Determination of mass transfer coefficients for packing materials used in biofilters and biotrickling filters for air pollution control—2: Development of mass transfer coefficients correlations

Correlations that allow determination of gas film mass transfer coefficients (k_Ga_t, k_Ga_w) and liquid film mass transfer coefficients (k_La_w) for packing materials used in biofilters and biotrickling filters for air pollution control are presented. Lava rock, polyurethane foam cubes (PUF), Pall rings, porous ceramic beads, porous ceramic Raschig rings, and various compost-woodchips mixtures were used as packing materials. The functionality of gas and liquid velocity on mass transfer coefficients (k_Ga_t,k_Ga_w,k_La_w) obtained experimentally (see Part 1 of this paper) was correlated using modified Onda-type equations. The correlation equations helped to better understand the sensitivity of gas and liquid velocities on mass transfer, and the effects of packing wetting. Each packing had a different functionality with gas and liquid velocity and different wetting property, hence different correlation equations were needed for the different packing materials. Most of the fitted data fell within ±20% of the experimental values.     

Determination of the interfacial area and mass transfer coefficients in the Taylor gas–liquid flow in a microchannel

The interfacial area in the Taylor (slug) gas–liquid flow in a microchannel was measured by the Danckwerts' (chemical) method, using CO₂ absorption from the CO₂/N₂ mixture into KHCO₃/K₂CO₃ buffer solutions, containing NaOCl as a catalyst. The rate of absorption was determined and the Danckwerts' plots were constructed. Reasonable agreement with the geometrical area measured photographically was obtained. This fact allowed to determine for the first time the mass transfer coefficients separately for liquid film and liquid caps. A correlation for the calculation of mass transfer coefficients has been proposed.     

Vapour- and liquid-side volumetric mass transfer coefficients measured in distillation column. Comparison with data calculated from absorption correlations

Volumetric mass transfer coefficients in liquid and vapour phases in distillation column were measured by the method consisting of a fitting of the concentration profile of liquid phase along the column obtained by the integration of a differential model to the experimental one. The mathematical model of distillation process includes mass and energy balances and the heat and mass transfer equations. The film model flux expressions with the convective transport contributions have been considered in the transfer equations. Vapour and liquid phases are supposed to be at their saturated temperatures along the column. Effect of changes of phase flows and physical properties of phases on the mass transfer coefficients along the column and non-ideal thermodynamic behaviour of the liquid phase have been taken into account. The concentration profiles of liquid phase are measured in the binary distillation of the ethanol-water and methanol-ethanol systems at total reflux on metal Pall Rings and Intalox saddles 25 mm in the column with diameter of 150 mm. The distillation mass transfer coefficients obtained by the fitting procedure are compared with those calculated from absorption data using Onda's, Billet's and Linek's correlations. The distillation heat transfer coefficients calculated from the model assuming saturated temperatures in both phases are compared with those calculated from the Chilton-Colburn and penetration model analogy between mass and heat transfer. The results have confirmed an agreement neither between distillation and from absorption correlations calculated mass transfer coefficients nor between analogy and from enthalpy balance calculated heat transfer coefficients. Also the concentration profiles obtained by the integration of the differential model of the distillation column using the coefficients from absorption correlation have differed from the experimental profiles considerably.     

Mass transfer coefficients of styrene and oxygen into silicone oil emulsions in a bubble reactor

The absorption of oxygen and styrene in water-silicone oil emulsions was independently studied in laboratory-scale bubble reactors at a constant gas flow rate for the whole range of emulsion compositions (0-10% v/v). The volumetric mass transfer coefficients to the emulsions were experimentally measured using a dynamic absorption method. It was assumed that the gas phase contacts preferentially the water phase. In the case of oxygen absorption, it was found that the addition of silicone oil hinders oxygen mass transfer compared to an air-water system. Decreases in k_La_oxygen of up to 25% were noted. Such decreases in the oxygen mass transfer coefficient, which imply longer aeration times to transfer oxygen, could represent a limiting step in biotechnological processes strongly dependent on oxygen concentration. Nevertheless, as the large affinity of silicone oil for oxygen enables greater amounts of oxygen to be transferred from the gas phase, it appears that the addition of more than 5% silicone oil should be beneficial to increase the oxygen transfer rate. In the case of styrene absorption, it was established that the volumetric mass transfer coefficient based on the emulsion volume is roughly constant with the increase in the emulsion composition. In spite of the relatively high cost of silicone oil, water-silicone oil emulsions remain relevant to treat low-solubility volatile organic compounds, such as styrene, in low-concentration gas streams.     

Design and operation of gas–liquid slug flow in miniaturized channels for rapid mass transfer

The influences of operating parameters such as channel size, flow rate, and void fraction on the mass transfer rate in the gas–liquid slug flow are investigated to establish a design method to determine the parameters for rapid mass transfer. From the experimental results, the turnover index, including the slug linear velocity, its length, and the channel size that represents the turnover frequency of the internal circulation flow, is proposed. For PTFE tube in which no liquid film exists in slug flow, a master curve is derived from the relationship between the mass transfer coefficient and the turnover index. For each channel material, the Sherwood number is also roughly correlated with the Peclet number. These correlations make it possible to arbitrarily determine a set of operating parameters to achieve the desired mass transfer rate. However, the turnover index and the Peclet number include the slug length, which cannot be controlled directly. The relationship between the slug length and the operating parameters is also investigated. The slug volume mainly depends on the inner diameter (i.d.) of a union tee. At a fixed union tee i.d., the slug length is controlled through the exit i.d. of the channel connected to the union tee and the void fraction. Thus, the final slug length depends on the union tee and exit channel inner diameters. At low flow rates, the gas and liquid collision angle is significant in determining the slug length.     

Hydrodynamics and mass transfer in a packed column: Case of toluene absorption with a viscous absorbent

Volatile organic compounds (VOCs) cause nuisance to humans and the environment. Recent legislation encourages industrialists to set up equipment for treating their VOC-loaded gaseous effluents. This piece of research studies the absorption process, using a viscous organic absorbent (di(2-ethylhexyl) adipate=DEHA) to treat a toluene-loaded vent gas, in terms of hydrodynamics and mass transfer. It is shown that DEHA does not lead to an excessive pressure drop. Correlations predicting hydrodynamic parameters from previous literature are summarised and tested against experimental results. It is shown that acceptable prediction accuracy can be achieved for counter-current pressure drop and liquid hold-up. Treatment efficiency for the toluene-loaded vent gas is shown to be very good. Calculation of mass transfer constants (k_La) enables to test literature correlations against the experimental results. The mass transfer is supposed to be limited by the liquid-side resistance. Our experimental results showed that the k_La of the system depends on the liquid velocity but also on the gas velocity. This behaviour has also been observed by the few authors who have used viscous fluids in their experiments, but is contrary to all the authors who have work on low-viscosity fluids. It is therefore clear that the influence of viscosity on the phenomenon is considerable. Not one current correlation is currently accurate in the case of a viscous absorbent.     

Computation and measurements of mass transfer and dispersion coefficients in fluidized beds

Conventional design of circulating fluidized beds requires the knowledge of dispersion and mass transfer coefficients, expressed in dimensionless forms as Sherwood numbers. However, these are known to vary by five or more orders of magnitude. Furthermore, the Sherwood numbers for fine particles reported in the literature are several orders of magnitude lower than the Sherwood number of two for diffusion to a single particle. We have shown that by replacing the particle diameter in the conventional Sherwood number with cluster or bubble diameter, the modified Sherwood number is again of the order of two.We have also shown that the kinetic theory based computational fluid dynamics codes correctly compute the dispersion and mass transfer coefficients. Hence, the kinetic theory based computational fluid dynamics codes can be used for fluidized bed reactor design without any such inputs.     

Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors

In this work, the effects of surface-active contaminants on mass transfer coefficients k_La and k_L were studied in two different bubble contactors. The oxygen transfer coefficient, k_L, was obtained from the volumetric oxygen transfer coefficient, k_La, since the specific interfacial area, a, could be determined from the fractional gas holdup, ε, and the average bubble diameter, d₃₂. Water at different heights and antifoam solutions of 0.5- were used as working media, under varying gas sparging conditions, in small-scale bubble column and rectangular airlift contactors of 6.7 and capacity, respectively. Both the antifoam concentration and the bubble residence time were shown to control k_La and k_L values over a span of almost 400%. A theoretical interpretation is proposed based on modelling the kinetics of single bubble contamination, followed by sudden surface transition from mobile to rigid condition, in accordance with the stagnant cap model. Model results match experimental k_L data within ±30%.     

Mechanism of enhanced gas absorption in presence of fine solid particles. Effect of molecular diffusivity on mass transfer coefficient in stirred cell

Desorption of oxygen and hydrogen from various liquids (water, 0.8 molar sodium sulphate solution) containing suspended particles of activated carbon at various solid loading was investigated. The desorption was used to avoid supersaturation effect which was observed during oxygen and hydrogen absorption into liquid saturated with nitrogen. Experiments were carried out in a stirred cell with flat gas-liquid interface at and atmospheric pressure. An increase of k_L upon addition of the particles was observed. Enhancement factor increases with increasing contact time of the particles with liquid reaching maximum steady-state value of approx. 3 after sufficiently long time (a few hours) regardless of solid loading , agitator frequency and solute gas (O₂,H₂). The results fit the correlation (e is specific power dissipated by agitator in liquid and D is molecular diffusivity of gas absorbed) with the exponent for liquids without and for the liquids with the particles. It indicates that the interface is rigid in absence of particles and hinders the motion of liquid along the interface forming boundary layer while in the presence of particles the interface is completely mobile and surface renewal proceeds according to the penetration model. These results confirm a finding of Kaya and Schumpe (2005) that the enhancement of mass transfer in the cell at the presence of hydrophobic solids is due to clean-up of the interface from surfactants by their adsorption on hydrophobic solids rather than by a “shuttle mechanism” exerted by particles with a high adsorption capacity for the transfer component.     

Determination of mass transfer resistance during absorption of carbon dioxide by mixed absorbents in PVDF and PP membrane contactor

In this study, the absorption of carbon dioxide by the absorbent which was composed of 2-amino-2-methyl-l-propanol (AMP) + piperazine (PZ) or methyldiethanolamine (MDEA) + piperazine (PZ) in polyvinylidinefluoride (PVDF) and polypropylene (PP) membrane contactors werewas examined. Three resistances were considered in each hollow fiber, i.e., liquid-film diffusion, membrane diffusion, and gas-film diffusion. The mass transfer resistance of membrane k_m was influenced by the wetting ratio using an absorbent with higher reaction rate. The wetting ratio was affected by contact angle between the membrane and absorbent and the viscosity of absorbent. The calculated absorption rates considering wetting ratio of membrane and using the modified correlation equation of gas-phase mass transfer coefficient were reasonably agreeable to those of measured ones (standard deviation, 4%). The fractional resistance of each transport step during the experiments was then determined. The rate-controlling step was dominated by the resistance of gas-film diffusion with mixed absorbents. The absorption rates of CO₂ increase with the increasing of gas flow rates in the most experimental cases. The resistance of liquid-film diffusion was only important using an absorbent with lower reaction rate. The rate-controlling step was the membrane diffusion only at higher gas flow rate with the absorbent composed of AMP and PZ in PVDF hollow fiber membrane contactor.     

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.     

Determination of the Henry's constant and the mass transfer rate of VOCs in solvents

Absorption of hydrophobic volatile organic compounds (VOCs): dimethylsulfide (DMS), dimethyldisulfide (DMDS) and toluene, in organic solvents: di-(2-ethyl)hexyladipate (DEHA), n-hexadecane, oleyl alcohol and PEG 400, was studied. In order to characterise the absorption capacity of various VOC/solvent systems, the Henry's constant (H) was determined. DMS was found to be the least absorbable in all the selected solvents. Amongst these solvents, DEHA was found to be the most efficient to absorb the considered VOCs. The effect of water addition to the considered solvents (emulsions) on the Henry's constants was examined and confirmed a decreasing VOC absorption for an increasing amount of water in solvent. Finally, to quantify the process rapidity, the absorption rate (N) and the overall liquid mass transfer coefficient (K_La) were measured for some selected couples VOC/solvent and revealed a superior efficiency of DEHA compared to other solvents in trapping DMS, DMDS and toluene.     

Experimental and numerical study of mass transfer efficiency in new wire gauze with high capacity structured packing

ABSTRACT

Experimental and numerical studies were conducted on the mass transfer efficiency of new wire gauze structured packing. For serving this purpose, various operational conditions were studied to assess the optimal parameters such as HETP of PACK-2100 in the distillation column. The results indicate that the HETP values are enhanced in comparison to conventional ones. In addition, the HETP slowly increases from 4 to 6 cm as mass flow rates of air and liquid flow are increased. The numerical simulations were also performed to describe the performance of the PACK-2100. The Eulerian-Eulerian multiphase approach is applied to calculate the value of HETP and pressure drop. The computational results confirmed that our experimental results. The average relative error between CFD predictions and the experimental data for the prediction of mass transfer efficiency is 20.45%.     

Heat and mass transfer in multicylinder drying: Part I. Analysis of machine data

A mathematical model describing the heat and mass transfer in the dryer section of a paper machine has been applied to the production data from four paper machines. Model predictions for the machine speed are compared to actual machine speeds for a total of 163 data sets. The mathematical model assumes that the temperature and moisture content remain homogeneous in the thickness direction of the sheet. For three paper machines producing paper with basis weights ranging from 0.056 to 0.159 kg d.s./m² the model predictions are adequate. For the paper machine producing the heaviest grades with basis weights ranging from 0.189 to 0.390 kg d.s./m² the model predictions are flawed by a systematic error. For low machine velocities/high basis weights the machine velocity is over-predicted and for high machine velocities/low basis weights the machine velocity is under-predicted. This systematic error is caused by the assumption of homogeneous moisture content and temperature within the sheet being severely in error for thick sheets.     

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.     

Numerical investigation of hydrodynamics and mass transfer for in-line fiber arrays in laminar cross-flow at low Reynolds numbers

In this work, mass transfer at the shell side of an in-line hollow fiber array subjected to cross-flow is simulated by applying the domain decomposition method combined with orthogonal grid generation. Two-dimensional Navier-Stokes equations written in stream function-vorticity variables, were separately solved along with a species conservation equation for different arrays. The main factors influencing the concentration fields, local mass transfer rates and global mass transfer rates in the laminar flow of Re=10-200 and Pe=10-300 with pitch to tube diameter ratios of 1.45, 1.50, 1.75, 1.85 and 2.00 are discussed in detail. Mass transfer correlations obtained from the numerical simulations show good agreement with typical empirical correlations proposed earlier.     

Assessment of mass transfer coefficients in coalescing slug flow in vertical pipes and applications to tubular airlift membrane bioreactors

One of the operational challenges associated with membrane bioreactors (MBRs) is the fouling of the membranes. In tubular side-stream MBRs, fouling reduction can be achieved through controlling the hydrodynamics of the two-phase slug flow near the membrane surface. The two-phase slug flow induces higher shear stresses near the membrane surface, which generate high mass transfer coefficients from the surface to the bulk region. However, measuring the mass transfer coefficient is difficult in complex heterogeneous mixtures like activated sludge and existing techniques (e.g. electrochemical methods) cannot be applied directly. As an alternative, in this work, a multidisciplinary approach was selected, by exploiting dimensionless analysis using the Sherwood number. Mass transfer coefficients were measured at various superficial velocities of gas and liquid flow in a tubular system. Due to the variability of the mass transfer coefficient obtained for each experimental condition, the results were compiled into, mass transfer coefficient histograms (MTH) for analysis. A bimodal MTH was observed, with one peak corresponding to the mass transfer induced by the liquid flow, and the other peak induced by the gas flow. It was noted that coalescence of bubbles affects the MTH. Coalescence increased the “width” of the peaks (i.e. the estimate of the variability of the mass transfer coefficient) and the height of the peak (i.e. amount of time that a mass transfer coefficient of a given value is maintained). A semi-empirical relationship based on the Lévêque relationship for the Sherwood number (mass transfer coefficient) was formulated for the laminar regime. A test case comparison between water and activated sludge was performed based on full-scale airlift MBR operational conditions. It was found that the Sherwood number in the non-Newtonian case is 8% higher than that in the Newtonian case.     

Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid-liquid extraction columns

A comprehensive model for predicting the interacting hydrodynamics and mass transfer is formulated on the basis of a spatially distributed population balance equation in terms of the bivariate number density function with respect to droplet diameter and solute concentration. The two macro- (droplet breakage and coalescence) and micro- (interphase mass transfer) droplet phenomena are allowed to interact through the dispersion interfacial tension. The resulting model equations are composed of a system of partial and algebraic equations that are dominated by convection, and hence it calls for a specialized discretization approach. The model equations are applied to a laboratory segment of an RDC column using an experimentally validated droplet transport and interaction functions. Aside from the model spatial discretization, two methods for the discretization of the droplet diameter are extended to include the droplet solute concentration. These methods are the generalized fixed-pivot technique (GFP) and the quadrature method of moments (QMOM). The numerical results obtained from the two extended methods are almost identical, and the CPU time of both methods is found acceptable so that the two methods are being extended to simulate a full-scale liquid-liquid extraction column.     

Methanation in a fluidized bed reactor with high initial CO partial pressure: Part I—Experimental investigation of hydrodynamics, mass transfer effects, and carbon deposition

An extensive experimental study on the methanation reaction was carried out in a gas–solid fluidized bed reactor at 320 °C with a stoichiometric ratio of H₂/CO=3. By means of spatially resolved measurements of the axial gas species concentration and temperatures along the fluid bed the effects of different catalyst loadings, gas velocities and dilution rates were observed and analyzed. By applying this technique, it was found that most of the reaction (CO and H₂ conversion) proceeds in the first 20 mm of the bed depending on the experimental conditions. For a few cases, the temperature increases by up to 80 °C from 320 to 400 °C within the first 3 mm of the bed. By increasing the inlet volume flow only by a factor of 1.4, the temperature hotspot diminishes and isothermal behavior develops. For all experiments, a CO conversion of practically 100% was achieved. The experimental data indicate that the dense phase of the fluidized bed is probed and that mass transfer between bubble and dense phase is dominating in the upper part of the bed. It could be shown that both hydrodynamic and chemical boundary conditions influence the methanation reaction inside the fluidized bed reactor.