Reactor dynamic model

The analysis of the transient behavior of the packed bed reactor is fairly recent in the literature 142-145)- There is no published reactor dynamic model for the monolith or the screen bed, which compares well with experimental data. 

The performance of the robust estimators has been tested on the same CSTR used by Liebman et al (1992) where the four variables in the system were assumed to be measured. The two input variables are the feed concentration and temperature while the two state variables are the output concentration and temperature. Measurements for both state and input variables were simulated at time steps of 1 (scaled time value corresponding to 2.5 s) adding Gaussian noise with a standard deviation of 5% of the reference values (see Liebman et al, 1992) to the true values obtained from the numerical integration of the reactor dynamic model. Same outliers and a bias were added to the simulated measurements. The simulation was initialized at a scaled steady state operation point (feed concentration = 6.5, feed temperature = 3.5, output concentration = 0.1531 and output temperature = 4.6091). At time step 30 the feed concentration was stepped to 7.5. 

Pollock, M. J., MacGregor, J. F., and Hamielec, A. E. (1981) Continuous poly (vinyl acetate) emulsion polymerization reactors dynamic modeling of molecular weight and particle size development and application to optimal multiple reactor system design. Computer Applications in Applied Polymer Science, (ed. T. Provder), ACS, Washington, pp. 209-20. 

Steady state models of the automobile catalytic converter have been reported in the literature 138), but only a dynamic model can do justice to the demands of an urban car. The central importance of the transient thermal behavior of the reactor was pointed out by Vardi and Biller, who made a model of the pellet bed without chemical reactions as a onedimensional continuum 139). The gas and the solid are assumed to have different temperatures, with heat transfer between the phases. The equations of heat balance are ... 

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

Sandelin, F., Salmi, T., and Murzin, D. (2006) Dynamic modelling of catalyst deactivation in fixed bed reactors skeletal isomerization of 1-pentene on ferrierite. Ind. Eng. Chem. Res., 45, 558-566. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

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. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

The coupling of the component and energy balance equations in the modelling of non-isothermal tubular reactors can often lead to numerical difficulties, especially in solutions of steady-state behaviour. In these cases, a dynamic digital simulation approach can often be advantageous as a method of determining the steady-state variations in concentration and temperature, with respect to reactor length. The full form of the dynamic model equations are used in this approach, and these are solved up to the final steady-state condition, at which condition... 

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. 

Program THERM solves the dynamic model equations. The initial values of concentration and temperature in the reactor can be changed after each run using the ISIM interactive commands. The plot statement causes a composite phase-plane graph of concentration versus temperature to be drawn. Note that for comparison both programs should be used with the same parameter values. 

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

General. In this section, a mathematical dynamic model will be developed for emulsion homopolymerization processes. The model derivation will be general enough to easily apply to several Case I monomer systems (e.g. vinyl acetate, vinyl chloride), i.e. to emulsion systems characterized by significant radical desorption rates, and therefore an average number of radicals per particle much less than 1/2, and to a variety of different modes of reactor operation. 

The development of on-line sensors is a very costly and time-consuming process. Therefore, if one has available a dynamic model of the reactor which predicts the various polymer (or latex) properties of interest, then this can be used to guide one in the selection and development of sensors. Ideas from the optimal statistical design of experiments together with the present model expressed in the form of a Kalman filter have been successfully used (58) to select those combinations of existing or hypothetical sensors which would maximize the information that could be obtained on the states of the polymerization system. Both the type of sensors and the precisions necessary for them are easily investigated in this way. By changing the choice of the measurement matrix and... 

A dynamic model has been developed to simulate the behavior of a Pseudomonas sp. 0X1 biofilm reactor for phenol and azo-dye conversion during the aerobic-anaerobic cyclic operation. Phenol and oxygen were considered as the limiting substrates for growth kinetics. 

Use a dynamic model for a tank reactor to verify the values calculated by this program. Do the same for a steady state and dynamic tubular reactor model. 

As mentioned earlier, reformate from a fuel processor often needs addition processing to reduce the carbon monoxide levels. Researchers at the Stevens Institute of Technology are developing a microscale preferential oxidation (FrOx) reactor to decrease the carbon monoxide level in the reformate stream to below 100 ppm. As part of their research, they used advanced computational fluid dynamic modeling. 

Therefore, there is a strong motivation to develop a dynamic model of the SCR monolithic reactor suitable for extended temperature operation and to study the fast SCR reaction in view of future possible applications. In the following, we will focus on these two issues. 

Figure 13.9 Validation of the dynamic model ofthe monolith SCR reactor during ESC and ETC tests. All concentrations are normalized by the respective maximum inlet valueduringthe test cycle. Dotted black lines, inlet values solid black lines, outlet measurements gray lines, outlet simulations. Adapted from ref. [62].

This chapter presents an analysis of the development of dynamic models for packed bed reactors, with particular emphasis on models that can be used in control system design. Our method of attack will be first to formulate a comprehensive, relatively detailed packed bed reactor model next to consider the techniques available for numerical solution of the model then, utilizing... 

Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena. Wiley, New York, 1960. Bonvin, D., Dynamic Modeling and Control Structures for a Tubular Autothermal Reactor at an Unstable State. Ph.D. thesis, University of California, Santa Barbara (1980). 

Until very recently fluid dynamical models of multiphase reactors were considered intractable. This situation is rapidly changing with the development of high performance computers. Today s workstations allow new approaches to. .. modeling. 

Kinetics packages also exist which take calorimetric data and fit kinetics correlations to them. These kinetic expressions can then be used within dynamic models of a venting reactor. Care must be taken when using such packages, particularly if the data are extrapolated above the measurement temperature, to ensure that the reaction kinetics still apply at the increased temperature. 

---