Residence Time Distribution Experiments Research Articles

Dynamic tank-in-series modelling and simulation of gas-liquid interaction in trickle bed reactor designed for gas fermentation

Trickle bed reactors (TBR), historically utilized in petroleum processing and wastewater treatment, now extend their applicability in biological gas conversions, including syngas biomethanation for renewable methane production. Despite operational benefits, optimizing TBR design and scale-up demands a good understanding of the reactor's hydraulic behavior and mass transfer phenomena. This study's novelty is TBR's hydraulic characterization in respect to liquid and gas flowrates and simulation of the gas-liquid interaction by a dynamic gas-liquid transfer model. Residence time distribution (RTD) experiments in 220 mL lab- and 5000 mL pilot-scale TBRs with co-current flow of gas and liquid were conducted to determine the liquid and gas working volume and the number of tanks for a dynamic tank-in-series (TIS) model. RTD experiments revealed 2–6 tanks for varying liquid flowrate (constant gas flowrate) and 5–8 tanks for varying gas flowrate (constant liquid flowrate). A dimensionless equation, fitted to RTD experimental data, predicted the liquid working volume of a TBR at various liquid flowrates and reactor configurations. TBR simulation by TIS model considering 8 well mixed gas and liquid phase tanks connected in series, resulted in an excellent model validation with an R2 at 0.99. Finally, the model simulated the mass transfer kinetics of H2, CO, and CO2 in water under varying gas and liquid flowrates for lab- and pilot-scale TBRs. Simulation results showed increased dissolved gas concentration with higher gas flowrate (constant liquid flowrate) for both scales TBR. It was also noticeable that under constant gas flowrate, the dissolved gas concentration initially decreased (0.01 < ReL < 17), then increased (17 < ReL < 34), and again decreased (34 < ReL < 105). This behavior was the same for both scales TBR and revealed an optimum ReL value irrespective of TBR size.

Residence time distribution experiments in a hybrid anaerobic blanket reactor treating real pharmaceutical wastewater

BackgroundThe phenomena of mixing is considered important due to its involvement in modelling and design of reactors. MethodsThe residence time distribution (RTD) experiments to find out the mixing characteristics were conducted in hybrid anaerobic blanket reactor (HABR) with four different OLRs of pharmaceutical wastewater using lithium chloride as tracer by means of stimulus-response technique. The mean hydraulic retention time, dispersion and Peclet number for various OLRs in HABR were determined. Significant findingsThe experimental COD removal efficiencies in HABR and the theoretical performance were found out using the axial dispersion flow model (ADFM) and plug flow model (PFM). The estimated theoretical chemical oxygen demand (COD) removal efficiencies, using the ADFM were 92.4%, 82.0%, 63.0% and 41.7% and the values respectively for PFM were 97.27%, 93.92%, 83.47% and 59.34%. The error percentage detected was less than 7% in ADFM which exhibited better flow representation in HABR. Furthermore, the value of correlation coefficient (R2 = 0.9956) between the theoretical COD removal efficiencies and experimental values confirmed the suitability of the ADF model.

Microreactor designed for efficient plasma-liquid segmented flows.

Microreactors were designed for gas-liquid plasma chemical processes and operated under segmented flows in a high aspect ratio (8.76) rectangular microchannel. First, the hydrodynamics of the gas-liquid flows generated at a T-junction was investigated for fifteen solvents commonly used in organic synthesis. The classical literature scaling laws were revised to describe the dependence of bubble and slug lengths, and bubble residence time on the liquid nature by introducing their liquid vapour pressure. Liquid film thickness and liquid residence time were estimated from residence time distribution experiments. Secondly, plasma could be successfully generated in these segmented flows for all the liquids. Due to the plasma dissipation of thermal energy, gas phase temperature increased and induced the lengthening of bubbles and the decrease in bubble residence time. The flow pattern was also impacted by the gas temperature increase. A flow map describing the evolution of the flow pattern under plasma conditions was built, enabling prediction of the flow pattern based on the liquid boiling point and dielectric constant. These microreactors have demonstrated great potential, and by adapting the synthesis solvent or the operating plasma conditions, they could find promising applications in gas-liquid plasma chemical processes.

Experimental and numerical investigation on the influence of wall deformations on mixing quality of a Multifunctional Heat Exchanger/Reactor (MHER)

This study focuses on the mixing performance enhancement in laminar flow equipment by investigating the generation of chaotic advection using wall deformations in annular geometries. The results presented concern the mixing quality in two different geometries, one with a deformed sinusoidal wall “DT” (Deformed Tube), and the other with a combination of deformed sinusoidal external wall and a swirled core “DETSC” (Deformed External Tube and Swirled Internal Core). The goal is to evaluate the influence of the swirled core on the mixing, and to determine if this combination of wall deformations could improve the mixing quality for Reynolds numbers ranging from 800 to 2000. To provide a comprehensive analyse, the evaluation is conducted based on two aspects: the process engineering aspect, through experimental Residence Time Distribution (RTD) to gain an overview of the dispersion of fluid particles in the reactors, and the fluid mechanics aspect, using various numerical tools such as the mixing rate, Poincaré sections, and particle trajectories to better analyse the secondary flows resulting from wall deformations and assess the mixing in terms of concentration. These two aspects allow to characterize the mixture globally and locally. The findings demonstrated that the combined geometry induced chaotic advection, resulting in a perfect mixing rate of 100% across the entire range of Reynolds numbers studied, compared to the DT configuration where the maximum achieved mixing rate reaches 70% at Re = 2000.

Hydrodynamic modelling and performance assessment of continuous-flow single-channel reactor for river water turbidity removal using electrocoagulation process

A hydrodynamic modelling of a continuous-flow single-channel (CFSC) reactor was highlighted by means of Residence Time Distribution (RTD) experimental approach using stimulus response technique and three inlet flowrates (43.66, 79.40 and 115.10 L.h−1). Axial dispersion model (ADM) was applied for approximating the RTD experimental curves in order to check the flow patterns homogeneity and identify the possible flow deviations. The CFSC reactor was then evaluated for river water treatment by electrocoagulation process. At 43.66 L.h−1, dead zones were diagnosed within the CFSC reactor and corresponding experimental RTD curve deviated from ADM. At high inlet flowrates, the hydrodynamic behaviour was highly plug-flow (Pe > 100) without flow malfunctions and a satisfactory agreement was obtained between RTD experimental curves and ADM. In contrast, at 43.66 L.h−1, the CFSC reactor exhibited higher turbidity removal (of about 91.7%) compared to high inlet flowrates, indicating that the treatment efficiency depends mainly on coagulant dose electro-dissolved per unit of time rather hydrodynamic condition. However, the associated operating cost was relatively high at 43.66 L.h−1. As for the effect of initial water quality, it was observed that, for the same coagulant dose electro-dissolved, the treatment efficiency dropped as the initial turbidity of water decreased.

Effect of lifter shape and operating parameters on the flow of materials in a pilot rotary kiln: Part IV. Improvement of the hydrodynamics-related dimensionless correlations

Non-spherical particles are widely processed in industrial-scale rotary kilns. There is nonetheless a lack of simple tools that make it possible to predict their hydrodynamic behavior inside rotary kilns. This article thus focuses on the hydrodynamics of crozets flowing inside a pilot-scale rotary kiln. Thirty-eight experiments were conducted with this product. Experimental Residence Time Distribution curves were successfully obtained with a tracer pulse methodology using painted crozets. Both the experimental mean residence time and the axial dispersion coefficient were obtained by fitting the analytical expression of E(t) for the open-open boundary condition with the experimental E(t) curves. The hydrodynamic behavior observed was qualitatively in agreement with the literature. Our dimensionless models were then re-identified with all of the experimental data and simplified through statistical analysis. This study provides more robust dimensionless hydrodynamic models that can be used to reliably predict the behavior of non-spherical particle flow inside an industrial kiln.

Enhanced scale-up performance on residence time distribution by integrated microcapillaries with high size uniformity

Continuous tubular flow reactors are widely used by virtue of their simple structures, controllable reaction conditions, enhanced heat and mass transfer, etc. Microreactors present specific microscale characteristics including laminar flow, reduced diffusion path, enhanced mixing degree and high surface area to volume ratio. Microcapillary reactors combined the advantages of continuous processing and microscale reactions. However, the scale-up of microreactions is still a very challenging task for the loss of enhanced transport characteristics in microscale. Residence time distribution (RTD) is a vital research method to investigate the flow behaviors of microreactors. Microcapillary films (MCFs) containing several parallel microcapillaries provide a strategy to multiplex the microreactions. Nevertheless, the low size uniformity of microcapillaries in MCF strips hinders their application in microreactions. We carried out Computational Fluid Dynamic (CFD) simulations with experimental RTD validation to investigate the effects of dimension, convection and diffusion on RTD and the relationship between the RTD diversity and the size uniformity of microcapillaries under fixed velocities and volumetric flow rates. MCFs with high size uniformity were manufactured by liquid-assisted extrusion, and the coefficient of variance of the mean residence times of the microcapillaries in the MCF strip was only 2.8%. Neutralization reaction also showed the consistence of reaction performances among microcapillaries. With the enhanced scale-up performance on RTD and microreactions, MCFs are expected to have broad applications in large-scale microreactions in chemical engineering industry.

The study on the effect of hydrodynamic flow on the photocatalytic performance of photocatalytic reactors.

The scalability of photocatalytic reactor is the major challenge due to the inability of the light penetration when the laboratory scale reactors are ascended. It is well known that the characteristic length of photocatalytic reactor is one of the influential parameters determining the efficiency of light penetration and also affects the hydrodynamic fluid flow behaviour inside the reactor. This study visualizes hydrodynamic flow behaviour of three differently configured photocatalytic reactors through numerical simulation of the fluid mass transport inside the reactors. The three photocatalytic reactors are (1) concentric cylindrical glass tube micro-reactor (CGTR), (2) UV-LED strip photocatalytic reactor (STR) and (3) classical annular reactor (CAR) from our previous work. The simulations of flow behaviour confirmed that CGTR exhibited plug flow regime, STR exhibited arbitrary flow (in-between continuously stirred tank reactor and plug flow reactor) and CAR behaved like continuously stirred tank reactor. Also, interpretations of numerical modelling were validated through plotting experimental residence time distribution curve. Furthermore, the comparison of performance parameters revealed that the highest modified space time yield (STYmodified) 225s-1and highest modified photocatalytic space time yield (PSTYmodified) 9.375s-1/kW/m3 was obtained for plug flow reactor when compared to continuously stirred tank reactor (CAR) and arbitrary flow reactor (STR). The study confirms that decrease in characteristic length of photocatalytic reactor onsets plug flow regime, which has highest photocatalytic performance efficiency.

A DEM model to evaluate refill strategies of a twin-screw feeder

Residence time distribution (RTD) modeling has proven to be a valuable tool for material tracking in continuous pharmaceutical processes. Refilling is thoroughly studied in the literature, but the main focus lies on the feed rate disturbances. The impact of the feeders themselves on intermixing of different material batches is often overlooked. Since the experimental methods to measure the RTD feeder discharging processes feeder are complex and material intensive, there is only limited experimental RTD data available in the literature. A DEM (discrete element method) simulation of a discharge of a twin-screw feeder shows that a large fraction of material that is moved and intermixed by the agitator. In addition to the intermixing, there is a tendency to discharge material located above the agitator early. In order to predict the behavior during multiple refill events, three models in order of increasing complexity are presented: (1) A simple exponential RTD assuming perfect intermixing of material batches; (2) a RTD model based on DEM results; (3) particle-level material tracking by extrapolation of the DEM results. All three of these models are able to predict the survival function of old material for late refills at low fill levels, however, earlier refills at high fill levels require more complex models to accurately represent the dynamics inside the hopper of the feeder.

Hydrodynamics of a rotor–stator spinning disk reactor: Investigations by large-eddy simulation

In this work, computational fluid dynamics are used to study the hydrodynamics in a complete rotor–stator spinning disk reactor with throughflow. Large-eddy simulations of OpenFOAM 9 were used to capture the turbulent structures of the flow in combination with the wall-adapting local eddy viscosity sub-grid-scale model. The method was validated based on residence time distributions (RTDs) for a range of rotational Reynolds numbers (Re = ωRD2ν−1 = 3.2–52 × 104) and a dimensionless flow rate (Cw = Q ν−1RD−1) of 150 and G = 0.0303 (G = h RD−1). The experimental RTD was obtained from tracer experiments with UV/VIS flow cells. From the RTD, the plug flow (PFR) volume fraction, the Péclet number, and the radial position (rtrans) where the flow changes from PFR into ideally mixed were determined by using an engineering model based on axial dispersion. For the turbulent cases, good agreement based on the RTD curve, PFR volume, the Péclet number, and rtrans was found. Furthermore, the boundary layer thickness on the rotor and stator and the entrainment coefficient were in good agreement with the literature. Finally, the turbulent intensity was analyzed illustrating a high intensity at the rim of the rotor and was 10% larger in centripetal flow compared to centrifugal flow.

Modelling of powder hydrodynamics in a screw reactor

Screw reactors are largely used devices in the industry. Very few studies focus on the powder hydrodynamics in screw reactors. The overflow point, a filling degree value when the powder passes over the shaft, was determined for different conditions and a dimensionless model was fitted to predict this parameter. The residence time distribution (RTD) has been measured with a pulse injection of salty powder. The influence of operating conditions and geometry parameters on the RTD has been studied. It appeared that the Hausner ratio, the pitch length and the filling degree mostly influence the RTD shape. Two models for the RTD have been compared: the compartment model was the most accurate and has one parameter of adjustment. A dimensionless model was developed and fitted with 51 experimental RTD results, predicting the RTD shape. The dimensionless model predicts with good accuracy other experimental data from the literature.

Micromixing Performance and Residence Time Distribution in a Miniaturized Magnetic Reactor: Experimental Investigation and Machine Learning Modeling

Miniaturization of mixers is a hot topic in process intensification, but efficient mixing at operational conditions with relatively large viscosity μ and large flow rate ratio R between two mixed solutions is still a great challenge for micromixers. Herein, a miniaturized magnetic reactor (MMR) is developed, and its micro- and macromixing performances are characterized by the Villermaux/Dushman reaction and residence time distribution experiments, respectively. The results show that the miniaturization of the premixing unit and the stirred unit is vital. By arranging the stirred units in series, the MMR is effective in reducing axial dispersion, intensifying mixing at operational conditions with large μ and R and achieving efficient energy utilization without introducing extra energy input. The micromixing time tm in the optimized MMR ranges from 0.24 to 1.42 ms when 4.72 mPa·s < μ < 73.30 mPa·s and 8 < R < 20, indicating superior micromixing performance. Moreover, machine learning models are established and compared for predicting tm with excellent accuracy and guiding mixer design, and the SHAP method is adopted for model interpretation.

Solid Phase Macromixing Study in a Pilot-Scale Geldart Group B Circulating Fluidized Bed Riser Using Single Particle RTD and RPT Measurements

Solid flow in a Geldart’s group B circulating fluidized bed (CFB) riser is complex, and it exhibits backflow and recirculation in the riser. A single radioactive tracer particle is used to measure the overall and sectional residence time distribution in a CFB riser at a gas velocity of 7.6–9.2 m/s and a solid flux of 100–200 kg/m2s. At the same time, radioactive particle tracking (RPT) data are used to measure the trajectories of the tracer particle and its length distribution at the bottom and middle sections of the riser. Both residence time distribution (RTD) and trajectory length distribution data obtained from RPT and RTD experiments are processed and compared. Results show that the bottom section has higher back mixing than the middle section. The results also show that back mixing in both the sections reduces with an increase in the gas inlet velocity and reduces marginally with an increase in the solid flux. Results confirm that RPT and RTD data are highly correlated and can be used with the same accuracy to quantify the macromixing behavior of any process vessel/reactor.

Performance evaluation of oscillatory baffle Bunsen reactor in iodine sulfur thermochemical process for hydrogen production

&lt;abstract&gt; &lt;p&gt;Hydrogen is an environmentally attractive transportation fuel that can replace fossil fuels. The iodine-sulfur (I-S) thermo-chemical process involves three reaction steps. The Bunsen reaction is one of the main reaction steps of I-S process and plays an important role in defining overall process efficiency. Different types of reactors are being studied, including the oscillatory baffle Bunsen reactor. The reactor selection is based on process intensification and process integration, i.e., reaction and separation in the single equipment. Simulations are performed for two-dimensional cases by solving incompressible Navier-Stokes equations along with continuity equation, the geometry chosen is of single section in the column and diameter of 50 mm and baffle spacing of 50, 75,100 mm i.e. 1, 1.5 and 2 times the diameter of column and baffle free area 22%. The residence time distribution experiments are carried out in a metallic reactor with NaCl as a tracer operated at different frequencies, amplitudes and flow rates. D/uL is evaluated from experimental curves. The power per unit mass is compared for oscillatory baffled column and stirred tank for a semi-batch process. From the numerical simulations, good eddy interactions are present at higher frequencies and amplitudes and at a baffle spacing of 1.5 times the diameter of the column. Residence time distribution analysis gives a lower dispersion number at medium frequencies and higher amplitudes with constant flow rate. If the flow rates are high, then it is better to operate at higher frequencies and amplitudes to achieve plug flow behavior. Power per unit mass is less for oscillatory baffle column compared to the stirred tank of given configuration. With better mixing performance and less power per unit volume, the oscillatory baffle column is a good alternative to other columns.&lt;/p&gt; &lt;/abstract&gt;

Impact of ball size distribution, compartment configuration, and classifying liner on cement particle size in a continuous ball mill

A true unsteady-state simulator (TUSSIM), based on a cell-based Population Balance Model (PBM) with a differential algebraic equation (DAE) solver, was used for modeling a full-scale open-circuit cement ball mill for better understanding the industry best practices of employing number of mill compartments, classifying liners, and ball mixtures. Model parameters for the particle breakage and classification action with/without the classifying liner were obtained from the available literature for cement clinker. Experimental residence time distribution data for a full-scale cement ball mill was fitted by the cell-based PBM to determine the number of cells and axial back-mixing ratio. Dynamic simulations, conducted to determine the temporal evolution of the particle size distribution and mass hold-up, demonstrate that milling with a ball mixture outperforms milling with a single ball size. Single-compartment milling can achieve desirable product fineness if the feed is pre-milled. Having the same length, a two-compartment mill obviates the need for pre-milling and performs similarly or better than a three-compartment mill, depending on the ball sizes used. For a given set of ball sizes, a distribution with uniform mass of balls, as opposed to that with a uniform number of balls, achieves 8% increase in cement specific surface area. The use of a classifying liner achieves a negligibly finer cement product compared to uniformly mixed balls. Overall, these results agree with experimental observations, lending credence to TUSSIM, while providing rationale to best practices in the cement industry, offering various process insights and a toolbox to optimize existing open-circuit continuous ball mills.

Residence time distribution and micromixing efficiency of a dynamic inline rotor–stator mixer

An industrially available dynamic inline–mixer which operates on the rotor–stator principle was investigated for aqueous solutions with a total volume flow rate of up to 40 L/h to gain valid insight into the mixing behavior. In residence time distribution (RTD) experiments, mean residence times ranging between 29 and 305 s and Bodenstein numbers ranging between 1.4 and 5.1 were measured. Micromixing efficiency was investigated with the Villermaux–Dushman reaction at varying rotational speeds, total volume flow rates and injection inlets. The results suggest that micromixing processes are especially complex in a continuous rotor–stator mixer. As expected, the injection inlet had a decisive influence on micromixing efficiency. Surprisingly, even at higher volume flow rates backmixing was identified as a factor which significantly extends the micromixing time. A new method is proposed for estimating the degree of backmixing based on micromixing experiments. Micromixing times range between 3 · 10–4 and 4 · 10–3 s depending on the operating point.

Development and Use of a Residence Time Distribution (RTD) Model Control Strategy for a Continuous Manufacturing Drug Product Pharmaceutical Process.

Residence-time-distribution (RTD)-based models are key to understanding the mixing dynamics of continuous manufacturing systems. Such models can allow for material traceability throughout the process and can provide the ability for removal of non-conforming material from the finished product. These models have been implemented in continuous pharmaceutical manufacturing mainly for monitoring purposes, not as an integral part of the control strategy and in-process specifications. This paper discusses the steps taken to develop an RTD model design space and how the model was statistically incorporated into the product’s control strategy. To develop the model, experiments were conducted at a range of blender impeller speeds and total system mass flow rates. RTD parameters were optimized for each condition tested using a tank-in-series-type model with a delay. Using the experimental RTD parameters, an equation was derived relating the mean residence time to the operating conditions (i.e., blender impeller speed and mass flow rate). The RTD parameters were used in combination with real-time upstream process data to predict downstream API concentration, where these predictions allowed validation across the entire operating range of the process by comparison to measured tablet assay. The standard in-process control limits for the product were statistically tightened using the validation acceptance criteria. Ultimately, this model and strategy were accepted by regulatory authorities.

Why device design is crucial for membrane adsorbers

In preparative chromatography, a uniform flow distribution through the chromatography device is essential to get an effective ligand utilization and a breakthrough curve that is as steep as possible. Membrane adsorbers usually have a smaller aspect ratio (bed height to diameter ratio) than conventional columns. Upscaling devices with low aspect ratios is challenging due to the trade-off between easy-to-handle flow distribution and the pressure drop over the chromatographic membrane bed. This study aims to investigate the impact of membrane parameters (such as porosity and permeability) and device parameters (such as bed height, incident flow area, and dead volume) on the flow distribution by quantifying simulative and experimental residence time distributions (RTDs). In order to understand and develop a methodology to quantify the impact of the device geometry, the hydrodynamics of axial and radial devices are investigated using CFD simulations. The results show that the device configuration strongly influences the flow distribution. In contrast, the impact of the membrane characteristics on the flow distribution in the investigated small-scale devices with a cross-sectional area of up to 70mm2 is minor. However, membrane characteristics have a significant effect on the pressure drop over the stack. Experimental RTD data allow for evaluating only the impact of the whole device on signal responses. In this study, a purely model-based method was set up according to CFD simulations with the aim of separating the impact of membrane and membrane housing on the flow distribution. It has been shown that the investigated radial-flow devices have favorable hydrodynamic properties due to an optimized housing design and beneficial similar flow path lengths. Furthermore, an equivalent circuit of a CSTR and a DPFR was developed to predict the housing’s RTDs and, in the future, a model-based scale-up of devices.

Simulation on non-ideal behaviour of plug flow bioreactor based on the growth study of Lactobacillus species

ABSTRACT The physical properties of a biological system vary with time due to the growth of biomass, and thus the flowability of such a medium inside any bioreactor also changes with time. The present study aims to study the non-ideal behaviour of a plug flow bioreactor (PFBR) under non-reactive conditions for a biological system. Different physical parameters of this study have been incorporated from the batch growth study of Lactobacillus sp. The growth of bacteria culture was simulated using a PVA solution to conduct residence time distribution (RTD) experiments in pulse and step mode. Different parameters of the dispersion model were measured, and the non-zero variance indicated that dispersion always occurred along the path of reaction which led to turbulence and diffusion. The Peclet No was non-infinite; thus, PFBR always deviates from the ideal behaviour of the plug flow reactor. During the velocity distribution study, it had also been established that the Peclet number was decreased with the increase of Reynolds Number at a certain medium viscosity. Moreover, the non-ideality of PFBR further increased due to the change of physical properties of the medium. Here, a polynomial relation had been established between the Peclet number and medium viscosity. Therefore, the current study might be a value addition towards the designing of the plug flow bioreactor.

Residence time distribution and solids mixing of sawdust in a horizontal pulsed fluidized bed

A prototype horizontal pulsed fluidized bed (HPFB) has been built for continuous biomass torrefaction in our lab. Solids residence time distribution (RTD) of hemlock sawdust in the HPFB reactor was measured to study particle transport and mixing using a pulse injection of particle tracer. Effects of weir height, gas pulsation frequency, solids feed rate and gas velocity were investigated. A modified axial dispersion model was adopted to fit the experimental RTD curves, where horizontal dispersion coefficients were obtained. It is found that horizontal dispersion coefficients were slightly higher in the deeper bed. In the shallow bed, horizontal dispersion coefficients increased with increasing solids feed rate. The solids mixing intensity also found to increase with increasing the gas velocity. Horizontal solids dispersion coefficients obtained in the HPFB were significantly smaller than values calculated by literature correlations. A correlation in the shallow HPFB was established based on our experimental data.