Prediction Of Residence Time Distribution Research Articles

Residence time distribution in continuous virus filtration.

Regulatory authorities recommend using residence time distribution (RTD) to address material traceability in continuous manufacturing. Continuous virus filtration is an essential but poorly understood step in biologics manufacturing in respect to fluid dynamics and scale-up. Here we describe a model that considers nonideal mixing and film resistance for RTD prediction in continuous virus filtration, and its experimental validation using the inert tracer NaNO3. The model was successfully calibrated through pulse injection experiments, yielding good agreement between model prediction and experiment ( 0.90). The model enabled the prediction of RTD with variations-for example, in injection volumes, flow rates, tracer concentrations, and filter surface areas-and was validated using stepwise experiments and combined stepwise and pulse injection experiments. All validation experiments achieved 0.97. Notably, if the process includes a porous material-such as a porous chromatography material, ultrafilter, or virus filter-it must be considered whether the molecule size affects the RTD, as tracers with different sizes may penetrate the pore space differently. Calibration of the model with NaNO3 enabled extrapolation to RTD of recombinant antibodies, which will promote significant savings in antibody consumption. This RTD model is ready for further application in end-to-end integrated continuous downstream processes, such as addressing material traceability during continuous virus filtration processes.

Neural network prediction of residence time distribution for quasi-2D pebble flow

An important parameter in silo discharging is residence time distribution (RTD), which describes the time each pebble stays within the bed. RTD can be applied as a key indicator to estimate reaction processes, and a key analytical metric to assess the inherent safety of reactors. However, due to the difficulty in obtaining pebble trajectories, few studies on discharging processes have been carried out. In this research, a pilot experimental study is conducted to get quantitative data and prediction model on RTD with precise predictions. The feasibility of applying neural network methods to RTD prediction is also checked. The accuracy of neural network prediction is confirmed by comparing the error between predicted and experimental results. It is discovered that RTD isoline changes in different regions and characterized by intuitive physical models. Compared to DEM, the neural network has a significant advantage in computing speed while retaining acceptable prediction accuracy.

CFD simulation of solids residence time distribution for scaling up gas‐solid bubbling fluidized bed reactors based on the modified structure‐based drag model

AbstractSolids residence time distribution (RTD), which reflects the degree of solids mixing in bubbling fluidized bed (BFB), has become an essential parameter for the evaluation of reactor performances. In this paper, a modified structure‐based drag model was established to investigate the effect of the bed size and the correlation of bubble dimension on the gas‐solids hydrodynamics and solids RTD in three different scales of BFB. The result obtained from the modified structure‐based drag model shows better agreement with the experimental values and it can be used to predict the RTD properly. The deviation of flow field will cause a large difference in the RTD prediction. An accurate flow field is a prerequisite for calculating the RTD. For the cases of Geldart B particles, the Darton correlation is the best choice for low gas velocities. When scaling up a BFB, the RTD calculated by the modified structure‐based drag model is reduced in comparison with the experimental value, which is related to the increase of the bed size and the excessive estimation of the bubble size. On the other hand, the lack of consideration for the friction on both front and back walls in 2D simulation may lead to the over‐prediction of particle velocity and result in the deviation between calculated and experimental RTD value.

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.

Impact of material properties and process variables on the residence time distribution in twin screw feeding equipment

Screw feeders are integrated as dispensing units in most continuous manufacturing platforms. Hence, characterizing and modelling the residence time distribution (RTD) of materials in feeders is indispensable to understand the traceability of raw materials from the drum till tablet, enabling the separation of non-confirming material. The proposed methodology addressed this leap in knowledge by characterizing materials, performing RTD trials according to an experimental design, applying RTD models and establishing a partial least square (PLS) regression model that links the material properties and process variables with the RTD responses as outputs. Results showed that RTD in screw feeders can be represented by a combination of plug-flow and mixed-flow. Three variables were found to impact the residence time distribution in feeders: flow rate, hopper level and conditioned bulk density. Interestingly, the plug-flow fraction was not affected by variation in flow rate or material properties. Consequently, simple PLS models could be developed that use density and flow rate to predict RTD at a given hopper level. This approach is powerful for RTD prediction based on bulk density in the early phases of development when control strategies for clinical manufacturing need to be established and material availability is still limited.

Combination of axial dispersion and velocity profile in parallel tanks-in-series compartment model for prediction of residence time distribution in a wide range of non-ideal laminar flow regimes

The residence time distribution is an important characteristic in the analysis of non-ideal reactors. In micro- reactors that operate predominantly under low Reynolds number, the axial dispersion is important. Since the channel length or residence time of fluid is usually not long enough, the axial dispersion model cannot predict an accurate RTD of the fluid in micro-reactors. In order to overcome this dilemma, a new model has been developed in the present work that combines the axial dispersion and velocity profile using the parallel tanks-in-series compartment model. The model comprises of two parameters, including the velocity profile exponent and Peclet number. It can be used for Newtonian and non-Newtonian fluid flow in the reactors with a wide range of Reynolds number and in all ranges of flow regime, including plug, laminar, perfectly mixed, and other profiles between these regimes. After verifying the model, the effects of velocity profile and Peclet number on the RTD of fluid in the tube for m-laminar and y-laminar velocity profiles were evaluated. Then, the RTDs of some previously reported systems such as straight Polytetrafluoroethylene (PTFE) tube, multi-laminated/elongational flow micro-mixer (MEFM-4) and standard T-junction micro-mixer (TjM) were adjusted to the proposed model.

Residence time distribution in an internal loop airlift reactor: CFD simulation versus digital image processing measurement

Residence time distribution (RTD) curve as the global flow characteristic in a rectangular internal loop airlift reactor (ALR) was obtained using Computational Fluid Dynamics (CFD) technique. CFD analysis of the laboratory ALR with a working volume of 2400 cm3 has been conducted under unsteady state conditions at low superficial gas velocities. Simulations were performed with water and air as the liquid and gas phase, respectively. To determine RTD, a pulse injection of a colored tracer was considered at top of downcomer and its concentration was obtained theoretically at different cross-sections of the reactor. The numerical Eulerian–Eulerian laminar two-fluid model was applied in transient 3D modeling of the fluids. RTD predictions using CFD simulation were compared with the experimental results obtained using Digital Image Processing (DIP) technique. For superficial gas velocities ranging from 0.01 to 0.03 m/s, there was a good agreement between the predictions and the experimental values. Results of this study indicate the potential of CFD simulation in describing the fluid hydrodynamics of rectangular ALRs with internal circulation loop.

Prediction of Residence Time Distribution of Solid Wastes in a Rotary Dryer

The residence time distribution (RTD) of heterogeneous citrus waste particles was determined in a semi-pilot-scale rotary dryer with concurrent flow under several operational conditions. The experimental methodology was based on the stimulus-response technique, which consisted of injecting pulse-like tracers in the dryer feed stream. Measurements of RTD were performed to build up experimental curves that were numerically integrated to provide the mean residence time. A perfectly-stirred-tank in series model and a neural network model were derived. In addition, empirical and semi-empirical correlations from the literature were used to estimate residence time and the influence of operating conditions on this variable was investigated.

Production of Silver Nanoparticles in a Continuous Stirred Tank Reactor Based on Plant-Mediated Biosynthesis: Flow Behaviors and Residence Time Distribution Prediction by Computational Fluid Dynamics Simulation

Here, biosynthesis of silver nanoparticles (AgNPs) in a continuous stirred tank with C. Platycladi extract serving as both reducing and capping agents was investigated, which for the first time provided a successful green protocol for synthesis of AgNPs in a continuous stirred tank. Residence time distributions (RTDs) of the tank for both liquid and the AgNPs were measured experimentally to evaluate the performance of the tank. In addition, the flow behaviors in the tank varied with rotor speed and the performance of the RTD at sufficient rotor speed (360 rpm) was simulated then analyzed using the computational fluid dynamics (CFD) tool. The results showed that the mean and variance of the RTD deviate from the ideal values at low rotor speed, indicating that the rotor speed is a crucial factor for the continuous stirred tank. In addition, the liquid RTD was very close to the granular RTD, and the predicted RTD by CFD was similar to that measured experimentally. Finally, AgNPs with different size distributions were successfully synthesized in the tank by regulating technical parameters such as feeding flow rates of the reaction solutions, the concentration of C. Platycladi extract, and reaction temperature. The present work is anticipated to play an important role toward continuous production and industrialization of AgNPs using biosynthetic technique.

Residence Time Distribution Determination of a Continuous Stirred Tank Reactor using Computational Fluid Dynamics and its Application on the Mathematical Modeling of Styrene Polymerization

Abstract The continuous operation of a stirred tank reactor for styrene polymerization was modeled. The proposed approach consists of an iterative procedure between two modules that considers the fluid-dynamics and kinetics respectively. The kinetic module considers a complex kinetic mechanism and is used to predict the time evolution of global variables, such as conversion and species concentrations, physicochemical properties and molecular structure characteristics of the final product. In order to obtain a 3D representation of the flow field, the simulation of the hydrodynamics of the reactor was carried out with the aid of a commercial computational fluid dynamics (CFD) software package. Because CFD is capable to predict the complete velocity distribution in a tank, it provided a good alternative to carry out residence time distribution (RTD) studies. It was found that the stimulus-response tracer method is reasonably accurate to obtain a complete RTD compared to the particle tracking method. The obtained RTD results showed a good agreement when validated with experimental data and literature information.From the estimates of the kinetic module and the RTD predictions, a statistical calculus allows the determination of the average properties at the reactor outlet. The convergence of the iterative procedure was tested and reasonable predictions were achieved for an industrial reactor.

A Particulate Method for Determining Residence Time in Viscous Flow Processes

AbstractIt is well known that residence time distribution (RTD) is a significant parameter in material processing, therefore, its accurate prediction is essential. From a numerical standpoint, one of the most widespread simulation methodologies is based on the combination of computational fluid dynamics (CFD) and particle tracking techniques. Within this framework, the novelty of this contribution is that the RTD is built upon a minimization of a least square criterion ensuring an accurate prediction of the mean residence time, as well as a smooth RTD function. In addition, a computational procedure is developed to estimate the thickness of the near‐wall region, which must be free of particles otherwise the RTD predictions will diverge. The relevance of the proposed method is assessed on analytical flow test cases and the Kenics static mixer for both Newtonian and non‐Newtonian fluids. Good agreement is found between numerical and corresponding theoretical mean residence times. magnified image

Numerical and experimental mixing studies in a MEMS-based multilaminated/elongational flow micromixer

Improvement of mixing quality in microchannel mixers or reactors has been recognized as a relevant technical issue critical to the development and application of integrated microchemical processing systems. Silicon micro- electro mechanical systems (MEMS) technology was successfully used to fabricate a novel multichannel micromixer. This improved micromixer design basically used the mechanisms of fluid multilamination, elongational flow, and geometric focusing for mixing enhancement. The fabricated triple-stack (Pyrex™/silicon/Pyrex™) multilaminated/elongational flow micromixer (herein referred to as MEFM-4) was evaluated for its mixing performance using residence time distribution (RTD) measure in conjunction with UV–vis absorption spectroscopy detection technique. Using a semi-empirical model and the so-called convolution–deconvolution theorem, a model description of the experimental RTD data was obtained for the flow/mixing unit. This result was compared with numerical RTD predictions based on computational fluid dynamics (CFD) simulations. The simulation results are in good agreement with the experimental data, especially in the low flow-rate range (Reynolds number <13 in this study). However, as expected, the accuracy of the CFD simulations is generally limited at higher flow rates (high Peclet number) because of unavoidable numerical diffusion. This paper describes the efficient design, fabrication and characterization of an effective microchannel mixer for microchemical systems’ applications.

Numerical analysis of high-pressure fluid jets: Application to RTD prediction in supercritical reactors

Computational fluid dynamics is becoming a very important tool in the research and design of new processes. At high pressures, the fluid dynamics behaves very differently than when reduced pressure is lower than unity. The aim of this work is to do an assessment of turbulence models to discern which is the most suitable choice when dealing with supercritical fluids. Two different studies have been carried out: First, an analysis of a turbulent submerged nitrogen jet, secondly a RTD (Residence Time Distribution) analysis of a supercritical carbon dioxide reactor. Both studies have been validated against experimental data. The results show that the Realizable k– ɛ model seems to be the most accurate choice for the simulation of high pressure systems, providing average deviations lower than 18% from experimental values. A methodology based on the solution of a transport equation for the residence time has been used. Using this method, the presence and location of undesirable backmixing zones inside the reactor are better identified. These backmixing zones correspond to the larger eddies present in the reactor, responsible for the long tail of the RTD data, this affect directly to conversion and selectivity.

Application of a multiphase CFD modelling approach to improve ozone residual monitoring and tracer testing strategies for full-scale drinking water ozone disinfection processes

A multiphase computational fluid dynamics (CFD) model has been developed to address the major components of ozone disinfection processes: contactor hydraulics, ozone decay and mass transfer. The model was applied to simulate ozone profiles and tracer residence time distributions of ozone contactors at the DesBaillets Water Treatment Plant (WTP) in Montreal, Canada. The modelling results showed that ozone residuals at the cross-section of the outlet of each chamber in the ozone contactors were very sensitive to monitoring point selection. The optimum locations were significantly affected by multiple operational parameters including water/gas flow rates, ozone dosage and baffling conditions. The modelling results suggested that multiple monitoring points should be used to obtain more representative ozone residuals. The CFD model was also used to study the factors affecting tracer residence time distribution (RTD). It was observed that the method of tracer injection could slightly affect tracer RTD results while sampling location had a significant influence on tracer RTD prediction or measurement. Therefore, it is suggested that multiple sampling points should be employed during tracer tests if possible.

Indepth diagnosis of a secondary clarifier by the application of radiotracer technique and numerical modeling

To make an indepth diagnosis of a full-scale rectangular secondary clarifier, an experimental and numerical study has been performed in a wastewater treatment facility. Calculation results by the numerical model with the adoption of the SIMPLE algorithm of Patankar are validated with radiotracer experiments. Emphasis is given to the prediction of residence time distribution (RTD) curves. The predicted RTD profiles are in good agreement with the experimental RTD curves at the upstream and center sections except for the withdrawal zone of the complex effluent weir structure. The simulation results predict successfully the well-known flow characteristics of each stage such as the waterfall phenomenon at the front of the clarifier, the bottom density current and the surface return flow in the settling zone, and the upward flow in the exit zone. The detailed effects of density current are thoroughly investigated in terms of high SS loading and temperature difference between influent and ambient fluid. The program developed in this study shows the high potential to assist in the design and determination of optimal operating conditions to improve effluent quality in a full-scale secondary clarifier.

CFD Simulation of RTD and Mixing in the Annular Region of a Taylor−Couette Contactor

Flow between two concentric cylinders, with either or both of them rotating, has potential advantages over the conventional process equipment. This flow, also termed as Taylor-Couette flow, which reveals a variety of flow regimes, is studied using computational fluid dynamics (CFD) simulations. The vortex motion causes mixing in the annulus, which necessitates the understanding of residence time of the fluid in the annulus and the mixing time. A systematic study of residence time distribution (RTD) and the mixing phenomenon in the annular region of the Taylor-Couette contactor has been carried out. The RTD predictions have been found to be in good agreement with the established experimental results. Axial dispersion in the Taylor vortex regime and the turbulent regime has been predicted, and it can be said that, with an increase in the radial mixing, the effect of velocity profile on the dispersion parameter significantly reduces at higher rotational speeds. Effect of axial flow, annular gap width, and rotational speed has been investigated on the axial dispersion. The dispersion number and the dispersion coefficient have been predicted.

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1–0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298–323 K and 0.01–0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient ( D L ). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas–liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.

Prediction of Residence Time Distribution for Different Screw Configurations of a Ko-Kneader by using a Cluster Model

Abstract Prediction of residence time distribution (RTD) in the modular type screw extruders has always been one of the most attractive subjects for predicting. In the present work an attempt was made to establish a method with functionality similar to additive rule for predicting RTD of the modular screw extruders with different configurations such as Buss Ko-Kneader. Results predicted from this method, which was named as cluster model, were compared with the results predicted based on our previously reported trajectory method as well as experimental results. A reasonability good agreement was found between these results justified reliability of the cluster model for being used as a new approach to predict the RTD of the modular screw extruders.

Prediction of Residence Time Distribution in EZ and KE Element of a Ko-Kneader by using CFD Method

Abstract Residence time distribution is among the important parameters of the Buss Ko-Kneader which allows one to better understand the flow conditions inside the system and to get information on mixing efficiency. However it has always been a difficult task to predict the RTD of complex geometries such as Buss elements. The aim of the present work was to estimate the residence time distribution in EZ and KE element of the Buss Ko-Kneader by utilizing an elemental tracing method performed on the flow fields in the same elements which were analysized by CFD method. The effects of rotating and reciprocating motions of the screw have been taken into account in three dimensional flow analysis. It was demonstrated that these results can provide valuable information on mixing performance of these two elements.

CFD Simulation of Mixing and Dispersion in Bubble Columns

Liquid phase mixing time was measured in 0.2 and 0.4 m i.d. columns over a wide range of superficial gas velocity (0.07–0.295 ms–1) and height-to-diameter ratio (1–10). A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The predictions agree favourably with all the experimental data published in the literature. Complete energy balance was established in all cases. The validated CFD model was extended for the simulation of the macro-mixing process by incorporating the effects of both the bulk motion and the eddy diffusion. Excellent agreement was observed between the CFD predicted and experimental values of the mixing time over the entire range of D, VG and HD/D covered. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (DL). The predicted values of DL were found to agree very well with all the experimental data published in the literature.