Liquid Phase Axial Dispersion Research Articles

Experimental study on spray diffusion characteristics at various biodiesel-butanol blended ratios and ambient conditions

The depletion of fossil fuels and stringent emission regulations have encouraged the development of renewable fuels, especially biodiesel and alcohols fuels. The aim of the investigation is to explore the spray diffusion characteristics at different biodiesel-butanol blended ratios (0, 10%, 30%, and 50%), ambient temperatures (600 K, 700K, and 800 K), and pressures (1 MPa, 3 MPa, and 5 MPa). The experiment was carried out in a constant volume combustion chamber. The liquid- and vapor-phase spray images were captured by backlight illumination and schlieren imaging technique, respectively. The axial, radial, and spatial diffusion characteristics were analyzed, including spray penetration, cone angle, area, R-parameter, and perimeter ratio. Results show that in the case of biodiesel mixed with 10% n-butanol, for liquid-phase spray, the liquid-core spray with high concentration has the largest impact on axial diffusion, and for vapor-phase spray, axial dispersion is slower and radial diffusion is faster. The fuel density and ambient temperature have a more significant impact on the liquid-phase axial dispersion at the steady state compared with ambient pressure and injection pressure. At lower ambient pressures, increasing the injection pressure can accelerate the radial diffusion and increase the spray cone angle, which is opposite of the variation law at higher ambient pressures. The radial spray has a faster diffusion with adding a small or middle proportion of n-butanol, and the maximum values of liquid- and vapor-phase cone angles appear at biodiesel blended with 30% and 10% n-butanol, respectively. Moreover, the axial diffusion plays a dominant role in the spray spatial dispersion.

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.

Investigation of liquid phase axial dispersion in Taylor bubble flow by radiotracer residence time distribution analysis

A gas-liquid Taylor bubble flow occurs in small diameter channels in which gas bubbles are separated by slugs of pure liquid. This type of flow regime is well suited for solid catalyzed gas-liquid reactors in which the reaction efficiency is a strong function of axial dispersion in the regions of pure liquid. This paper presents an experimental study of liquid phase axial dispersion in a Taylor bubble flow developed in a horizontal tube using high speed photography and radiotracer residence time distribution (RTD) analysis. A parametric dependence of axial dispersion on average volume fraction of gas phase was also investigated by varying the relative volumetric flow rates of the two phases. 137m Ba produced from a 137 Cs/ 137m Ba radionuclide generator was used as radiotracer and measurements were made using the NaI(Tl) scintillation detectors. Validation of 137m Ba in the form of barium chloride as aqueous phase radiotracer was also carried out. Axial Dispersion Model (ADM) was used to simulate the hydrodynamics of the system and the results of the experiment are presented. It was observed that the system is characterized by very high values of Peclet Number (Pe∼10 2 ) which reveals an approaching plug type flow. The experimental and model estimated values of mean residence times were observed in agreement with each other.

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.

Effects of Gas Redispersion and Liquid Height on Gas–Liquid Hydrodynamics in a Multistage Bubble Column

The influence of staging, superficial gas velocity, u g, and clear liquid height, h, on the values of volumetric mass transfer co-efficient, k L a, gas hold-up, ɛ g and liquid phase axial dispersion co-efficient, D L, of a 14 cm diameter and 98 cm tall bubble column were studied. The mass transfer parameter, k L a, was estimated by using the electrical conductivity method of Panja and Rao (1991) which consists of measuring the changes in electrical conductivity of water as a function of time obtained by absorbing pure carbon dioxide in water and using the measured data to infer the value of the mass transfer parameter with the help of a mathematical model. The parameter, D L, was determined by conducting tracer mixing experiments and fitting the dispersion model. From the results of the present work, the staging of the column was found to cause an increase in the value of k L a by about 60%, an increase in the value of ɛ g by about 5–10%. and a decrease in the value of D L by about 68–78, while the increase in the power input due to staging was found to be only 2.5% over the range of u g equal to 0.3–4.5 cm s −1 It was also found that in the absence of a gas redistributor, the values of k L a and D L decreased with increase in h. For identical values of gas flow rates and h, the values of k L a obtained under desorption conditions were found to be much higher than the values obtained under absorption conditions. Also, experiments were carried out on absorption of pure CO 2 into an aqueous solution of NaOH under batch and continuous co-current up-flow conditions with CO 2 as limiting reactant, and a preliminary mathematical model was proposed to explain the experimental results.

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.

The combined use of in-bed monitoring and an adsorption model to anticipate breakthrough during expanded bed adsorption

Tighter control of expanded bed adsorption (EBA) separations is shown to be possible through the combined use of on-line monitoring of samples abstracted from within a column and an adsorption model. A 5 cm diameter EBA column was modified to allow liquid sampling from within the fluidized bed during the adsorption of pure lysozyme and bovine serum albumin (BSA) on STREAMLINE SP and STREAMLINE DEAE, respectively. The developing breakthrough curve was measured at various positions along the bed. The adsorption model incorporated terms for liquid dispersion, film mass transfer, pore diffusion and adsorption. Parameters obtained by fitting the model to the experimental in-bed breakthrough curves were subsequently used to predict breakthrough at the bed exit. Comparison of the actual breakthrough curves at the bed exit ( 40 cm sample port) with those predicted based on the fit of the model to the experimental breakthrough data obtained from the 25 cm sample port, demonstrated that on-line, in-bed monitoring of the progress of the front of non-bound protein can provide information for tighter control of EBA separations. The accuracy of the model predictions was improved by employing information on the axial variations in the bed voidage, liquid phase axial dispersion and dynamic capacity for the top and bottom zones within the column. Ten per cent breakthrough at the 40 cm sample port was predicted to within 2% and 5% of the breakthrough time observed for the experimental runs for lysozyme and BSA, respectively.

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.

Ozone mass transfer in water treatment: hydrodynamics and mass transfer modeling of ozone bubble columns

Most of the mathematical models that are employed to model the performance of bubble columns are based on the assumption that either plug flow or complete mixing conditions prevail in the liquid phase. Although due to the liquid-phase axial dispersion, the actual flow pattern in bubble columns is usually closer to being mixed flow rather than plug flow, but still not completely mixed flow. Therefore, the back flow cell model (BFCM), that hypothesises both back flow and exchange flow to characterise the liquid-phase axial dispersion, is presented as an alternative approach to describe the hydrodynamics and mass transfer of ozone bubble columns. BFCM is easy to formulate and solve. It is an accurate and reliable design model. Transient BFCM consists of NBFCM ordinary-first-order differential equations in which NBFCM unknowns (Yj) are to be determined. That set of equations was solved numerically as NBFCM linear algebraic equations. Steady-state BFCM consists of 3 × NBFCM non-linear algebraic equations in which 3 × NBFCM unknowns (qG,j, Xj, and Yj) are to be determined. Those non-linear algebraic equations were solved numerically using Newton–Raphson technique. Steady-state BFCM was initially tested using the pilot-scale experimental data of Zhou. BFCM provided excellent predictions of the dissolved ozone profiles under different operating conditions for both counter and co-current flow modes.

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.