Residence Time Distribution Measurements Research Articles

Mechanistic modeling and simulation of grinding iron ore pellet feed in pilot and industrial-scale ball mills

Various approaches have been used over the years to describe quantitatively ball milling, with different levels of success. The present work presents the application and validation of a mechanistic model to describe ball milling of iron ore pellet feed. The approach started by estimating selected parameters describing the ore characteristics by back-calculation from batch grinding tests, followed by validation of the model in batch grinding as well as continuous open-circuit ball milling at a pilot-scale operating at a variety of solids concentrations, both with overflow and grate discharge. An industrial ball mill was then laser scanned and surveyed, including measurements of residence time distribution. Simulations using the discrete element method were then conducted and the model was applied to simulate closed-circuit operation, resulting in good agreement between measured and predicted size distributions and circulating load ratio.

Heat Transfer and Residence Time Distribution in Plug Flow Continuous Oscillatory Baffled Crystallizers.

Heat transfer coefficients in a continuous oscillatory baffled crystallizer (COBC) with a nominal internal diameter of 15 mm have been determined as a function of flow and oscillatory conditions typically used under processing conditions. Residence time distribution measurements show a near-plug flow with high Peclet numbers on the order of 100–1000 s, although there was significant oscillation damping in longer COBC setups. Very rapid heat transfer was found under typical conditions, with overall heat transfer coefficients on the order of 100 s W m–2 K–1. Furthermore, poor mixing in the COBC cooling jacket was observed when lower jacket flow rates were implemented in an attempt to decrease the rate of heat transfer in order to achieve more gradual temperature profile along the crystallizer length. Utilizing the experimentally determined overall heat transfer coefficients, a theoretical case study is presented to investigate the effects of the heat transfer rate on temperature and supersaturation profiles and to highlight potential fouling issues during a continuous plug flow cooling crystallization.

Kinetic study of phenol hydroxylation by H2O2 in 3D Fe/SiC honeycomb monolithic reactors: Enabling the sustainable production of dihydroxybenzenes

The chemical kinetics of phenol hydroxylation by hydrogen peroxide (H2O2) to produce dihydroxybenzenes was studied using a 3D printed monolithic reactor. The monoliths were manufactured by the Robocasting technique. They consisted on honeycomb-structured Fe/SiC nanoparticles (13.5 mm in diameter and 14.8 mm in length) with triangle cell geometry and staggered interconnected channels (71 cells per cm2). The isothermal reactor was constituted by three stacked monoliths and was operated as an ideal plug flow reactor, according to the measured residence time distribution. The hydroxylation experiments were carried out at CPHENOL,0 = 0.33 M, phenol:H2O2 molar ratio 1:1, τ(space time) = 0–254 g h L-1, T = 80, 85 and 90 °C and water as unique solvent.Experimental results showed no mass transfer limitations. The best fits were obtained for H2O2 decomposition with a Langmuir-Hinshelwood-Hougen-Watson kinetic model and for phenol hydroxylation, as well as, catechol and hydroquinone production, with an Eley-Rideal kinetic model. The hydroxylation reaction mechanism underling to the developed model involved three elementary reactions: (1) adsorption of H2O2 molecules on the iron active sites, (2) chemical surface H2O2 decomposition into the hydroxyl radical species, and (3) reaction between adsorbed radical species and phenol in solution leading to the dihydroxybenzene formation and freeing the iron catalytic active sites (rds).This work contributes to the implementation of outstanding 3D Fe/SiC honeycomb monolithic reactors, with a dihydroxybenzene selectivity above 99% at 80 °C, for the sustainable production of hydroxylated aromatics.

A new method for continuous measurement of residence time distribution in spray drying

The residence time distribution of particles is one of the most important parameters during spray drying, since it directly impacts the thermal damage of a potential product. Due to insufficiencies of previous approaches for measuring the residence time distribution, a new method for continuous measurements was developed. This method simultaneously allows the determination of the residence time distribution of individual particle size fractions. The impact of air mass flow rate and particle size on the residence time distribution during spray drying was investigated. The mean particle residence time decreased with increasing air mass flow rate from 15.8 s for 190 kg/h, to 13.0 s for 210 kg/h and to 7.1 s for 230 kg/h, which is significantly shorter than the mean air residence time of 35.3 s, 31.9 s and 29.1 s, respectively. The mean particle residence time decreased with increasing particle size, with this effect being more pronounced for lower air flow rates. If the particle size is smaller than 105 µm, the presented technique can be transferred to any kind of single-stage spray dryer.

Residence time distribution study in a pilot-scale liquid phase catalytic exchange (LPCE) column packed with a mixture of hydrophobic and hydrophilic catalysts

Residence time distribution (RTD) measurements were carried out in a packed bed column designed for exchange of hydrogen isotopes. The main objective of the study was to characterize the liquid phase mixing under various processes and operating conditions. The packed bed was composed of a mixture of two different types of catalytic packing materials, i.e., a hydrophobic material and a hydrophilic material. Technitium-99m (99mTc) as sodium pertechnetate was used as a radiotracer for RTD measurements. From the measured RTD curves, mean residence times (MRTs), liquid holdup and degree of mixing of liquid phase were evaluated. An axial dispersion model exchange with stagnant zones was used to simulate the measured RTD curves. The results of model simulation showed that volume fraction of hydrophobic to hydrophilic packing and gas/liquid superficial velocities affect the liquid holdup, bed pressure drop and liquid phase dispersion/mixing characteristics. The results of the present study will help to screen packing, optimize the volume of the packing fractions, design and construct the catalyst and optimize the operating conditions for scale up of the isotope exchange process.

Electrochemical Residence Time Distribution As a Diagnostic Tool for Electrodes in Redox Flow Batteries

Redox flow batteries (RFBs) are a burgeoning technology for use in grid-scale energy storage; however, broad adoption is stymied by large capital costs.1,2 Housed within the reactor, porous electrodes are critical components to system performance and cost, as they provide surfaces for redox reactions, void space for electrolyte passage, and conductive solids for electron transport.3 Carbon papers, cloths, and felts are commonly used in RFBs, despite their tailored design and function towards the governing physics as fuel cell gas diffusion layers. Consequently, when coupled with geometrically varying flow field structures, these carbon substrates underperform in RFBs with forced liquid advection, resulting in uneven flow and current distributions. These inhomogeneities lead to inefficient operation, motivating the investigation of electrode morphologies and flow conditions that enable more uniform reactions throughout the reactor.One promising approach to assessing electrode performance is the measurement of residence time distribution, a traditional chemical reactor efficacy metric for quantifying flow pathways and hydraulic short-circuiting.4 Currently, most residence time estimations in flow cells assess the fluid dynamic spreading of a known solution leaving a reactor, using both experiments and computational fluid dynamics.5 However, in the absence of complementary electrochemical performance measurements, hydrodynamic calculations can only serve as a proxy for possible surface accessibility. Additionally, sole measurements of the reactor effluent are susceptible to added variance, which can obscure experimental results6 as opposed to spatial quantities within the reactor.Herein, we present an electrochemical method to measure spatially averaged electrochemical residence times in a small-scale flow cell. Using two disparate flow fields each with carbon cloth and paper electrodes, we compare electrochemical residence time responses to conventional steady-state polarization measurements to capture performance scaling relationships. Further, we present complementary modeling approaches, depicting multi-scale residence time calculations to contextualize the experimental values. Together, these approaches have the potential to elucidate the effects of electrode microstructure and flow field selection on cell-level fluid dynamics and electrochemical performance, which, in turn, may be used to advance RFB reactor design.AcknowledgmentsThis work was funded by the Joint Center for Energy Storage Research, an Energy Innovation Hub of the U.S. Department of Energy, Office of Science, Basic Energy (De-AC02-06CH11357). K.M.T. recognizes additional support from the U.S. NSF Graduate Research Fellowship (1122374).References A. Z. Weber et al., J. Appl. Electrochem., 41, 1137 (2011).C. Minke, U. Kunz, and T. Turek, J. Power Sources, 361, 105–114 (2017).K. J. Kim et al., J. Mater. Chem. A, 3, 16913–16933 (2015).A. E. Rodrigues, Chem. Eng. Sci., 230, 116188 (2021).G. Aparicio-Mauricio, F. A. Rodríguez, J. J. H. Pijpers, M. R. Cruz-Díaz, and E. P. Rivero, J. Energy Storage, 29, 101337 (2020).A. Bérard, B. Blais, and G. S. Patience, Can. J. Chem. Eng., 98, 848–867 (2020).

Parametric Study of Residence Time Distributions and Granulation Kinetics as a Basis for Process Modeling of Twin-Screw Wet Granulation.

Twin-screw wet granulation is a crucial unit operation in shifting from pharmaceutical batch to continuous processes, but granulation kinetics as well as residence times are yet poorly understood. Experimental findings are highly dependent on screw configuration as well as formulation, and thus have limited universal validity. In this study, an experimental design with a repetitive screw setup was conducted to measure the effect of specific feed load (SFL), liquid-to-solid ratio (L/S), and inclusion of a distributive feed screw on particle size distribution (PSD) and shape as well as residence time distribution of a hydrophilic lactose/microcrystalline cellulose based formulation. An intermediate sampling point was obtained by changing inlet ports along the screw axis. Camera-based particle size analysis (QICPIC) indicated no significant change of PSD between the first and second kneading section, except for low L/S and low SFL where fines increase. Mean residence time was approximated as a bilinear fit of L/S and SFL. Moreover, large mass flow pulsations were observed by continuous camera measurements of residence time distribution and correlated to hold-up of the twin-screw granulator. These findings indicate fast granulation kinetics and process instabilities for high mean residence times, questioning current standards of two kneading compartments for wet granulation. The present study further underlines the necessity of developing a multiscale simulation approach including particle dynamics in the future.

A counter-current flow micro-packed-bed DBD plasmatron for the synthesis of a methylated cobaloxime

An atmospheric, dielectric-barrier discharge µ-plasmatron was designed, fabricated, and applied to synthesize a methylated organometallic complex. The design comprises counter-current flow to packed-bed microstructures to facilitate gas–liquid and plasma–liquid mixing. Micropillars arranged in a staggered configuration served as a porous media for the optimum 2D mixing of components that replenish plasma-liquid interfaces. Longitudinal dispersion was characterized through residence time distribution (RTD) measurements. The experimental RTD data were then described by an axial dispersion model with a time delay parameter. Levenspiel number (lv) indicating the intensity of axial dispersion was estimated in the range of 20.1–374, indicating that a dispersion model should be accounted for in plasma-assisted reaction kinetics development. Stable plasma excitation of methane-helium gas mixtures was observed within the 2D porous media, by in-situ optical emission spectra, while applying an alternating high voltage across the dielectric barrier. This novel technique made it possible to confirm in-situ formations of methyl radicals. Interestingly, the porous media served as a static mixer as no discrete plasma streamers were observed. To investigate its utility, an example homogeneous cobalt catalyst was injected into the µ-plasmatron and methylated. Our findings potentially introduce a new plasma-assisted reactor design and methodology for the synthesis of methylated cobaloxime.

A novel technique for residence time distribution (RTD) measurements in solids unit operations

This work presents a novel technique with fast response for Residence Time Distribution (RTD) measurements in gas-solid unit operations (e.g., fluidized bed reactors). This technique is based on an optical method which eliminates the requirement of knowing the velocity and concentration profiles at the exit section of the system. Experiments were carried out with SiC particles and a phosphorescent pigment used as a tracer. A concentration measurement system was developed to measure the tracer concentration in SiC/pigment mixtures. The corresponding pigment concentrations were evaluated at the bottom of this system using a photomultiplier. The pigment concentration was derived from the integral of the signal intensity received by the photomultiplier. Then, a calibration curve was established which provided the empirical relationship between the integral and pigment concentration. In order to validate this RTD measurement technique, a series of experiments was performed in a bubbling fluidized bed and the effect of the bed height was studied. It was shown that the experimental RTD curves were in good agreement with the theoretical RTD of bubbling fluidized beds. This solids RTD measurement technique can be used to provide a better understanding of the hydrodynamics of complex solids unit operations.

Continuous blending monitored and feedback controlled by machine vision-based PAT tool

In a continuous powder blending process machine vision is utilized as a Process Analytical Technology (PAT) tool. While near-infrared (NIR) and Raman spectroscopy are reliable methods in this field, measurements become challenging when concentrations below 2 w/w% are quantified. However, an active pharmaceutical ingredient (API) with an intense color might be quantified in even lower quantities by images recorded with a digital camera. Riboflavin (RI) was used as a model API with orange color, its Limit of Detection was found to be 0.015 w/w% and the Limit of Quantification was 0.046 w/w% using a calibration based on the pixel value of images. A calibration for in-line measurement of RI concentration was prepared in the range of 0.2−0.45 w/w%, validation with UV/VIS spectrometry showed great accuracy with a relative error of 2.53 %. The developed method was then utilized for a residence time distribution (RTD) measurement in order to characterize the dynamics of the blending process. Lastly, the technique was applied in real-time feedback control of a continuous powder blending process. Machine vision based direct or indirect API concentration determination is a promising and fast method with a great potential for monitoring and control of continuous pharmaceutical processes.

A method for measuring the residence time distribution of particles in a fluidized bed based on digital image analysis

Abstract Traditional methods for measuring the residence time distribution (RTD) of particles in a fluidized bed are complex and time-consuming. To this regard, the present work proposes a new measurement method with remarkable efficiency based on digital image analysis. The dyed tracers are recognized in the images of the samples due to the difference of colors from bed materials. The HSV and the well-known RGB color space were employed to distinguish the tracers. By enhancing the Saturation and the Value in HSV and adjusting the gray range of images, the recognition error is effectively reduced. Then the pixels representing the tracers are distinguished, based on which the concentration of the tracers and RTD are measured. The efficiency, accuracy and repeatability of the method were validated by RTD measurements experiments. The method is also fit for distinguishing the target particles from multi-component systems consisting of particles of different colors.

Choosing the right packing in millipacked bed reactors under single phase gas flow

Packed bed reactors with diameters below 1 cm, millipacked beds hereafter, are often used to test catalysts. The prospect of using these reactors for catalytic kinetic measurements is quite attractive, but it requires a better knowledge of the flow characteristics of these reactors. This study focuses on the main hydrodynamic features of millipacked bed reactors in single phase gas flow. The effects of the bed length, gas velocity, reactor/particle diameter ratio (δ) and the use of fine inert powder as porosity filler are investigated via residence time distribution measurements and reactive tests. When using spherical particles, for values of reactor/particle diameter ratios between 1 < δ < 3, the behavior of the Peclet number, Pe, is not monotonous. Lower values of the Pe number for specific values of δ corresponding to large void spaces between the particles and/or between the particles and the walls, have been observed. For values of δ > 3 higher Pe numbers are observed, in particular at high gas velocities, due to the transition to a more uniform packing where the walls are no longer the major constraint. When using cylindrical particles, higher dispersion is observed when the cylinders align on each other along the reactor axis, as compared to when they are randomly arranged in the reactor. A criterion to calculate the maximum conversion that can be achieved neglecting dispersion effects has been proposed, highlighting the situations where it has to be used with caution. The dispersion in these reactors can often be neglected. In case the criterion is not fulfilled, filling the porosity of the beds with powder reduces the dispersion. Using porosity fillers in reactors with internal diameters between 2 and 4 mm showed an improvement of the conversions for n-heptane reforming and methylcyclohexane dehydrogenation, which is attributed to external mass transfer improvement. Fine and spherical powders fill better the porosity and yield lower dispersion and higher mass transfer.

Flow of a moderately cohesive FCC catalyst in two pilot-scale rotary calciners: Residence time distribution and bed depth measurements with and without dams

Powder flow and heat transfer in rotary calciners are difficult to predict, which can result in reduced product quality. This work attempts to improve our understanding of powder flow in a rotary calciner. We compare experimental results to existing models. In this study, a moderately cohesive fluid catalytic cracking (FCC) powder was passed through two pilot plants rotary calciners with and without dams. Residence time distributions were measured, and the resulting mean residence times and axial dispersion coefficients were compared to predictive models. It observed that increasing the calciner incline and speed of rotation resulted in decreased mean residence time (MRT) and feed rate only had a small effect on MRT and axial dispersion. Increasing the height of dams increases the mean residence time and lowers the dispersion coefficient. Bed depth profiles at various operating conditions and geometries, with and without dams, were also determined and compared to available models.

Mathematical Modeling of Hydrodynamics in Bioreactor by Means of CFD-Based Compartment Model

This study presents the procedure of deriving a compartmental model (CM) based on an analysis obtained from the computational fluid dynamics (CFD) model of a bioreactor. The CM is composed of two parts, a structural (that takes into account the architecture of the mathematical model), and a parametric part (which contains the extrinsic parameters of the model). The CM is composed of the branches containing the set of perfectly mixed continuous stirred-tank reactors (CSTRs) in a configuration that matches the bioreactor’s flow patterns. Therefore, this work’s main objective was to develop a mathematical model that incorporated the flow field obtained by CFD technique. The proposed mathematical model was validated by means of the experimental data in the form of the residence time distribution (RTD) measurements.

Validation of a filtered drag model for solid residence time distribution (RTD) prediction in a pilot-scale FCC riser

Computational fluid dynamics (CFD) is a powerful tool for prediction and analysis of complex multiphase flow hydrodynamics and residence time distribution (RTD) in chemical reactors. This study presented the validation and application of a filtered drag model for solid RTD prediction in a pilot-scale fluid catalytic cracking (FCC) circulating fluidized bed (CFB) riser with Geldart A particles. First, the filtered drag model implemented in the open-source MFiX-TFM solver was validated for flow hydrodynamics simulation in a FCC CFB riser. After that, the model was further employed to validate its ability for solid RTD prediction in the same riser by comparing the simulation results with the experimental data. The simulation with the filtered drag model well reproduced the tracer response experiment which is more accurate than that with the Gidaspow drag model. Simulations with both pulse and step tracer injection methods were compared, which reveals the limitation of solid RTD measurement using a pulse tracer injection method in the experiment.

Correction of residence time distribution measurements for short holding times in pasteurization processes

Abstract When in-line cells are used for obtaining residence time distribution (RTD) data from systems with short residence time, the signal distortion caused by the cell can compromise the results. A procedure to correct such distortion using convolution of signals in the time domain is proposed. First, the RTD of the cell is characterized, and then the E-curve of an RTD model is convoluted with the cell curve. The convoluted E-curve is fitted to the experimental data by adjusting the mean time and the model parameter. The procedure is demonstrated using a pilot scale pasteurization unit with two heaters, one cooler and six options of holding tube. Pulse experiments were performed, E-curves were obtained for each process step and five RTD models were tested. The convolution procedure was successful in removing the distortion caused by the detection cell, which was very significant for the holding tubes.

κ-Carrageenan-Fe2O3 superporous composite adsorbent beads for application in magnetic field expanded bed chromatography adsorption

One of the authentic separation methods to purification of bioproducts is expanded bed adsorption (EBA). The magnetic field expanded bed adsorption (MFEBA) can be used to improve the efficiency of the EBA process. New type adsorbent beads composed as κ-Carrageenan-Fe2O3 (KC-Fe2O3) and superporous κ-Carrageenan- Fe2O3 (SP-KC-Fe2O3) have been prepared and well-studied by w/o emulsification method followed by morphological, physical and hydrodynamic investigations. The optical microscopy (OM) and field emission scanning electron microscopy (FESEM) were applied to the morphology study of the adsorbent particles. A suitable spherical morphology and porosity have been detected for the fabricated composite beads. A suitable wet density between 1.278 and 1.895 g/mL has been detected for the composite adsorbent. The beads porosity and egg (EA) albumin effective porosity were measured for SP-KC-Fe2O3-3 with the values of about 97.83% and 75.62% respectively. In order to study the hydrodynamic behavior of KC-Fe2O3 and SP-KC-Fe2O3 composite adsorbents in expanded bed adsorption process, the residence time distribution (RTD) measurements were carried out. The results indicated that suitable physical and hydrodynamic properties of the fabricated matrices in proof the potential of their application in high flow rate magnetic field expanded bed adsorption.

Flow and residence time distribution in small-scale dual-layer depth filter capsules

Depth filtration is widely used for clarification of liquid feeds, including the purification of biopharmaceuticals. The performance characteristics of these depth filters can be strongly influenced by the local flow and pressure distribution within the filter capsule, but there is currently little information on these phenomena in commercial depth filter modules. This work used a combination of computational fluid dynamics (CFD), residence time distribution (RTD) measurements, and dye binding experiments to obtain detailed information on the pressure and flow distribution within a small-scale Supracap™ depth filtration capsule, containing two layers of depth filter media with different pore size, that is of high interest in bioprocessing. The results confirmed the presence of four distinct flow paths through the capsule, with less than 40% of the flow passing completely through both layers of the depth filter media and nearly 11% bypassing the large pore size prefilter layer. Model calculations were in good agreement with the measured RTD and images of dye binding, providing further confirmation of the flow phenomena. These studies provide important insights into the performance characteristics of these depth filters, while providing a framework that can be applied to analyze the pressure and flow distribution in other membrane and depth filtration modules.

Experimental analysis and compartmental modeling of the residence time distribution in DN6 and DN15 continuous oscillatory baffled crystallizer (COBC) systems

Compartment models (CMs) are widely used to capture typical hydrodynamic features of systems, generally having low computational cost. The main building blocks of the CMs are the continuous stirred tank reactor and plug flow reactor models. In this study, the hydrodynamics of two laboratory scale continuously oscillated baffled crystallizer systems were investigated: the commercially available DN15 and a scaled down version known as the DN6. CM structures were identified based on residence time distribution (RTD) measurements by direct fitting method for both the DN6 and DN15 systems, which showed superior performance compared to the traditional tank in series CM structure determination. To attain a more accurate CM calibration, the piston and pump flowrates obtained by the typical peristaltic pump configurations were thoroughly analyzed.The investigations revealed that the behavior of the systems varies based on the oscillation amplitudes and frequencies, so the number of compartments required for an adequate model was identified based on measurement with different amplitudes and frequencies. It is shown that adaptive tank in series CMs are needed to capture the measured RTD characteristics over a broad piston operation range. Not only the RTD curves but the calculated compartment numbers follow similar trends in DN6 and DN15. This enabled the generalization of the CM structure for the DN6 and DN15 systems.

Measurement of Residence Time Distributions in a Continuously Operated Spouted Bed

AbstractContinuous gas‐solid processes are applied in many industries with particulate products, e.g. for granulation or coating. In this contribution, the residence time behavior in a continuously operated prismatic spouted bed was determined by applying an impulse of magnetizable tracer particles. Experiments were performed with the original configuration and with separation plates including mouse holes of varying size between the different chambers of the ProCell 25 apparatus. It is shown that the shape of the residence time distribution is influenced by the separation plates. In order to quantify the backmixing between the chambers, discontinuous experiments were performed, and the bed mass distribution and the distribution of the tracer were measured and compared to the initial conditions.