Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces

Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, C_S, as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737-1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965-2000] to account for the bubble-induced turbulence in the k-ε model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with C_S=0.08 and 0.10 agree well with the measurements. When C_S is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio (H/D=3 and H/D=6), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results.     

Intrinsic kinetics of the oxidative reaction of dichloroacetic acid employing hydrogen peroxide and ultraviolet radiation

In a previous work it has been shown that the combination of H₂O₂ and low wavelength UV radiation is a suitable process for degrading dichloroacetic acid (DCA). The final result provided a validated and complete reaction scheme. That proposal included two possible ways for the hydroxyl radical to react with DCA [Zalazar, C., Labas, M., Brandi, R., Cassano, A., 2007. Dichloroacetic acid degradation employing hydrogen peroxide and UV radiation. Chemosphere 66, 808-815].This work was directed to a single objective: to derive, from the previous reaction sequence, a mathematical model able to represent the kinetics of DCA oxidation and validate its predictive quality with experiments. This representation of the reaction must include all the required variables for an ulterior reactor design and scale-up and, consequently, the kinetic model parameters must be independent of the shape, size and configuration of the laboratory reactor.Working with a complete set of experimental runs that included all the involved variables, the unknown kinetics parameters of the DCA degradation were obtained by comparing predicted concentrations by the model (represented by a set of two ordinary differential equations and two algebraic equations coupled with a mass and a radiation balance inside the reactor) with the experimental values, employing a multi-parameter non-linear regression analysis. Experimental values confirmed the validity of the proposed mechanism. Additionally, an optimal concentration ratio of hydrogen peroxide with respect to DCA was obtained (r=CH₂O₂/C_DCA≈8).The intermediate results of the numerical solution of the complete system of differential and algebraic equations representing the proposed complete reaction mechanism were useful to find simplified, analytical expressions for the reaction rates of DCA and H₂O₂. The obtained rates resulting from these simplifications were compared with those of the complete system showing a very satisfactory concordance. This outcome is, at the same time, a clear indication of the significant influence of the radical in the reaction evolution.     

Characterization of flow phenomena induced by ultrasonic horn

Mean flow and turbulence parameters have been measured using laser Doppler anemometer (LDA) in ultrasound reactor. The effects of the ultrasonic power have been investigated over a power density (P/V) range of 15-. The liquid circulation velocities are dominant in the zone nearer to the source of energy and are substantially low at the walls and at the bottom of the reactor. The levels of turbulence kinetic energy and dissipation rate are high near the horn and decrease rapidly with increasing distance from the horn. Average turbulent normal stresses are larger than the turbulent shear stresses. However, they are much lower than stirred reactors when compared at the same power consumption per unit mass. Comparisons of LDA measurements and computational fluid dynamics (CFD) predictions have been presented. The good agreement indicates the validity of the CFD model. The flow information has been extended for the prediction of mixing time. For uniform mixing in ultrasound-assisted reactors, optimum power density and diameter of the vessel is needed, yet it is far less effective than conventional stirred vessel. The possibility of optimization has been suggested in terms of power dissipation and the vessel size.     

Heat transfer in rotary kilns with interstitial gases

While slow granular flows have been an area of active research in recent years, heat transfer in flowing particulate systems has received relatively little attention. We employ a computational technique that couples the discrete element method (DEM), computational fluid dynamics (CFD), and heat transfer calculations to simulate realistic heat transfer in a rotary kiln. To maintain simplicity, while simulating the cylindrical kiln, we use a non-uniform grid in our code. Different materials, particle sizes, and rotation speeds are used to track the transition from convection-dominated heat transfer to conduction-dominated heat transfer. At low particle conductivities, the heat transfer is dominated by gas-solid conduction; however, at higher particle conductivities solid-solid conduction plays a more important role. Moreover, our results suggest that the rate of change of the average bed temperature can display a transition as the conductivity of the interstitial medium is increased. At low interstitial transport rates, such as in vacuum, high conductivity, high heat capacity particles get heated most rapidly, but with increased interstitial transport coefficients, lower heat capacity material may get heated faster despite lower values of conductivity.     

The study on the conductivity of styrene-maleic anhydride copolymer electrolytes based on poly(ethylene glycol)400 and LiClO4

Polyelectrolytes, in this study were synthesized from styrene-maleic anhydride (SMA) copolymer, poly(ethylene glycol)400 (PEG400), and lithium perchlorate (LiClO₄). Fourier transform infrared spectroscopy (FTIR), and magic angle spinning (MAS) solid-state NMR were used to monitor the interaction between Li⁺ ions and polymer. The results of FTIR and MAS solid-state NMR indicate the Li⁺ ions are preferentially coordinated to the ether oxygen of PEG. The T_g of the PEG segments in polyelectrolyte increases with LiClO₄ concentration, as determined by differential scanning calorimetry (DSC), indicating that solubility of the Li⁺ ions in the host polymer increases with the PEG content. Impedance spectroscopy (IS) shows that the bulk conductivity of polyelectrolytes and the conductivity behavior obeys the Vogel-Tamman-Fulcher (VTF) equation.     

Numerical simulation of temperature and concentration distributions in fluidized beds with liquid injection

In this paper a numerical simulation study of dynamic behavior of a fluidized bed with liquid injection is presented. A continuum model has been developed taking into account the mass and energy balances of solid, gas as well as liquid to describe the temperature and concentration distributions in gas-solid-fluidized beds. The model considers the deposition efficiency of the liquid droplets as well as the influence of the spray nozzle region. For solving the non-linear partial differential equations with discrete boundary conditions a finite element method is used. Numerical computations have been done with two different schemes of time integration, a fully implicit and a semi implicit scheme. The complex correlations of mass and liquid flow rates, mass and heat transfer, drying, and transient two-dimensional air humidity, air temperature, particle wetting, liquid film temperature and particle temperature were simulated. The model was validated with transient measurements of the air temperature and air humidity at the outlet of a fluidized bed with water injection.     

A mechanism study of chloride and sulfate effects on Hg reduction in sulfite solution

This paper studied the effects of sulfate and chloride ions on bivalent mercury (Hg²⁺) absorption and reduction behaviors in a simulated WFGD system. The aqueous mercuric ion-sulfite system reduction behaviors were monitored and investigated using a UV-visible spectrum. Thereafter, the mechanism of Hg²⁺ reduction in the presence of sulfate and chloride ions was proposed. Experimental results revealed that both sulfate and chloride ions had inhibition effects on aqueous Hg²⁺ reduction to Hg⁰. The inhibition was assumed due to the formation of (in the presence of ) and / (in the presence of Cl⁻). And it was found that complex was more stable than in excess of Cl⁻. The formation of the above-mentioned complexes in the presence of and Cl⁻ would damp the formation of HgSO₃, whose decomposition was assumed to be the key step of Hg²⁺ reduction.     

Analysis of a cathode catalyst layer model for a polymer electrolyte fuel cell

A macroscopic model for a non-isothermal cathode catalyst layer (CL) in a proton exchange membrane (PEM) fuel cell is presented, in which liquid water in the CL pores is neglected. The model couples three phases: an electrically conductive carbon/platinum phase, gas pores, and a proton-conducting Nafion phase. The reaction-diffusion dynamics are described by a nonlinear system of differential equations which, due to the wide range of physical parameters, is very stiff. To reduce the stiffness of the system, an appropriate scaled model is introduced. A numerical algorithm consisting of two embedded Newton loops, specifically developed to handle the stiffness, is presented. Several numerical results are used to investigate the dynamics of the layer and the validity of the interface reduction, or zero CL thickness limit, which is often used in large fuel cell computations. In the limit of infinite water adsorption rate between ionomer phase and pore, a boundary layer emerges at either side of the CL, in which the water sorption equilibrium [Zawodzinski, T., Derouin, C., Radzinski, S., Sherman, R., Smith, V., Springer T., Gottesfeld, S., 1993. A comparative study of water uptake by and transport through ionomeric fuel cell membranes. Journal of the Electrochemical Society 140, 1981-1985] between ionomer and pore is violated.     

Formation and behavior of composite CO2 hydrate particles in a high-pressure water tunnel facility

Sinking CO₂ composite particles consisting of seawater, liquid CO₂, and CO₂ hydrate were produced by a coaxial flow injector fed with liquid CO₂ and artificial seawater. The particles were injected into a high-pressure water tunnel facility to permit determination of their settling velocities and dissolution rates. Injections were performed at fixed pressures approximately equivalent to 1200-m, 1500-m, and 1800-m depths and at temperatures varying from approximately 2 to 5 °C. Immediately after injection, the cylindrical particles were observed to break away from the injector tip and often aggregated into sinking clusters. The seawater flow in the tunnel was then adjusted in a countercurrent flow mode to suspend the particles in an observation window so that images of the particles could be recorded for later analysis. The flow would often break or cause rearrangement of some of the clusters. Selected individual particles and some clusters were studied until they became too hydrodynamically unstable to follow. In general, the flow required to suspend clusters or individual particles decreased with time as the particles dissolved. For example, one particle was produced and observed for over 6 min at an average pressure of 15.022 MPa and an average temperature of 5.1 °C. Its sinking rate, determined from the flow required for stabilization, changed from 37.2 to 3.3 mm/s over this time. Particle sinking rates were compared to correlations from the literature for uniform cylindrical objects. Reasonable agreement was observed for short times; however, the observed decrease in sinking velocity with time was greater than that predicted by the correlations for longer times. Particle dissolution rates, based on changes in diameter, were also determined and varied from 5 to . A pseudo-homogeneous mass transfer model was used to predict single-particle dissolution rates. Good agreement was achieved between experimental dissolution data and the modeling results.     

Systematics of salt precipitation in complexes of polyethylene oxide and alkali metal iodides

Conductivity measurements in PEO₃₀MI polymer electrolytes with M=Li, Na, K, Rb, or Cs over the temperature range from about 65 to 200 °C show an increasing tendency for salt precipitation with increasing cation size. The salt precipitation in these complexes upon heating is revealed by the decrease of the dc conductivity starting at a critical temperature T_c. Whereas LiI and NaI complexes do not show precipitation effects, T_c monotonically decreases from about 140 to 65 °C when changing the salt component from KI via RbI to CsI. For the PEO-RbI system, precipitation is further investigated by nuclear magnetic resonance (NMR) and tracer diffusion experiments. NMR analysis unambiguously demonstrates the onset of RbI salt precipitation and the increase of the precipitate fraction with increasing temperature. In diffusion experiments on PEO₃₀RbI with the radiotracers and , the precipitation effect is manifested by anomalous features in the penetration profiles, however, without noticeable changes in their depth range. Combining the resulting tracer diffusion coefficients with the dc conductivity data enables us to assess crucial parameters characterizing ionic transport in PEO₃₀RbI.     

Assessment of a redox alkaline/iron-chelate absorption process for the removal of dilute hydrogen sulfide in air emissions

The oxidative absorption of hydrogen sulfide (H₂S) into a solution of ferric chelate of trans-1,2- diaminocyclohexanetetraacetate (CDTA) was studied in a counter-current laboratory column randomly packed with 15 mm plastic Ralu rings. The present investigation takes concern about the Kraft pulping situation where dilute H₂S concentrations are omnipresent in large-volume gas effluents. A fractional two-level factorial approach was instigated to determine the significance of six operating variables, namely the solution's alkalinity (pH; 8.5-10.5), the liquid mass flow rate (L;1.73-), the solution's ionic strength (I_C;0.01-), the gas mass flow rate (G;0.19-), the inlet H₂S concentration (C_H2S,0;70-430 ppm) and the initial ferric CDTA concentration (C_Fe,0;100 -). Initially, a Plackett-Burman design matrix of seven duplicated experiments revealed that pH is the leading factor controlling the H₂S conversion rate while the ionic strength and ferric CDTA concentration effects remained negligible within the factorial domain. Surface response analysis based on 11 duplicated factorial experiments plus 10 central composite trials revealed that the H₂S conversion significantly increases with liquid flow rate but decreases with growing H₂S load up. Further examination about the influence of ferric CDTA on H₂S absorption rate was set up over a broader concentration range (C_Fe,0;0- at pH of 9.5 and 10.5. It showed good potential at as H₂S conversion increased by a significant 25% for both pH values in comparison to pure alkaline solutions containing no ferric CDTA.     

Recent advances in biomolecular process intensification

Escherichia coli has been the most popular cellular biofactory for the production of many biomolecules including recombinant proteins whose bioactivities are not dependent on complicated post-translational modifications such as glycosylation. Despite many advantages of protein production using E. coli, the formation of insoluble inclusion bodies (IBs) poses a major challenge to harnessing E. coli as a host of choice. Furthermore, the complicated processing steps associated with IB extraction, solubilisation of IBs and refolding of the solubilised-denatured IB proteins, which are typically encountered in the traditional IB processing flowsheet, significantly compromise process economics of IB-route protein production using E. coli. In this paper, many recent advances in innovative IB processing technologies are reviewed with a special emphasis on their potential to contribute to process intensification, which is critical to achieve better process economics in the IB-route recombinant protein production using E. coli.     

Mass transfer across the falling film: Simulations and experiments

Mass transfer across the thin falling film gas-liquid interface is a very important process as in chemical engineering and other fields, and yet there is still a lack of general predictability of the transfer quantity based on basic hydrodynamic parameters and independent of the geometrical setup. In this work, a numerical simulation is carried out for a vertical falling film arrangement. The wave dynamics and the associated mass transfer phenomena are discussed and compared with previous experimental empirical relationships. Based on the validity of the simulated results for wave parameters, numerical experiments for mass transfer were carried out with the aim of comparing to the empirical relation based on a single hydrodynamic parameter β (the gradient of the vertical fluctuating velocity at the interface) established previously by Law and Khoo [2002. Transport across a turbulent gas-liquid interface. A.I.Ch.E. Journal 48(9), 1856-1868.] and Xu et al. [2006. Mass transfer across the turbulence gas-water interface. A.I.Ch.E. Journal 52, 3363-3374] with various non-falling film experiments. Separately, experiments in an inclined plate thin falling film apparatus were carried out to determine the β distribution and associated mass transfer. It is found that there is reasonable concurrence with the mentioned empirical relation, hence suggesting the general applicability of β characterizing the scalar transport across the gas-liquid interface independent of the means of turbulence generation.     

A multi-scale approach for CFD calculations of gas-liquid flow within large size column equipped with structured packing

This work has been carried out in the framework of post-combustion CO₂ capture process development. Considering the huge amount of gases to be treated and the constraints in terms of pressure drop, it appears that the absorption column will be equipped with high efficiency high capacity packings such as structured packings. The present paper focuses on the CFD modellisation of the two-phase flow within this complex geometry. For limited computational resources reasons, it is presently impossible to run computations at large scales taking into account the gas-liquid interaction and the real geometry of the packing and original approaches must be developed. In the present work, a multi-scale approach is proposed. It first considers liquid-wall and liquid-gas interaction at small scale via two-phase flow calculations using the VOF method. Second, the latter results are used in three-dimensional calculations run at a meso-scale corresponding to a periodic element representative of the real packing geometry. Last, those results are further used at large scale in three-dimensional calculations with a geometry corresponding to a complete column. Results are compared with experimental data and with other CFD simulations in terms of liquid hold-up, pressure drop and unit operation. Some suggestions are made for further development.     

Dynamic modeling and simulation of absorption of carbon dioxide into seawater

In order to elucidate the dynamic performance of the CO₂ ocean disposal process, effects of operating parameters, such as gas flow rate, salinity and temperature, on the absorption of CO₂ into seawater were examined. The rate-based model consisting of the rates of chemical reaction and gas-liquid mass transfer was developed for simulating dynamic process of CO₂ ocean disposal. In modeling, non-ideal mixing characteristics in the gas and liquid phases are described using a tanks-in-series model with backflow. Experiments were performed to verify dynamic CO₂ absorption prediction capability of the proposed model in a cylindrical bubble column. The operation was batch and continuous with respect to liquid phase and gas phase, respectively. Experimental results indicate that the CO₂ gas injection rate increased the absorption rate but the increase in salinity concentration caused inhibition of the absorption of CO₂. The proposed model could describe the present experimental results for the dynamic changes and the steady-state values of dissolved CO₂ concentration and hydrogen ion concentration. The proposed model might effectively handle the prediction of the absorption of CO₂ into seawater in the CO₂ ocean disposal.     

Absorption of carbon dioxide into aqueous blends of 2-amino-2-methyl-1-propanol and monoethanolamine

This work presents an investigation of CO₂ absorption into aqueous blends of 2-amino-2-methyl-1-propanol (AMP) and monoethanolamine (MEA). The acid gas mass transfer has been modeled using equilibrium-mass transfer-kinetics-based combined model to describe CO₂ absorption into the amine blends according to Higbie's penetration theory. The effect of contact time and relative amine concentration on the rate of absorption and enhancement factor were studied by absorption experiment in a wetted wall column at atmospheric pressure. The model was used to estimate the rate coefficient of the reaction between CO₂ and monoethanolamine at 313 K from experimentally measured absorption rates. A rigorous parametric sensitivity test has been done to identify the key systems’ parameters and quantify their effects on the mass transfer using the mathematical model developed in this work. The model predictions have been found to be in good agreement with the experimental rates of absorption of CO₂ into (AMP+MEA+H₂O).     

Gas mass transfer to AOT-based microemulsions

The present paper analyses the gas/liquid mass transfer process employing carbon dioxide as gas phase and ternary water in oil microemulsions as absorbent liquid phases. The liquid phases were obtained by a direct mixing of water, 2,2,4-trimethylpentane and sodium bis(2-ethylhexyl)sulfosuccinate (Aerosol OT). The characteristics of the microemulsions employed as liquid phase have been analysed to interpret the experimental results observed in the absorption process. More specifically, they have been analysed in relation to the percolation phenomenon and the effects produced by this phenomenon upon the different physical properties. Characteristic results have been observed for the gas/liquid mass transfer using microemulsions, because ternary microemulsions with high viscosity values in relation to pure water show a faster absorption process than the carbon dioxide/water system. This characteristic behaviour has been explained on the basis of the microemulsions internal dynamics.     

Kinetics of absorption of carbon dioxide into aqueous blends of 2-(1-piperazinyl)-ethylamine and N-methyldiethanolamine

The kinetics absorption of CO₂ into aqueous blends of 2-(1-piperazinyl)-ethylamine (PZEA) and N-methyldiethanolamine (MDEA) were studied at 303, 313, and 323 K using a wetted wall column absorber. The PZEA concentrations in the blends with MDEA varied from 0 to to see the effect of PZEA as an activator in the blends with two different total amine concentrations (1.0 and ). Based on the pseudo-first-order condition for the CO₂ absorption, the overall second-order reaction rate constants were determined from the kinetic measurements. The kinetic rate parameters were calculated and presented at each experimental condition.     

The effect of specific surface area on the activity of nano-scale ceria catalysts for methanol decomposition with and without steam at SOFC operating temperatures

Nano-particulate high surface area CeO₂ was found to have a useful methanol decomposition activity producing H₂, CO, CO₂, and a small amount of CH₄ without the presence of steam being required under solid oxide fuel cell temperatures, 700-1000 °C. The catalyst provides high resistance toward carbon deposition even when no steam is present in the feed. It was observed that the conversion of methanol was close to 100% at 850 °C, and no carbon deposition was detected from the temperature programmed oxidation measurement.The reactivity toward methanol decomposition for CeO₂ is due to the redox property of this material. During the decomposition process, the gas-solid reactions between the gaseous components, which are homogeneously generated from the methanol decomposition (i.e., CH₄, CO₂, CO, H₂O, and H₂), and the lattice oxygen on ceria surface take place. The reactions of adsorbed surface hydrocarbons with the lattice oxygen ( can produce synthesis gas (CO and H₂) and also prevent the formation of carbon species from hydrocarbons decomposition reaction (C_nH_m⇔nC+m/2H₂). V_O^·· denotes an oxygen vacancy with an effective charge 2⁺. Moreover, the formation of carbon via Boudouard reaction (2CO⇔CO₂+C) is also reduced by the gas-solid reaction of carbon monoxide with the lattice oxygen .At steady state, the rate of methanol decomposition over high surface area CeO₂ was considerably higher than that over low surface area CeO₂ due to the significantly higher oxygen storage capacity of high surface area CeO₂, which also results in the high resistance toward carbon deposition for this material. In particular, it was observed that the methanol decomposition rate is proportional to the methanol partial pressure but independent of the steam partial pressure at 700-800 °C. The addition of hydrogen to the inlet stream was found to have a significant inhibitory effect on the rate of methanol decomposition.     

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues

Robust MIMO PID controllers tuning based on complex/real ratio of the characteristic matrix eigenvalues is proposed. It is showed that this tuning criterion is equivalent to H_∞ optimal control. Under the proposed criterion, the tuning problem is stated as an optimization problem, in which the complex/real ratio of the characteristic matrix eigenvalues, a Lyapunov quadratic index, and the spectral abscissa were simultaneously minimized. Proposed criterion was applied to the multivariate controls of a distillation column, and a non-linear chemical reactor, both reported in the literature.