Lattice Boltzmann modelling of unsteady-state 2D concentration profiles in adsorption bed

This study describes a lattice Boltzmann model (LBM) developed to simulate two-dimensional (2D) unsteady-state concentration profiles, including breakthrough curves, in a tubular column packed with adsorbents. The model using d3q19 (three dimensions and 19 speeds) lattice solves the 3D time-dependent convection-diffusion-adsorption equation for an ideal binary gaseous mixture assuming different velocity profiles in the column, including radially flat (plug flow) and non-uniform across the column's cross-section. The simulation results show significant concentration gradient across the cross-section depending upon the d/d_p ratio. The model results corroborate the experimental measurements made in the adsorption bed that the concentration due to breakthrough may be larger near the wall than at the core of the column due to the relatively larger local velocity in the vicinity of the wall. The LBM results have significance from the perspective of the physical understanding of the concentration profiles prevalent in the adsorption bed as well as effective design of a large-scale column. The model results are validated with the analytical solution to 1D axial dispersion problem, and to a few simple flow problems, such as Poiseuille and Couette flows.     

Simulation of 3D velocity and concentration profiles in a packed bed adsorber by lattice Boltzmann methods

Full 3D simulations of velocity and concentration profiles were carried out for the several ordered packing arrangements of spherical particles with small tube-to-particle diameter ratio (<10) using lattice Boltzmann methods. The effects of voids and diffusion coefficients on the adsorption concentration profiles in a packed bed of circular cross-section were investigated. In particular, the radial (r) and circumferential (θ) dependencies of the concentrations due to non-uniform velocity and particle voids across tube's cross-section, especially near the walls, were ascertained. The lattice Boltzmann technique allows simultaneous solution to velocity and concentration fields at all locations inside the packed tube without using any empirical correlations for certain transport parameters, for example, dispersion coefficient. Depending upon the packing arrangements and the magnitudes of diffusion coefficient, the concentration gradients in r- and θ-directions were found to be significant. The lattice model simulation results were also compared to the tomographic data obtained in a tubular adsorber packed with the zeolites coated glass beads and were found to be in reasonably good agreement.     

Simulation of temperature fields in a narrow tubular adsorber by thermal lattice Boltzmann methods

Significant temperature gradients may exist in packed bed adsorbers due to the exothermic heat of adsorption. In this study we investigate temperature fields in a narrow tubular packed bed adsorber having tube to particle size ratio <10. Theoretical calculations are carried out using lattice Boltzmann methods (LBM) to simulate three-dimensional concentration and temperature profiles in macro- as well as micro-pores of the adsorption bed. Model simulation results show non-uniform temperature gradients across the tube's cross-section. Zones of significantly high temperature are observed within macro-voids. Temperature gradient is found to be primarily dependent on the amount of heat released, internal BET surface area, and hydrodynamic conditions prevailing in the adsorber. Agreement between the model results and the experimental data obtained with the aid of the tomography technique for a tubular adsorber is observed to be reasonable. The study is important from the point of view of a realistic design of packed bed adsorbers.     

On the influence of particle shape and process conditions in the pressure drop and hydrodynamics in a wall-effect fixed bed

A low tube-to-particle diameter ratio (d_t/d_e,p) fixed bed, packed with spherical and nonspherical catalyst supports, was used to investigate pressure drop at varying temperature (298–673?K) and inlet pressure (245–294?kPa). The d_t/d_e,p ranged from 3 to 6, namely, a large wall-effect fixed bed, with an average void fraction between 0.38 and 0.61. These conditions pertain to multitubular fixed-bed reactors used for exothermic reactions. The pressure drop was notably influenced by the particle size and morphology as well as temperature. The use of particles with d_t/d_e,p?0.55) appeared suitable for pressure drop control. The fluid velocity profiles were calculated by applying the Navier–Stokes–Darcy–Forchheimer equation computing the respective permeability parameters with refitted state-of-the-art pressure drop correlations. The fluid flow exhibited different velocity zones across the fixed bed, the highest velocity zone being located near the reactor wall. The axial velocity component was influenced by the catalyst morphology, as well as temperature and inlet pressure.     

Application of wave propagation theory to adsorption breakthrough studies of toluene on activated carbon fiber beds

Based on the wave propagation theory, a dynamics model that combines the nonlinear equilibrium isotherm and the linear mass-transfer equation has been developed to predict the breakthrough behaviour of toluene adsorption in a fixed bed packed with activated carbon fibers. The experimental results showed that the constant-pattern wave model using the Langmuir isotherm equation could capture the dynamic behaviour of the adsorption column. Two important parameters, the half breakthrough time (t_1/2) and the volumetric mass-transfer coefficients (k_Gα) in the model were obtained from linear fitting of the model to experimental breakthrough data. k_Gα was found to be insensitive to the initial concentration and increased with the increasing the superficial velocity. It was also observed that t_1/2 decreases with increasing the superficial velocity and the initial concentration, and increases with increasing the bed height. A sensitivity analysis showed that external mass-transfer had a much stronger influence on the breakthrough curve than internal mass-transfer, confirming that the overall mass-transfer for toluene adsorption onto activated carbon fibers in fixed bed is controlled by external mass-transfer.     

Modeling solvent extraction of vegetable oil in a packed bed

A one-dimensional model was developed for solvent extraction of oil from a packed bed of oil-bearing vegetable materials. The equilibrium relationship between the residual oil content of marc and oil concentration of stagnant miscella in pores of the bed material was generated through experiments with rice bran and hexane. The nondimensional parameters recognized from the model describing extraction were initial Reynolds number (Re_i), initial Schmidt number (Sc_i), bed void fraction (ε_b), particle porosity (ε_p), ratio of bed diameter to particle diameter (D_t/d_p), ratio of bed depth to bed diameter (L/D_t), ratio of particle surface area to bed cross-section (a_pAL/A=a_pL), and recycle of solvent and equilibrium distribution coefficient (EDC). For reducing the time required to extract to the same residual oil content of marc, higher values of Re_i, ε_b, and a_pL were beneficial, whereas higher values of Sc_i, ε_p, D_t/d_p, L/D_t, and EDC were detrimental.     

Performance of fixed-bed KOH impregnated activated carbon adsorber for NO and NO2 removal in the presence of oxygen

KOH-impregnated activated carbon (K-IAC) was used in this study. This paper contains observation the adsorption behavior of NO and NO₂ with/without oxygen and with different bed depths of adsorbent. The paper also defines surface chemical changes due to NO_x adsorption. By using a simple design of adsorber, the packed amount of adsorbent for NO_x abatement for 6 months on a pilot scale was calculated. When oxygen was present, NO and NO₂ had a great improvement in adsorptivity. Adsorption of NO₂ forms a oxide crystal on the surface of the K-IAC and at the same time produces NO, which acts to bring about increased adsorptivity. The higher the bed of adsorbent was, the more NO was produced and the longer the breakthrough time took. The adsorber was designed in a scale-up condition where NO, NO₂ and O₂ were applied to K-IAC. The adsorbate that consumed the least packed amount was NO₂-air followed by NO₂-N₂, NO-air and NO-N₂. The results of the experiment demonstrated that with regard to adsorption of NO and NO₂ on K-IAC, the presence of oxygen and the bed depth of adsorbent were the biggest variables to adsorptivity.     

Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model

Using an illustrative sphere packing assembly, it is demonstrated that flow structure and wall heat transfer patterns in low aspect ratio fixed bed reactors are more realistically modelled by properly accounting for the discrete void fraction variations. A 3D network-of-voids (NoV) model has been devised to characterise and examine the discrete flow and heat transfer phenomena in a low aspect ratio packed bed with d_t/d_p = 1.93. The model as formulated is deliberately designed to be not too complicated so as not to place severe demands on computational resources. Hence, the model can potentially easily be applied to simulate the typically large sets of tubes (often comprising more than 10,000) in the case of industrial multi-tubular reactors, where every tube is different due to the random insertion of the packing particles. Because of its simplicity, the model offers an opportunity of coupling the individual catalyst pellet level transport with the complex interstitial flows at the reactor scale. Illustrative studies of this NoV model on a random packed bed of spheres predict large variations of discrete in-void angular velocities and consequently wall heat transfer coefficients within a single tube. The wide variations of wall heat transfer coefficients imply that the different angular sections of the tube will transfer heat at radically different rates resulting in potentially large temperature differences in different segments of the tube. This may possibly result in local temperature runaway and/or hot spot development leading to several potentially unanticipated consequences for safety and integrity of the tube and hence the reactor. The NoV model predictions of the overall pressure drop behaviour are shown to be consistent with the quantitative and qualitative features of correlations available in the literature.     

Magnetic Resonance Visualisation of Flow and Pore Structure in Packed Beds with Low Aspect Ratio

Different NMR techniques were combined to obtain the structure and velocity information for a systematic investigation of fixed beds with low aspect ratio (tube diameter to particle diamter, d_t/d_p) in the range 1.4 to 32. The structure of the void space was determined for a variety of packed beds of glass beads or regular and irregular porous pellets by magnetic resonance imaging (MRI). Based on the images the radial distribution of the voids within the bed was obtained. Ordering effects were found even for non‐spherical and polydisperse particles, and a maximum of the fluid density near the tube wall was confirmed for all pellet geometries and sizes. By combining MRI with velocity encoding, velocity profiles and distributions of flow velocity components of a single fluid phase through packed beds have been acquired. The radial velocity distribution follows an oscillatory pattern which largely reflects the ordering of the particles, which can be accessed from the density distribution of the interparticle fluid. Maximum velocities of up to four times the average value were found to occur near the tube wall. This wall effect was observed for all but the smallest particles, where the aspect ratio was d_t/d_p = 32. Moreover, a visualisation of flow pattern in the presence of packed particles was achieved by using a tagging technique, and the stationary flow field could be identified for an experimental time of several hours.     

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.     

Mass transfer in gas-fluidized beds: measurement of actual driving forces

Concentration profiles of naphthalene vapors were measured in the flow of air through fluidized beds of naphthalene spheres. Seven different sizes of spheres were used in this study and ranged from 0.02480 to 0.2000 cm. To avoid saturation conditions in the air leaving the bed, the naphthalene spheres were diluted in a matrix of inert beads (styrene divinylbenzene copolymer) of the same size and density as the naphthalene spheres. The established concentration profiles were graphically integrated to produce from them actual mass transfer coefficients. These transfer coefficients were then used to calculate j_d, mass transfer factors, for this fluidized bed system and also the product j_dRe_f which has been found to depend on Re_mf, the corresponding Reynolds number at minimum fluidization conditions. Actual driving forces, (Δp)_a were normalized with the corresponding log-mean values, (Δp)_m, to produce the driving force factor, F = (Δp)_a/(Δp)_m. This factor has been correlated with the parameters of the system and can be predicted with a certainty of 10.5%.     

Radial gas dispersion in a column packed with screen cylinders

Gaseous eddy diffusivity measurements were made by a point injection technique in a 6.5-in. column packed with open-end screen cylinders varying in size from 3/8-in. to 1 1/2-in. diameter, and made from wire cloth varying from 4 to 28 mesh/in. Oxygen was used as the tracer gas. Only packings made from 4 to 10 mesh/in. produced concentration profiles which were symmetric. The latter data show that turbulent diffusivity increases linearly with gas flow rate, but decreases with decreasing mesh opening and wire diameter. A correlation is presented for turbulent diffusivities as a function of the Reynolds number, d_muρ/m?, and the ratio d_w/d_m.     

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 bed void volume on pressure vacuum swing adsorption for air separation

The effects of a poorly packed bed on the pressure vacuum swing adsorption (PVSA) process were investigated experimentally and theoretically by a five-step two-bed PVSA system. At first, the adsorption dynamics of a zeolite LiX bed for air separation (78 mol% N₂, 21 mol% O₂ and 1 mol% Ar) was studied at various adsorption pressures and flow rates. In breakthrough results, the effect of adsorption pressure on variations in bed temperature was greater than that of the feed flow rate. A combined roll-up of Ar and O₂ by N₂ propagation was observed and the roll-up plateau reached about 4 mol%. The fluid dynamic behavior of the poorly packed bed was simulated at each step in the PVSA process. The pressure and velocity profiles in the non-isobaric steps were clearly different from those of a normally packed bed. The two-bed PVSA process using one poorly packed bed with additional 1% void volume in feed end of bed could produce a purity of 92.3mol% O₂ from air, which was almost 1% purity lower than the PVSA with normal two beds. Even small asymmetry between beds, due to poor bed packing, could greatly reduce the product purity in the PVSA process.     

A study of particle shape and size effects on hydrodynamic parameters of trickle beds

Uniform-spherical and cylindrical-extrudate particles are employed to study air-water downflow in a packed bed of 14 cm i.d. The effect of particle shape, neglected in the literature so far, is shown to be very significant. A packed bed of extrudates displays significantly greater global dynamic liquid holdup h_d and pressure drop, as well as a trickling-to-pulsing transition boundary at higher gas flow rates, compared to beds of spheres of comparable size. Moreover, packed extrudates exhibit a significant increase of holdup, h_d, in the axial flow direction, a trend reported for the first time as there are no similar data available in the literature; on the contrary beds of spherical particles are characterized by practically constant h_d in the axial direction. Although an explanation for this h_d axial variation is not obvious, one might attribute it to the anisotropy and non-uniformity of interstitial voids of packed cylindrical particles. For beds of uniform spheres, in the diameter range examined (3-6 mm), the effect of size on both dynamic holdup and pressure drop, although quite pronounced, is not as significant as the effect of particle shape. An extensive survey of literature data, obtained with similar spherical particles, suggests that small bed diameters have an appreciable influence on trickling-to-pulsing transition boundary. Comparisons are reported with literature methods for predicting the measured parameters; discrepancies between data and predictions may be partly due to the inadequacy of a single “equivalent” diameter to represent both shape and size of non-spherical particles; predictive methods performing best are also identified.     

Mass transfer from the wall in small diameter packed beds

Measurements are reported for the rate of mass transfer from the wall to the fluid in packed beds of the kind employed for exothermic reactions in small diameter tubes surrounded by coolant. Correction is made for the varying pressure in the tube from inlet to exit when mercury is vaporised into a nitrogen stream. The transport parameters were then estimated from the experimental axial concentration profiles by a non-linear least squares fitting procedure. The Biot number, Bi, characterizing transfer at the wall was found as a function of the particle Reynolds number: Bi = b Re_p^−k valid over the range of Re_p observed. The Peclet number characterizing radial transfer in the bed was found on the assumption that it was constant over the corresponding range of Re_p. Such sets of parameters were found for six different particle sizes.     

CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion

CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d_p, is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.     

Propylen/Propan‐Trennung im Festbettadsorber und durch Membranpermeation

The metal‐organic framework Mg₂(dhtp) with the linker dihydroxyterephthalate is known as MOF‐74 or CPO‐27. Mg₂(dhtp) has been synthesized as powder to measure breakthrough curves in a fixed‐bed adsorber and adsorption isotherms, and as a supported thin membrane layer for permeation studies. The measurement of the breakthrough curves of the binary propylene/propane mixture shows that separation with the fixed bed adsorber is possible. Propylene shows a higher affinity to Mg₂(dhtp). Although the single gas propane flux is slightly higher than the one of propylene, the binary propane/propylene mixture is not separated.     

Wall effect in laminar flow of non-Newtonian fluid through a packed bed

Experiments were conducted on laminar flow of non-Newtonian fluid through a packed bed of low column to packing particle diameter ratio (3.8) to elucidate the wall effect on pressure drop and mass flux. Carboxy methyl cellulose (CMC) at different concentrations was passed through the packed bed and the pressure drop was measured at different CMC concentrations and flow rates. It was found that the pressure drop increases with the increase in CMC flow rate. The pressure drop also increases with the increase in CMC concentration for a given flow rate. The friction factor is plotted against Reynolds number and the data for different CMC concentration are found to be scattered around a line expressed as f=1.03/Re^0.87. The tri-regional model of Cohen and Metzner [1] predicted correctly the mass flux in the packed bed at different pressure drop values and CMC concentrations with parameters K₀ (related to pore geometry) value of 1.5 and L_e/L (related to effective path length) value of 1.2, respectively.