A pseudo-dynamic optimization of a dual-stage methanol synthesis reactor in the face of catalyst deactivation

This paper presents an optimization investigation on methanol synthesis reactor in the face of catalyst deactivation using multi-objective genetic algorithms. Catalyst deactivation is a challenging problem in the operation of methanol synthesis reactor and has an important role on productivity of the reactor. Therefore, determination of the optimal temperature profile along the reactor could be a very important effort in order to cope with catalyst deactivation. Our previous studies clarify the benefits of a two-stage reactor over a single stage reactor. In this study, an optimal temperature trajectory is obtained for each stage of the corresponding two-stage reactor. Here, steady state optimization is performed in six different activity levels by maximizing the yield and minimizing the temperature of the first stage of the reactor. Multi-objective genetic algorithms are used to solve this two-objective optimization. The set of optimal solutions obtained for six activity levels represents an optimal temperature trajectory for each stage, which has been extended and proposed as a dynamic optimization. This optimization resulted in an additional 3.6% yield, during the course of 4-year process.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

Two-phase modeling of a gas phase polyethylene fluidized bed reactor

A two-phase model is proposed for describing the behavior of a fluidized bed reactor used for polyethylene production. In the proposed model, the bed is divided into several sequential sections where flow of the gas is considered to be plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Voidages of the emulsion and bubble phases are estimated from the dynamic two phase structure hydrodynamic model. The kinetic model employed in this study is based on the moment equations. The hydrodynamic and kinetic models are combined in order to develop a comprehensive model for gas-phase polyethylene reactor. The results of the model are compared with the experimental data in terms of molecular weight distribution and polydispersity of the produced polymer. A good agreement is observed between the model predictions and actual plant data. It has been shown that about 20% of the polymer is produced inside the bubble phase and as such cannot be neglected in modeling such reactors.     

Simulation of Hydroisomerization of <Emphasis Type="Italic">n</Emphasis>-Pentane into 2-Methylbutane on a Palladium-Containing Mordenite Catalyst

A stepwise mechanism for the isomerization of n-pentane into 2-methylbutane on a bifunctional palladium-containing mordenite catalyst is proposed and a corresponding kinetic model is built. Kinetic experiments are performed in a flow catalytic reactor. During the experiments, the reactor pressure varied from 10 to 30 atm, the reactor temperature varied from 603 to 640 K, and the hydrogen/n-pentane molar ratio varied from 2 to 10. The contact time (the ratio of the catalyst weight to the mass flow rate of the raw material) varied from 0.5 to 2 h. From the data of the kinetic experiment, the kinetic constants of the model and the constants of the distribution density of the observation errors are estimated by the maximum likelihood (ML) method. A sequential design of the kinetic experiment is implemented in order to precisely estimate the model constants and the kinetic model allowing us to predict the experimental results with an accuracy exceeding that of the starting experiments. The model is shown to be adequate for the experimental data obtained.     

Study on the enzymatic hydrolysis of racemic methyl ibuprofen ester

The hydrolysis of racemic methyl ibuprofen ester in the presence of lipase from Candida rugosa was investigated in shake flasks. Experiments were performed to study the effect of temperature, pH and shaking speed on the reaction rate. Different hydrophobic co‐solvents were screened for the highest reaction rate and the presence of enzyme inhibition by substrate and products was examined. A kinetic expression was then proposed to describe the reaction. Kinetic parameters were determined for the optimum operating conditions and the proposed model was verified with the experimental results. Next, this reaction was scaled up to a fed batch stirred tank reactor. Batch reactor and fed batch reactor configurations were compared for better conversions. The effects of aqueous phase hold‐up, substrate concentration and feed flow rate on the conversion of the reaction were also studied. Higher conversions were obtained in a fed batch reactor when compared with the batch reactor. In the fed batch reactor, increased conversions were observed with lower feed flowrates and high aqueous phase hold‐up. © 2001 Society of Chemical Industry     

旋风反应器内传热的研究

研究了旋风反应器内壁与气体之间的传热过程，提出了一套数学模型，对实验数据进行关联。结果表明，模型计算结果与实验数据基本一致，计算误差一般在１０％以下。     

Modeling and simulation of dynamics of chemical reactors

The rate of the homogenous exothermic hydrolysis reaction of acetic anhydride catalyzed by sulfric acid in solvent acetic acid was estimated from nonisothermal experimental batch reactor transient temperature data. Rate equations based on three different reaction mechanisms of hydrolysis published in the literature were fitted to the experimental rate data. The experimental results on runaway and limit cycle behavior obtained with this reaction were explained by using the mechanism-based rate equations for hydrolysis in the reactor dynamic models, and good agreement was obtained between the predicted and the experimental dynamic data.     

Melt polycondensation of poly(ethylene terephthalate) in a rotating disk reactor

A multicompartment model is proposed for a semibatch melt polycondensation of poly(ethylene terephthalate) in a rotating disk polymerization reactor and compared with laboratory experimental data. The reactor is a horizontal cylindrical vessel with a horizontal shaft on which multiple disks are mounted. The reactor is assumed to comprise N equal sized compartments and each compartment consists of a film phase on the rotating disk and a bulk phase in which disks are partially immersed. The effects of disk rotating speed, number of disks, reaction temperature, and pressure were investigated. It was observed that ethylene glycol is predominantly removed from thin polymer layers on the rotating disks and the enhanced interfacial area exerted by ethylene glycol bubbles accounts for about 30–50% of the total available interfacial mass transfer area. Although the rate of polymerization increases as more disks are used, the maximum number of disks in a reactor must be determined properly in order to prevent the formation of thick polymer films that result in a reduced specific interfacial area and reduced polymerization efficiency. At a fixed reaction pressure, the equilibrium conversion is reached but the rate of reaction can be further increased by increasing the reaction temperature. The results of the proposed multicompartment model are also compared with those predicted by a simple one-parameter model. © 1995 John Wiley & Sons, Inc.     

A modeling study of the effect of reactor configuration on the cycle length of heavy oil fixed-bed hydroprocessing

This article analyses how the configuration of an industrial fixed-bed reactor affects the cycle length of a heavy oil hydroprocessing unit. It is well-known that during the hydroprocessing of heavy feeds, catalyst aging is counterbalanced by continuously increasing reaction temperature. In addition, the exothermality of the reaction provokes a huge temperature rise along the reactor, which is why quenching is necessary. Thus, there is an increasing temperature profile that evolves with time until a maximum allowable temperature is reached and then the operation is shut down. For this reason, there is an optimum reactor configuration (i.e. number of quenches and their positions) that must be established when designing new processes in order to maximize unit run length. To evaluate this problem, a reactor performance model with time varying catalyst activity was constructed. Kinetic and catalyst aging data were obtained from bench-scale tests. The model showed to reproduce sufficiently well the experimental data set. The analysis of various reactor designs indicated that for this process the use of single-bed or double-bed reactors is unpractical in terms of cycle length. A more complex configuration consisting of multiple beds of increasing lengths is necessary to delay shut down.     

Pyrolysis of the mixture of biomass and plastics in countercurrent flow reactor Part I: Experimental analysis and modeling of kinetics

A shaft kiln is considered to be a promising pyrolysis device for the efficient decomposition of municipal wastes. In this device, the temperature distributions of the gas and solid phases can be separately controlled, thereby leading to considerably different profiles for both the phases. The temperature controllability in a shaft kiln helps us to obtain a suitable profile of the gas-phase temperature for the decomposition of tar that evolves from the solid phase. By leveraging this advantage of the shaft kiln, we performed further pyrolysis and steam reforming of the volatiles formed from the pyrolysis of biomass and several polymers using a two-stage reactor that was maintained at different temperatures. The amount of tar decreased with an increase in the temperature in the upper reactor in the absence of a catalyst. By using the experimental results, we developed a lumped kinetic model for secondary gas-phase reactions and performed a kinetic analysis of the reactions that proceeded in the upper reactor. It is confirmed that the simulation model is successful in reproducing the product distribution of the gas-phase reactions of volatiles from biomass and polymers.     

2-甲基-6-乙酰基萘液相催化氧化反应动力学

In this paper,a kinetics model for the liquid-phase oxidation of 2-methyl-6-acetyl-naphthalene to 2,6-naphthalene dicarboxylic acid catalyzed by cobalt-manganese-bromide is proposed.The effects of the reaction temperature,catalyst concentration and ratio of catalyst on the time evolution of the experimental concentration for the constituents including raw material,intermediates and product are investigated.The model parameters are determined in a nonlinear optimization,minimizing the difference between the simulated and experimental time evolution of the product composition obtained in a semi-batch oxidation reactor where the gas and liquid phase were well mixed.The kinetics data demonstrate that the model is suitable to the liquid-phase oxidation of 2-methyl-6-acetyl-naphthalene to 2,6-naphthalene dicarboxylic acid.     

Estimation of heating time in tubular supercritical water reactors

Reactor efficiency and product distribution in supercritical water (SCW) reactors is greatly influenced by the design of the heating section of these reactors. However, little experimental or theoretical work is available to estimate the rate of heat transfer in such systems. In the present study, CFD modeling of the heat transfer in tubular SCW reactors has been performed. Effects of various operating parameters; i.e. reactor temperature and pressure, flow rate, reactor diameter, and the external heating mechanism, on the heating time constant, the temperature profile along the reactor, and reactor residence time are investigated. Based on numerical simulations, a semi-theoretical model is proposed to estimate the heating time constant as a function of reactor operating conditions. Results of this study provide useful insights for designing continuous supercritical water reactors as well as for the analysis of experimental data obtained from such systems.     

Fluid dynamic simulation in a chemical looping combustion with two interconnected fluidized beds

Flow behavior of gas and particles is simulated in a 2-D chemical-looping combustion (CLC) process with two interconnected fluidized beds. A Eulerian continuum two-fluid model is applied for both the gas phase and the solid phase. Gas turbulence is modeled by using a k-ε turbulent model. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. Instantaneous and local velocity, concentration of particles and granular temperature are obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in the air reactor. Flow behavior of bubbles is predicted in the fuel reactor and pot-seal. Computed leakage qualitatively agrees with experimental data in the fuel reactor and pot-seal.     

Experimental investigation of vinyl chloride polymerization at high conversion—reactor dynamics

A series of suspension polymerizations of vinyl chloride monomer (VCM) was carried out in a 5-L pilot plant reactor over the temperature range, 40–70°C. The reactor pressure and monomer conversion were monitored simultaneously every 7–8 min. The critical conversion X_f, at which the liquid monomer phase is consumed, was considered to occur when the reactor pressure fell to 98% of the vapor pressure of VCM for suspension at the polymerization temperature. The reactor model predictions of pressure are in excellent agreement with the experimental data over the entire conversion and temperature ranges studied. The mechanism of reactor pressure development for VCM suspension polymerization is discussed herein in some detail. For isothermal batch polymerization, the reactor pressure falls in two stages due to the effect of polymer particle morphology on pressure drop. The first stage is due to the volume increase of the vapor phase as a result of volume shrinkage due to conversion of monomer to polymer. The monomer phase is not yet consumed at this stage, but it is trapped in the interstices between primary particles creating a mass transfer resistance; therefore, the reactor pressure drops slowly. The second stage is due to both the volume increase of the vapor phase and to the monomer in the vapor phase diffusing into the polymer phase because of the subsaturation condition with respect to monomer in the polymer phase. The reactor pressure drops dramatically with an increase in monomer conversion at this stage. The present model can be used to predict reactor dynamics during suspension polymerization under varying temperature and pressure conditions.     

Lexicographic optimization based MPC: Simulation and experimental study

Multi-variable prioritized control study is carried out using model predictive control (MPC) algorithms. The conventional MPC algorithm implements multi-variable control through one augmented objective function and requires weights adjustment for required performance. In order to implement explicit prioritization in multiple control objectives, we have used lexicographic MPC. To achieve better tracking performance, we have used a new MPC algorithm, by modifying the lexicographic constraint, referred to as MLMPC, where tuning of weights is not required. The effectiveness of MLMPC algorithm is demonstrated on a PMMA reactor for controlling the number average molecular weight and the reactor temperature. We have also verified the benefits of proposed algorithm on an experimental single board heater system (SBHS) for controlling temperature of a thin metal plate. These simulation and experimental studies demonstrate the superiority of the proposed method over conventional MPC and lexicographic MPC. Finally, we have presented generalized mathematical solutions to the optimization problem in MLMPC.     

Estimation of the micromixing time in the torus reactor by the application of the incorporation model

On the basis of previous experimental results in a torus reactor, micromixing time is determined using the incorporation model. Obtained results allowed the characterisation of the performances of this new configuration of reactor in comparison to other reactors, such as the stirred tank reactor. In addition, a correlation is proposed for each incorporation law, in order to determine the micromixing time from the experimental micromixedness ratio (α). Finally, in terms of Kolmogorov's turbulence theory, a relationship between micromixing time and the local energy dissipation rate is obtained and compared to those previously published.     

High temperature fluidized bed reactor: measurements,hydrodynamics and simulation

This paper was made possible through the development of a novel high temperature optical fiber probe to study the hydrodynamics of a high temperature fluidized bed reactor. The experimental results show that the hydrodynamic parameters considerably change with bed temperature when fluidizing FCC particles. For a given superficial gas velocity, the average local particle concentration, the dense phase fraction and the particle concentration in the dense phase decrease with increasing bed temperature. As a result of an increase in temperature, the fluidized behavior of the FCC particles progressively shifts from typical Geldart A towards B. Consequently, a modified two-phase model, based on the simple two-phase model, integrating the effects of temperature and superficial gas velocity on the hydrodynamics, is proposed. Simulation of a reactive catalytic system using a conventional simple two-phase model and the modified model is achieved. The predicted reactor performances strongly differ for each model. In the present case, the simple two-phase model underestimates the reactor performance by inadequately accounting for the solid fractions in the bubble and dense phases and their dependence on temperature and superficial gas velocity. This suggests that the hydrodynamic models should take into account the effects of temperature and superficial gas velocity when simulating the performance of a high temperature fluidized bed reactor.     

转鼓反应器中油酸氧化裂解制备壬二酸的研究

在转鼓反应器中实现了油酸臭氧氧化裂解制备壬二酸的连续化操作。考察了转鼓转速、液体流量、气体流量对转鼓反应器内气液传质反应速率的影响。在双膜理论的基础上,利用恩田公式来计算气相传质系数、液相传质系数,建立了转鼓反应器中两步反应速率模型,并将模型预测值与实验值进行了比较。实验结果表明:在转鼓反应器中,油酸氧化裂解反应速率分别随转鼓转速和液体流量的增大,先增大后趋于平缓;随着气体通量的增加,转鼓反应器内油酸氧化裂解反应速率先增大然后减小;在转鼓转速为1 699 r/min、液体流量为45 mL/min、气体流量为3 L/min时,在转鼓内油酸氧化裂解可获得最大的气液传质反应速率。模型预测值与实验值比较,两者吻合得较好,验证了模型的可靠性。