Analysis and interpretation of residence time distribution experimental curves in FM01-LC reactor using axial dispersion and plug dispersion exchange models with closed-closed boundary conditions

The liquid phase mixing flow pattern at low (20 < Re < 120) and intermediate liquid flow rate (120 < Re < 400) was studied by means of residence time distribution (RTD) experimental curve in an up-flow Filter Press electrochemical reactor (FM01-LC) bench scale. For this purpose, a plastic turbulence promoter was used with stainless-steel and platinised titanium structural meshes as electrodes in channel configuration. To visualize and determine the mixing flow pattern in the liquid phase, the stimulus-response technique was employed using dextran blue (D_M = 1.058 × 10⁻¹¹ m² s⁻¹, 25 °C, in water) as model tracer. A theoretical analysis and approximation RTD experimental curves with axial dispersion model (ADM) and plug dispersion exchange model (PDE), with “closed-closed vessel” boundary conditions were used in order to establish a better approximation of the axial dispersion, stagnant zones, channelling and by-pass (preference flow) effects present at low and intermediate Re. RTD curves show that the liquid flow pattern in the FM01-LC deviates considerably from axial dispersion model at low Re, where the FM01-LC exhibits large channelling, stagnant zones, and dead zone. The PDE model represents fairly this deviation from ideal flow (less dead zone).     

Liquid backmixing in oscillatory flow through a periodically constricted meso-tube

This paper deals with the measurement and modelling of axial liquid dispersion in a 4.5 mm internal diameter tube provided with smooth-periodic constrictions (meso-tube) in steady and oscillatory flow conditions. The residence time distribution (RTD) in the meso-tube was monitored for a range of fluid oscillation frequency (f) and amplitude (x₀) at laminar flow. The RTD response was modelled with three hydrodynamic models: (i) tanks-in-series, (ii) tanks-in-series with backflow and (iii) plug flow with axial dispersion. The steady flow through the meso-tube at flow rates up to 21.30 ml/min resulted in broad RTDs, mainly due to the parabolic velocity profile. The use of fluid oscillations allowed a fine-control of the axial liquid dispersion in the meso-tube due to generation of secondary flow in the regions between the constrictions. The axial dispersion coefficient D was reduced by up to 13-fold in comparison with the steady flow situation. Values of x₀ ≤ 1 mm and f = 10 Hz generally resulted in a maximum reduction in axial dispersion through, therefore maximum improvements in RTD. The tanks-in-series model was generally not capable of predicting RTDs in the meso-tube. The potential of this platform for the continuous, sustainable production of added-value products is herein demonstrated.     

Residence time distribution in a packed bed bioreactor containing porous glass particles: Influence of the presence of immobilized cells

An experimental investigation of the liquid phase residence time distribution (RTD) in a packed bed bioreactor containing porous glass particles is presented. For Re < 1, intraparticle forced convection is negligible and only diffusion, characterized by an effective diffusion coefficient, must be considered to describe the mass transfer process between the extraparticle and the intraparticle fluid phase. For Re > 1, the mass transfer rate becomes dependent on the liquid flow rate, indicating the existence of intraparticle convection. A model including axially dispersed flow for the external fluid phase and an ‘apparent’ effective diffusivity that combines diffusion and convection, predicts experimental RTD data satisfactorily. Yeast cells immobilized inside the porous glass beads did not affect the mass transfer rate at low biomass loading. At high biomass loading (0·02 g yeast cells g^?1 carrier), the mass transfer rate between the extraparticle and intraparticle fluid phase was significantly decreased. Comparison of the RTD data from experimets performed in the presence and absence of cells in the external fluid phase revealed that the mass transfer rate is influenced by the cells immobilized inside the porous particles and not by the cells present in the external fluid phase.     

Electrochemical incineration of p-cresol and o-cresol in the filter-press-type FM01-LC electrochemical cell using BDD electrodes in sulfate media at pH 0

This work shows a comparative study of the incineration of 2-mM p-cresol and o-cresol in 1 M-H₂SO₄ in aqueous media. Microelectrolysis studies indicated that both the p-cresol and o-cresol oxidation were carried out via hydroxyl radicals (OH) formed by water oxidation in the boron-doped diamonds (BDD)-H₂O-H₂SO₄-p-cresol and o-cresol interface. In both cases, the potential and current density ranges, where great amounts of OH are formed, were between 2.3 V ≤ E ≤ 2.75 V versus SHE and J = 10 mA cm⁻². Electrolyses in an undivided FM01-LC reactor were performed at different Reynolds values 27,129 ≤ Re ≤ 42,631, and at J = 10 mA cm⁻². For p-cresol and o-cresol, the rate of degradation was slow, however it increases slightly as a function of the Re, indicating that the oxidation involves a complex pathway; current efficiency also rises as a function of the Re. For p-cresol, the mineralization at Re = 42,631 reached 90%, with 71% current efficiency and an energy consumption of 7.84 kWh m⁻³; whereas o-cresol was mineralized to 84%, with 67% current efficiency and an energy consumption of 6.56 kWh m⁻³. The results obtained in this work demonstrated that o-cresol is more recalcitrant than p-cresol.     

Residence time distributions in short tubular vessels

The results of an experimental study of the influence of vessel dimensions and fluid velocity on residence time distributions (RTD's) are presented. Length to diameter ratio (L/D) exerts the major influence on the RTD for the range of sizes and velocities studied. At L/D ≤ 2.6, the RTD resembles the response of a well stirred vessel with by-passing to a pulse signal. Both Reynolds No. (N_Re) and nozzle to vessel diameter ratio (d/D) effect the RTD. At L/D ≥ 5.2, the RTD resembles the response of stirred tanks in series to a pulse. N_Re and d/D do not effect the RTD and can be neglected for scale-up. The second and third moments of the RTD's and parameters of a finite stage model fitted to the RTD relate qualitatively to L/D, d/D and N_Re, but neither the moments or the particular finite stage model used are satisfactory for quantitative correlations.     

Continuous screening of base-catalysed biodiesel production using New designs of mesoscale oscillatory baffled reactors

Base-catalysed biodiesel production was continuously screened using new designs of mesoscale oscillatory baffled reactors. Experiments were carried out at very low flow rates, less than 2 ml/min, which would be in the laminar flow regime in non oscillatory, steady state. Initially central disc baffles and helically wound wires were used, but provided insufficient mixing at this scale as demonstrated by glycerol settling. A new design of sharp-edged, helically baffled reactor was developed specifically for this application, which exhibited homogeneous mixing in the two-phase liquid reaction even at these low flow rates and low oscillatory Reynolds numbers. Methyl ester (biodiesel) was produced at a consistent quality and there were clear responses to variations in input conditions. A clear step-change between various steady state molar ratios of methanol to oil and dynamic screening was observed in these mesoscale oscillatory baffled reactors. Rapid screening technique such as this has the potential to significantly reduce process development, operating costs and environmental impact.     

A simplified correlation for fixed bed pressure drop

An experimental study was conducted on the pressure drop characteristics of a variety of vertical packed beds in turbulent flow of air. The materials of different particle diameter, D_p, with a range of sphericity Φ, 0.55 ≤ Φ ≤ 1.00 were used in random loose packing to produce beds of different lengths, L, with a range of porosity, ε, 0.36 ≤ ε ≤ 0.56. In the covered test cases the cross-sectional velocity distribution at the exit plane of the packed beds and the pressure drop ΔP_Bed were measured in a particle Reynolds number range of Re_p, 675 ≤ Re_p ≤ 7772. The particular emphasis of the study was given to determine the influence of ε, Φ, D_p, L, Re_p on ΔP_Bed. In this respect the measurements of ΔP_Bed were compared with the well-known Ergun's Equation and the data were expressed in terms of correlations through introduced dimensionless parameters of pressure coefficient, ΔP^? and exit Reynolds number Re_exit. The proposed correlations of ΔP^? = ΔP^?(εRe_pD_p / L) and Re_exit = Re_exit(Re_pD_p / L) are found to be appropriate for the determination of ΔP_Bed and mean exit velocity, U, respectively with an acceptable fit of experimental data in an error margin less than ± 20%. The methodology is presented in this paper as an alternative approach to the available literature on packed beds.     

Smart RTD for multiphase flow systems

A relatively new concept is presented for evaluation of the fluid age distribution a = a(x,t) within the interior of an apparatus. In the standard RTD approach, the tracer study is performed and the residence time distribution is obtained. In the new approach denoted as SRTD, the fluid age is considered as the field quantity and the governing equation is formulated for its spatio-temporal distribution within the flow domain. There are only few studies devoted to this alternative approach, which typically concern only the single-phase flow systems. In this contribution we investigate its applicability also to multiphase systems. In the case of a bubble column, both the RTD and SRTD concepts are employed and discussed. The results are calculated numerically and compared with the experimental observations.     

Improving the dynamic performance of continuous-flow mixing of pseudoplastic fluids possessing yield stress using Maxblend impeller

The strategic approach of this article is to characterize the continuous-flow mixing of pseudoplastic fluids possessing yield stress in a stirred reactor with the Maxblend impeller. Dynamic experiments were carried out through the frequency-modulated random binary input of a brine solution to determine the extent of non-ideal flows. Mixing quality was determined on the basis of the extent of channeling and fully mixed volume. The effects of important parameters such as impeller speed (25–500 rpm), absence of baffles, fluid rheology (0.5–1.5%), fluid flow rate (3.20–14.17 L min⁻¹), and the locations of inlet/outlet on the dynamic performance of the continuous-flow mixing vessel were explored. The performance of the Maxblend impeller was then compared to the performances of various types of impellers such as close-clearance (an anchor), axial-flow (a Lightnin A320), and radial-flow (a Scaba 6SRGT) impellers. It was found when the channeling approached zero and the fully mixed volume approached the total fluid volume in the vessel, the power drawn by the A320 impeller and the Scaba impeller were about 2.9 and 4.3 times greater than that of the Maxblend impeller. Thus, the Maxblend impeller was able to drastically improve the performance of continuous-flow mixing with huge power savings. The mixing quality was further improved by optimizing the impeller speed, decreasing the fluid flow rate, decreasing the fluid concentration, and using bottom inlet- top outlet configuration. The flow non-ideality of the mixing system increased in the absence of the baffles. Thus, better mixing quality and more energy savings can be achieved by employing the findings of this study.     

RTD studies in trickle bed reactors packed with porous particles

The residence time distribution (RTD) for liquid phase in a trickle bed reactor (TBR) has been experimentally studied for air-water system. Experiments were performed in a 15.2 cm diameter column using commerical alumina extrudates with D/d_p ratio equal to 75 to eliminate the radial flow differences. The range of liquid and gas flow rates covered was 3.76 < Re_L < 9.3 and 0 < Re_G < 2.92. The axial dispersion model was used to compute axial dispersion coefficient. The effect of liquid and gas flow rates on total liquid holdup and axial dispersion was investigated. The total liquid holdup has been correlated to liquid and gas flow rates.     

Electrochemical synthesis and characterization of mixed molybdenum-rhenium oxides

The electrodeposition of Mo_xRe_1−xO_y films (0.6 ≤ x ≤ 1) on indium-tin oxide (ITO) coated glass substrates from acidic peroxo-polymolybdo-perrhenate solutions is described. Trends in film growth were established as a function of potential from +0.4 V to −0.7 V vs Ag/AgCl by analyzing the composition and stoichiometry of the deposit using inductively coupled plasma mass spectrometry (ICPMS) and X-ray photoelectron spectroscopy (XPS). These experiments show that the concentration of rhenium increases linearly with the deposition potential and that the deposits are mixed-valent containing up to five different metal oxidation states (i.e., Mo^IV, Mo^V, Mo^VI, Re⁰, Re^IV). Electroanalytical techniques were used to explore the deposition mechanism, including chronocoulometry, cyclic voltammetry, spectroelectrochemistry, and electrochemical quartz crystal nanogravimetry (EQCN). At potentials positive to −0.26 V, perrhenate (Re^VIIO₄⁻) behaves as a redox mediator to accelerate the deposition of a mixed-valent molybdenum oxide, but at more negative potentials mixed molybdenum-rhenium oxides are produced.     

Modelling of Self-Induced Oscillations in the Mixing Head of a RIM Machine

In this paper, the self-induced oscillations in the mixing head of a RIM machine were modelled. An analytical and simple correlation was derived between the Strouhal number and the averaged pressure drop along the amplitude of the oscillation in the mixing chamber. This correlation theoretically identified that the frequency of the oscillations could be well correlated by the jet Reynolds number, Re_d, and the dimensionless distance between the two jets as proposed by Denshchikov et al., Fluid Dyn. 3 , 460-462 (1983). The flow field dynamics in the mixing head was simulated successfully by Fluent and the computed pressure fluctuations were used to calculate the frequencies of the oscillations in the mixing head. The calculated Strouhal numbers are in good agreement with the dominant frequency from the power spectra of the measured velocity component u_x (Santos, 2003). Finally, the effect of Re_d and Froude number, Fr, on the Strouhal number was investigated in the impingement region. The average Strouhal number showed a decrease with the Reynolds numbers, due to the increasing randomness of flow field in the impingement region. It was also found that the operations at lower values of Fr presented an increasing stability up to the point where the system is unable to present dynamic evolution. The model in this paper provides a theoretical starting point towards understanding of the quantities of the oscillatory flow in the mixing head, as well as a numerical approach to evaluate the dominant frequency in the mixing chamber.     

Numerical investigation of the hydrodynamics of split‐and‐recombination and multilamination microreactors

The hydrodynamics and residence time distribution (RTD) of two microreactors based on the split‐and‐recombination (SAR), and multilamination mixing mechanisms, respectively were investigated. It was found that the design of the distribution manifolds of the SAR mechanism produces an unbalanced flow distribution. For feeding ratios different than one, bypassing and recirculation occur within the SAR manifolds. For equal flow rates the SAR flow behavior can be accurately described by the pure convection model. The manifold used in the multilamination microreactor achieves a homogeneous distribution of flow and its interdigital mixing structure generates an alternated pattern of fluid layers which is maintained for Re < 140. After this point the ordered arrangement is broken and two large segregated zones are formed. In the absence of molecular diffusion both microreactors reach limiting values of scale and intensity of segregation that were found to be independent of the energy applied to the system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 988–1001, 2013     

Effect of blockage on drag and heat transfer from a single sphere and an in-line array of three spheres

The effect of blockage ratio on the steady flow and heat transfer characteristics of incompressible fluid over a sphere and an in-line array of three spheres placed at the axis of a tube has been investigated numerically. The Navier-Stokes and thermal energy equations have been solved numerically using FLUENT for the following ranges of parameters: for a single sphere, 2 ≤ β ≤ 10; 1 ≤ Re ≤ 100; for the three-sphere system, for two values of sphere-to-sphere distance, namely s = 2 and 4. All computations were carried out for two values of the Prandtl number, i.e., 0.74 and 7, corresponding to the flow of air and water respectively. Extensive results on streamline patterns, wake characteristics (angle of separation and recirculation length), drag coefficient and Nusselt number are presented to elucidate the interplay between the blockage and the Reynolds number and their influence on drag and Nusselt number.     

Reduced power consumption compared to a traditional stirred tank reactor (STR) for enzymatic saccharification of alpha-cellulose using oscillatory baffled reactor (OBR) technology

Enzymatic saccharification of pure α-cellulose was conducted in oscillatory baffled (OBR) and stirred tank (STR) reactors over a range of mixing intensities requiring power densities (P/V) from 0 to 250 Watts per cubic metre (W/m³). Both reactor designs produced similar saccharification conversion rates at zero mixing. Conversion increased with increasing mixing intensity. The maximum conversion rate occurred at an oscillatory Reynolds number (Re_o) of 600 in the OBR and at an impeller speed of between 185 and 350 rpm in the STR. The OBR was able to achieve a maximum conversion rate at a much lower power density (2.36 W/m³) than the STR (37.2–250 W/m³). The OBR demonstrated a 94–99% decrease in the required power density to achieve maximum conversion rates and showed a 12% increase in glucose production after 24 h at 2.36 W/m³.     

Residence Time and Concentration Distribution in a Kenics Static Mixer

Static mixers, often referred to as motionless mixers, are in-line mixing devices that consist of mixing elements inserted into a length of pipe. Most of the experimental works in this field have concentrated on establishing design guidelines and pressure drop correlations. Due to experimental difficulties, few articles have been published on the investigation of the flow and mixing mechanisms. In this work, a Kenics KMX static mixer was utilized to study concentration and residence time distribution (RTD) and effect of Reynolds number on mixing. The static mixer had six mixing elements arranged in-line along the length of the tube, and the angle between two neighboring elements was 90°. The length of the mixer was 0.98 m with internal and external diameters of 5.0 cm and 6.0 cm, respectively. The main continuous fluid was water, and NaCl solution was used as a tracer. All experiments were conducted with three replications at three Reynolds numbers, Re = 1188.71, 1584.95, and 1981.19. A dispersion model was used to model the RTD data. The experimental results were compared with the model results and reasonable agreement was achieved.     

VK管内锥形挡板结构最优化的计算机辅助设计

采用有限差分法求解二维流动的控制方程，计算出二维流场的径向混合、速度分布及停留时间分布，从理论上阐明了消除死角的方法。对挡板倾斜角、相邻两挡板的间距及开孔率的最优化进行了具体讨论。     

CFD study of effect of inclination angle on transport and reaction in hollow cylinder catalysts

This work examines how the angle to the flow of a 1-hole catalyst particle impacts its catalytic performance. Computational fluid dynamics (CFD) simulations are reported for flow past a single equilateral hollow cylinder under methane steam reforming conditions, for 1000 ≤ Re ≤ 10,000, and for approach angles from 0° to 90°. The simulations show that at 0°, the flat end of the particle causes separation and formation of a large wake region, while a jet-like flow results through the center hole. These flows result in a pattern of vortices behind the particle, with reverse flow along the particle length. These features are distorted as the approach angle increases, with boundary-layer formation on the upstream side of the particle and a complex vortex pattern on the downstream side. The flow through the particle hole decreases with incidence angle. Surface heat and mass fluxes decrease for the flat ends and the inside curved surface, and increase on the outside curved surface. Both reactant consumption and energy uptake show maxima as a result of the changes in transfer rates through the various particle surfaces, caused by the incident flow.     

The confined impeller stirred tank (CIST): A bench scale testing device for specification of local mixing conditions required in large scale vessels

A new stirred tank geometry, the confined impeller stirred tank (CIST), was designed to provide repeatable testing of the effect of mixing on the performance of chemical additives at the bench scale. The CIST (T = 0.076 m, H = 3T) is filled with five or six impellers. Three impeller geometries were tested: A310, Rushton and Intermig. This paper presents the following hydrodynamic characteristics of the CIST: power number, flow number, momentum number, velocity profiles at different locations in the tank and the transition point from fully turbulent to transitional flow. Based on the scaled velocity profiles, the CIST was able to keep the flow turbulent at Re < 2000 for Rushton turbines and 3200 for Intermigs. The ratio ?_max/?_average was lower for the CIST than for a conventional stirred tank, indicating that the energy dissipation is more uniformly distributed in the CIST. The CIST consistently maintains turbulent flow down to a Reynolds number 10× smaller than that needed in a conventional stirred tank.     

Volumetric power consumption in baffled shake flasks

For the cultivation of microorganisms, baffled shake flasks are employed when increased levels of oxygenation and mixing are required. Their use has been discouraged, however, due to the danger of a wetted sterile plug and the lower reproducibility of the experimental results. Consequently, there are only few studies dealing with this type of shaken bioreactor, and there is practically no characterization of this reactor type from a chemical engineering viewpoint. Therefore, a systematic study to elaborate the basic characteristics of the volumetric power consumption and the unfavorable out-of-phase phenomenon in baffled shake flasks is undertaken. A new type of measuring device was developed to measure the volumetric power consumption in a single shake flask. The volumetric power consumption was found to increase with increasing shaking frequency and with decreasing filling volume. Further, an independency of power consumption on the shaking diameter was observed as long as the fluid motion is in-phase. A comparison of two different baffle geometries demonstrated that deeper baffles cause more resistance to fluid flow. For the commonly employed shaking diameter of 25 mm, the investigated baffled flask types may not be operated in the in-phase state. A larger shaking diameter must therefore be employed. It was found for the first time that for all in-phase conditions, the dimensionless Newton number Ne^′ is independent of the Reynolds number Re. Power consumption in baffled shake flasks may therefore be described by a characteristic Ne^′ only dependent on the filling volume V_L and the flask type. Even though there are quantitative differences, a qualitative similarity between fluid flow in stirred tanks and shake flasks has been demonstrated.