Simulation Examples

Models may be used in training and education. Many important aspects of reactor operation can be simulated by the use of simple models. These include process start-up and shut down, feeding strategies, measurement dynamics, heat effects and control. Such effects are easily demonstrated by computer, as shown in the accompanying simulation examples, but are often difficult and expensive to demonstrate in practice. 

Full details of the ISlM digital simulation programming language can be found in the appendix, and by reference to the ISIM programs associated with the simulation examples of Chapter 5. 

How these and other relationships are incorporated within the development of particular modelling instances are illustrated, throughout the text and in the simulation examples. 

The steady-state condition of constant volume in the tank (dV/dt = 0) occurs when the volumetric flow in, Fq, is exactly balanced by the volumetric flow out, Fi. Total mass balances therefore are mostly important for those modelling situations in which volumes are subject to change, as given in simulation examples CONFLO, TANKBLD, TANKDIS and TANKHYD. 

However, with a time variant flow of liquid into the tank, then analytical solution is not so simple. The above problem is treated in more detail by the simulation example TANKDIS. 

Energy balances are formulated by following the same set of guidelines as those given in Sec. 1.2.2 for mass balances. Energy balances are however considerably more complex, because of the many processes which cause temperature change in chemical systems. The treatment considered here is somewhat simplified, but is adequate to understand the non-isothermal simulation examples. The various texts cited in the reference section, provide additional advanced reading in this subject. 

Further examples of the use of dimensionless terms in dynamic modelling applications are given in Sec. 1.2.5.1, Sec. 4.3.6.1 and 4.3.7 and in the simulation examples KLADYN, DISRET, DISRE, TANKD and TUBED. 

Here K is the thermodynamic chemical equilibrium constant. If AH is constant, direct integration yields an explicit expression. If AH is a function of temperature, as described in Sec. 1.3.3, then its dependancy on Cp can be easily included and integration is again straight forward. A calculation with varying AH and Cp being functions of temperature is given in the simulation example REVTEMP. 

Equilibrium data correlations can be extremely complex, especially when related to non-ideal multicomponent mixtures, and in order to handle such real life complex simulations, a commercial dynamic simulator with access to a physical property data-base often becomes essential. The approach in this text, is based, however, on the basic concepts of ideal behaviour, as expressed by Henry s law for gas absorption, the use of constant relative volatility values for distillation and constant distribution coeficients for solvent extraction. These have the advantage that they normally enable an explicit method of solution and avoid the more cumbersome iterative types of procedure, which would otherwise be required. Simulation examples in which more complex forms of equilibria are employed are STEAM and BUBBLE. 

All the above changes are easily implementable in dynamic simulations, using ISIM and other digital simulation languages. The forms of response obtained differ in form, depending upon the system characteristics and can be demonstrated in the various ISIM simulation examples. The response characteristics of real systems are, however, more complex. In order to be able to explain such phenomena, it is necessary to first examine the responses of simple systems, using the concept of the simple, step-change disturbance. 

The effects of measurement dynamics are demonstrated in the simulation examples KLADYN, TEMPCONT and CONTUN. 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

Simulation example TRANSIM is based on the solution of a complex transfer function. 

U is the heat transfer coefficient, M the mass, Cp the heat capacity and A the heat transfer area. A knowledge and understanding of the appropriate time constants is important in interpreting many of the simulation examples. 

Process control is highly dynamic in nature, and its modelling leads usually to sets of differential equations which can be conveniently solved by digital simulation. A short introduction to the basic principles of process control, as employed in the simulation examples of Sec. 5.7, is presented. 

The components of the basic feedback control loop, combining the process and the controller can be best understood using a generalised block diagram (Fig. 2.29). The information on the measured variable, temperature, taken from the system is used to manipulate the flow rate of the cooling water in order to keep the temperature at the desired constant value, or setpoint. This is illustrated by the simulation example TEMPCONT, Sec. 5.7.1. 

Simple control strategies form an integral part of many of the simulation examples, including RELUY, COOL, DEACT, REFRIG, RUN, and COLCON and the special control examples in Sec. 5.7, TEMPCONT, TWOTANK and CONTUN. 

The purpose of controller tuning is to choose the correct controller constants to obtain the desired performance characteristics. This usually means that the control variables should be restored in an optimal way to acceptable values, following either a change in the set point or the appearance of an input disturbance. Simulation examples TEMPCONT and CONTUN, provide exercises for controller tuning using the methods explained below. 

An example of cascade control could be based on the simulation example DEACT and this is shown in Fig. 2.35. The problem involves a loop reactor with a deactivating catalyst, and a control strategy is needed to keep the product concentration Cp constant. This could be done by manipulating the feed rate into the system to control the product concentration at a desired level, Cjet- In this cascade control, the first controller establishes the setpoint for flow rate. The second controller uses a measurement of flow rate to establish the valve position. This control procedure would then counteract the influence of decreasing catalyst activity. 

Model instability is demonstrated by many of the simulation examples and leads to very interesting phenomena, such as multiple steady states, naturally occurring oscillations, and chaotic behaviour. In the case of a model which is inherently unstable, nothing can be done except to completely reformulate the model into a more stable form... 

For a fuller treatment of dynamic stability problems, the reader is referred to Walas (1991), Seborg et al. (1989), Habermann (1976), Perlmutter (1972) and to the simulation examples THERM, THERMPLOT, COOL, STABIL, REFRIG 1 and 2, OSCIL, LORENZ, HOPFBIF and CHAOS. 

Heat transfer is usually effected by coils or jackets, but can also be achieved by the use of external loop heat exchangers and, in certain cases, by the vaporisation of volatile material from the reactor. The treatment, here mainly concerns Jackets and coils. Other instances of heat transfer are illustrated in the simulation examples of Chapter 5. 

As shown in several of the simulation examples, the fact that Q is now a function of the flow rate, Fj, provides a convenient basis for the modelling of cooling effects, and control of the temperature of the reactor by regulation of the flow of coolant. 

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. 

Thus the respective rate expressions depend upon the particular concentration and temperature levels, that exist within reactor, n. The rate of production of heat by reaction, rg, was defined in Sec. 1.2.5 and includes all occurring reactions. Simulation examples pertaining to stirred tanks in series are CSTR, CASCSEQ and COOL. 

The types of system behaviour predicted, by the above analysis are depicted in Figs. 3.16 and 3.17. The phase-plane plots of Fig. 3.17 give the relation of the dependant variables C and T. Detained explanation of phase-plane plots is given in control textbooks (e.g., Stephanopoulos, 1984). Linearisation of the reactor model equations is used in the simulation example, HOMPOLY. 

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. 

Two simple forms of a batch reactor temperature control are possible, in which the reactor is either heated by a controlled supply of steam to the heating jacket, or cooled by a controlled flow of coolant (Fig. 3.18) Other control schemes would be to regulate the reactor flow rate or feed concentration, in order to maintain a given reaction rate (see simulation example SEMIEX). 

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