Ideal Continuous Stirred Tank Reactor Research Articles

Kinetic-hydrodynamic models considering climatic influence on the domestic sewage treatment by constructed wetlands in tropical country

Typical constructed wetlands (CW) sizing methods in tropical countries rarely considers climate parameters as evapotranspiration (EPT) and rainfall (Ra), even though high levels of EPT and Ra can change the pollutant removal kinetic and Wastewater hydrodynamic. This paper aims to evaluate the climatic influences (EPT and Ra) on fit of several kinetic-hydrodynamic models used to describe the sewage organic matter removal in a real scale vertical (VSSF-CW) and horizontal (HSSF-CW) subsurface flow constructed wetland. Sewage quality (Biochemical Oxygen Demand - BOD and Chemical Oxygen Demand - COD) and sewage flow rates data were applied of First Order, Grau-Second Order, Monod, Monod Multi and Stover-Kincannon kinetic models, combined with ideal continuous stirred-tank reactor (CSTR) and plug-flow reactor (PF) hydrodynamic models. Monod, Monod Multi and Stover-Kincannon models (in CSTR) were more able to represent organic matter removal in CWs. Models considering EPT and Ra were more adequate or with no statistical difference compared with conventional models (that don’t consider EPT and Ra), except for BOD in VSSF-CW.

Transient heat transfer during startup of a thermal plasma chamber: Numerical insights

Thermal plasma pyrolysis of radioactive waste is a recommended technique to manage large volume of combustible radioactive waste comprising of rubber and plastics. A lumped parameter based numerical model, to predict the thermal behavior of a plasma pyrolysis chamber during startup, is reported in this work. The model takes into account the non-ideal flow conditions inside the plasma chamber which are specific to the geometry of the chamber. Three different non-ideal models – a Continuous Stirred Tank Reactor (CSTR) having exchange with a separate perfectly mixed CSTR like geometry, two parallel CSTRs, and two parallel CSTRs with exchange, as well as an ideal single CSTR model have been compared. The models consider heat transport from plasma chamber interior to the walls through convection as well as radiation. Resistance offered by five successive layers of insulation of different materials has been considered. The predictions from the models are compared against experimentally determined evolution of chamber temperature during startup for three different power ratings of the plasma torch. The model formulation of two parallel CSTRs with exchange (a two-parameter model) is observed to fit the experimental data the best. A detailed sensitivity analysis has been carried out and the optimum model parameters are determined. Temperature evolution of different insulation layers has also been obtained. The validated model has been used to study the temperature response of the chamber during two different types of operating transients, viz. step changes in torch power and sinusoidal variation in torch power.

Systematic calibration of N2O emissions from a full-scale WWTP including a tracer test and a global sensitivity approach

Nitrous oxide (N2O) is a greenhouse gas (GHG) emitted during biological nitrogen removal from wastewater treatment plants (WWTPs). Some modelling tools have been proposed to predict N2O emissions during the design and operation of WWTPs. In this study, the novel ASM2d-N2O model, which accounts for the production of N2O in nutrient removal WWTPs, was used to study the associated emissions from a full-scale WWTP with two independent lines. Firstly, the hydraulics of the WWTP was characterized by a residence time distribution test, showing the flow was equally divided into the two treatment lines (49.3 vs. 50.7%), that each reactor worked as an ideal continuous stirred tank reactor and the secondary settler model flux was similar to a plug-flow reactor. The ASM2d-N2O model was then calibrated using experimental data obtained under dynamic conditions. A global sensitivity analysis was used to select, among 59 model parameters, five candidates that resulted to be related to nitrifying organisms. Different parameter subsets up to four parameters were evaluated, being the subset [µNOB, qAOB_AMO, KO2_NOB, KNO2_NOB] the best, achieving 53.3% reduction of the calibration cost function. The model fit obtained provided a reasonably description of nutrients and N2O emission trends, considering the inherent operational variability suffered in full-scale WWTPs. Finally, a simulation-based study showed that, for the given WWTP and operational conditions, an unbalanced distribution of flow-rate between the two treatment lines did not result in a significant increase on N2O emissions. The results obtained show that this model can be a suitable tool for predicting N2O emissions in full-scale WWTPs, and can therefore be used to find operational conditions that help to minimise these emissions.

Simulation of ethylene polymerization in continuous slurry reactors

A large volume of polyethylene is manufactured in continuous slurry reactors at an industrial scale. A complete reactor model of the polyethylene slurry reactors consists of the kinetic model, intraparticle diffusion model and the mass balance equations for individual species. In this paper, a modified polymeric multigrain model (PMGM) is used to describe the intraparticle monomer transport, rate of polymerization, particle growth and polymer yield in an ideal continuous stirred tank reactor (CSTR) using a single-site, non-deactivating catalyst. The effect of parameters such as the original catalyst size, ethylene partial pressure and the gas–liquid mass transfer coefficient on the radial monomer concentration profile, the rate of polymerization, polymer yield, reactor safety factor and the polydispersity index of the macroparticle is discussed.

Dry Powder Mixing Is Feasible in Continuous Twin Screw Extruder: Towards Lean Extrusion Process for Oral Solid Dosage Manufacturing.

Using discrete element method (DEM) modeling and near-infrared (NIR) spectroscopy, the feasibility of powder mixing in the initial pre-melting zones of a twin screw extruder using two independent feeders was studied. Previous work in the pharmaceutical and food industry has focused on mixing when materials are melted or on material homogeneity at the extruder's output. Depending on the formulation, ensuring a fully blended formulation prior to melting may be desired. Experiments were conducted using a Coperion ZSK-18 extruder to evaluate if blend uniformity can be achieved by exploring screw configuration, screw speed, and powder feed rate. As powder exited the extruder and deposited on a conveyor belt, an in-line NIR spectrophotometer measured spectra of material. Chemometric-based models predicted unknown concentrations to evaluate if blend uniformity was achieved. Using the EDEM software, Hertz-Mindlin contact model, and dimensions of the extruder, DEM simulations complemented the experimental work. The DEM computational models provided understanding of mixing patterns inside the extruder at particle scale and helped select the screw configuration before doing experimentation. The simulations showed good axial mixing for all the screw configurations studied, while good cross (radial) mixing was only observed for the screw configuration with 90-degree kneading elements. Therefore, the screw configuration with two 90-degree kneading elements was chosen for the experimental study. The RTD profiles when using a screw configuration with only conveying screw elements are comparable to a plug flow reactor (PFR), while the profiles when using kneading elements are more comparable to an ideal continuous stirred tank reactor (CSTR). For the screw configuration with 90 degrees kneading elements, the mean residence time (MRT) decreases with an increase in the screw speed. Experimental NIR spectra showed that concentrations can be predicted with an error of 2%. It was demonstrated that the twin screw extruder can provide proper dry powder mixing of two powder feed streams based on a unit dose scale, enabling continuous powder mixing prior to the melting zone in the extruder for the formulation studied with a cohesive API. This setup may also work for other types of formulations. These studies can help in developing lean hot melt as well as wet extrusion/granulation processes using twin screw extruders for the continuous manufacturing of oral solid dosage products.

Analysis of Proportional Integral Derivative Controller Parameters for CSTR

Continuous Stirred Tank Reactor (CSTR) plays a vital role and presents a various scope of researchers in the field of control and chemical engineering which exhibits of highly nonlinear behaviour and has wide operating ranges. Different control methods have been implemented on CSTR to control these parameters. Tragically, in the realcase, the behaviour of the CSTR is very different from that expected ideal CSTR which leads to the outcomes of the wrong product. However, it is a challenging task for every engineer to control the CSTR.PID controller has been proposed for adjust enhanced PID parameters in a CSTR operation utilizing a weighted mix of target capacities. Streamlining of PID controller parameters is the key objective of concoction and biochemical businesses. PID controllers have restricted the working scope of procedures with effective nonlinearity. This work considers some issues in CSTR and presents the efforts of existing researchers and it comes into view as an essential new method to adjust the control parameters. This work plans to investigate the various techniques in CSTR along with its solutions and these schemes have been surveyed in this work. This survey presents the comparison of various methods for optimizing parameters in CSTR are employed and compared with certain parameters.

Continuous Mixing Technology: Characterization of a Vertical Mixer Using Residence Time Distribution.

Continuous powder mixing technology (CMT) application during continuous direct compression has emerged as a leading technology used in the development and manufacture of solid oral dosage forms. The critical quality attributes of the final product are heavily dependent on the performance of the mixing step as the quality of mixing directly influences the drug product quality attributes. This study investigates the impact of blend material properties (bulk density, API particle size distribution) and process parameters (process throughput, hold up mass and impeller speed) on the mixing performance. Mixing of the blend was characterized using the Residence Time Distribution (RTD) of the process by trending the outlet stream of the mixer using a near-infrared (NIR) probe after the injection of a small mass of tracer at the inlet stream. The outcomes of this study show that the RTDs of the mixer with throughput ranging between 15 and 30kg/h; impeller speed ranging between 400 and 600rpm and hold up mass (HUM) ranging between 500 and 850g can be described by a series of two ideal Continuous Stirred Tank Reactors (CSTRs) with different volumes, and correspondingly, different mean residence times. It is also observed that the mixing is mainly occurring in the lower chamber of the CMT and the normalized RTDs of the mixer are similar across the range of process conditions and material attributes studied. The results also showed that the formulation blend with different API particle sizes and bulk properties, like bulk density and flowability, provide insignificant impact on the mixing performance. The CMT allows independent selection of target set points for HUM, impeller rotational speed and line throughput and it shows great robustness and flexibility for continuous blending in solid oral dose manufacturing.

Data-Driven Linear Parameter-Varying Model Identification Using Transfer Learning

This letter proposes transfer learning methods to address a challenge in state-space linear parameter-varying (LPV-SS) model identification/learning using kernelized machine learning, when the distributions of the training and testing sets are different. Kernel mean matching is first employed to correct sample bias by resampling the data in the training set before the states in state-space model are estimated. Moreover, transfer component analysis is adopted to find a state-space basis transformation such that the transformed states follow similar distributions. The proposed methods are validated by testing on an ideal continuous stirred tank reactor (CSTR) model. Simulation results show that the proposed learning methods can enhance the accuracy of model identification and reduce the efforts involved in hyperparameters tuning.

Development of the Crank’s diffusion model for the case of material-gas feedback regime in gas flow reactors. Advanced methodology of oxygen partial pressure relaxation for the kinetics of oxygen exchange in nonstoichiometric oxides

• The Crank model may give incorrect k and D in case of vigorous reaction. • Extended samples require consideration of convective and diffusion gas transfer. • Models taking into account these factors are developed in this study. In order to determine the kinetic parameters of oxygen exchange between nonstoichiometric oxides and the gas phase, the rate constant of surface exchange k and the coefficient of bulk oxygen diffusion in the oxide D , one needs to model the kinetics of relaxation occurring under mixed diffusion-reaction control. It is shown that the widely used Crank model can misestimate the k and D values as it does not take into account such factors as (i) changes in oxygen partial pressure p O 2 in the reactor caused by vigorous reaction, (ii) the non-uniform distribution of p O 2 over the elongated oxide sample. Models taking into account these factors are discussed sequentially in this work: the ideal continuous stirred-tank reactor (CSTR) model where p O 2 varies over time as reaction proceeds; the tanks-in-series (TIS) model imitating the non-uniform distribution of p O 2 over the sample under approximation of convective gas transfer; and the model of tanks-in-series with diffusion-convective gas transfer (TSD). The TIS and TSD models (the latter one being used for low gas flow rates), which take into account all of the above factors, give the most reasonable results: the scatter of the values of the kinetic constants k and D determined at different rates of gas flow in the reactor does not exceed the reasonable experimental error. An expression is proposed for estimating k TIS , which corrects the k values obtained from the Crank model.

Experimental Study on the Solids Residence Time Distribution in Multiple Square-Based Spouted Beds

The present work aims at investigating the residence time distribution (RTD) of a multiple spouted bed reactor, which will be applied for the pyrolysis and gasification of residual biomass. The unit is composed of square-based spouted beds, placed in series and at descending heights, and communicating with each other through an opening in the lateral wall. The gas is fed evenly in parallel. The experimental analysis is based on tracer experiments in cold-flow units, assessing the influence of the number of units and the bed height. The tests proved the good mixing properties of the spouted beds, which create a stable fluidization regime and do not feature dead zones. Each spouted bed can generally be well assimilated to an ideal continuous stirred tank reactor (CSTR). The RTD of the device seems adequate for the application, and also seems to be well tuneable through the selection of the bed height and number of units. Given the good similarity with ideal reactor networks, these represent a valid tool to estimate the final behavior in terms of RTD.

A shallow cross-flow fluidized-bed solar reactor for continuous calcination processes

A laboratory-scale solar reactor prototype dedicated to calcination processes of non-metallic mineral particles is tested and characterized. The prototype consists of an indirect heating shallow cross-flow fluidized-bed reactor-receiver. It is composed of 4 compartments in series in which the particles are thermally treated with solar power in order to drive the endothermic calcination reaction. The particles are fluidized in the reactor with preheated air and are heated up to 800 °C through the front wall of the reactor receiving the concentrated solar flux (about 200 kW/m2). The tests are carried out at the 1-MW Odeillo’s solar furnace (France). The thermal decomposition of a continuous stream of 9.4 kg/h of dolomite (CaMg(CO3)2) is investigated in this paper. The half decomposition of dolomite (CaMg(CO3)2 → CaCO3 + MgO + CO2) is performed with a degree of conversion of 100%. The complete decomposition of dolomite (CaMg(CO3)2 → CaO + MgO + 2CO2) is not reached because, with respect to the CO2 partial pressure in the reactor, the temperature of particles is not high enough to decompose the calcium carbonate. The calculated thermochemical efficiency (i.e. the energy absorbed by the endothermic calcination reaction compared to the solar energy provided to the system) is 6.6%. This low efficiency is neither surprising nor critical since the reactor design was not optimised with respect to energy efficiency but designed to the control of particle flow and front wall solar flux distribution. A numerical model considering the 4 compartments of the reactor as 4 ideal continuous stirred tank reactors in series is developed. The model accounts for the mass and the energy balances, as well as the reaction kinetics of the half decomposition of dolomite. The model gives consistent results compared to the experimental data. These results are a proof of concept of continuous calcination reaction using concentrated solar energy in a cross-flow fluidized-bed reactor.

A Study on the Hydraulic Behavior in Moving Bed Biofilm Reactor for Water Treatment (I) - Observation through Tracer Tests -

The purpose of this study was to investigate the optimum condition of hydraulic behavior in MBBR (Moving Bed Biofilm Reactor) process under various operating conditions. As results of the tracer tests, it was found that the air injection amount/rate had an important influence on the hydraulic behavior in the reactor. However, the filling rate of the carrier did not affect the hydraulic flow. It is also observed that the selective operation of the air injection pipeline has little effect on the hydraulic behavior. The operation of the internal circulators reduces the short-circuit flow and the dead flow, and by inclining them, causing the up-down flow causes improve flow condition into to that of the ideal CSTR (Continuous Stirred Tank Reactor). Key words: MBBR (Moving Bed Biofilm Reactor), tracer test, short circuit flow, eddy flow, CSTR (Continuos Stirred Tank Reactor)

Acetylene pyrolysis in a jet-stirred-reactor for low pressure gas carburizing process – Experiments, kinetic modeling and mixing intensity investigations by CFD simulation

Low-pressure gas carburizing is used to harden steel, it has been shown to be a source of considerable PAH (Polycyclic Aromatic Hydrocarbon) pollution. Some PAH, like benzo[a]pyrene, are carcinogenic, and activities such as furnace maintenance and cleaning operations may thus represent a risk to workers. Occupational exposure during these operations should therefore be reduced. Benzene is a specific chemical marker of PAH, and the aim of the study was to understand its formation. Acetylene pyrolysis was experimentally performed in a jet-stirred-reactor in the laboratory, in conditions close to those encountered in industrial processes (1173 K and 8 kPa). Products of pyrolysis were analyzed by gas chromatography (TCD, FID) at the outlet from the reaction zone. The influence of residence time in the reactor was studied. A detailed kinetic model assuming an ideal continuous stirred tank reactor was used to describe the formation of chemical compounds and validate experimental data. CFD simulations were performed to characterize the reactor’s hydrodynamics by applying the theory of the free jet. They allowed putting forward one explanation to understand the deviation between experiments and the kinetic model.

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

AbstractThis work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.

Integration of CFD and polymerization for an industrial scale cis-polybutadiene reactor

ABSTRACTA computational fluid dynamics (CFD) approach, coupled with anionic polymerization kinetics, was used to investigate the solution polymerization in a 12 m3 industrial scale cis-polybutadiene reactor. The kinetic model with double catalytic active sites was integrated with CFD by a user-defined function. The coupled model was successfully validated by the plant data and then used to investigate the key operating variables. Also, predictions of CFD model were compared with those of continuous stirred tank reactor (CSTR) model. Although the reaction mixture is well mixed in the middle and at the top of the reactor, there exists a poor mixing feeding zone at the bottom, which leads to serious deviations from the ideal CSTR. The polymerization process with nonideal mixing is very sensitive to the inlet temperature and the feeding rate. Enhancing the mixing performance in the feeding zone could be an effective way to improve the product quality.

Kinetic investigations of the steam reforming of methanol over a Pt/In2O3/Al2O3 catalyst in microchannels

A kinetic study of methanol steam reforming over bimetallic Pt/In2O3/Al2O3 catalyst was carried out. The kinetic measurements were performed in a microstructured monolithic reactor with an external recycle free of temperature and concentration gradients. By the help of residence time distribution measurements it could be verified that the reactor showed the behaviour of an ideal continuous stirred tank reactor (CSTR). The absence of external and internal concentration gradients could be proven by corresponding experiments and theoretical diagnostic criteria.The kinetic measurements performed by variation of the reactant inlet partial pressures revealed that in the temperature range from 310°C to 355°C the molar rate of methanol consumption mainly depends on the methanol partial pressure, especially at higher temperatures, whereas there is only minor dependence on the water partial pressure. Carbon dioxide has no inhibiting effect, whereas hydrogen showed a weak inhibiting effect.Two power laws and three Langmuir-Hinshelwood rate equations were created for the modelling of the kinetic data. Power laws could not be fitted to the measured values. Therefore the uses of Langmuir-Hinshelwood rate laws with temperature dependent sorption constants are inevitable for the modelling. The model discrimination revealed that the rate law derived from a mechanism, which assumes the dehydrogenation of an adsorbed methoxy-species as rate determining step, described the measured kinetic data second best. Optimum agreement between observed and predicted molar rates of methanol consumption was obtained when applying a Langmuir-Hinshelwood rate law assuming dissociative methanol and molecular water adsorption on the catalyst surface. Dissociative adsorption of water and methanol at the same active site may be excluded. This leads to a better evaluation of the models that assume molecular water adsorption at the same site where methanol ties or the ones with no participation of water in the rate determining step (RDS) under discrimination.

Stochastic Modeling of Polymer Microstructure From Residence Time Distribution

Stochastic modeling constitutes a powerful technique to obtain complete distributions of microstructural properties of polymer materials and may help to synthesize polymers with well‐defined microstructure, as in the case of controlled radical polymerizations (CRP). However, these techniques have been often applied to describe polymerizations performed in batch or idealized continuous plug flow conditions. The present manuscript describes a Monte Carlo technique that can be used to calculate microstructural properties in polymerization systems performed continuously with arbitrary residence time distributions (RTD), under regime of complete micromixing segregation. The technique approximates the continuous system by a set of batch reactors, operated independently, whose volumes and batch times can be related to the discretized version of the RTD. The technique is applied successfully to describe a styrene‐based CRP reaction carried out in an ideal continuous stirred tank reactor and a tubular non‐ideal tubular reactor.

Relationship between residence time distribution and forces applied by paddles on powder attrition during the die filling process

Abstract The die filling process, which happens prior to the compaction step, affects directly the quality of the final product (tablets). As paddles pass through the powder bed inside the feed frame, shear is applied to particles. Therefore, it is important to establish a relationship between residence time distribution (RTD) and forces applied by the feed frame paddles on powder attrition and overlubrication during the die filling process. The pulse injection method was used to study the RTD. The discrete element method (DEM) was also used to measure the RTD of particles by size ranges and the mean residence time (MRT) inside the feed frame. The experimental and DEM simulation design of experiments included 2 paddle wheel speeds (24 and 72 rpm) and 2 die disk speeds (29 and 57 rpm). Experimental results show that higher paddle wheel speeds lead to lower mean residence time, narrower RTD profiles, and larger number of paddle passes. The simulations RTD profiles are similar to an ideal continuous stirred tank reactor (CSTR) profile with a sharp peak and a tail. Operating conditions, feed frame exit contributions, and outlet mass flow rate affect the MRT. The RTD analysis by particle size shows that particle size segregation occurs where the smaller particles are leaving the feed frame faster. The level of powder confinement inside the feed frames can have a significant effect on powder attrition. As particle size increases, the compressive and tangential force applied to it increases. The tangential force data show that the level of attrition is also affected by the paddle wheel speed. This study explains in detail different factors that can affect the residence time distribution and the force applied to particles that can ultimately cause particle breakage and powder overlubrication.

Differentiation criteria study for continuous stirred tank reactor and plug flow reactor

All reactors in reality are not ideal plug flow reactor (PFR) or ideal continuous stirred tank reactor (CSTR). They are difficult to differentiate. This study was to investigate the reactor analysis of PFR and CSTR through tracer response curves, residence time distributions (RTD) and several hydraulic performance indexes. We set up the differentiated value of each index. The tracer response curve showed that our lab-scale CSTR was close to ideal CSTR and got 99.9% recovery. In the RTD curves, the results could significantly recognize the PFR nature of high rate pond (HRP). With hydraulic performance indexes study, every selected index demonstrated that the studied HRP was closer to PFR than the studied CSTR. Based on the lab-scale study results, this study established the cutting point between the PFR and CSTR in each index; we were looking through the different types of reactors in literature and we confirmed the criteria with all literature reactors with the “graphic method”. The method helped us to establish those important values to help us to differentiate the reactor types in practice and to understand the designs better.

Experimental study and mathematical modeling of the residence time distribution in magnetic mixer

This study reports on research results in the field of a mixing process under the action of a transverse rotating magnetic field (TRMF). The main objective of this paper is to present the effect of this type of a magnetic field on residence time distribution (RTD) measurements. This paper evaluates the performance of a magnetic mixer by comparing the results of an experimental investigations in a pilot set-up and theoretical values obtained from mathematical model. This model consisting of the set of ideal continuous stirred tank reactors (CSTR) fitted well the experimental data.