A double linear driving force approximation for non-isothermal mass transfer modeling through bi-disperse adsorbents

The aim of this paper is to derive a double LDF non-isothermal model to describe mass transfer through a fixed bed of bi-disperse adsorbent pellets. Firstly, we perform an analysis concerning the different way the composition within the pellets can be described and the consequence on the model structure and compactness. Secondly, we present a bed model including a simplified intra-particle model that is based on a double LDF approximation. This bi-disperse pellet model reduces the number of variables and parameters that are needed. This simplified model is used to simulate breakthroughs of a methane/carbon dioxide mixture over a 5 A zeolite and of a 2,2-dimethylbutane/2-methylpentane mixture over a silicalite molecular sieve. It is also compared with a more detailed model based on Stefan-Maxwell theory that we have previously developed.     

Modeling of multicomponent mass diffusion in porous spherical pellets: Application to steam methane reforming and methanol synthesis

The main purpose of this paper is the derivation and evaluation of various diffusion flux models. For this aim, a comprehensive catalyst pellet problem has been simulated for two test cases: the steam methane reforming (SMR) and the methanol synthesis, as these two important chemical processes cover various aspects of a chemical reaction. The pressure, temperature, total concentration, species composition, viscous flow, mass and heat fluxes within the porous spherical pellet are included in the transient pellet model. Mass diffusion fluxes are described according to the rigorous Maxell–Stefan and dusty gas models, and the respectively simpler Wilke and Wilke–Bosanquet models. Simulations are performed with these fluxes defined according to both the molar averaged and mass averaged definitions. For the mass based pellet equations, a consistent set of equations is obtained holding only the mass averaged velocity. On the other hand, the closed set of molar based pellet equations hold both the molar averaged and mass averaged velocities as the fundamental energy balance and the momentum balance (Darcy law) are derived according to the mass averaged velocity definition, whereas the diffusion fluxes are defined relative to the molar averaged velocity. Identical results of the molar and mass based pellet equations were not obtained; however, the deviations are small. It is anticipated that these discrepancies are due to some unspecified numerical inaccuracies. However, efficiency factors have been computed for both processes and the values obtained compare well with the available literature data. Furthermore, efficiency factor sensitivity on parameters like pore diameter, tortuosity, temperature and pressure have been accomplished, and the classical simplifications of the pellet equations have been elucidated: isothermal condition, constant pressure, and neglecting viscous flow. The following conclusions are established for the reactor operating conditions used in the present work. The methanol synthesis: The simulation results of the methanol synthesis indicate that the classical assumptions are very fair for this process. Moreover, both Wilke and Wilke–Bosanquet models are good replacements for the more rigorous Maxwell–Stefan and dusty gas models. However, the simulation results are affected by Knudsen diffusion, thus the diffusion flux is most appropriately described by the Wilke–Bosanquet model. The SMR process: Knudsen diffusion hardly influences the results of the highly intraparticle diffusion limited SMR process. As the Wilke model does not necessarily conserve mass, we recommend the Maxwell–Stefan model because the simpler Wilke closure deviates with several percents. However, it is not elucidated whether these deviations are numerical problems arising from the large gradients of this process, or related to the choice of diffusion model. Isothermal and isobaric conditions can be assumed within the particle, but significant external temperature gradients are observed. Convective fluxes are much less than the diffusive fluxes, hence viscous flow can be neglected.     

Values of the mass transfer coefficient of the linear driving force model for VOC adsorption on activated carbons

Modelling of activated carbon cartridges is essential in personal protective equipments against toxic gases in order to know the duration of protection. The linear driving force model seems to be more adapted than the actual Wheeler–Jonas model because it has more physical significance. The difficulty is that the mass transfer coefficient can not be calculated a priori. Values of the LDF mass transfer coefficient are disseminated in the literature and thus there is no overview of the range and variations with different adsorbents, adsorbates and concentrations. The object of this paper is thus twofold: obtaining values of the mass transfer coefficient at different concentrations and adsorbates in order to have a comprehensive view of variations and appreciating the validity of the LDF constant pattern model.     

Low to moderate Peclet mass transport in assemblages of spherical particles for a realistic adsorption-reaction-desorption mechanism

A theoretical model and the associated numerical simulations for the mass transport from a moving Newtonian fluid to an assemblage of spherical solid absorbers are presented here. In particular, we present results from the numerical solution of the convection-diffusion equation in the simplified sphere-in-cell geometry and in stochastically constructed 3-D spherical particle assemblages for low to moderate Peclet numbers (Pe < 100) and relatively high porosities (? > 0.7). A realistic adsorption/reaction/desorption mechanism is used to describe the adsorption of diluted mass on the particles surface as opposed to the assumption of instantaneous and Langmuir-type adsorption that has been adopted in previous works. We also attempt to compare the effect of considering different sorption mechanisms in terms of adsorption efficiency. In all cases, the adequacy of the simplified sphere-in-cell approach is tested against the predictions from the numerical study in sphere assemblages. It is found that higher adsorption efficiencies correspond to lower porosities while increasing Peclet numbers lead to lower λ₀ values. Finally, it is shown that the assumption of instantaneous adsorption leads to severe overestimation of the adsorption efficiency in comparison with that obtained by using the more realistic adsorption-reaction-desorption model.     

Oxygen mass transfer in a gas/membrane/liquid system surrogate of membrane blood oxygenators

Oxygen mass transfer in a membrane blood oxygenator (MBO) surrogate system has been addressed in this work. It consists of a slit for water circulation as a surrogate blood flow channel and a constant pressure oxygen chamber separated by an integral asymmetric hemocompatible polyurethane‐based membrane. The oxygenated stream enters a well‐mixed reservoir of constant volume, V, for the oxygen average concentration, , measurement as a function of time, t. In a range of short times, the linearity of vs. t allows the direct determination of the permeation fluxes , with no recourse to dimensionless correlations for the determination of mass‐transfer coefficients. The experimental fluxes are in very good agreement with the predictions based in unidimensional axial convection and unidimensional transversal diffusion. This custom‐made benchmark system allows the optimization of the flow and oxygen mass transfer for the design of a novel flat‐sheet MBO. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3756–3763, 2018     

A numerical study of pellet model consistency with respect to molar and mass average velocities,pressure gradients and porosity models for methanol synthesis process: Effects of flux models on reactor performance

The objective of this work is to compare mass- and mole based diffusion flux models, convection, fluid velocity and pore structure models for methanol synthesis process. Steady-state models have been derived and solved using least-squares spectral method (LSM) to describe the evolution of species composition, pressure, velocity, total concentration and diffusion fluxes in porous pellets for methanol synthesis. Mass diffusion fluxes are described according to the rigorous Maxwell Stefan model, dusty gas model and the more simple Wilke model. These fluxes are defined with respect to molar- and mass averaged velocities. The different effects of choosing the random- and parallel pore models have been investigated. The effects of Knudsen diffusion have been investigated. The result varies significantly in the dusty gas model. The effectiveness factors have been calculated for the methanol synthesis process for both mass- and mole based pellet models. The values of effectiveness factors for both mass- and mole based pellet models do not vary so much. The effect of Wilke-, Maxwell–Stefan- and dusty gas mass diffusion fluxes on the reactor performance have been studied. Steady-state heterogeneous fixed bed reactor model is derived where the intra-particle mass diffusion fluxes in the voids of the pellet are described by Wilke-, Maxwell–Stefan- and dusty gas models. Furthermore, the total computational efficiency of the heterogeneous fixed bed reactor model is calculated with several closures for the intra-particle mass diffusion fluxes. The model evaluations revealed that:

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The mass- and mole based pellet models are not completely consistent. However, the small deviation (less than 2%) between mass- and mole based pellet models is due to the model equations are not fully consistent. If one pellet model is to be chosen for the methanol synthesis process, the optimal diffusion flux model is the Maxwell–Stefan model.     

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     

The role of under-rib convection in mass transport of methanol through the serpentine flow field and its neighboring porous layer in a DMFC

Numerical simulation of a direct methanol fuel cell (DMFC) operating under discharging conditions is challenged by the difficulties in modeling of complicated liquid-gas two-phase flows and coupled electrochemical kinetics. Under open-circuit conditions, the net electrochemical reactions in the DMFC anode cease, but, owing to the methanol concentration difference between the anode and cathode, the mass transport of methanol remains, creating a mass transport process of methanol in a single-phase liquid flow with no electrochemical reactions in the DMFC anode. Consequently, an accurate simulation of mass transport of methanol under such open-circuit conditions becomes possible. In this work, we performed a 3D numerical simulation of mass transport of methanol in the DMFC anode under open-circuit conditions and obtained the mass flux of methanol through the porous layer for different values of permeability. We also measured the mass flux of methanol permeation from the anode flow field to the cathode under open-circuit conditions. The comparison between the numerical and measured mass flux of methanol made it possible to in situ determine the permeability of the typical commercial porous layer. Using this in situ determined permeability, we then investigated numerically the effect of methanol feed rates on mass transport and found that the in-plane under-rib convection plays an important role, even at low methanol feed rate, to make the reactant evenly distributed over the entire catalyst layer.     

Effect of the Re number on heat and mass transport in a catalytic monolith

The numerical investigation of inter-phase heat transfer in a catalytic combustor, under laminar flow regime at different values of the Re number, is performed by means of a 2D axi-symmetric model of a single monolith channel. Numerical results highlight that axial diffusion comes to play an important role in the ignition region also at high convective fluxes (high Re) due to the strong flow perturbation accompanying light-off, with the consequences that: (a) the ignition position is not a linear function of contact time, as it would be expected at high Re; (b) the heat and mass transfer between surface and bulk gas phase are non-linearly affected by Re, especially in the entrance and in the ignition regions.A previously developed correlation for Nu and Sh is, hence, extended to include the effect of the Re number on heat and mass fluxes, enabling the prediction of the local value of Nu and Sh in the main features, and in particular the enhancement in the ignition region and the dependence on Re.     

A dynamic forward mixing model for evaluating the mass transfer performances of an extraction column

It is well known that the droplet behavior of the dispersed phase in extraction equipments has a strong influence on the mass transfer performances. It is, and will continuously be a key project for design and scaling up of extraction columns. In this work, a dynamic mass transfer model, considering the effect of forward mixing led by the drop size distribution and the axial mixing of the continuous phase, has been developed, by which the axial mixing characteristic can be easily evaluated when a stimulus-response dynamic curve is obtained. In order to test the mass transfer model and to study in the effect of droplet coalescence on mass transfer performance, a typical experimental system of 30% tributyl phosphate (in kerosene)-nitric acid-water with interface intension of 0.00995 N/m was chosen to investigate the mass transfer in a coalescence-dispersion pulsed-sieve-plate extraction column (CDPSEC) with 150 mm in diameter. The two-point dynamic method was applied to get the stimulus-response curves. With these results the axial mixing of the CDPSEC were evaluated. The calculated results showed that the response curves could be predicted with the new mass transfer model very well. The model has marked advantages over the traditional diffusion model. It is closer to the practice, easier to solve for the mathematical equations and boundary conditions, and has only one parameter to be optimized. The calculated results also showed that the influence of local coalescence of droplets on mass transfer performances is obvious.     

A numerical study of multicomponent mass diffusion and convection in porous pellets for the sorption-enhanced steam methane reforming and desorption processes

Mass-based mathematical models have been formulated to describe the evolution of species mass fraction, pressure, velocity, density and mass diffusion flux in porous pellets for steam methane reforming (SMR) and sorption-enhanced steam methane reforming (SE-SMR) with CO₂ capture and desorption. The internal- and overall effectiveness factors have been calculated for the steam methane reforming, the sorption-enhanced steam methane reforming with a CaO-based adsorbent and the desorption processes. The accuracy of choosing the Wilke model to describe multicomponent diffusion instead of using the more costly Maxwell–Stefan- and Dusty gas models have been investigated. The different effects of choosing the random pore-, multi-grain- and the parallel-pore models have been investigated. Using an average size of the micro-particle the results obtained by in the multi-grain model, are slightly different than those for the parallel-pore model.The model evaluations revealed that:

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  The rate determining steps for the SMR process are basically the chemical kinetics, but the internal diffusion flux rate is also important as the main conversion takes place close to the external surface of the pellet. The SE-SMR process is basically chemical kinetics controlled. The approximate values of the efficiency factors for SE-SMR processes are around 1 and for the desorption it is around 0.02.

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  In general, the optimal diffusion flux model is the dusty gas model.

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  The multi-grain model is optimal pore model for the SMR and SE-SMR pellets.

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  There is a uniform temperature within the pellet.

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  The diffusion fluxes dominate over the convective fluxes. The pressure gradients and velocity vanish due to the imposed symmetry conditions.

     

Diffusional mass transfer model for the adsorption of food dyes on chitosan films

The adsorption kinetics of erythrosine B and indigo carmine on chitosan films was studied by a diffusional mass transfer model. The experimental curves were obtained in batch system under different conditions of stirring rate (80–200 rpm) and initial dye concentration (20–100 mg L⁻¹). For the model development, external mass transfer and intraparticle diffusion steps were considered and the specific simplifications were based on the system characteristics. The proposed diffusional mass transfer model agreed very well with the experimental curves, indicating that the surface diffusion was the rate limiting step. The external mass transfer coefficient (k_f) was dependent of the operating conditions and ranged from 1.32 × 10⁻⁴ to 2.17 × 10⁻⁴ m s⁻¹. The values of surface diffusion coefficient (D_s) increased with the initial dye concentration and were in the range from 0.41 × 10⁻¹⁴ to 22.90 × 10⁻¹⁴ m² s⁻¹. The Biot number ranged from 17.0 to 478.5, confirming that the intraparticle diffusion due to surface diffusion was the rate limiting step in the adsorption of erythrosine B and indigo carmine on chitosan films.     

Hollow fiber membrane contactor transient experiments for the characterization of gas/liquid thermodynamics and mass transfer properties

We present results from experiments and numerical simulations of contact between a non-reactive gas (N₂O and CO₂) and a physical solvent (H₂O) occurring in a polypropylene (PP) hollow fiber membrane contactor. The closed-loop liquid flow within the experimental setup provides transient curves representing the progressive saturation of the solvent by the gas. We develop an in-house numerical model to fully characterize the gas/liquid mass transfer both in the non-wetted and in the wetted modes, i.e., when the liquid starts partially wetting the pores of the membrane. Using experiments and numerical simulations, we show that the Henry constant (H) and the molecular diffusion coefficient of a non-reactive gas absorbing into a liquid solvent can be extracted by parameter estimation. Both parameters are obtained within a single experiment at a constant temperature and the comparison with temperature-dependant correlations yields excellent agreement over the whole range of temperature studied in this work. Simulations show a partial wetting of the membrane pore by the liquid meniscus during a contact between CO₂ and H₂O, possibly due to the plasticizer effect of CO₂ inside the membrane contactor fibers.