RTD Curves Research Articles

Development of a high-fidelity digital twin using the discrete element method for a continuous direct compression process. Part 2. Validation of calibration workflow

This paper is the second in a series of two that describes the application of discrete element method (DEM) and reduced order modeling to predict the effect of disturbances in the concentration of drug substance at the inlet of a continuous powder mixer on the concentration of the drug substance at the outlet of the mixer. In the companion publication, small-scale material characterization tests, a careful DEM parameter calibration and DEM simulations of the manufacturing process were used to develop a reliable RTD models. In the current work, the same calibration workflow was employed to evaluate the predictive ability of the resulting reduced-order model for an extended design space. DEM simulations were extrapolated using a relay race method and the cumulative RTD was accurately parameterized using the n-CSTR model. By performing experiments and simulations, a calibrated DEM model predicted the response of a continuous powder mixer to step changes in the inlet concentration of an API. Thus, carefully calibrated DEM models was used to guide and reduce experimental work and to establish an adequate control strategy. In addition, a further reduction in the computational effort was obtained by using the relay race method to extrapolate results. The predicted RTD curves were then parameterized to develop reduced order models and used to simulate the process in a matter of seconds. Overall, a control strategy evaluation tool based on high-fidelity DEM simulations was developed using material-sparing small-scale characterization tests.

New Understanding on Relationship Between RTD Curve and Inclusion Behavior in the Tundish

New Understanding on Relationship Between RTD Curve and Inclusion Behavior in the Tundish

Plate structure optimization and performance study of a new continuous flow electrocoagulation reactor

Electrocoagulation (EC) process is an environmentally friendly and effective water treatment method. A folded plate EC reactor has been developed to remove pollutants such as azo dyes and COD from wastewater. There is a dead zone in the corner position of this electrocoagulation reactor, so this study aims to improve this problem and strengthen the EC mass transfer process in the reactor. A circular perforation treatment at the corner of the folded plate electrode is proposed to promote the exchange between the dead zone and the active zone and enhance the mixing strength. Taking methyl orange as the target pollutant, the effects of perforation diameter, perforation spacing and plate arrangement were considered, and these parameters were optimized by Box-Behnken model. The results show that the removal efficiency of 92.16% is obtained when the perforation diameter is 4 mm, the perforation spacing is 20 mm and the plate arrangement is 0.5 L height difference between the front and back plates. In addition, the RTD curve shows that the dead zone of the perforated electrode is lower, the dimensionless variance is larger, and the mixing effect is better. The cost was reduced by perforation design and optimization of operating parameters, and the COD removal efficiency of 16.8% and the decolorization efficiency of 17.4% were increased in pharmaceutical wastewater.

New insight into relationship between casting speed and inclusion removal in the tundish

The tundish is the last refractory metallurgical reactor during the continuous casting process, and the fluid flow in the tundish is one of the key factors to control inclusion collision-coalescence and its removal. Thus, numerical method is applied to obtain the flow field, the RTD curve and the inclusion field. Numerical results showed that the predicted RTD curve and the inclusion number density agree well with the experimental data. In the case of different fluid velocity at tundish inlet, the volume fraction of plug zone, dead zone and well-mixed zone keep unchanged, but the dimensionless tundish inclusion volume concentration, the dimensionless tundish inclusion radius and the inclusion removal ratio have the exponential relation to the fluid velocity at tundish inlet. Further, there is maximum inclusion removal rate for the specific tundish. Another interesting phenomenon is about the inclusion behavior and the characteristic time of the RTD curve. The inclusion removal ratio and the dimensionless tundish inclusion radius have the linear relation to the minimum residence time, the peak concentration time and the average residence time.

Numerical Study on Gas Blown in Tundish Side Walls

The performance of gas blown in side walls of a single strand tundish is numerically simulated. Three cases are studied, i.e. tundish without gas blown, tundish with gas blown from the right side wall, and from the front wall. The vortex circulating flow is the main flow structure in tundish without gas blown. The gas blown from the right side wall of tundish will significantly change the flow field. The short-circuit flow that the tracer flow along the bottom of tundish to the outlet is becoming the main flow pattern. The RTD curve shows a rapid increase tendency. An anticlockwise flow near the top surface is formed. The mixing of tracer in the tundish is delayed and the dead volume fraction is increased when compared with the tundish without gas blown case. In contrast, the gas blown from the front wall of tundish will divide the tundish into two parts. The strong circulation flow in two parts is formed. Besides, the mixing of tracer is faster and the dead volume fraction is lower than that of the case without gas blown. This case may be an optimized gas blown technology in tundish.

Effect of Flow Field Optimization of an Asymmetric Multi-Strand Tundish on the Quality Consistency of Cracking Con-Rod Steel.

Cracking con-rod is an advanced high-precision connecting structure based on brittle expansion, breaking and reconnection of steel, to solve the problem of assembly circle missing. High carbon micro-alloyed steel C70S6, as a dominant material for the production of cracking con-rod, has extremely strict requirements on non-metallic inclusions in steel and microstructure stability. Continuous casting tundish plays an important role in removing large-sized inclusions and stabilizing casting quality. Aiming at the inconsistent casting quality of C70S6 steel produced by a three-strand asymmetric tundish and the frequent occurrence of slag entrapment problems in Xining Special Steel, the tundish structure was optimized by means of physical modelling combined with numerical simulation, and the quality of the bloom castings and subsequent hot-rolled products before and after optimization were compared based on volume production. The results show that a new flow control design to the tundish can effectively improve the consistency of its metallurgical effect for each of the three strands and the following overall product quality, in which the flow field and temperature field in the tundish are more uniform. This is due to the adoption of a vortex inhibitor and an optimized wall structure according to the measured RTD curve, ink trajectory and numerical simulation on the 3-D streamline contours and temperature distribution in the tundish. The peak concentration of outlet 1 is decreased from 6.5 before optimization to less than 2.0 after optimization, which means the elimination or alleviation of the local short-circuit flow. The maximum temperature difference of C70S6 molten steel measured at the outlets of the tundish three strands is decreased from 2–5 °C to 1–3 °C, which is in good agreement with the numerical simulation results. The difference in columnar crystal ratio of the corresponding bloom castings is decreased from 2.27–3.17% to 1.26–1.85%, and the consistency of central carbon segregation index is also significantly improved. In addition, the difference in oxygen content among the three strand blooms is decreased from 1.7–3.5 ppm to 0.8–1.9 ppm. As a result, the overall mechanical properties and microstructure stability of the hot-rolled products are improved statistically, in which the hardness fluctuation is decreased from 84 HBW to 60 HBW, the inclusion grade of types B + C + D + Ds is reduced to 1.105, and the occurrence rate of Ds dropped to 0.118%. Accordingly, the failure rate of the cracking con-rod is controlled stably within 4‰, and the fracture is generally smoother than that before tundish optimization. In summary, the flow field optimization to a multi-strand asymmetric tundish has a clear effect on improving the overall quality of its bloom castings and rolled products, which should be paid more attention industrially. Meanwhile, the present study provides a reliable theoretical and experimental reference for the improvement of metallurgical effects of an asymmetric-typed tundish commonly used in special steel production.

Further analysis of the near-plug gas flow conditions in micro gas-solid fluidized beds

This work presents a theoretical analysis of the near-plug gas flow conditions in micro gas-solid fluidized beds based on the simple one-dimensional dispersion model. The analysis is validated by comparison with the experimental results reported in the literature. It concludes that gas flows can be considered near-plug flow only when: 1) the gas RTD curve is symmetrically shaped; 2) the product of RTD peak height E(t)h and variance σt (i.e., E(t)hσt) approximates 0.4; and 3) E(t)h is greater than 1.0 s−1 (dimensionless Eθ,max > 2.82) or σt2 < 0.25 s2 (and (dimensionless σθ2 > 0.02). This work further improves the criterion for the near-plug flow of gas in micro fluidized beds originally proposed by Geng et al. (CEJ, 351 (2018) 110–118).

On-Line Optical Monitoring of the Mixing Performance in Co-Rotating Twin-Screw Extruders.

The use of real-time techniques to evaluate the global mixing performance of co-rotating twin-screw extruders is well consolidated, but much less is reported on the specific contribution of individual screw zones. This work uses on-line flow turbidity and birefringence to ascertain the mixing performance of kneading blocks with different geometries. For this purpose, one of the barrel segments of the extruder was modified in order to incorporate four sampling devices and slit dies containing optical windows were attached to them. The experiments consisted in reaching steady extrusion and then adding a small amount of tracer. Upon opening each sampling device, material was laterally detoured from the local screw channel, and its turbidity and birefringence were measured by the optical detector. Residence time distribution curves (RTD) were obtained at various axial positions along three different kneading blocks and under a range of screw speeds. It is hypothesized that K, a parameter related to the area under each RTD curve, is a good indicator of dispersive mixing, whereas variance can be used to assess distributive mixing. The experimental data confirmed that these mixing indices are sensitive to changes in processing conditions, and that they translate the expected behavior of each kneading block geometry.

Ecuaciones de diseño de un reactor electroquímico tubular con electrodos concéntricos de mallas expandidas a través de un análisis teórico del micro/macromezclado de curvas de DTR

In the present work, the liquid flow pattern in a Tubular Electrochemical Reactor (TC-ECR) with concentric cylindrical expanded meshes as electrodes and inlet/outlet distributors of shower‑sprinkler type was evaluated. It was found that the CFD theoretical results describe the experimental F(t)-curves obtained with the methodology of “step-signal input”. Later, the F(t)-curves estimated with CFD for each reactor zone were adequately approximated with global parametric models for the development of the TER design equations. The Stagnant Zone Model with mass exchange with the anodic zone turns out to be adequate for the reactor shell zone. However, for the cathode and anode meshes, the Axial Dispersion Model with mass exchange between them proves to be appropriate. For all liquid flow rates (0.37 to 4.0 L min-1), the dispersion numbers (Nd) are in a magnitude order of small dispersion. This confirms that the incorporation of inlet/outlet distributors in a T-ECR improve considerably the liquid flow pattern behaviour. This experimental methodology, coupled with micro/macromixing theoretical analysis of RTD curves with CFD, can be a good alternative for the reactor design.

Numerical and experimental evaluation of the general performance in a modular electrochemical reactor and its feasibility for electro-chlorination purposes: Effect of the different electrode assembly configurations

Evaluation of electrochemical reactors consisting of different electrode assemblies, stacks, or modular units, by the employing of computational techniques and its comparison with experimental data is desirable for its applications and scaling up for electrochemical processes like the mediated electro-chlorination. This work aimed to evaluate the effect of three different electrode configurations (flat, interspersed, and C-stack assemblies) on the general performance of a homemade modular reactor, based on former ElectroSyn design with an improved inlet-outlet system, through studies of hydrodynamics, electrical characteristics, and mass transfer. Additionally, a secondary potential-current distribution study was carried out to evaluate the feasibility of different electrode configurations tested for the electro-chlorination process, that can be applied mainly for environmental purposes like mediated oxidation of organic pollutants and disinfection by the production of active chlorine species.From the hydrodynamic study, velocity profiles and RTD curves obtained in all electrode configurations tested, suggest that the flat electrode configuration exposes a low fluid dispersion and resistance than the other configurations, because of the diminishing of the high-velocity zones and by its higher cross-sectional area, which was confirmed by the pressure drop measurements. On the other hand, calculation of primary and secondary current distribution suggests that the presence and modification of edge effect in the different configurations tested generate strong non-uniformities in the electrode corners and the reactor walls, which could affect the distribution of reaction rate during the mass transport evaluations. Also, the secondary potential-current distribution study indicates that the flat and C-stack configurations are the more electrical feasible configurations (since the effect of the flow field and mass transfer was not taken into account) to be applied in the electro-chlorination process.

Residence time distribution studies on recycle reactor with recirculation

Abstract Residence time distribution (RTD) experiments provide very important information about the performance of reactors. In the present work, RTD experiments were performed with varying recycle and recirculation rates to see their effect on mean residence time (MRT), flow bypassing and stagnant volume in the reactor. A computer program was developed to solve the model equations using fourth-order Runge–Kutta method. A low bypass flow (&lt;5%) was observed from the experimental RTD curves obtained at different operating conditions. A change in the MRT from 1.2 to 1.8 h was observed at different recycle and recirculation rates. At maximum recycle and maximum recirculation, in the study ranges, a 37% stagnant volume (with exchange) was predicted. In the absence of recycle and recirculation, a 53% stagnant volume (with exchange) was predicted corresponding to the best fit of the experimental RTD data.

Mechanistic understanding of the effects of process and design parameters on the mixing dynamics in continuous twin-screw granulation

Wet granulation is a size enlargement process in which fine powders are agglomerated into larger granules via the presence of a liquid binder. Among various types and modes of granulation processes, twin-screw granulation is a popular continuous wet granulation technique. The typical residence time that powders spend in a twin-screw granulator are in the order of seconds, hence, the rigorous mixing of solid and liquid particles across particle sizes and equipment geometry becomes even more important. This study aims to improve the mechanistic understanding of the effect of process and screw parameters on the mixing dynamics inside a twin-screw granulator using dispersion coefficient as a key metric. The dispersion coefficient quantifies the dispersion and is directly proportional to the extent of mixing occurring inside the granulator. An analysis of the experimentally obtained dispersion coefficient is performed to understand the effect of key process and design parameters such as feed rate, screw speed, number of kneading elements and, stagger angle. A semi-mechanistic model that incorporates these parameters was developed to estimate and predict the dispersion coefficient. The model accurately predicts the dispersion coefficient values and the goodness-of-fit values (R2) for the test set and full data set were found to be equal to 0.920 and 0.932 respectively. This model was further tested by predicting the complete RTD curves using the predicted dispersion coefficients. The average goodness-of-fit value (R2) for the prediction of RTD curves for all the experimental runs was calculated to be equal to 0.698.

Steel Cleanliness Depends on Inflow Turbulence Intensity (in Tundishes and Molds)

Economically, steel cleanliness is important. Cleaner steel contains fewer inclusions. Inclusions are removed, and thus cleanliness improves when steel is molten. Consequently, simulation of steel flow must be as accurate as possible. Steel flow in tundishes and molds is turbulent. In most turbulent flows, it is assumed that turbulence is generated inside the flow rather than entering with inflow. Due to this assumption, inflow turbulence intensity ( $$I_{\text{in}}$$ ) is sometimes not reported. If $$I_{\text{in}}$$ is reported, its values differ greatly among different papers. The present study shows, for the first time, that $$I_{\text{in}}$$ must be accurately specified because it affects steel cleanliness. In other words, the inclusions’ interaction (RTD curves), slag turbulence intensity and other factors concerning steel cleanliness depend on $$I_{\text{in}}$$ . This dependence is proved numerically by applying different $$I_{\text{in}}$$ s to steel flows in two industrial tundishes, two industrial molds and water models of a tundish and a mold. In addition to revealing this dependence, the results also disclose interesting facts regarding steel cleanliness. For example, this article illustrates that a tundish’s performance can change with $$I_{\text{in}}$$ . Therefore, a tundish’s performance depends on the design of the upstream devices as well as its own design.

CFD modeling of residence time distribution and experimental validation in a redox flow battery using free and porous flow

Abstract The successful use of clean energy sources will rest, in part, on the availability of efficient energy storage systems. Thus, the present work examines two critical factors (flow patterns and residence time distribution, RTD) affecting the performance of one of the most promising energy storage systems: redox flow batteries (RFBs). The goal is to develop a methodology for analyzing the hydrodynamic and mass transport behavior within a commercial redox flow battery (CRFB). This methodology includes modeling of the flow behavior as well as its experimental validation with RTD. The CRFB consisted of a square geometry with an interdigitated flow field design. Experimental residence time distribution curves for this device were obtained at four different flow rates using the stimulus-response technique with step signal. Theoretically, the flow behavior within the CRFB was approximated by an axial dispersion model (ADM), and a plug dispersion exchange model (PDE), as well as by solving the hydrodynamic equations (Navier–Stokes and Brinkman equations) and the mass transport equation (convection-diffusion) using COMSOL Multiphysics® 5.3. The calculated RTD curves are in good agreement with the experimental RTD curves. Our theoretical and experimental analysis resulted in better approximations of the axial dispersion, and the presence of stagnant zones, and channeling and by-pass (i.e., preferential flow) effects at low and intermediate Reynolds numbers (Re). The experimental RTD curves show that the liquid flow pattern in the CRFB deviates considerably from the axial dispersion model at low Re, conditions under which the CRFB exhibits significant channeling effects, as well as stagnant and dead zones. The PDE model was able to describe the deviation from ideal flow pattern caused by channeling, recycling, or by the presence of stagnant regions in the CRFB. The mass transport in the CRFB was determined by measuring the distribution of tracer molecules at different time points after the initial (step) tracer injection. The interdigitated flow field geometry exhibited a homogeneous flow distribution, featuring an increased mean electrolyte velocity inside the electrode. This simulation allowed locating stagnant zones that would locally affect the mass transport properties and globally lead to a reduction of the RFB conversion efficiency.

Optimization of injected radiotracer volume for flow rate measurement in closed conduits

In chemical processes it is essential that the flow in the process is accurately defined. Fluid velocity measurements are important for fluid flow quality performance in flow systems. This study focuses on determination of the volumetric flow rate and its standard (relative) deviation for calibration of conventional flow meters by using a radiotracer approach. The measurements for flow meter calibration were performed at a pilot-scale flow rig using Technetium-99 m (99mTc) as a radiotracer in the form of pertechnetate ion (99mTcO4-). The measured data were analyzed, and precision of the experimental setup was investigated under two different approaches ? IAEA?s RTD software and sum approximation of raw data. For the first time, the variation of standard deviation of calculated flow rate with the injection volume and activity of the radiotracer was determined. Plug flow with axial dispersion was used to simulate the measured RTD curves and investigate the flow dynamics of the flowing water. The results of the study have shown the possibility of in situ calibration of flow meters with a relative error lower than 1 %. They also revealed a slight dependency of the precision of output results on the injection volume as well as similar results for manual and specialized RTD software data processing.

Hydraulic performance evaluation of a quasi-two dimensional constructed wetland microcosm using tracer tests and Visual MODFLOW simulation

Hydraulic conditions of constructed wetlands (CWs) are crucial to pollutant removal and are influenced by factors such as influent loading rates, influent or effluent position or porous media size. The performance evaluation of CWs in real application, however, is difficult and a visualization analysis is difficult due to the black-box effect. In this paper, a nonopaque microcosmic horizontal subsurface flow constructed wetland (HSSFCW) reactor was built in the laboratory for an efficient and intuitive assessment of the influences of such parameters on the hydraulic performance of CWs. Chloride tracer tests were carried out to obtain parameters on hydraulic performance by considering hydraulic loading rates and different flow inlet-outlet configurations, while dye tracer tests were designed for the visualization of solute transport and diffusion. In parallel, an identical design of the HSSFCW reactor was modeled using the Visual MODFLOW (VM) software in order to detect the tracer movement and solute concentration field. Results show that the inflow rate and the inlet-outlet configuration have significant impacts on the hydraulic performance of a CW influencing RTD curve shape, flow path, dead zone distribution and hydraulic efficiency. The dead zone and flow path have been visualized and analyzed by comparing the dye tracer experiments of VM solute concentration field and particulate path-line tracking. In addition, the feasibility and reliability of the VM simulation has been verified. The application of VM in this study has been robust indicating a possible application for further investigations on the influencing factors of real CWs.

Experimental study and mathematical modeling of two phase flow with a Eulerian approach in a continuous gas evolving electrochlorinator

Electrochlorination systems have become popular. Their hydrodynamic behavior affects the efficiency and power consumption but the reaction environment is complex due to the complex flow arising from gas evolution at the electrodes. Water reduction at the stainless steel cathode generates a large amount of small hydrogen bubbles being then, the only evolving gas at the electrodes that can modify the flow pattern inside the reactor. (Cl2(g) generated at anode is rapidly hydrolyzed into hypochlorous acid or hypochlorite ion). This paper considers the hydrodynamic behavior of the two-phase flow using experimentally and modeled RTD curves, via a weakly coupled Euler-Euler model. Experimental data are in a qualitative agreement with the RTD model.

Determination of RTD Curves for Aluminium Refining Process Conducted in Batch Reactor – Physical Modelling

Determination of RTD Curves for Aluminium Refining Process Conducted in Batch Reactor – Physical Modelling

Phenomenological behavior coupling hydrodynamics and electrode kinetics in a flow electrochemical reactor. Numerical analysis and experimental validation

Parallel plate electrochemical reactors are frequently used in industry because its high range of applications in several electrochemical processes related with electrosynthesis, environment electrochemistry and energy storage systems. In such sense, the aim of this work is deal with the reaction environment characterization of a parallel plate flow reactor having a net-like spacer, by the employment of original experimental and theoretical techniques in order to evaluate the influence of transport phenomena on overall reactor performance. Flow distribution is analyzed by the use of automatic measurement of flow paths using image processing techniques, based on mathematical morphology theory. On the other hand, a theoretical model of current-potential distribution under intermediate kinetics control (tertiary current-potential distribution) based on numerical solution of turbulent diffusion-convection and binary electrolyte theory is proposed. In this case, concentration at electrode surface was determined in terms of dimensionless Damkhöler number, obtained from a mass balance at electrode-electrolyte interface in steady state. RTD curves obtained by image processing techniques describes correctly the fluid dynamics behavior in electrochemical reactor. Meanwhile, correspondence between calculated and experimental polarization curves using the oxidation of chloride ions to chlorine as model electrochemical reaction was made with an error values lesser than 7%, indicating a good agreement between theoretical model and experimental tests. Results founded in the parallel plate flow electrochemical reactor used here, evidenced that the methodology proposed to analyze the hydrodynamic and electrochemical behavior are adequate to its use in other electrochemical devices, particularly, when they work under intermediate kinetic and limiting current conditions.

Numerical optimization of membrane module design and operation for a full-scale submerged MBR by computational fluid dynamics

The hydrodynamics in the membrane module of a full-scale sMBR at 500 m3/d was simulated by computational fluid dynamics (CFD) in this study. Several key indexes, including membrane distance (d), aeration design, height of gas-liquid dispersion hm, and freeboard height hf and operational conditions, including SADp and liquid viscosity, were optimized through investigating their impacts on water velocity distribution and membrane shear stress. The CFD model was validated by comparing the simulated trace element RTD curves with experimental results. The optimal design and operational parameters for the full scale sMBR are as following: membrane distance d = 35 mm, air diffusers parallel located 75–100 mm under the bottom of the membrane module, the free board height hf adjusted to 400 mm, and the SADp recommended as 20 in the full-scale MBR studied.