Residence Time Distribution Measurements Research Articles

Mixing efficacy and residence time distribution measurement in heavy water upgradation plant using radiotracer

To evaluate the efficiency of catalyst packing and to characterize the liquid phase flow dynamics in a heavy water distillation column, a series of residence time distribution (RTD) measurements were carried out using radiotracer. For a RTD measurement, about 1 mCi (37 MBq) of 82Br as ammonium bromide was injected as an impulse and its movement was monitored by thirty NaI(Tl) detectors at the inlet and outlet of the five catalyst cages present in the distillation column. The tracer measurements were carried out at varying liquid phase flow rate from 80 to 180 LPH. From the radiotracer data, it was concluded that radial distribution of the liquid phase at the top and bottom of the five cages was uniform. However, a slight non uniformity was observed in the middle cages. The residence time of the heavy water in the five cages varying the liquid flowrate was found to be varying from 4.2 min to 36.7 Min. To characterize the liquid mixing in each section of the distillation column, axial dispersion model was used using convolution method. The model parameter peclet number (Pe) was used to characterize the mixing. The Pe values for the five sections were found to be varying from 7 to 35. The Pe value suggests that flow of the liquid phase in the column was close to the plug flow in bottom three sections as desired.

Innovative fixed bed bioreactor platform: Enabling linearly scalable adherent cell biomanufacturing with real-time biomass prediction from nutrient consumption.

Scalable single-use adherent cell-based biomanufacturing platforms are essential for unlocking the full potential of cell and gene therapies. The primary objective of this study is to design and develop a novel fixed bed bioreactor platform tailored specifically for scaling up adherent cell culture. The bioreactor comprises a packed bed of vertically stacked woven polyethylene terephthalate mesh discs, sandwiched between two-fluid guide plates. Leveraging computational fluid dynamics modeling, we optimized bioreactor design to achieve uniform flow with minimal shear stress. Residence time distribution measurements demonstrated excellent flow uniformity with plug flow characteristics. Periodic media sampling coupled with offline analysis revealed minimal gradients of crucial metabolites (glucose, glutamine, lactate, and ammonia) across the bioreactor during cell growth. Furthermore, the bioreactor platform demonstrated high performance in automated cell harvesting, with ≈96% efficiency and ≈98% viability. It also exhibited linear scalability in both operational parameters and performance for cell culture and adeno-associated virus vector production. We developed mathematical models based on oxygen uptake rates to accurately predict cell growth curves and estimate biomass in real-time. This study demonstrates the effectiveness of the developed fixed-bed bioreactor platform in enabling scalable adherent cell-based biomanufacturing with high productivity and process control.

A new method for solids residence time distribution measurement in continuous fluidized beds

Accurate measurement of solids residence time distribution (RTD) is an important and challenging issue in developing fluidized bed reactors with continuous solids feeding and discharging. In this study, we proposed a new method for measuring solids residence time distribution, where coked bulk material was used for solids tracer and high-precision element analyzers were used to determine solids tracer fraction. A calibration procedure was established to achieve high-accuracy measurement of solids tracer fraction. The following validation tests had successfully proved the pseudo-CSTR solids flow pattern under different operating conditions and the staging effect of an inserted horizontal baffle in a small laboratory-scale fluidized bed cold model, which demonstrate the feasibility and advantages of this new solids RTD measurement method.

Reduction of Taylor dispersion in a capillary by spin-up flow—Theoretical insights

We have developed a theoretical framework to characterize the transport and mixing of a passive scalar in a capillary tube. In this configuration, a suspension of magnetic nanoparticles undergoes Poiseuille flow, while a rotating magnetic field is applied around the tube’s revolution axis, inducing a secondary flow in the azimuthal direction. This secondary flow facilitates the mitigation of concentration gradients and radial dispersion associated with the axial parabolic Poiseuille profile. The improvement in mixing is emphasized by a new dimensionless parameter, the mixing factor, which is incorporated into the scalar transport equation. Such a factor acts as a quantitative measure of the effect of the tangential motion induced by the spin-up flow on the overall mixing efficiency of the liquid and the observed reduction of the Taylor dispersion in the measured residence time distributions. Recognizing the mixing factor as a crucial parameter advances our understanding of the mechanisms governing scalar transport and provides a valuable tool for predicting and optimizing mixing in laminar capillary flows subjected to spin-up motion.

Statistical data treatment for residence time distribution studies in pharmaceutical manufacturing

Residence time distribution (RTD) method has been widely used in the pharmaceutical manufacturing for understanding powder dynamics within unit operations and continuous integrated manufacturing lines. The dynamics thus captured is then used to develop predictive models for unit operations and important RTD-based applications ensuring product quality assurance. Despite thorough efforts in tracer selection, data acquisition, and calibration model development to obtain tracer concentration profiles for RTD studies, there can exist significant noise in these profiles. This noise can make it challenging to identify the underlying signal and get a representative RTD of the system under study. Such concerns have previously indicated the importance of noise handling for RTD measurements in literature. However, the literature does not provide sufficient information on noise handling or data treatment strategies for RTD studies. To this end, we investigate the impact of varying levels of noise using different tracers on measurement of RTD profile and its applications. We quantify the impact of different denoising methods (time and frequency averaging methods). Through this investigation, we see that Savitsky Golay filtering turns out to a good method for denoising RTD profiles despite varying noise levels. The investigation is performed such that the key features of the RTD profile (which are important for RTD based applications) are preserved. Subsequently, we also investigate the impact of denoising on RTD-based applications such as out-of-specification (OOS) analysis and RTD modeling. The results show that the degree of noise levels considered in this work do not significantly impact the RTD-based applications.

Role of Gas Aspiration through Ladle Shroud and Influence on Tundish Hydrodynamic Performances: A Physical and Mathematical Modeling Study

Gas aspiration through ladle shroud, during the teeming of a ladle into a tundish, has been investigated via physical and mathematical modeling. To this end, a volume of fluid‐based two‐phase turbulent flow model (in conjunction with the standard k–ε turbulence model) and a full‐scale two‐strand bloom casting tundish have been applied. Both flow and residence time distribution measurements are carried out in the full‐scale tundish system, adopting well‐established measurement techniques. Computational results, supported appropriately with experimentally measured data, indicate that gas aspiration alters flow and turbulence profoundly in the vicinity of the shroud entry zone. Early reversal of jetting flow toward the free surface, due to the buoyancy of the entrained gas, increases the overall intensity of motion in the tundish, creating more mixing flow volumes at the expense of plug flow volume. Most importantly, however, gas aspiration through shroud tends to drastically cut down interactions between the down coming liquid jet metal and the pouring box, making the specific design and shape of a pouring box redundant toward desirable flow modification. Finally, it is shown that strong surface flows and turbulence, generated due to gas aspiration, can be suitably damped by deploying a set of weirs, increasing plug flow volume in tundish.

A paradigm shift for biocatalytic microreactors: Decoupling application from reactor design

Microreactors have been successfully applied to execute a broad range of biotransformations in flow. However, microreactors have typically been designed with a specific biotransformation or a specific biocatalyst immobilization method in mind, constraining their wider applicability. Furthermore, their design is typically either applicable for whole-cell or for enzyme biocatalysis, but not for both. We present a novel microreactor design which offers cartridge-like insertion of both immobilised enzymes and cells. A T-shaped lid opens and closes the reaction chamber (whilst leaving the rest of the microreactor unchanged), enables the easy insertion of immobilised biocatalysts, and thus allows the user to configure different reactor types. We demonstrated this novel concept showing three different reactor types: a hydrogel microreactor containing entrapped E. coli cells overexpressing transketolase (volumetric productivity of 2.23 ± 0.83 mmoll-ERY Lvoid1 min1), a packed-bed microreactor containing commercial beads with immobilised Candida antarctica lipase B (volumetric productivity of 317.69 ± 96.74 mmolBB Lvoid1 min1), and a micropillar microreactor containing surface-immobilised ω-transaminase (volumetric productivity of 0.08 ± 0.02 mmolACP Lvoid1 min1). The proposed design showed consistency and robustness for 10 consecutive T-shaped lid ‘open and close’ cycles and withstood the pressure of at least 4 bar. Design analysis further included Computational Fluid Dynamics models and Residence Time Distribution measurements. The presented design offers a standardised approach for multiple applications, underpinning process development and paving the way for off-the-shelf microreactor technology for biocatalysis.

Effects of operating parameters on residence time distribution in a REFLUX flotation cell

Residence time distribution (RTD) is a critical parameter in design and optimization of flotation processes and machines. RTD measurements provide valuable indication into the distribution of residence times experienced by particulates (e.g., particles, oil droplets) within the system, enabling the identification of flow regimes and potential issues such as short-circuiting, dead zones or inadequate mixing. While previous studies in the literature have generally focused on RTD measurements in mechanical flotation cells, there are limited experimental studies available for pneumatic flotation cells. In this study, RTD measurements were performed to characterize the type of flow regime in the REFLUXTM Flotation Cell (RFC), and to investigate the impacts of operational parameters, including bias, feed flux, and gas flux, using a laboratory-scale RFC-100. An impulse-response methodology was employed with a KCl solution used as a tracer in a two-phase (liquid–gas) system. Large and Small Tanks in Series (LSTS), N-mixer in Series, and Perfect Mixer models were applied to a database created by experimental results. The results revealed that the fluid behavior in RFC-100 approached a plug-flow pattern rather than perfect mixing in the two-phase (liquid–gas) system. Furthermore, an increase in bias resulted in a decrease in mean residence time (MRT), and the tracer concentration inside the cell could be adjusted by varying the gas flux under the same feed flux.

Twin-screw granulation: Mechanistic understanding of the effect of material properties on key granule quality attributes through the analysis of mixing dynamics and granulation rate mechanisms

This study focuses on understanding the effect of material properties on granule quality attributes through the analysis of mixing dynamics and granulation rate mechanisms. Powder wettability, binder viscosity, and liquid-to-solid (L/S) ratio were the factors that were investigated in this study. The mixing occurring inside the twin-screw granulator (TSG) was quantitatively assessed by obtaining the axial dispersion coefficient from the experimentally measured residence time distribution (RTD) curves. It was observed that the quality of the nuclei fed to the kneading zone significantly affected the mixing dynamics. The quality of nuclei was governed by nucleation kinetics, which in turn was principally affected by the liquid saturation of the nuclei and the ratio of drop penetration time and encounter time, which in turn were affected by the L/S ratio and binder viscosity respectively. The hydrophobicity of the blend mainly affected the extent of nucleation. The type of nuclei entering the kneading zone and mixing dynamics in the TSG also determined whether the granulation growth mechanism was “layering-dominant” or “viscous-dominant”. It was also shown that the resultant granule quality attributes were a reflection of the growth mechanisms. Ultimately, a mechanistic link between material properties, mixing dynamics, granulation rate mechanisms, and granule quality attributes was established.

Residence Time Distribution Measurements and Modeling in an Industrial-Scale Siemens Flotation Cell

This short communication presents residence time distribution (RTD) measurements and modeling in a 16 m3 Siemens flotation cell, as the first RTD characterization in an industrial-scale pneumatic cell. The Siemens cell was installed as a pre-rougher machine in a Cu-Mo selective plant. This plant recovered molybdenite as an enriched product, depressing copper-bearing minerals. Irradiated non-floatable solid and Br82 in water solution were employed as solid and liquid tracers, respectively. The tracers were instantly injected into the Siemens cell, and the inlet and outlet concentrations were directly measured by external non-invasive detectors. From the flotation literature, three model structures for the RTDs were evaluated, including perfect mixing, one large perfect mixer and one small perfect mixer in series (LSTS), and N perfectly mixed reactors in series. A transport delay was incorporated for all models. The LSTS representation was more consistent with the experimental data, showing that the Siemens cell RTDs presented significant deviations with respect to perfect mixing and plug-flow regimes. From the industrial measurements, mean residence times of 4.1–5.2 min were estimated.

Synthesis and characterization of supermacroporous cryogel with immobilized p-aminobenzenesulfonamide as affinity ligand for the purification of lactoperoxidase from whey.

This study proposed the development of a monolithic supermacroporous affinity column for direct capture of lactoperoxidase, a glycoprotein present in milk, whey, and colostrum, with several applications due to its wide antimicrobial activity. A poly(acrylamide)-based cryogel was produced by radical co-polymerization of monomers in frozen aqueous solution and activated with p-aminobenzenesulfonamide as a ligand for specific interaction with the lactoperoxidase. The axial liquid dispersion coefficients at different liquid flow rates were determined by measuring residence time distributions using the tracer pulse-response method. The axial dispersion coefficient was low and the height equivalent to theoretical plate was not dependent on the flow velocity. The adsorptive capacity of affinity cryogel was studied as a function of flow velocity and the best condition was 0.9cm/min. The response surface methodology was applied to optimize the capture of the enzyme, as a function of pH and salt concentration. Higher purification factor value was found at a salt concentration of 80mmol/L and pH of 8.0 (p<0.05). There was no influence of the variables under study on the yield (p>0.05). The results indicated that affinity cryogel is a promising chromatography support for the use in high-throughput one-step purification of lactoperoxidase from whey.

Evaluation of mixing performance and validation of CFD simulations in baffled anaerobic digesters using radiotracer technique

The anaerobic digesters find usage in treating the huge amount of waste such as trash, garbage, human waste and animal waste. The sustained performance of an anaerobic digester depends on the flow pattern and mixing behaviour in the digester. A cylindrical digester tank with vertical baffles can provide flow behaviour approaching that of a plug flow reactor. However, the presence of dead zones and recirculating regions cause non-ideal flow in the digester. In this work, the mixing behaviour in two scaled-down models of baffled digester tanks is characterized by measurement of residence time distribution (RTD) using a radioactive tracer. While the first design has three vertical baffles, the second design include horizontal static flaps on the baffles. The flow behaviour in the digester is also simulated using computational fluid dynamics (CFD) and RTD is obtained computationally. The comparison of RTD curves obtained from CFD simulations with those obtained from radiotracer experiments show good agreement between them. There appear to be only minor difference in the flow behaviour and the RTD curves in the two digester designs. Using the RTD curve data, two commonly used RTD models, tank-in-series and dispersion models, have been fitted and both models are able to predict the RTD in the digester qualitatively.

Characterization and propagation of RTD uncertainty for continuous powder blending processes

Residence time distribution (RTD) is a probability density function that describes the time materials spend inside a system. It is a promising tool for mixing behavior characterization, material traceability, and real-time quality control in pharmaceutical manufacturing. However, RTD measurements are accompanied with some degree of uncertainties because of process fluctuation and variation, measurement error, and experimental variation among different replicates. Due to the strict quality control requirements of drug manufacturing, it is essential to consider RTD uncertainty and characterize its effects on RTD-based predictions and applications. Towards this end, two approaches were developed in this work, namely model-based and data-based approaches. The model-based approach characterizes the RTD uncertainty via RTD model parameters and uses Monte Carlo sampling to propagate and analyze the effects on downstream processes. To avoid bias and possible reduction of uncertainty during model fitting, the data-based approach characterizes RTD uncertainty using the raw experimental data and utilizes interval arithmetic for uncertainty propagation. A constrained optimization approach was also proposed to overcome the drawback of interval arithmetic in the data-based approach. Results depict probability intervals around the upstream disturbance tracking profile and the funnel plot, facilitating better decision-making for quality control under uncertainty.

Investigation of aqueous phase dynamics in a uranium stripping unit using radioactive tracer

Mixer-setters units are widely used in uranium purification processes. For efficient operations of mixer-settler units, it is essential to measure the hydrodynamics parameters of the different phases involved. The residence time distribution (RTD) measurement is commonly used method to estimate the hydrodynamics parameters of process reactors. In the present study, RTD of the aqueous phase was measured in different stages mixer-settler unit (mixers, settlers and mixer-settler units) used for stripping operation using Iodine-131 as a radiotracer. For the RTD measurements, radiotracer was injected as an impulse in aqueous phase feed line and its movement was monitored at different locations in the stripping unit using NaI(Tl) detectors. The mean residence times (MRTs) of the aqueous phase were estimated from measured RTD curves. For quantification of the degree of mixing, suitable flow models were proposed based on design and nature of the measured RTD curves and subsequently used for simulation. Based on the results of the RTD study, the mixing of aqueous phase was characterized and design of the stripping unit and its sub-units were validated. The optimum conditions were identified for efficient for the operation of the stripping unit.

The Use of Radioactive Tracers to Detect and Correct Feed Flowrate Imbalances in Parallel Flotation Banks

This work presents the application of radioactive tracers to detect and correct feed flowrate imbalances in parallel rougher flotation banks. Several surveys were conducted at Minera Los Pelambres concentrator, in banks consisting of 250 m3 mechanical flotation cells. The feed pulp distribution was estimated from the mean residence times, which were obtained from residence time distribution measurements. The tracer was injected in the feed distributor and the inlet and outlet tracer signals of cells 1 and 2 were measured by on-stream sensors. The baseline condition for the pulp distribution was defined by the valve settings in the feed distributor, which led to an unbalanced condition for two parallel rougher banks, with 34% of the pulp being fed to bank A and 66% to bank B. New valve configurations were evaluated, with a fraction of the feed being directed to the rougher bank C, which was not initially fed from the same distributor. The feed distribution was finally balanced with 49% of the pulp being fed to bank A versus 51% to bank B. Thus, the radioactive traces proved to be a powerful tool to industrially detect and improve feed distributions in parallel flotation circuits.

Residence Time Distribution of Non-Spherical Particles in a Continuous Rotary Drum

The motion of non-spherical particles with sharp edges, as they are commonly involved in practice, was characterized by residence time distribution (RTD) measurement in a continuous drum. Particles with two sizes, 6 and 10 mm, and two densities, 750 and 2085 kg/m3, were used in the experiments. The effects of rotation speed (3–11 rpm), incline angle (2–4°), feed rate, and mixture composition were investigated and compared to the results of other researchers on particles without sharp edges. We also fitted the RTD with an axial dispersion model to obtain a better insight into the flow behavior. MRT of non-spherical particles with sharp edges depends on ω−α similar to other shapes, while the value of alpha is higher for particles with sharp edges (0.9 &lt; α &lt; 1.24), especially at high incline angles. The MRT depends on incline angle, β−b, where b varies between 0.81 (at low ω) and 1.34 (at high ω), while it is close to 1 for other shapes. Feed rate has a slight effect on the MRT of particles with sharp edges and the effect of particle size diminishes when rotation speed increases. The MRT linearly increases with volume fraction of light particles in a mixture of light and heavy particles (from pure heavy to pure light particles).

Non-Idealities in Lab-Scale Kinetic Testing: A Theoretical Study of a Modular Temkin Reactor

The Temkin reactor can be applied for industrial relevant catalyst testing with unmodified catalyst particles. It was assumed in the literature that this reactor behaves as a cascade of continuously stirred tank reactors (CSTR). However, this assumption was based only on outlet gas composition or inert residence time distribution measurements. The present work theoretically investigates the catalytic CO2 methanation as a test case on different catalyst geometries, a sphere, and a ring, inside a single Temkin reaction chamber under isothermal conditions. Axial gas-phase species profiles from detailed computational fluid dynamics (CFD) are compared with a CSTR and 1D plug-flow reactor (PFR) model using a sophisticated microkinetic model. In addition, a 1D chemical reactor network (CRN) model was developed, and model parameters were adjusted based on the CFD simulations. Whereas the ideal reactor models overpredict the axial product concentrations, the CRN model results agree well with the CFD simulations, especially under low to medium flow rates. This study shows that complex flow patterns greatly influence species fields inside the Temkin reactor. Although residence time measurements suggest CSTR-like behavior, the reactive flow cannot be described by either a CSTR or PFR model but with the developed CRN model.

Heat Transfer and Residence Time in Lean Direct Injection Fuel Galleries

Abstract In radially staged lean direct injection (LDI) systems, pilot fuel plays an important role in cooling the mains fuel gallery in regions of the flight envelope where the mains fuel is stagnant. Under these conditions, managing wetted wall temperatures is vital to avoid the formation of carbonaceous particles, which become deposited on the surfaces of the fuel gallery and can lead to a deterioration in system performance. The prediction of wetted wall temperatures therefore represents an important aspect of the injector design phase. Such predictions are often based on injector thermal models, which tend to rely on the application of convective boundary conditions from empirical heat transfer correlations. The use of these correlations leads to questions over the accuracy of predicted wetted wall temperatures and therefore uncertainty over the probability of deposition. This paper seeks to improve on the current situation by applying the inverse conduction technique to determine heat transfer coefficients (HTCs) specific to the pilot fuel gallery. These HTCs are crucial for determining wetted wall temperatures in the pilot and mains fuel galleries and principally govern the risk of deposition in the stagnant mains. The pilot heat transfer data are further examined alongside measurements of the pilot residence time distribution, which together control the risk of pilot deposition at low fuel flow rates. Both the heat transfer and residence time measurements demonstrate the opportunity for future fuel gallery design refinement and provide the supporting data to facilitate this.

Comparative Study of Two Identical Industrial Digesters Using Radiotracer‐Based Residence Time Distribution Measurement

AbstractRadiotracer‐based residence time distribution (RTD) measurements were performed for two identical wheat straw pulping digesters to evaluate and compare their performances. The radiotracer technetium (99mTc) as sodium pertechnetate was used to follow the liquid phase inside the digester. The product quality of both digesters was not identical for similar sets of operating conditions. Temperature, pressure, and mass flow rates were the influencing parameters, and the experimental and theoretical mean residence time (MRT) were compared. A significant amount of flow abnormalities was observed in the second digester as compared to the first one, including channeling, dead volume, scaling, and bypassing. The axial dispersion model and tank in series with the back‐mixing model were suitable for modeling the obtained RTD data.

Investigation of Oxy-Fuel Combustion through Reactor Network and Residence Time Data

Oxy-fuel combustion is a promising strategy to minimize the environmental impact of combustion-based energy conversion. Simple and flexible tools are required to facilitate the successful integration of such strategies at the industrial level. This study couples measured residence time distribution with chemical reactor network analysis in a close-to-reality combustor. This provides detailed knowledge about the various mixing and reactive characteristics arising from the use of the two different oxidizing streams.