Batch reactor, model simulation

In order to simulate the concentration-time data and evaluate the kinetic parameters in equations 6 - 8, a batch reactor model was used. Under isothermal conditions, the variation of the liquid phase concentration of crotonaldehyde and butyraldehyde with time can be described by the following set of mass balance equations. 

Table 17.1. Simulation parameters for fed-batch reactor model.

In order to evaluate the rate parameters in the kinetic model, the observed concentration time data were simulated using a batch reactor model under isothermal conditions as described below ... 

The hquid-phase chlorination of benzene is an ideal example of a set of sequential reactions with varying rates from the single-chlorinated molecule to the completely chlorinated molecule containing six chlorines. Classical papers have modeled the chlorination of benzene through the dichlorobenzenes (14,15). A reactor system may be simulated with the relative rate equations and flow equation. The batch reactor gives the minimum ratio of... 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

In this chapter the simulation examples are described. As seen from the Table of Contents, the examples are organised according to twelve application areas Batch Reactors, Continuous Tank Reactors, Tubular Reactors, Semi-Continuous Reactors, Mixing Models, Tank Flow Examples, Process Control, Mass Transfer Processes, Distillation Processes, Heat Transfer, and Dynamic Numerical Examples. There are aspects of some examples which relate them to more than one application area, which is usually apparent from the titles of the examples. Within each section, the examples are listed in order of their degree of difficulty. 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

Thus, the design of a batch reactor can be based on the optimization of a temporal superstructure. Given a simulation model with a mathematical formulation, the next step is to determine the optimal values for the control variables of a batch reaction system. 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

Some typical results from their simulations are presented in Fig. 16 in which the yield XQ of the product Q from the slow reaction of a set of two competitive reactions in a fed batch reactor has been plotted vs. impeller speed for two micromixing models, viz. their own CSV model and Bourne s EDD model their simulation results are compared with experimental data from Bourne and Yu (1991). For the cases shown, the CSV model may perform better than Bourne s EDD model, in particular when A is fed near to the impeller where mixing is most intense. 

Industrially relevant consecutive-competitive reaction schemes on metal catalysts were considered hydrogenation of citral, xylose and lactose. The first case study is relevant for perfumery industry, while the latter ones are used for the production of sweeteners. The catalysts deactivate during the process. The yields of the desired products are steered by mass transfer conditions and the concentration fronts move inside the particles due to catalyst deactivation. The reaction-deactivation-diffusion model was solved and the model was used to predict the behaviours of semi-batch reactors. Depending on the hydrogen concentration level on the catalyst surface, the product distribution can be steered towards isomerization or hydrogenation products. The tool developed in this work can be used for simulation and optimization of stirred tanks in laboratory and industrial scale. 

Zaldivar, J.M., Hernandez, H. and Barcons, C. (1996) Development of a mathematical model and a simulator for the analysis and optimisation of batch reactors Experimental model characterisation using a reaction calorimeter. Thermochimica Acta, 289, 267-302. 

First, the detailed model is used to simulate the behavior of the real system, and a set of simulated isothermal experimental data is generated including the total heat released by reaction. Then, these data are used to estimate the kinetic parameters of the reduced models and the heats of reaction of the lumped reactions. Finally, the reduced kinetic models are tested in a validation procedure which simulates the operation of a batch reactor and allows one to identify the best reduced model. 

In Chaps. 5 and 6 model-based control and early diagnosis of faults for ideal batch reactors have been considered. A detailed kinetic network and a correspondingly complex rate of heat production have been included in the mathematical model, in order to simulate a realistic application however, the reactor was described by simple ideal mathematical models, as developed in Chap. 2. In fact, real chemical reactors differ from ideal ones because of two main causes of nonideal behavior, namely the nonideal mixing of the reactor contents and the presence of multiphase systems. 

The main physicochemical processes in thin-film deposition are chemical reactions in the gas phase and on the film surface and heat-mass transfer processes in the reactor chamber. Laboratory deposition reactors have usually a simple geometry to reduce heat-mass transfer limitations and, hence, to simplify the study of film deposition kinetics and optimize process parameters. In this case, one can use simplified gas-dynamics reactor such as well stirred reactor (WSR), calorimetric bomb reactor (CBR, batch reactor), and plug flow reactor (PFR) models to simulate deposition kinetics and compare theoretical data with experimental results. 

Knowledge of these types of reactors is important because some industrial reactors approach the idealized types or may be simulated by a number of ideal reactors. In this chapter, we will review the above reactors and their applications in the chemical process industries. Additionally, multiphase reactors such as the fixed and fluidized beds are reviewed. In Chapter 5, the numerical method of analysis will be used to model the concentration-time profiles of various reactions in a batch reactor, and provide sizing of the batch, semi-batch, continuous flow stirred tank, and plug flow reactors for both isothermal and adiabatic conditions. 

Model. A difference equation for the material balance was obtained from a discrete reactor model which was devised by dividing the annulus into a two dimensional array of cells, each taken to be a well stirred batch reactor. The model supposes that axial motion of the mobile phase and bed rotation occur by instantaneous discontinuous jumps, between cells. Reaction occurs only on the solid surface, and for the reaction type A B + C used in this work, -dn /dt = K n - n n. Linear isotherms, n = BiC, were used, and while dispersion was not explicitly included, it could be simulated by adjusting the number of cells. The balance is given by Eq. 2, where subscript n is the cell index in the axial direction, and subscript m is the index in the circumferential direction. 

Various levels of models can be used to describe the behavior of pilot-scale jacketed batch reactors. For online reaction calorimetry and for rapid scale-up, a simple model characterizing the heat transfer from the reactor to the jacket can be used. Another level of modeling detail includes both the jacket and reactor dynamics. Finally, the complete set of equations simultaneously describing the integrated reactor/jacket and recirculating system dynamics can be used for feedback control system design and simulation. The complete model can more accurately assess the operability and safety of the pilot-scale system and can be used for more accurate process scale-up. 

Batch Reactors. The model for a batch reactor is obtained easily from the continuous flow reactor model by setting the liquid flow rate equal to zero wherever it occurs in the material balances. Simulation results showing the effects of varying the inhibition constant, initial organism concentration, and pH control will not be presented since the general effects of these at constant pH have been demonstrated previously (J). The results of these previous simulations indicated that in... 

The study demonstrates that particle swam optimisation is a powerful optimisation technique, especially when the objective function has several local rninirna. Conventional optimisation techniques could be trapped in local minima but PSO could in general find the global rninimrun. Stacked neural networks can not only given better prediction performance but also provide model prediction confidence bounds. In order to improve the reliability of neural network model based optimisation, an additional term is introduced in the optimisation objective to penalize wide model prediction confidence bormd. The proposed technique is successfully demonstrated on a simulated fed-batch reactor. 

Other steps used in the model assume that the heterogeneous conversion of methane is limited to the gas-phase availability of oxygen, O2 adsorption is fast relative to the rate of methane conversion, and heat and mass transports are fast relative to the reaction rates. Calculations for the above model were conducted for a batch reactor using some kinetic parameters available for the oxidative coupling of methane over sodium-promoted CaO. The results of the computer simulation performed for methane dimerization at 800 °C can be found in Figure 7. It is seen that the major products of the reaction are ethane, ethylene, and CO. The formation of methanol and formaldehyde decreases as the contact time increases. 

The authors found that the model-predicted As concentration is close to the leachate concentrations from the column packed with dust from the continuous reactor (1 120 H.gL-1 versus 1 330 xgL-1), when the solubility product of scorodite from Robins (1990) and the triple layer model is used. Only 11% As in the system was sorbed onto hydrous ferric oxide surfaces. Arsenic concentrations in the leachate are largely controlled by scorodite solubility. It should also be pointed out that simulations using solubility only and without including surface adsorption resulted in a closer match (1 270 n-gL-1 versus 1330 piglA1). For the simulation of the column experiments using wastes from the batch-reactor, the triple layer model predicted too low an As concentration (33 jigL-1 versus 120 pigL-1). 

A proper fit of the time-courses of some batch reactor experiments at different starting concentrations represents an appropriate test of the rate equation. This implies that numerical integration of the rate equation (e. g. by the Runge Kutta method11121), yielding a simulated time-course, has to fit the data of the measured time-course over the whole range of conversion (compare to Fig. 7-17 B). Examples of these methods will be given after the presentation of the basic kinetic models. 

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