Continuous Stirred Tank Reactor Model Research Articles

CODIMENSION-TWO BIFURCATION ANALYSIS OF THE CONTINUOUS STIRRED TANK REACTOR MODEL WITH DELAY

The aim of this paper is to research the dynamical behaviors of the continuous stirred tank reactor (CSTR) model with delay. Firstly, we discuss the situation that its related characteristic equation has a simple zero root and a pair of purely imaginary roots. Secondly, the center manifold method and the normal form method are used to reduce the equation of CSTR model. Finally, some characteristics about the CSTR model can be obtained. We analyze three different topological structure and give entire bifurcation diagrams and phase portraits, which are innovative phenomenon. At the end, we obtain the stable and unstable periodic solutions by numerical simulation.

Experimental Study and Mathematical Modeling of Self-Sustained Kinetic Oscillations in Catalytic Oxidation of Methane over Nickel.

The self-sustained kinetic oscillations in the oxidation of CH4 over Ni foil have been studied at atmospheric pressure using an X-ray diffraction technique and mass spectrometry. It has been shown that the regular oscillations appear under oxygen-deficient conditions; CO, CO2, H2, and H2O are detected as the products. According to in situ X-ray diffraction measurements, nickel periodically oxidizes to NiO initiating the reaction-rate oscillations. To describe the oscillations, we have proposed a five-stage mechanism of the partial oxidation of methane over Ni and a corresponding three-variable kinetic model. The mechanism considers catalytic methane decomposition, dissociative adsorption of oxygen, transformation of chemisorbed oxygen to surface nickel oxide, and reaction of adsorbed carbon and oxygen species to form CO. Analysis of the kinetic model indicates that the competition of two processes, i.e., the oxidation and the carbonization of the catalyst surface, is the driving force of the self-sustained oscillations in the oxidation of methane. We have compared this mechanism with the detailed 18-stage mechanism described previously by Lashina et al. (Kinetics and Catalysis 2012, 53, 374-383). It has been shown that both kinetic mechanisms coupled with a continuous stirred-tank reactor model describe well the oscillatory behavior in the oxidation of methane under non-isothermal conditions.

Optimized deep learning neural network predictive controller for continuous stirred tank reactor

In this paper, a deep learning neural network model predictive controller (DLNNMPC) is designed to analyse the performance of a non-linear continuous stirred tank reactor (CSTR) that performs parallel and series reactions. The data generated employing the state space model of CSTR is used to train the designed deep learning neural network controller. Deep Learning Neural Network (DLNN) progresses the training with its weights tuned by the proposed hybrid version of evolutionary algorithms – Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA). The developed hybrid PSO – GSA based DLNN model of continuous stirred tank reactor is employed in this paper for model predictive controller design. The effectiveness of the proposed DLNNMPC tuned by hybrid PSO – GSA for CSTR is validated for its performance on comparison with that of other designed Proportional – Integral (PI) and Proportional – Integral – Derivative (PID) controllers as available in early literatures for the same problem under consideration.

Vapor-fed bio-hybrid fuel cell

BackgroundConcentration and purification of ethanol and other biofuels from fermentations are energy-intensive processes, with amplified costs at smaller scales. To circumvent the need for these processes, and to potentially reduce transportation costs as well, we have previously investigated bio-hybrid fuel cells (FCs), in which a fermentation and FC are closely coupled. However, long-term operation requires strictly preventing the fermentation and FC from harming each other. We introduce here the concept of the vapor-fed bio-hybrid FC as a means of continuously extracting power from ongoing fermentations at ambient conditions. By bubbling a carrier gas (N2) through a yeast fermentation and then through a direct ethanol FC, we protect the FC anode from the catalyst poisons in the fermentation (which are non-volatile), and also protect the yeast from harmful FC products (notably acetic acid) and from build-up of ethanol.ResultsSince vapor-fed direct ethanol FCs at ambient conditions have never been systematically characterized (in contrast to vapor-fed direct methanol FCs), we first assess the effects on output power and conversion efficiency of ethanol concentration, vapor flow rate, and FC voltage. The results fit a continuous stirred-tank reactor model. Over a wide range of ethanol partial pressures (2–8 mmHg), power densities are comparable to those for liquid-fed direct ethanol FCs at the same temperature, with power densities >2 mW/cm2 obtained. We then demonstrate the continuous operation of a vapor-fed bio-hybrid FC with fermentation for 5 months, with no indication of performance degradation due to poisoning (of either the FC or the fermentation). It is further shown that the system is stable, recovering quickly from disturbances or from interruptions in maintenance.ConclusionsThe vapor-fed bio-hybrid FC enables extraction of power from dilute bio-ethanol streams without costly concentration and purification steps. The concept should be scalable to both large and small operations and should be generalizable to other biofuels and waste-to-energy systems.

Integration of simulated moving bed chromatography and enzymatic racemization for the production of single enantiomers

Integration of enantioseparation by simulated moving bed (SMB) and mild enzymatic racemization enables the production of single enantiomers from a racemic mixture in theoretically 100% yield and hence overcomes the 50% yield limitation of conventional SMB processes. We implemented such a process consisting of a Chirobiotic TAG column-SMB, an amino acid racemase-containing enzyme membrane reactor, and a nanofiltration unit for concentration of the distomer-enriched SMB raffinate prior to racemization on lab-scale for the production of enantiopure D-methionine. The integrated process scheme was operated continuously for over 30h without significant variations in product concentration and purity and with a yield of 93.5%, demonstrating the feasibility of this integrated process concept. Furthermore, a rational analysis of the integrated process on the basis of a short-cut model was conducted. The process model consists of a true moving bed equilibrium stage model to represent the SMB, a continuous stirred tank reactor model with reversible Michaelis–Menten kinetics to represent the enzyme membrane reactor, a nanofiltration model and feed node mass balances, and enabled the identification of optimal operating points (flow rate ratios, enzyme concentration) at a variety of process specifications and objectives. Optimal operating points were calculated for different cost distributions between the applied materials such as stationary phase, enzyme, solvent, and nanofiltration membrane. By assigning plausible pricing data and lifetimes to the respective materials, variable costs for the specific process considered in this work were estimated.

Kinetic Studies on State of the Art Solid Oxide Cells: A Comparison between Hydrogen/Steam and Reformate Fuels

Electrochemical reaction kinetics at the electrodes of Solid Oxide Cells (SOCs) were investigated at 700°C for two cells with different fuel electrode microstructures as well as on a third cell with a reduced active electrode area. Three fuel mixtures were investigated – hydrogen/steam and model reformate fuels–hydrogen/carbon-dioxide and hydrogen/methane/steam. It was found that the electrode kinetics at the fuel electrode were exactly the same in both reformates. The hydrogen/steam fuel displayed 5–7% faster kinetics than the reformate fuels. 19% faster kinetics were recorded for the cell with a finer microstructure. The measured gas conversion impedance was compared with models in literature for both the 16- and the 2 cm2 cells. The continuously stirred tank reactor (CSTR) AC model approximated the overpotential of the smaller cells (2 cm2) with greater accuracy in the current density range 0–0.5 A/cm2 while the plug flow reactor (PFR) model although derived for the case of zero DC bias predicted the 16 cm2 cell ASR better than the zero bias CSTR model. Furthermore, the gas conversion impedance in the hydrogen/steam fuel split into two processes with opposing temperature behavior in the reformate fuels. By using a 87.5% smaller active electrode area the gas conversion impedance was diminished in the hydrogen/steam fuel at (the same absolute) high fuel flow rates. In both reformates, the second and third lowest frequency processes merged into a single process as the gas conversion was reduced. The SOC with finer electrode microstructure displayed improved kinetics.

Towards efficient and inherently safer continuous reactor alternatives to batch-wise processing of fine chemicals: CSTR nonlinear dynamics analysis of alkylpyridines N-oxidation

This paper demonstrates the integration of process safety concepts (e.g., reactive chemicals, inherently safer design) with classical reaction engineering/system fundamentals (e.g., first-principles reactor modeling, system dynamics and stability) for identifying economically viable and safe continuous stirred tank reactor (CSTR) designs for scale-up of batch-wise fine chemical and pharmaceutical syntheses. As an illustrative and industrially relevant example, the homogeneous catalytic exothermic N-oxidation of alkylpyridines is investigated using a jacketed CSTR model. Reactor steady-state multiplicity and oscillation phenomena, which may bring about serious incidents, are analyzed based upon system equations. Reactor design and operation conditions as well as start-up strategies and worst-case scenarios are systematically investigated to address process safety concerns and balance reactor efficiency.

Model-based cost optimization of a reaction–separation integrated process for the enzymatic production of the rare sugar d-psicose at elevated temperatures

The integration of biocatalysis with continuous separation of product and substrate constitutes an attractive option for overcoming the intrinsic yield limitation in enzymatic reactions that suffer from an unfavourable position of the equilibrium. One example is the recently established continuous process combining enzymatic epimerization in an enzyme membrane reactor (EMR), simulated moving bed (SMB) chromatography and nanofiltration for the high-yield production of the rare sugar d-psicose from its bulk epimer d-fructose with recycling of the unused epimer to the EMR. In this work, we present a first, comprehensive analysis of this novel reaction-separation process concept on the basis of an integrated process model. Therefore, a process model consisting of a continuous stirred tank reactor model with reversible Michaelis–Menten kinetics for representation of EMR operation, a transport-dispersive true moving bed model for representation of SMB operation and an ideal filtration model was constructed. As enzyme costs are particularly difficult to estimate due to their strong dependence on the reactor temperature, we further established a model-based procedure for characterizing the biocatalyst in terms of operational stability and activation as a function of the reactor operating temperature. The integrated process model then enabled the identification of optimum operating points for a fully integrated process operation. First, the established design procedure was used to implement a highly productive run on our existing lab-scale plant (i.e. 2.3kg of d-psicose per L of SMB column volume and day and 4.5kg d-psicose per g enzyme and day), where Dpsicose was produced both at high purity (≈ 98%) and at remarkable yield (96%). Next, the established process model was used for the optimization of the overall process economics. Therefore, a comprehensive analysis of the process in terms of suitable reactor temperatures was performed based on a multi-objective function addressing important cost contributions in the integrated process (i.e. enzyme, desorbent, solid phase, substrate). The presented integrated process scheme can be easily adapted to a number of similar isomerization and epimerization reactions enabling economic production of (almost) the complete set of C6 sugars.

Two-stage parameter estimation applied to ordinary differential equation models

A two-stage (TS) parameter estimation method for identifying ordinary differential equation (ODE) models, which minimizes the squared residuals between the derivatives of the fitted values of available measurements and the rate changes of the states, is presented. The model is an alternative to the traditional method, in which the measured squared residuals and measurements of state are used to obtain near-optimal estimated parameters for ODEs in the first stage of the TS method. Therefore, the problem of ill-conditioning, encountered in integrating the system equations, can be ignored. The second stage of the TS method minimizes the squared residuals in the model's traditional integrated form by using the estimated parameter values from the first stage as initial guesses. Three examples were examined, and the results confirmed the utility of the developed TS parameter estimation method for easy programming and low computation time. The first example is a semi-batch reactor model of toluene hydrogenation, while a continuous stirred-tank reactor model is used for the second example. Finally, a batch-process model focused on the synthesis of glycerol ether synthesis from glycerol and tert-butyl alcohol is examined.

On the relaxing dissipation of dissipative pseudo Hamiltonian models

This paper further explores the link between irreversible thermodynamics and system theory, and its use for port-based modeling for reaction systems. More specifically we show here that a pseudo Hamiltonian representation with R(x) > 0 can be obtained by considering the Brayton-Moser formulation via a unified potential function that verifies a thermodynamic evolution criterion. As a consequence, it gives additional degrees of freedom (i.e. to construct alternate pseudo Hamiltonian models with new passive outputs) usable for further studies on the control design. A representative example of irreversible processes via the non isothermal continuous stirred tank reactor model is used to illustrate the theoretical developments.

An integrated predictive model with an on-line updating strategy for iron precipitation in zinc hydrometallurgy

Iron precipitation by goethite plays an important role in zinc hydrometallurgy. The ferrous ion concentration, which is a key index for assessing the iron removal rate and process control results, cannot be measured on-line. In this study, an integrated predictive model of the ferrous ion concentration is established by integrating the mechanism model and error compensation model, which is based on data identification. The mechanism model is proposed based on an analysis of the process reaction and considering the reaction unit as a continuous stirred tank reactor model. For unknown parameters in the mechanism model, a double-particle swarm optimization algorithm based on information exchange and dynamic adjustment of the feasible region is developed for optimal selection. To improve the adaptive capability of the integrated model, we propose a model-updating strategy and parameter calibration method based on a sensitivity analysis to accomplish on-line adaptive updating of the predictive model. The simulation results demonstrate that the proposed model can effectively track the variation tendency of the ferrous ion concentration and successfully improve the adaptability of the integrated model.

Model Driven Process Design and Development for a Continuous Process

This paper presents a case study where kinetic models were used to drive process development of an amination reaction in a continuous process. The kinetic model was first used to optimize the process by minimizing impurity formation. Then, the kinetic parameters were put into a two-in-series CSTR (continuous stirred tank reactor) model and a separate PFR (plug flow reactor) model to guide reactor selection and optimize the reactor design. Once the model predictions were validated with experimental data, the simulated impurity profile from each reactor type was compared. While the results showed that both reactors delivered similar impurity profiles at steady state, the model was used to conduct perturbation analysis on the two reactors to assess the impurity and operational control strategy. The simulations showed that the CSTR can tolerate a process upset time up to 10% of its residence time with materials meeting product specification as compared to the PFR. Since the CSTR offers additional buffering ca...

Identification of LPV Models with Non-uniformly Spaced Operating Points by Using Asymmetric Gaussian Weights

In this paper, asymmetric Gaussian weighting functions are introduced for the identification of linear parameter varying systems by utilizing an input–output multi-model structure. It is not required to select operating points with uniform spacing and more flexibility is achieved. To verify the effectiveness of the proposed approach, several weighting functions, including linear, Gaussian and asymmetric Gaussian weighting functions, are evaluated and compared. It is demonstrated through simulations with a continuous stirred tank reactor model that the proposed approach provides more satisfactory approximation.

사연댐 수위조절시 수질변화 분석

울산시의 주요 생활용수공급댐인 사연댐 상류 수몰지역 내에 국보 285호인 반구대 암각화가 위치하고 있다. 표고 53~57 m에 위치한 암각화 보존을 위한 여러 가지 방안 중, 사연댐 수위를 60 m에서 52 m로 낮추어 물 밖으로 끄집어내는 안이 주로 검토되어 왔다. 댐의 수위를 인위적으로 조절하는 경우 저수량 및 용수공급량 감소와 더불어 부영양화로 인해 수질이 나빠지게 된다. 본 연구에서는 사연댐 수위조절에 따른 수질악화로 댐의 기능상실과 수질변화로 인해 예상되는 여러 가지 문제점을 검토하였다. Vollenweider 모델과 CSTR (Continuous Stirred Tank Reactor) 모델을 이용하여 수위조절시 변화가 예측되는 대표적인 수질지표인 BOD 및 COD 그리고 조류성장의 주 원인이 되는 총인과 총질소의 농도변화를 분석하였다. 그 결과 사연댐의 수위를 60 m에서 52 m로 조절하는 경우, COD의 농도는 약간 낮아지지만 총질소와 총인은 약 130% 이상 농도가 증가되는 것으로 나타났다. 이러한 변화는 심각한 조류문제를 일으킬 수 있으며, 사연댐의 수질관리를 영양염류의 농도를 대상으로 하는 경우 수질이 악화되는 것으로 나타났다. The Bangudae Petroglyphs, national treasure No. 285 is located within submerged upper districts of Sayeon dam supplying the main residential water in Ulsan. Of the many ways for the reservation of Petroglyphs located the altitude at 53~57 m, the plan that we take it out of the water lowering the water level from 60 m to 52 m has been examined mainly in case of controlling artificially the water level of the dam. In this paper, we examined expected problems from the loss of dam function and the change of water quality from water deterioration caused by the water level control of the Sayeon dam. Using the model of Vollenweider and CSTR (Continuous Stirred Tank Reactor), we analyzed the density change of BOD and COD, representative water quality index and the TP and TN, the main reason of algae growth. The result showed that the density of COD lowered a little but the density of TP and TN went up over 130% when controlling the water level from 60 m to 52 m. These changes cause a serious algae problem and if doing the water quality management as the density of TN and TP, the water quality would become worse. Water storage and supply residential water decreases, and the water quality becomes worse because of eutrophic state.

Stability analysis and controller design of interval type-2 fuzzy systems with time delay

The type-2 fuzzy models can handle the system uncertainties directly based on the type-2 fuzzy sets. In this paper, the Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 (IT2) fuzzy systems with time-varying delay. Delay-dependent robust stability criteria are developed in terms of linear matrix inequalities by using the improvement technique of free-weighting matrices. Less conservative results are obtained by considering the information contained in the footprint of uncertainty. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results. One is provided to show the merits of the proposed method, the other based on the continuous stirred tank reactor model is given to illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.

Thermal Oscillations in the Decomposition of Organic Peroxides: Identification of a Hazard, Utilization, and Suppression

The purpose of this research is to identify and characterize oscillatory thermal instability in organic peroxides that are used in vast quantities in industry and misused by terrorists. The explosive thermal decompositions of lauroyl peroxide, methyl ethyl ketone peroxide, and triacetone triperoxide are investigated computationally, using a continuous stirred tank reactor model and literature values of the kinetic and thermal parameters. Mathematical stability analysis is used to identify and track the oscillatory instability, which may be violent. In the mild oscillatory regime it is shown that, in principle, the oscillatory thermal signal may be used in microcalorimetry to detect and identify explosives. Stabilization of peroxide thermal decomposition via Endex coupling is investigated. It is usually assumed that initiation of explosive thermal decomposition occurs via classical (Semenov) ignition at a turning point or saddle-node bifurcation, but this work shows that oscillatory ignition is also characteristic of thermoreactive liquids and that Semenov theory and purely steady state analyses are inadequate for identifying a thermal hazard in such systems.

Determination of the sorption and desorption kinetics of perfume raw materials in the liquid phase with vesicular dispersion: Application of SIFT-MS

Perfume raw materials such as coumarin, hexyl acetate and octanal are used in domestic fabric softeners together with cationic quaternary ammonium surfactants during the last rinsing step of a wash cycle. Selected ion flow tube mass spectrometry (SIFT-MS) is used to analyze the gas phase concentration of these perfume raw materials in an experiment, mimicking this rinsing step when fabric softeners are applied together with a vesicular diethyl ester dimethyl ammonium chloride (DEEDMAC) dispersion in a bubble column. A continuous stirred tank reactor (CSTR) model is proposed to obtain sorption and desorption kinetics for the mass transfer between the liquid phase and the vesicular dispersion from experimental gas phase concentration data. Sorption coefficients of (4.8±0.3) 10−3, (9.4±0.1) 10−3 and (4.0±0.1) 10−3s−1 are obtained for coumarin, hexyl acetate and octanal. Desorption coefficients for these components are respectively reported as (5.4±0.6) 10−5, (1.8±0.1) 10−5 and (3.5±0.2) 10−5s−1. From an engineering point of view, SIFT-MS is considered to be a promising experimental technique to evaluate the dynamic behavior, i.e., the sorption and desorption kinetics, of molecules in a vesicular dispersion using the proposed CSTR model.

ON THE NUMERICAL CONTINUATION OF ISOLAS OF EQUILIBRIA

We present a numerical strategy to compute one-parameter families of isolas of equilibrium solutions in ODEs. Isolas are solution branches closed in parameter space. Numerical continuation is required to compute one single isola since it contains at least one unstable segment. We show how to use pseudo-arclength predictor–corrector schemes in order to follow an entire isola in parameter space, as an individual object, by posing a suitable algebraic problem. We continue isolas of equilibria in a two-dimensional dynamical system, the so-called continuous stirred tank reactor model, and also in a three-dimensional model related to plasma physics. We then construct a toy model and follow a family of isolas past a fold and illustrate how to initiate the computation close to a formation center, using approximate ellipses in a model inspired by the van der Pol equation. We also show how to introduce node adaptivity in the discretization of the isola, so as to concentrate on nodes in region with higher curvature. We conclude by commenting on the extension of the proposed numerical strategy to the case of isolas of periodic orbits.

Model comparisons for tracer experiments at a clear water storage tank

A fluoride tracer experiment was conducted to investigate mixing processes and residence times in a cylindrical clear water storage tank at the Stromlo Water Treatment Plant, Canberra, ACT. Four different modelling techniques have been used to simulate the experimental results: computational fluid dynamics (CFD), a single continuously stirred tank reactor (CSTR), two CSTRs in series, and a series/parallel combination of two CSTRs (NM). Flow of a conservative tracer through the tank has been simulated at the rated flow from the works using the PHOENICS (CFD) program. The CFD simulation agrees closely with the measured fluoride concentrations and requires no fitted parameters. The agreement with the experimental data for NM is comparable with the CFD and a little better than two CSTRs in series. The poorest agreement was obtained with a single CSTR model.

Model Comparisons for Tracer Experiments at a Clear Water Storage Tank

A fluoride tracer experiment was conducted to investigate mixing processes and residence times in a cylindrical clear water storage tank at the Stromlo Water Treatment Plant, Canberra, ACT. Four different modelling techniques have been used to simulate the experimental results: computational fluid dynamics (CFD), a single continuously stirred tank reactor (CSTR), two CSTRs in series, and a series/parallel combination of two CSTRs (NM). Flow of a conservative tracer through the tank has been simulated at the rated flow from the works using the PHOENICS (CFD) program. The CFD simulation agrees closely with the measured fluoride concentrations and requires no fitted parameters. The agreement with the experimental data for NM is comparable with the CFD and a little better than two CSTRs in series. The poorest agreement was obtained with a single CSTR model.