Liquid Phase Axial Dispersion Coefficient Research Articles

Novel multistage solid–liquid circulating fluidized bed: liquid phase mixing characteristics

Liquid phase axial mixing studies have been carried out in the novel solid–liquid circulating fluidized bed (SLCFB). The SLCFB primarily consists of a single multistage column (having an inner diameter of 100 mm i.d. and length of 1.40 m) which is divided into two sections wherein both the steps of utilization, namely loading (e.g., adsorption and catalytic reaction) and regeneration of solid phase, can be carried out simultaneously in continuous mode. Weak base anion exchange resin was used as the solid phase, whereas water as the fluidizing medium. The effects of physical properties of solid phase, superficial liquid velocity, and solid circulation rate on liquid phase axial dispersion coefficient were investigated. The dispersion coefficient increases monotonically with an increase in the size of solid particle, superficial liquid velocity, and solid circulation rate. The axial dispersion model (ADM) was used to model experimental residence time distribution (RTD) data. A good agreement was found between ADM predictions and the experimental measurements. A unified correlation has also been proposed to determine dispersion coefficient as a function of physical properties of solid and liquid phases, superficial liquid velocity, and solid circulation rate based on all previous and present experimental data on multistage SLCFB.

Liquid phase axial mixing in solid–liquid circulating multistage fluidized bed: CFD modeling and RTD measurements

Liquid phase residence time distribution (RTD) studies have been performed in conventional solid–liquid fluidized bed (SLFB) and solid–liquid circulating multistage fluidized bed (SLCMFB). The riser column was made up of 50mm i.d. and 2m long glass pipe while the multistage down comer column (glass) consisted of seven stages of 100mm i.d. and 100mm long sections each having perforated plate as a distributor (having 480 holes of 2mm diameter). RTD experiments for SLFB were carried out in the column having the same diameter as the downcomer of SLCMFB. RTD has been estimated for both the riser column and the multistage column of SLCMFB. Computational fluid dynamic (CFD) simulations of SLFB and riser section of SLCMFB have been performed to predict the RTD. In all the above cases good agreement was found between the CFD predictions and the experimental measurements. Ion exchange resins and glass beads were used as a solid phase and water as a fluidizing medium. The dispersion characteristics of SLFB and SLCMFB have been investigated for resin particles with size range of 0.36–0.72mm and glass beads with size range of 0.1–0.7mm. It was observed that the liquid phase axial dispersion coefficient depends strongly on superficial liquid velocity, particle size and particle density. Based on the experimental data, empirical correlations have been proposed for liquid phase axial dispersion coefficient and have been found to be applicable to all the available data in the published literature.

Gas Holdup and Liquid-Phase Dispersion in Packed Bubble Columns

The gas holdup and liquid phase axial dispersion coefficient are measured in two semi batch packed bubble columns, 10 and 15 cm diameter for an air–water system, at atmospheric conditions. The experiments were carried out using a transient method (the tracer response method). The dispersion coefficient was obtained by adjusting the experimental profiles of tracer concentration with the predictions of the model. Experiment results of packed bubble column, shows a considerable reduction of the back mixing. The investigations have been carried out using RTD measurements and the back mixing is usually characterized by the axial dispersion coefficient obtained from the one-dimensional axial dispersion model. Also, a decrease in superficial gas velocity reduces the liquid back mixing. It is observed that the liquid circulation comprises an upward flow in the column core and a downward flow along the wall. It also seen that the transition from the bubbly flow to the pulsation flow regime occurred at 5-6 cm/s superficial gas velocity.

Liquid-Phase Back mixing in Bubble Columns

Liquid-phase axial dispersion coefficients have been measured for air-water system in bubble columns of 10, 15 and 30 cm diameter. The experiments are carried out using a transient method (the tracer response method). Dispersion coefficient is obtained by adjusting the experimental profiles of tracer concentration with the predictions of the model. The experimental results show that one-dimensional axial dispersion coefficient, Dax,L, reveal strong scale dependence. Backmixing of liquid phase increases with the increase of reactor diameter and superficial gas velocity. Axial dispersion coefficient for large column reactors can be easily predicted from the developed relation . Comparison of calculated with the experimental data and with the published data of other authors shows good agreement which ensure the reliability and confusability of the adopted correlations to be used in further design and scale-up purposes.

Liquid-Phase Back mixing in Bubble Columns

Liquid-phase axial dispersion coefficients have been measured for air-water system in bubble columns of 10, 15 and 30 cm diameter. The experiments are carried out using a transient method (the tracer response method). Dispersion coefficient is obtained by adjusting the experimental profiles of tracer concentration with the predictions of the model. The experimental results show that one-dimensional axial dispersion coefficient, D ax,L, reveal strong scale dependence. Backmixing of liquid phase increases with the increase of reactor diameter and superficial gas velocity. Axial dispersion coefficient for large column reactors can be easily predicted from the developed relation . Comparison of calculated with the experimental data and with the published data of other authors shows good agreement which ensure the reliability and confusability of the adopted correlations to be used in further design and scale-up purposes.

The Effect of Superficial Gas Velocity and Aerated Liquid Height on the Spatial Distribution of Local Liquid-Phase Axial Dispersion Coefficients in a Bubble Column

The spatial liquid-phase concentrations were measured by means of an electrical conductivity probe in a 0.289-m ID bubble column operated at superficial gas velocities (ug) of 0.018, 0.031 and 0.038 m/s, respectively. The column was equipped with a perforated plate gas distributor (0.002 mo × 31 holes). Carbon dioxide was used as a tracer gas, whereas deionized water was used as a liquid phase. The local liquid-phase axial dispersion coefficient EL was derived from the local liquid-phase concentrations by means of the graphical method developed by Khang and Kothari (1980). It was found that the spatial distribution of the local EL coefficients becomes radially non-uniform as a function of ug. At the regime transition velocity (Utrans = 0.031 m/s) between bubbly and transition flow regimes the mean, EL coefficient for the upper zone (UZ) becomes identical to the one for the lower zone (LZ). At both lower and higher ug values EL(UZ) is systematically higher than EL(LZ). The same result also holds if the overall bubble bed (BB) is divided into core and annulus regions. It was proven that, in the bubbly flow regime (ug Utrans), EL (annulus region) > EL (core region). The effect of the aerated liquid height L on the spatial distribution of the local EL coefficients was studied, as well. Three different BBs, viz. L = 0.64 m (shallow BB), 1.28 m (medium BB) and 2.1 m (deep BB) were examined at ug = 0.038 m/s. The spatial distribution of the local EL coefficients was most scattered in the shallow BB (L = 0.64 m). In a medium BB with an aerated liquid height L = 1.28 m the existence of a well-developed helical flow structure was detected.It was shown that the graphically determined mean EL coefficient (for the overall BB) increases as a function of both the superficial gas velocity ug and aerated liquid height L, and a useful empirical correlation was derived. It covers the following range of bed aspect ratios: 2.1 ≤ L/Dc ≤ 7.3.

Mixing Time Studies in Multiple Impeller Agitated Reactors

AbstractMixing time studies have been carried in a 0.3m diameter and 0.9m tall vessel equipped with three impellers. Conductivity measurement technique has been used for the measurements of mixing time. Effect of the various parameters i.e. tracer density, tracer volume, speed of rotation and impeller combination on mixing time has been studied for two impeller combinations used viz. PTD‐PTD‐PTD and PTD‐PTD‐DT. A compartment model (with one fitted parameter, the exchange flow rate QE) with single compartment per agitation stage has been used to predict the conductivity response and the exchange coefficients are calculated from the model parameter. An attempt has been made to explain the experimental results on the basis of the liquid phase axial dispersion coefficient and cell residence time, calculated from the model parameter QE

Liquid phase mixing in 2-phase liquid–solid inverse fluidized bed

Liquid phase residence time distribution studies are reported in 2-phase inverse fluidized bed for the first time in the literature. Using a pulse tracer technique and deconvolution method of analysis, RTD of the system, residence time, Peclet number and dispersion coefficient are determined. The liquid phase axial dispersion coefficient increases with increase in liquid velocity and Archimedes number and is independent of static bed height. An empirical correlation has been proposed for liquid phase axial dispersion coefficient in 2-phase IFB.

Mass transfer analysis in ozone bubble columns

An impinging-jet bubble column has been tested for the ozone mass transfer applications in water treatment. Two venturi injectors were utilized to create turbulent gas-liquid jets in the ambient fluid by placing them at an intersecting angle of 125°. The intersecting of the jets caused an increase in the turbulence produced in the ambient fluid and therefore, increased the gas–liquid mass transfer rate. The steady-state one-phase axial dispersion model (1P-ADM) was applied to analyze the dissolved ozone concentration profiles measured in the bubble column by fitting these profiles to the predicted profiles, using the 1P-ADM, to determine the column-average overall mass transfer coefficient (kLa) and liquid-phase axial dispersion coefficient (DL). Two minimization approaches were applied to solve the differential equation representing the 1P-ADM: two-parameter (kLa and DL) and one-parameter (kLa) minimization techniques. To examine the sensitivity of the predicted kLa to changes in DL, DL was estimated first from the tracer experiments. Then, the one-parameter minimization technique was applied to determine kLa. As a result, kLa varied only slightly (<11%) between the two types of minimization techniques. Using the two-parameter minimization technique, kLa and DL values were correlated to the superficial gas and liquid velocities uG and uL, respectively) by power-law relationships. The following correlations were obtained: kLa = 20.54 uG1.13uL0.07 and DL = 2.94 x 10–2uG0.03uL0.18. The 1P-ADM has proven to be an accurate and easy-to use tool for describing the ozonation process in the impinging-jet bubble column as an excellent conformity between the measured and the predicted dissolved ozone concentration profiles was observed. Key words: axial dispersion model, impinging-jet bubble column, mass transfer, ozone.

Axial inhomogeneities in steady-state dissolved oxygen in airlift bioreactors: predictive models

Models were developed for prediction and interpretation of the observed steady-state axial dissolved oxygen concentration profiles in tall airlift bioreactors. The observed concentration profiles were non-linear because of a combination of hydrodynamic and mass transport factors. The profiles were influenced mainly by the liquid-phase axial dispersion coefficient, the volumetric overall gas–liquid mass transfer coefficient, the gas velocity, the induced liquid circulation velocity. The model-predicted concentration profiles agreed within ±2% with the measured data in a tall (working aspect ratio ∼15) airlift vessel operated under aeration regimens that are typically used during wastewater treatment. Axial inhomogeneities in dissolved oxygen increased with increasing aeration rate. This phenomenon may influence activated sludge processes in airlift and deep-shaft reactors. The maximum attainable concentration of dissolved oxygen at the bottom of a typically aerated airlift reactor, ≥3.5 m deep, always remained at <80% of air saturation value even when oxygen was not being consumed. Also, at steady state and without a net transfer of oxygen, the gas-phase mole fraction of oxygen varied by >10% axially up the reactor.

Liquid phase dispersion in bubble columns operating in the churn-turbulent flow regime

The objective of this paper is to develop a reliable, yet-simple, correlation for the liquid phase axial dispersion coefficient D ax,L in bubble column reactors. In order to develop this correlation we carried out measurements of the centre-line liquid velocity V L(0) and D ax,L in bubble columns of diameter D T=0.174, 0.38 and 0.63 m with the air-water system. The measurements were performed in the churn-turbulent regime of operation with superficial gas velocities U in the range 0.05–0.35 m/s. From the several literature correlations tested, the one proposed by Riquarts [Chem. Ing. Techn. 53, 1981, 60-61] can be recommended for estimation of V L(0) for air–water systems. The Riquarts correlation however anticipates the dependence of V L(0) on the kinematic viscosity of the liquid phase. Measurements of V L(0) were also carried out in the 0.38 m diameter column with Tellus oil as the liquid phase, with a kinematic viscosity 87 times that of water. Comparison of V L(0) measurements with water and Tellus oil shows a negligible influence of liquid viscosity, leading us to conclude that the best estimation procedure for V L(0) is to use the Riquarts correlation with properties of the water as the liquid phase. The above conclusions are also supported by Eulerian simulations of the bubble column hydrodynamics. Our measured data on the D ax,L and V L(0) were combined to develop a simple correlation: D ax,L=0.31 V L(0) D T; this correlation also provides a good description of experimental data from the literature.

Influence of scale on the hydrodynamics of bubble columns operating in the churn-turbulent regime: experiments vs. Eulerian simulations

The radial distribution of the liquid velocities, along with the liquid-phase axial dispersion coefficients, have been measured for the air–water system in bubble columns of 0.174, 0.38 and 0.63 m diameter. The experimental results emphasise the significant influence of the column diameter on the hydrodynamics, especially in the churn-turbulent regime. Computational fluid dynamics (CFD) is used to model the influence of column diameter on the hydrodynamics. The bubble column is considered to be made up of three phases: (1) liquid, (2) “small” bubbles and (3) “large” bubbles and the Eulerian description is used for each of these phases. Interactions between the gas phases and the liquid are taken into account in terms of momentum exchange, or drag, coefficients, which differ for these two gas phases. The drag coefficient between the small bubbles is estimated using the Harmathy correlation ( A.I.Ch.E. Journal 6 (1960) 281–288). The drag relation for interactions between the large bubbles and the liquid, is developed from analysis of an extensive data base on large bubble swarm velocities measured in columns of 0.051, 0.1, 0.174, 0.19, 0.38 and 0.63 m diameter using a variety of liquids (water, paraffin oil, tetradecane). The interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k– ε model. The three-phase description of bubble columns was implemented within the Eulerian framework of a commercial code CFX 4.1c of AEA Technology, Harwell, UK. Comparison of the experimental measurements with the Eulerian simulations show good agreement and it is concluded that the three-phase Eulerian simulation approach developed here could be a powerful design and scale-up tool.

Steady-state axial profiles of dissolved oxygen in tall bubble column bioreactors

A model is developed for prediction and interpretation of the observed steady-state axial dissolved oxygen concentration profiles in tall bubble columns. The observed concentration profiles are non-linear, unlike what would be expected if the hydrostatic pressure alone influenced the profiles. The non-linear profiles result from the axial mixing of liquid in the column. Several other factors influence the profiles, including the overall gas holdup, the volumetric overall gas–liquid mass transfer coefficient, and the static height of liquid in the column. The effect of mixing can be adequately accounted for using an axial dispersion coefficient. Because the axial dispersion coefficient is sensitive to the diameter of the column and to gas flow rate, the overall behavior of the profile is affected by the aspect ratio of the column and the superficial gas velocity in it. The mass transfer coefficient and the axial dispersion coefficient have mutually opposing effects on the shape of the profile. Because both those variables increase with increasing gas flow rate, the shape of the profile is affected less than would be the case if only mixing influenced the profile. The non-linearity of concentration profiles increases with increasing overall height of the column especially when the height exceeds about 2 m in a 0.24 m diameter column. The model-predicted axial concentration profiles agree closely – within ±3% – with the measured data. Using the measured profile, the model allows for calculation of the liquid-phase axial dispersion coefficients. This method does not require the use of tracers. Being a steady-state method, the operation of the bioreactor does not need to the interrupted in any way for the determination of the axial dispersion coefficient or the state of mixing. Consequently, the proposed method is particularly suited to characterizing the axial dispersion coefficient in an operating bioreactor without disturbing the operation. If the axial dispersion coefficient is known, the model allows for quantifying the spatial inhomogeneities in oxygen concentration in a bioreactor vessel.

Phase holdup, liquid dispersion, and gas-to-liquid mass transfer measurements in a three-phase magnetofluidized bed

The gas holdup, ε g , liquid-phase axial dispersion coefficient, D ax, and volumetric gas-to-liquid mass transfer coefficient, k l a, have been measured for a three-phase magneto-fluidized bed (MFB) as a function of gas superficial velocity, liquid superficial velocity, and magnetic field strength. The solid phase consisted of 4 mm diameter calcium alginate spheres within which magnetite powder was entrapped. The liquid and gas phases were water and air, respectively. An axial, direct-current magnetic field having a magnitude between 0 and 300 G was applied by an external solenoid. Six different bed operating regimes were distinguished by visual inspection. Local values of ε g were measured using a fiber-optic probe, and the average values of ε g were measured using the valve technique. Average ε g values decreased by as much as 20% with increasing field strength due to bed contraction and the formation of preferred channels. Local ε g measurements correlated well with average measurements at low field strengths but became erratic at high field strengths due to bubble channeling. The liquid-phase axial dispersion coefficient was measured using a salt tracer. A fourfold decrease in D ax was observed in the channel regime. The volumetric oxygen mass transfer coefficient ( k l a) was determined from measurements of the steady-state oxygen profile across the reactor. A 30% increase in k l a was observed in the chain-channel regime. The experimental results for the MFB were compared to published correlations for conventional fluidized bed systems.

Hydrodynamic characteristics of two-phase flow through fixed beds: Air/Newtonian and non-Newtonian liquids

An experimental investigation was carried out to determine the effects of gas and liquid flow rates and flow consistency index on the liquid-phase axial dispersion coefficient, pressure drop and the liquid holdup for two-phase downflow and upflow in a fixed bed. Water and non-Newtonian liquids were employed as liquid phase. The liquid-phase flow in a fixed bed was examined using the piston-diffusion-exchange (PDE) model. The time-domain analysis of tracer response data was used for the flow model parameter estimation.

Hydrodynamics and mixing in three-phase fluidized bed bioreactors

The effects of solid particles on hydrodynamics and mixing in a three-phase fluidized bed bioreactor were discussed. The gas holdup, bubble size, and liquid-phase axial dispersion coefficient were measured in a 0.25-m id bubble column bioreactors containing low-density particles. The presence of low-density solid particles slightly increased gas holdup. The decrease in average bubble diameter with solid presence was found. For the three-phase system, the liquid-phase axial dispersion coefficients were higher than for the two-phase system. We extended a model for a gas holdup developed for a gas-liquid two-phase bubble column bioreactor to a gas-liquid-solid three-phase fluidized bed bioreactor. Using the present data and available data in the literature, the predictions of the proposed model were examined. The proposed model agreed with a wide range of the experimental data. A theoretical correlation for liquid-phase axial dispersion coefficient was developed using Kolmogoroff's theory of isotropic turbulence. Reasonable agreement was obtained between the predicted and experimental values of axial dispersion coefficient.

Liquid-phase axial mixing in two-phase horizontal pipe flow

The liquid-phase axial dispersion coefficient and volume-averaged fractional phase hold-ups have been measured in two-phase horizontal pipe flow. Radioactive 99mTc—technetium-99 metastable—(as an aqueous solution of sodium pertechnate) was used as a tracer. The pulse technique with two-point measurement was employed. Superficial gas (air) and liquid (water) velocities were varied in the range 20–2300 and 30–800mm/s, respectively. The flow regimes covered were bubbly, elongated bubbly, stratified, wavy and slug. Experiments were also performed using single-phase pipe flow. The liquid-phase dispersion coefficient has been shown to depend upon the flow regime and the superficial gas and liquid velocities.

The influence of slight departures from vertical alignment on liquid dispersion and gas hold-up in a bubble column

The effects of vertical misalignment of a bubble column on the gas hold-up and the liquid-phase axial dispersion coefficient have been measured as a function of the superficial gas velocity in water-filled bubble columns of 22, 58 and 103 mm diameter with multi-holed gas spargers. From the measurements the following relationship between the axial dispersion coefficient E 1, the column diameter d, and the angle of inclination α, of the bubble column is found: ▪ with α < 0.04 rad; ν g < 0.05 m s −1 and C 1 = 1100 rad −1 m −1. The influence of inclination on the gas holdup ϵ g in the bubble columns is given by: ▪ with α < 0.04 rad and C 2 = 2.3 rad −1.

Liquid phase axial mixing in a bubble column with viscous non‐newtonian liquids

AbstractThis paper presents some new data for the liquid phase axial dispersion coefficient in a bubble column with highly viscous non‐Newtonian liquids (μL &gt; 0.03 Pa · s). The data were obtained in a 0.15 m diameter column operating in the slug flow regime, and the dispersion measurements were conducted using heat aas a tracer. The experimental results show that the dispersion coefficients increase with both gas and liquid velocities and quantitatively they are about three times higher than those obtained for the air‐water system. The results are explained based on a known hydrodynamic model of vertical gas‐liquid slug flow.

Axial dispersion in a rectangular bubble column

AbstractThis paper presents the results of an experimental study on the gas holdup and the liquid phase axial dispersion coefficient in a narrow packed and unpacked rectangular bubble column. In both cases the gas and liquid flow rates were varied and the data were obtained by employing standard tracer technique. The gas holdup and the axial dispersion coefficient for both the packed and unpacked columns were found to be dependent on the gas and liquid flow rates. For given gas and liquid velocities and a given packing size in the case of the packed column, the rectangular column gave significantly higher dispersion coefficients than a cylindrical column of the equivalent cross sectional area. This result agrees very well with the one predicted by the velocity distribution model. The correlations for the Peclet number, the axial dispersion coefficient, and the fluid holdup for both the unpacked and packed bubble columns are presented.