Tank heaters

Figure 10-4D. Vertical longitudinal finned-tube tank heater, which is used in multiple assemblies when required. (Used by permission Brown Fintube Co., A Koch Engineering Co., Bui. 4-5.)...

Many systems are shut down for periods of the year, either for process closure or if not required in winter. The advice of the supplier should be sought as to the correct procedure. In the case of refrigerant circuits, it is advisable to pump down into the receiver or condenser to minimize leakage losses. Water towers should be drained in winter in this climate, if not in use, and the tank heater disconnected. 

Temperature control in a stirred-tank heater is a common example (Fig. 2.9). We will come across it many times in later chapters. For now, we present the basic model equation, and use it as a review of transfer functions. 

Figure 2.9. A continuous flow stirred-tank heater.

A brief review is in order Recall that Laplace transform is a linear operator. The effects of individual inputs can be superimposed to form the output. In other words, an observed output change can be attributed to the individual effects of the inputs. From the stirred-tank heater example in Section 2.8.2 (p. 2-23), we found ... 

This section is a review of the properties of a first order differential equation model. Our Chapter 2 examples of mixed vessels, stined-tank heater, and homework problems of isothermal stirred-tank chemical reactors all fall into this category. Furthermore, the differential equation may represent either a process or a control system. What we cover here applies to any problem or situation as long as it can be described by a linear first order differential equation. 

It is important to understand that the time constant xp of a process, say, a stirred tank is not the same as the space time x. Review this point with the stirred-tank heater example in Chapter 2. Further, derive the time constant of a continuous flow stirred-tank reactor (CSTR) with a first-order chemical reaction... 

Consider the stirred-tank heater again, this time in a closed-loop (Fig. 5.4). The tank temperature can be affected by variables such as the inlet and jacket temperatures and inlet flow rate. Back in Chapter 2, we derived the transfer functions for the inlet and jacket temperatures. In Laplace transform, the change in temperature is given in Eq. (2-49b) on page 2-25 as... 

We now walk through the stirred-tank heater system once again. This time, we ll take a closer look at the transfer functions and the units (Fig. 5.5). 

With the stirred-tank heater, we know quite well by now that we want to manipulate the heating coil temperature to control the tank temperature. The process function Gp is defined based on this decision. In this simple illustration, the inlet temperature is the only disturbance, and the load function is defined accordingly. From Section 2.8.2 and Eq. (2-49b) on page 2-25, we have the first order process model ... 

The closed-loop characteristic equation of the stirred-tank heater system is hence ... 

When we developed the model for the stirred tank heater, we ignored the dynamics of the heating coil. Provide a slightly more realistic model which takes into consideration the flow rate of condensing steam. 

How we model the stirred tank heater is subject to the actual situation. At a slightly more realistic level, we may assume that heat is provided by condensing steam and that the coil metal is at the same temperature as the condensing steam. The heat balance and the Laplace transform of the tank remains identical to Chapter 2 ... 

Example 4—Selecting physically meaningful inputs to characterize stability. Consider a continuous stirred-tank heater modeled by the following equations, in continuous time ... 

A 200.0-liter water lank can withstand pressures up to 20.0 bar absolute before rupturing. At a particular time the lank contains 165.0 kg of liquid water, the fill and exit valves are closed, and the absolute pressure in the vapor head space above the liquid (which may be assumed to contain only water vapor) is 3.0 bar. A plant technician turns on the tank heater, intending to raise the water temperature to 155°C, but is called away and forgets to return and shut off the heater. Let be the instant the heater is turned on and the moment before the tank ruptures. Use the steam tables for the following calculations. 

Feed Tanks (T-i, T-IA). Figure B.2 depicts schematically the process flow around both emulsion feed storage tanks. The emulsion feed tank (T-1) is designed to hold 15,900 L (100 bbl). This horizontal tank is equipped with two identical mixers and a recirculation loop to ensure that emulsion feed is well mixed and consistent throughout a typical run. The tank is also equipped with a steam-plate coil-tank heater capable of raising the feed temperature to 70 (160 T) with a heat load of 18.3 kW (62,500 Btu/h)... 

Example 1.1 Controlling the Operation of a Stirred Tank Heater... 

Consider the tank heater system shown in Figure 1.1. A liquid enters the tank with a flow rate F, (ft3/min) and a temperature T, (°F), where it is heated with steam (having a flow rate F lb/min). Let F and T be the flow rate and temperature of the stream leaving the tank. The tank is considered to be well stirred, which implies that the temperature of the effluent is equal to the temperature of the liquid in the tank. 

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