Semi-batch Reactor Model Research Articles

Use of semibatch reactor technology for the investigation of reaction mechanism and kinetics: Heterogeneously catalyzed epoxidation of fatty acid esters

Heterogeneously catalyzed epoxidation of vegetable oils by hydrogen peroxide represents a greener route for the production of epoxides and a thermally safer reaction route compared to the classical Prileschajew epoxidation approach. The epoxidation kinetics of the heterogeneous system formed by aluminium oxide catalyst, hydrogen peroxide and methyl oleate as a model compound was studied with semibatch experiments in laboratory scale. It was found that semibatch operation improved the performance significantly compared to classical batch operation, a low and constant volumetric flowrate of hydrogen peroxide increased the final oxirane yield considerably. A semibatch reactor model and a kinetic model were developed, featuring the reaction temperature, the reactant molar ratio, the catalyst loading and the mass flow rate as the most significant experimental parameters. The mathematical model was able to well describe the experimental data. The approach can be applied to other liquid–solid catalyst systems in future in order to optimize the semibatch operation policy for complex reaction systems.

Modeling of atmospheric and vacuum petroleum residue hydroconversion in a slurry semi-batch reactor: Study of hydrogen consumption

In this work, Arabian light atmospheric residue and Safaniya vacuum residue were hydroconverted in a slurry phase semi-batch stirred tank reactor at 15 MPa for a wide range of temperatures (420–440 °C) and reaction times up to 4 h. Experimental data was used to develop a semi-batch reactor model including vapor-liquid equilibrium, gas-liquid mass transfer and gas phase hydrodynamics. Mass transfer and kinetic parameters were estimated by minimizing not only the total masses of products but also the outlet gas flow dynamics. Mass transfer and hydrogen consumption were compared against former studies using a batch reactor, a continuous stirred tank reactor and work by other authors, reported in the literature. Higher hydrogen consumption was achieved with the semi-batch reactor and no hydrogen mass transfer limitation was observed. Therefore, it was concluded that this setup is more suited and reliable for studying the chemical kinetics of slurry-phase hydroconversion of petroleum residues and permits improved representation of the role of hydrogen compared with current models.

A framework for modeling and optimizing dynamic systems under uncertainty

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.

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.

Targeting Copolymer Composition Distribution via Model-Based Monomer Feeding Policy in Semibatch RAFT Mini-Emulsion Copolymerization of Styrene and Butyl Acrylate

Copolymer composition distribution (CCD) is an important parameter of chain microstructure that has significant impact on the material properties of polymer products. Controlled/living radical polymerization (CLRP) has provided a great opportunity in producing polymers with predesigned CCDs through a model-based monomer feeding policy (MMFP) in homogeneous systems. In this work, the MMFP has been expanded to heterogeneous systems. Reversible addition–fragmentation transfer (RAFT) mini-emulsion polymerizations of styrene (St) and butyl acrylate (BA) were carried out with 3-benzyltrithiocarbonyl propionic acid (BCPA) used as a RAFT agent. A kinetic model was developed and correlated to the batch St/BA RAFT mini-emulsion experimental data for parameter estimation. The MMFP was then developed by combining the kinetic model with a semibatch reactor model and applied to the semibatch St/BA RAFT mini-emulsion copolymerization for the synthesis of targeted CCDs. The model agreed well with the polymerization kinetics. A series of St/BA copolymers with predesigned CCDs were successfully synthesized.

Gas absorption accompanied by chemical reaction in a system of three-phase slurry-foam reactors in series

Experiments have been performed in a semi-batch reactor for the absorption of carbon-dioxide gas in an aqueous foam-slurry containing suspended particles of calcium hydroxide. One each of cationic, anionic and non-ionic surfactants has been used as the foaming agent. Single-stage model for such a reactor, reported earlier by the present authors, agrees well with the present experimental data. The single-stage model was developed to account for the contribution of the storage section as well, instead of the foam section alone as reported in the literature, towards gas absorption and chemical reaction, considering that the storage constitutes 60–85 percent of the total liquid/slurry charged into the reactor. A system of continuous slurry-foam reactors in series has been simulated for the carbonation reaction mentioned above using the single-stage semi-batch reactor model and the material balance equations. Values of k sl and ε ¯ l , required for this, have been calculated from dimensionless correlations developed using the experimental data. Design charts have been presented in the form of figures. A comparison of a foam-bed reactor with other gas–liquid/gas–liquid–solid contactors in respect of important mass-transfer parameters and a critical review of the reported models of this reactor have also been presented.

Kinetic Modeling of Carbonylation of 1-(4-Isobutylphenyl)ethanol Using a Homogeneous PdCl2(PPh3)2/TsOH/LiCl Catalyst System

The kinetics of carbonylation of 1-(4-isobutylphenyl)ethanol (IBPE) were studied in a stirred semibatch reactor using a homogeneous PdCl2(PPh3)2/TsOH/LiCl catalyst system. A three-step reaction pathway that describes the formation of an active palladium(0) species, the formation of active carbonylation substrate, 1-(4-isobutylphenyl)ethyl chloride, and the main carbonylation catalytic cycle has been proposed. The effect of the catalyst, (TsOH/LiCl) and IBPE concentrations and the partial pressure of CO on the rate and semibatch reactor performance has been investigated over the temperature range of 378−398 K. An empirical semibatch reactor model was derived, and the reaction rate parameters were evaluated based upon a simplified scheme. The rate model was found to satisfactorily predict the concentration versus time profiles at all temperatures. An attempt was also made to develop a dynamic model that accounts for the change in concentration of all of the catalytic intermediate species as well as the reactants and products.

Optimal reaction conditions for the minimization of energy consumption and by-product formation in a poly(ethylene terephthalate) process

We determined the optimal reaction conditions to minimize the energy cost and the quantities of by-products for a poly(ethylene terephthalate) process by using the iterative dynamic programming (IDP) algorithm. Here, we employed a sequence of three reactor models: the semibatch transesterification reactor model, the semibatch prepolymerization reactor model, and the rotating-disc-type polycondensation reactor model. We selectively chose or developed the reactor models by incorporating experimentally verified kinetic models reported in the literature. We established the model for the entire reactor system by connecting the three reactor models in series and by resolving some joint problems arising when different types of reactor models were interconnected. On the basis of the simulation results of the reactor system, we scrutinized the cause and effect between the reaction conditions and the final quality of the polymer product. Here, we set up the optimization strategy by using IDP on the basis of the integrated reactor model, and the process variables with significant influence on the properties of polymer were selected as control variables with the help of a simulation study. With this method, we could refine the reaction conditions at the end of each iteration step by contracting the spectra of control regions, and the iteration process finally stopped when the profile of the optimal trajectory converged. We also took the constraints on the control variables into account to guarantee polymer quality and to suppress side reactions. Constituting six different strategies by setting weighting vectors differently, we examined the differences in optimal trajectories, the trend of optimality, and the quality of the final polymer product. For each of the strategies, we conducted the optimization to examine whether the number-average degree of polymerization approached the desired value. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 993–1008, 2002

A generic framework for integrated quality and profile control for industrial batch processes

Importance of batch processes has grown more in recent years as the increasing economic competition has pushed the manufacturing industries to pursue small quantity production of diverse high value-added products. Accordingly, system engineering study on advanced control and dynamic optimization of batch operation has drawn much attention recently.The purpose of this paper is to introduce recent advances in batch process control discuss possible extensions focusing on the contributions by the authors. For this, the so-called run-to-run approaches, that may play a breakthrough in batch operation problems and also the authors' work have been based on, are briefly reviewed first from control and optimization points of view. Then a novel MPC(Model Predictive Control)-like run-to-run batch control framework, called QBMPC, that can simultaneously perform prediction-based end-product quality and profile control is proposed aiming at a generic industrial batch control technique. Some possible extensions and modifications are discussed subsequently. Performance of QBMPC is demonstrated with a semi-batch reactor model.

Hydrocarbonylation of Methyl Acetate Using a Homogeneous Rh(CO)Cl(PPh3)2Complex as a Catalyst Precursor: Kinetic Modeling

The kinetics of hydrocarbonylation of methyl acetate to ethylidene diacetate (EDA) using the Rh(CO)Cl(PPh3)2/PPh3/MeI catalyst system was studied in a temperature range of 433−463 K. Concentration−time profiles were obtained for different reaction conditions such as concentrations of methyl acetate, methyl iodide, and catalyst and partial pressures of CO and hydrogen. Rate equations were proposed on the basis of a reaction mechanism with [Rh(CO)2I2]- as the catalytically active species. Activation energies for acetic anhydride (Ac2O) and EDA formation were found to be 80.72 and 91.79 kJ/mol, respectively. A semibatch reactor model was developed, and the effect of the carbon-monoxide-to-hydrogen ratio on the conversion of methyl acetate and selectivity to EDA is discussed.

Hydrogenation of nitrobenzene to p-aminophenol in a four-phase reactor: reaction kinetics and mass transfer effects

The kinetics of catalytic hydrogenation of nitrobenzene in acid medium to p-aminophenol was investigated in a batch slurry reactor in a temperature range of 323– 353 K . Aniline was formed as a byproduct (upto 20%). The initial rate data were analyzed to assess the mass transfer effects and it was found that gas–liquid mass transfer resistance was important under certain reaction conditions. A Langmuir–Hinshelwood type rate model has been proposed based on the initial rate data in the kinetic regime and considering the reaction taking place in both organic as well as aqueous phase. Since this was a four-phase system, the rate equation was suitably modified to include gas–liquid and liquid–liquid mass transfer steps. The kinetic parameters evaluated from a semibatch reactor model were found to represent the observed experimental data very well indicating the applicability of the proposed rate model.

A Technique for Integrated Quality Control, Profile Control, and Constraint Handling for Batch Processes

We propose a novel control technique for batch and semibatch processes. The main novelty of the technique lies in that it can accommodate several different aspects of industrial batch process control, such as the following of prespecified reference trajectories, the satisfaction of process constraints, and the meeting of product quality targets, altogether in a single framework. This simplifies the design and enables the user to make a systematic trade-off among the different objectives. Another novelty is the feature of iterative learning that allows the controller to use the information collected in the previous batches. This is done by establishing a batch-to-batch correlation model giving the integral control action with respect to the batch index. This feature allows the performance to be improved gradually as the batch run is repeated and makes it possible to attain precise control despite significant model errors and disturbances. The performance of the proposed technique is illustrated using a simple nonlinear semibatch reactor model.

Hydrogenation of 2,4-Dinitrotoluene Using a Supported Ni Catalyst: Reaction Kinetics and Semibatch Slurry Reactor Modeling

The kinetics of hydrogenation of 2,4-dinitrotoluene (2,4-DNT) using a 10% Ni supported on zeolite Y (10% Ni/HY) powdered catalyst (dp = 1 × 10-5 m) was studied experimentally in a semibatch slurry reactor over a temperature range of 333−363 K. The effects of reaction temperature, H2 pressure, concentration of 2,4-DNT and catalyst loading on the concentration−time and H2 consumption−time profiles were studied under isothermal conditions. To explain the rate behavior of this complex, consecutive, and parallel reaction, several rate expressions were derived based on Langmuir−Hinshelwood type rate mechanisms. The rate equations that were derived assuming the reaction between competitively adsorbed organic species and dissociatively adsorbed hydrogen as the rate-limiting step were found to represent the kinetics best. Quantitative analysis of the experiments performed under the chosen conditions (temperature, 333−363 K; H2 pressure, 1.3−5.4 MPa; 2,4-DNT concentration, 0.14−0.55 kmol/m3) indicated that the rate data obtained were under the kinetic regime. The rate and equilibrium parameters were evaluated for the different steps involved in the reaction network. A semibatch slurry reactor model has been developed to predict both integral concentration−time and H2 consumption−time profiles and was compared with experimental data at different sets of initial conditions. An excellent agreement between the model predictions and the experimental data was observed.

Hydrogenation of acetophenone using a 10% Ni supported on zeolite Y catalyst: kinetics and reaction mechanism

The kinetics of hydrogenation of acetophenone was studied using a 10% Ni supported on zeolite Y catalyst in a temperature range 353–393 K. The effect of H 2 pressure, initial concentration of acetophenone and catalyst loading on the concentration-time profiles was studied. Water formed during the course of hydrogenation showed a strong inhibiting influence on the rate of reaction. A rate equation has been proposed based on L–H type rate mechanism assuming that the reaction between the non-competitively adsorbed hydrogen and the adsorbed organic substrate as rate limiting step. A semi-batch reactor model was developed to predict the concentration-time, H 2 consumption-time profiles at different sets of initial conditions. The model predictions were found to agree with experimental data very well at all temperatures. This model incorporates the inhibition of hydrogenation rate due to water. The inhibiting effect of water is also explained based on quantum chemical calculations.

Effect of catalyst concentration and simulation of precipitation processes on liquid-phase catalytic oxidation of p-xylene to terephthalic acid

The influence of catalyst concentration, i.e. cobalt naphthenate, on product distribution and kinetic constants of the lumped kinetic scheme of liquid-phase p-xylene oxidation proposed in previous works (cf. Cao et al., 1994a, b) is investigated. The experiments involving various levels of catalyst concentrations (from 1.67 to 33.3 × 10−4 mol/kgl) are conducted in an isothermal semi-batch oxidation reactor where both the gas and the liquid phase are well mixed. The dependence of the kinetic constants of the lumped kinetic scheme on the catalyst concentration is examined. In addition, the interaction between the chemical reactions of the lumped kinetic scheme for p-xylene oxidation to terephthalic acid and the precipitation kinetics of both 4-carboxybenzaldehyde and terephthalic acid is analyzed theoretically. A semi-batch gas-liquid reactor model which incorporates the description of the above phenomena allows us to identify their interplay.

Experimental investigation of vinyl chloride polymerization at high conversion: semi-batch reactor modelling

A comprehensive semi-batch reactor model for suspension polymerization of vinyl chloride at high conversions has been developed. A series of kinetic experiments covering different pressure levels was carried out in a semi-batch process. The present model is in excellent agreement with the experimental data including monomer consumption, conversion history and accumulated number- and weight-average molecular weights and molecular weight distribution. The present model combined with our previous batch reactor model can be used to predict monomer feed rate, accumulated monomer consumption, polymerization rate, conversion history, reactor pressure, instantaneous and accumulated molecular weight averages and distribution and other kinetic features. The advantages of a semi-batch process operated at the vapour pressure of vinyl chloride include increased productivity, narrower molecular weight distributions and increased thermal stability of poly(vinyl chloride) (PVC) compared with a batch process taken to high conversions.