent CO:H₂ selectivities of 90:1 to >200:1 at H₂ recoveries of 20% to upwards of 40% may be achieved through appropriate design of the catalytic membrane and selection of operating conditions. Under these conditions, simulations predict an apparent hydrogen permeability of 2.3 × 10^?10 mol m^?1 Pa, which compares favorably against that of competing hydrogen‐permselective membranes. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4334–4345, 2013     

Particles mixing induced by bubbles in a gas‐solid fluidized bed

The effect of bubble injection characteristics on the mixing behavior of a gas‐solid fluidized bed is investigated using a discrete particle model. The effect of different parameters including gas injection time, velocity, and mode are studied. Simulation results show that injecting gas at a constant gas flow rate in the form of small bubbles results in a better overall particle mixing. It was also found that the injection velocities have limited effect on particle mixing behavior for the same total gas volume injected into the bed. Moreover, the mixing index (MI) of continuous gas jet bubbling regime is compared with the MI obtained in uniform gas injection regime and the results revealed that the MI of continuous jet bubbling regime has a larger value than that of uniform gas injection regime at the fixed total gas flow rate. In both regimes, z‐direction MI is larger than x‐direction index. The differences between two direction indices are more noticeable in continuous jet bubbling in comparison with the uniform gas injection regime. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1430–1438, 2016     

Impact of gravity on the bubble‐to‐pulse transition in packed beds

A model based on two‐phase volume‐averaged equations of motion is proposed to examine the gravity dependence of the bubble‐to‐pulse transition in gas‐liquid cocurrent down‐flow through packed beds. As input, the model uses experimental correlations for the frictional pressure drop under both normal gravity conditions and in the limit of vanishing gravity, as well as correlations for the liquid‐gas interfacial area per unit volume of bed in normal gravity. In accordance with experimental observations, the model shows that, for a given liquid flow, the transition to the pulse regime occurs at lower gas‐flow rates as the gravity level or the Bond number is decreased. Predicted transition boundaries agree reasonably well with observations under both reduced and normal gravity. The model also predicts a decrease in frictional pressure drop and an increase in total liquid holdup with decreasing gravity levels. © 2013 American Institute of Chemical Engineers AIChE J 60: 778–793, 2014     

Gas‐Liquid Mass Transfer in Fibrous Bed Reactor with Counter‐Current Liquid Recycle

In this work, the gas‐liquid mass transfer in a lab‐scale fibrous bed reactor with liquid recycle was studied. The volumetric gas‐liquid mass transfer coefficient, k_La, is determined over a range of the superficial liquid velocity (0.0042–0.0126 m.s^–1), gas velocity (0.006–0.021 m.s^–1), surface tension (35–72 mN/m), and viscosity (1–6 mPa.s). Increasing fluid velocities and viscosity, and decreasing interfacial tension, the volumetric oxygen transfer coefficient increased. In contrast to the case of co‐current flow, the effect of gas superficial velocity was found to be more significant than the liquid superficial velocity. This behavior is explained by variation of the coalescing gas fraction and the reduction in bubble size. A correlation for k_La is proposed. The predicted values deviate within ± 15 % from the experimental values, thus, implying that the equation can be used to predict gas‐liquid mass transfer rates in fibrous bed recycle bioreactors.     

Process intensification of catalytic hydrogenation of ethylanthraquinone with gas‐liquid microdispersion

In this article, to miniaturize the hydrogenation reactor and make the H₂O₂ production with more safety a gas‐liquid microdispersion system was generated to intensify the process of catalytic hydrogenation of ethylanthraquinone by passing the gas‐liquid microdispersion system through a generally packed bed reactor. A microdispersion device with a 5 μm pore size microfiltration membrane as the dispersion medium has been developed and microbubbles in the size of 10–100 μm were successfully generated. The reaction and mass transfer performance was evaluated. The conversion of ethylanthraquinone as much as 35% was realized in less than 3.5 s. The overall volume mass transfer coefficient in the microdispersion reaction system reached in the range of 1–21 s^?1, more than two orders of magnitude larger than the values in normal gas‐liquid trickle‐bed reactors. A mathematical model in the form of Sh = 2.0 + 54.7Sc^1/3We^1/2?^1/10 has been firstly suggested, which can well predict the overall mass transfer coefficient. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Studies on molecular transport of n‐alkanes through poly(tetrafluoroethylene‐co‐propylene) elastomeric membrane

Molecular transport of a series of n‐alkanes through commercial TFE elastomer (FA 150L) has been studied in the temperature range 30–50 °C using sorption‐gravimetric method. The Fickian diffusion equation was used to calculate the diffusion coefficients, which were dependent on the size of the alkanes and temperature. The diffusion coefficients at 30°C varied from 4.53 × 10^?8 cm²/s (n‐heptane) to 0.18 × 10^?8 cm²/s (n‐hexadecane). The liquid concentration profiles have also been computed using analytical solution of Fick's equation with the appropriate initial and boundary conditions and these were presented as a function of penetration depth of molecular migration and time of immersion. These results have been discussed in terms of molecular size of alkanes as well as temperature. In all the liquid penetrants, the transport phenomenon was found to follow the anomalous behavior. From the temperature dependence of diffusion and permeation coefficients, the Arrhenius activation parameters have been estimated. These parameters do not exhibit any systematic variation with the size of the penetrants. The resulting low diffusion coefficients, contribute to the superior barrier performance of the membrane, is due, in part, to the high glass transition temperature of Aflas? TFE elastomer. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2228–2235, 2006     

Preparation of polylactide microcapsules at a high throughput with a packed‐bed premix emulsification system

Core–shell polymer microcapsules are well known for their biomedical applications as drug carriers when they are filled with drugs and gas‐filled microcapsules that can be used as ultrasound contrast agents. The properties of microcapsules are strongly dependent on their size (distribution); therefore, equipment that allows the preparation of small and well‐defined microcapsules is of great practical relevance. In this study, we made polylactide microcapsules with a packed‐bed premix emulsification system that previously gave good results for regular emulsions. Here, we tested it for applicability to a system in which droplets shrank and solidified to obtain capsules. The packed‐bed column was loaded with glass beads of different sizes (30–90 µm) at various bed heights (2–20 mm), and coarse emulsions consisting of the polymer, a solvent, and a nonsolvent were pushed repeatedly through this system at selected applied pressures (1–4 bar). The obtained transmembrane fluxes (100–1000 m³ m^?2 h^?1) were much higher than those recorded for other membrane emulsification techniques. The average size of the obtained microcapsules ranged between 2 and 8 µm, with an average span of about 1; interestingly, the capsules were 2–10 times smaller than the interstitial voids of the beds. The droplets were larger when we used thicker beds and larger glass beads, and these effect correlated with the pore Reynolds number (Re_p). Two breakup mechanisms were identified: spontaneous droplet snap‐off dominated the system at low Re_ps, and localized shear forces dominated the system at higher Re_p. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43536.     

Structure and properties of ultra‐high molecular weight bisphenol a polycarbonate synthesized by solid‐state polymerization in amorphous microlayers

The structure and properties of ultrahigh molecular weight polycarbonate synthesized by solid‐state polymerization in micro‐layers (SSP_m) are reported. A low molecular weight prepolymer derived from the melt transesterification of bisphenol A and diphenyl carbonate as a starting material was polymerized to highly amorphous and transparent polycarbonate of molecular weight larger than 300,000 g mol^?1 in the micro‐layers of thickness from 50 nm to 20 µm. It was observed that when the polymerization time in micro‐layers was extended beyond conventional reaction time, insoluble polymer fraction increased up to 95%. Through the analysis of both soluble and insoluble polymer fractions of the high molecular weight polycarbonate by ¹H NMR spectroscopy and pyrolysis‐gas chromatography mass spectrometry (Py‐GC/MS), branches and partially crosslinked structures have been identified. The thermal, mechanical and rheological properties of the ultra‐high molecular weight nonlinear polycarbonates synthesized in this study have been measured by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and rheometry. The nonlinear chain structures of the polymer have been found to affect the polymer's thermal stability, mechanical strength, shear thinning effect, and elastic properties. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41609.     

Multicomponent gas diffusion in hardened cement paste at temperatures up to 350 °C

Diffusional gas transport of a H₂/CO₂ mixture versus N₂ in the pore system of hardened cement pastes was studied at four temperatures up to 350 °C in a Wicke-Kallenbach cell. The pastes possessed separation factors α_H2,CO2 from 1.42 to 3.43, i.e. the diffusion of hydrogen took place considerably faster than the diffusion of carbon dioxide. The separation factors depended on the threshold radii of the pastes, smaller threshold radii leading to higher separation factors. The Knudsen numbers of the controlling constrictions of the pore system and the temperature dependence of the effective diffusion coefficients of the gases show that gas transport in these constrictions takes place in the transient regime between Knudsen diffusion and bulk diffusion, smaller constriction widths leading to predominating Knudsen diffusion. It is therefore possible to use cement paste membranes to separate gas components of low molecular weight from higher weight components.