Control coolant flow

Open-Loop versus Closed-Loop Dynamics It is common in industry to manipulate coolant in a jacketed reacdor in order to control conditions in the reacdor itself. A simplified schematic diagram of such a reactor control system is shown in Fig. 8-2. Assume that the reacdor temperature is adjusted by a controller that increases the coolant flow in proportion to the difference between the desired reactor temperature and the temperature that is measured. The proportionality constant is K. If a small change in the temperature of the inlet stream occurs, then depending on the value or K, one might observe the reactor temperature responses shown in Fig. 8-3. The top plot shows the case for no control (K = 0), which is called the open loop, or the normal dynamic response of the process by itself. As increases, several effects can be noted. First, the reactor temperature responds faster and faster. Second, for the initial increases in K, the maximum deviation in the reactor temperature becomes smaller. Both of these effects are desirable so that disturbances from normal operation have... 

One such approach is called cascade control, which is routinely used in most modern computer control systems. Consider a chemical reactor, where reac tor temperature is to be controlled by coolant flow to the jacket of the reac tor (Fig. 8-34). The reac tor temperature can be influenced by changes in disturbance variables such as feed rate or feed temperature a feedback controller could be employed to compensate for such disturbances by adjusting a valve on me coolant flow to the reac tor jacket. However, suppose an increase occurs in the... 

For partial condenser systems, the pressure can be controlled by manipulating vapor product or a noncondensible vent stream. This gives excellent pressure control. To have a constant top vapor product composition, the condenser outlet temperature also needs to be controlled. For a total condenser system, a butterfly valve in the column overhead vapor line to the condenser has been used. Varying the condenser cooling by various means such as manipulation of coolant flow is also common. 

The HFBR core uses fully-enriched (93%) uranium oxide-aluminum cermet curved plates dad m aluminum. The core height is 0.58 m and the diameter is 0.48 m or a volume of 103.7 Itr. The U-235 weighs 9.83 kg supported by a grid plate on the vessel bottom. The coolant flow u downward. Iience. How reversal is necessary for natural circulation. It operating temperature and pressure are 60 ( and 195 psi. There are 8 main and 8 auxiliary control rod blades made of europium oxide (Lii A)o and dysprosium oxide (DyjO,), clad in stainless steel that operate in the reflector region. The scram system is the winch-clutch release type to drop the blades into the reflector region. Actuation of scram causes a setback for the auxiliary control rods which are driven upward by drive motors,... 

Close control of conditions may require diversion of the main air flow, see Figure 28.10, or moving human operatives outside the sensitive area. Coolant flow control should he modulating or infinitely variable, where possible. 

The parameters used in the program give a steady-state solution, representing, however, a non-stable operating point at which the reactor tends to produce natural, sustained oscillations in both reactor temperature and concentration. Proportional feedback control of the reactor temperature to regulate the coolant flow can, however, be used to stabilise the reactor. With positive feedback control, the controller action reinforces the natural oscillations and can cause complete instability of operation. 

Consider the case of a proportional controller, which is required to maintain a desired reactor temperature, by regulating the flow of coolant. Neglecting dynamic jacket effects, the reactor heat balance can then be modified to include the effect of the varying coolant flow rate, hj, in the model equation as ... 

Automatic primary coolant flow control (both total and loop flow controllers). 

If we were cooling instead of heating, we would want the coolant flow to increase when the temperature increased. But the controller action would still be reverse because the control valve would be an air-to-olosc valve, since wc want it to fail wide open. 

From Figure 16 it follows that the response of the reactor has no offset due to the integrators block. Another interesting aspect is that the incremental jacket temperature is lower than the incremental reactor temperature, so the heat transmission goes from the reactant to the coolant flow rate. The values of the control signals, i.e. the outlet and inlet flow rate deduced from Eq.(50), are shown in Figure 17. 

In this situation, a periodic variation of coolant flow rate into the reactor jacket, depending on the values of the amplitude and frequency, may drive to reactor to chaotic dynamics. With PI control, and taking into account that the reaction is carried out without excess of inert (see [1]), it will be shown that it the existence of a homoclinic Shilnikov orbit is possible. This orbit appears as a result of saturation of the control valve, and is responsible for the chaotic dynamics. The chaotic d3mamics is investigated by means of the eigenvalues of the linearized system, bifurcation diagram, divergence of nearby trajectories, Fourier power spectra, and Lyapunov s exponents. 

It is well known that a nonlinear system with an external periodic disturbance can reach chaotic dynamics. In a CSTR, it has been shown that the variation of the coolant temperature, from a basic self-oscillation state makes the reactor to change from periodic behavior to chaotic one [17]. On the other hand, in [22], it has been shown that it is possible to reach chaotic behavior from an external sine wave disturbance of the coolant flow rate. Note that a periodic disturbance can appear, for instance, when the parameters of the PID controller which manipulates the coolant flow rate are being tuned by using the Ziegler-Nichols rules. The chaotic behavior is difficult to obtain from normal... 

In this section we consider a CSTR with a very simple control system formed by two PI controllers. The first controller manipulates the outlet flow rate as a function of the volume in the tank reactor. A second PI controller manipulates the flow rate of cooling water to the jacket as a function of error in reactor s temperature. The control scheme is shown in Figure 12 where the manipulated variables are the inlet coolant flow rate Fj and the outlet flow rate F respectively. 

Exercise 6. Show that the equilibrium point of the model defined by Eq.(34) and the simplified model R given by Eq.(35), i.e. when the dynamics of the jacket is considered negligible, are the same. Deduce the Jacobian of the system (35) at the corresponding equilibrium point. Write a computer program to determine the eigenvalues of the linearized model R at the equilibrium point as a function of the dimensionless inlet flow 4 50. Values of the dimensionless parameters of the PI controller can be fixed at Ktd = 1-52 T2d = 5. The set point dimensionless temperature and the inlet coolant flow rate temperature are Xg = 0.0398, X40 = 0.0351 respectively. An appropriate value of dimensionless reference concentration is C g = 0.245. Does it exist some value of 2 50 for which the eigenvalues of the linearized system R at the equilibrium point are complex with zero real part Note that it is necessary to vary 2 50 from small to great values. Check the possibility to obtain similar results for the R model. 

In Eqs.(33), (34) and (35) the effect of the constrained coolant flow rate due to control valve saturation is not considered, however this limitation can be introduced in the mathematical model of the reactor as follows ... 

In this case it is not possible to reach any value of equilibrium dimensionless coolant flow rate X6e, because when xge is greater than xg ax, it is constrained to the maximum value xe ax due to the flow rate limitation through the control valve. From this moment, the derivative dx /dr) is zero and the flow rate cooling xq remains constant. Consequently, the coolant flow rate cannot decrease the reactor temperature, which reaches a value greater than the set point, and the corresponding reactant concentration will be smaller. From Eq.(43) the set point temperature must be equal to xse, and as a result it is impossible that the reactor temperature would be able to reach the set point temperature Xg, an consequently the control system cannot drive the reactor to the desired equilibrium point. The equilibrium values of dimensionless variables are given by the same Eqs.(45), (46) and (47), but making the substitutions ... 

It is interesting to note that in chaotic regime, the flow rate outlet stream, which is manipulated by the control valve CVl (see Figure 12), and the reactor volume, are driven by the PI controller to the equilibrium point without chaotic oscillations. However, the other variables have a chaotic behavior as shown in Figure 18. So it is possible to obtain a reactor behavior, in which some variables are in steady state and the others are in regime of chaotic oscillations, due to the decoupling or serial connection phenomena. In this case the control system and the volumetric flow limitation of coolant flow rate through the control valve VC2, are the responsible of this behavior. Similar results can be obtained from model. 

The non-linear dynamics of the reactor with two PI controllers that manipulates the outlet stream flow rate and the coolant flow rate are also presented. The more interesting result, from the non-linear d mamic point of view, is the possibility to obtain chaotic behavior without any external periodic forcing. The results for the CSTR show that the non-linearities and the control valve saturation, which manipulates the coolant flow rate, are the cause of this abnormal behavior. By simulation, a homoclinic of Shilnikov t3rpe has been found at the equilibrium point. In this case, chaotic behavior appears at and around the parameter values from which the previously cited orbit is generated. 

As a minimum, a distillation assembly consists of a tower, reboiler, condenser, and overhead accumulator. The bottom of the tower serves as accumulator for the bottoms product. The assembly must be controlled as a whole. Almost invariably, the pressure at either the top or bottom is maintained constant at the top at such a value that the necessary reflux can be condensed with the available coolant at the bottom in order to keep the boiling temperature low enough to prevent product degradation or low enough for the available HTM, and definitely well below the critical pressure of the bottom composition. There still remain a relatively large number of variables so that care must be taken to avoid overspecifying the number and kinds of controls. For instance, it is not possihle to control the flow rates of the feed and the top and bottom products under perturbed conditions without upsetting holdup in the system. 

The channel is a square-shaped tube fabricated from Zircaloy 4. The outer dimensions arc 5,518 inches (14 centimeters) by 5,518 inches (14 centimeters) by 166,9 inches (424 centimeters) long, The reusable channel makes a sliding seal lit on the lower tie plate surface. It is attached to the upper tic plate by the channel fastener assembly, consisting of a spring and a guide, and a cap screw secured by a lock washer. The fuel channels direct the core coolant flow through each fuel bundle and also serve to guide the control rods. 

Open-Loop versus Closed-Loop Dynamics It is common in industry to manipulate coolant in a jacketed reactor in order to control conditions in the reactor itself. A simplified schematic diagram of such a reactor control system is shown in Fig. 8-2. Assume that the reactor temperature is adjusted by a controller that increases the coolant flow in proportion to the difference between the desired reactor temperature and the temperature that is measured. The proportionality constant is Kc. If a small change in the temperature of the inlet stream occurs, then... 

Cascade control is one solution to this problem (see Fig. 8-36). Here the jacket temperature is measured, and an error signal is sent from this point to the coolant control valve this reduces coolant flow,... 

When reactor capacity is limited by heat removal, an often-recommended control structure is to run with maximum coolant flow and manipulate feed flowrate to control reactor temperature (Tr F0 control). This control scheme has the potential to achieve the highest possible production rate. However, if the feed temperature is lower than the reactor temperature, the transfer function between temperature and feed flowrate contains a positive zero, which degrades dynamic performance, as we demonstrate quantitatively in this section. The choice of a control structure for this process presents an example of the often encountered conflict between steady-state economics and dynamic controllability. 

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