The Level-Controlled Tank

The filling or draining of a tank is a relatively simple situation to model. If the tank has both input and output then it is a combination of the two previous cases and the differential equation for the rate of change of the level in the tank is as follows  

Atankcouldbeoperatedinsuchawaythattheinlefwasalwaysequaltotheoutlefwhen thetwowereattheirdesignedmagnitudes.Thusifq wasthedesigned flowrateinaCSTR, forexample,thenthesystemcouldbemaintainedatsomespedficdesignleveIh anddesign 

Suppose thatthe inlet flowratewasmostlyaconstantbutfromtimetotimeitsufferedan upset.Theupsetwouldeitherincreasetheinlet flowordecreaseit.lfthisweretooccupthen 

Thisequationistheonethatmustbeintegratedandtodosowemustknowhowthe upset behavesintime.Beforetheupsetfromt = Ountilsometimejustbelowtl,qpiszeroandh h(t)  

All DiracDelta and UnitStep functionality is now autoloaded. The package Calculus DiracDelta is obsolete. 

When the input flow rate is equal to the output flow rate, the system is at steady state and the level remains constant because = 0. 

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Where a flooded coil is located in a liquid tank, the refrigerant level will be within the tank, making it difficult to position the level control. In such cases, a gas trap or siphon can be formed in the lower balance pipe to give an indirect level in the float chamber. Siphons or traps can also be arranged to contain a non-voIatile fluid such as oil, so that the balance pipes remain free from frost. 

Liquid flows through a system of two tanks arranged in series, as shown below. The level control of tank 2 is based on the regulation of the inlet flow to the tank 1. This tank represents a considerable lag in the system. The aim of the controller is to maintain a constant level in tank 2, despite disturbances which occur in the flow F3. 

The feed flow-rate is often set by the level controller on a preceding column. It can be independently controlled if the column is fed from a storage or surge tank. 

Feedback is information in a closed-loop control system about the condition of a process variable. This variable is compared with a desired condition to produce the proper control action on the process. Information is continually "fed back" to the control circuit in response to control action. In the previous example, the actual storage tank water level, sensed by the level transmitter, is feedback to the level controller. This feedback is compared with a desired level to produce the required control action that will position the level control as needed to maintain the desired level. Figure 3 shows this relationship. 

In the water tank level control system in the example above, the level transmitter measures the level within the tank. The level transmitter sends a signal representing the tank level to the level control device, where it is compared to a desired tank level. The level control device then computes how far to open the supply valve to correct any difference between actual and desired tank levels. 

It might be worth noting that we could have considered the flow from the third tank fj as the forcing fijnction. Then the level in tank 3 would probably be maintained by the flow into the tank, f 2 Th Isvel in tank 2 would be controlled by fi, and tank 1 level by Fg. We would still have three equations. 

Suppose the flow rate Fq increases to the first tank in Fig. 7.14. The level in the first tank will start to increase. The level controller will start to increase Fi-When F has increased to the point that it is equal to Fo.-tflc level will stop changing since the tank is just an integrator. Now, if we use a P level controller, nothing else will happen. The level will remain at the higher level and the entering and exiting flows will be equal. 

Here, a variable-speed pump transfers the hot water from the production well into the steam separator. The speed of the pump is set by the tank level. (Variable-speed pump station controls are discussed in Section 2.17). The level control signal is corrected for steam pressure variations by multiplying the two. This is called a two-element feedwater system. 

A general knowledge of the symbols for flow, level, pressure, and temperature controllers, as given in Fig. 5.9.2, is needed to comprehend flow diagrams like the simple example presented in Fig. 5.9.3. In this vessel, with an inlet feed on top of the tank equipped with a flow controller, the level in the tank is maintained by a level controlling device. When the le el rises above the high level point, the level controller sends a signal to a valve actuator and the alve is opened to drop the le el. When the level approaches a specified value, the valve is closed. Complicated systems can be analyzed in the same manner used in this basically simple example. 

Continuous Starch Hydrolysis. A commercial continuous converter installation for dextrose manufacture employing a continuous, automatically controlled step for the hydrolysis of starch is now in operation. A flow diagram of a modem commercial installation for continuous starch hydrolysis is shown in Fig. 13-4. The starch converter consists of an 8-in. coil, 677 ft long, which is fed by a high-pressure centrifugal pump from a continuous starch make-up tank equipped for automatic control of density (Baumd), level, and acidity. The level controller regulates the addition of 20 B starch suspension, the Baum controller operates the water valve, and a conductivity instrument controls the addition of acid. The head end of the converter coil has an entry chamber to separate non-condensables, and the feed is instantaneously heated with live steam through a jet heater. 

The flow rate into the tank is measured. The flow signal is sent through a first-order lag with time constant t/t. The output of the lag is added to the output of the level controller. The sum of these two signals sets the outflow rate. Assume that the flow rate follows the setpoint signal to the flow controller exactly.,... 

For example, an equipment-oriented team might say The tank overflowed because the level controller failed. A people-oriented team may say The tank overflowed because the instrument technician did not service the level controller. A management-oriented team would say The tank overflowed because we did not have a good enough training program for our instrument technicians. ... 

It is critical that each LOPA scenario have just one cause and one consequence. There will always be a temptation to combine those causes that lead to the same consequence to save time in the analysis and documentation. However, the different causes will occur with different frequencies and may use different IPLs. For example, high level in a tank could be caused by failure of the level control instrument or by failure of the tank s discharge pump. These causes will have different frequencies of occurrence. They will also utilize different IPLs for the first scenario an IPL could be a self-testing mechanism on the level instrument, for the second scenario an IPL could be an ammeter signal telling the operator that the pump had shut down. 

Extending off from one of the discharge pipes 102 is a level control pipe 165 projecting downwardly into the sump 164 and terminating close to the bottom of the sump. A two-way operating pump 166 driven by a reversible motor 167 is provided in the level control pipe "0 165. The purpose of this level control pipe 165 is to convey heavy water back and forth between the sump 164 and the active portion 19 of the reactor 18 in response to the action of the pump 166 so as to control the level of the heavy water in the tank 20. This may... 

The rationale behind the definitions of iow demand mode and high demand or continuous mode in lEC 61508 is based on the failure behaviour of a safety-related system due to random hardware faults. Underlying much of the reasoning is the distinction between safety-functions that only operate on demand and those that operate continuously . A safety function that operates on demand has no influence until a demand arises, at which time the safety function acts to transfer the associated equipment into a safe state. A simple example of such a safety function is a high level trip on a liquid storage tank. The level of liquid in the tank is controlled in normal operation by a separate control system, but is monitored by the safety-related system. If a fault develops in the level control system that causes the level to exceed a pre-determined value, then the safety-related system closes the feed valve. With such a safety function, a hazardous event (in this case, overspill) will only occur if the safety function is in a failed state at the time a demand (resulting from a failure of the associated equipment or equipment control system) occurs. A failure of the safety function will not, of itself, lead to a hazardous event. This model is illustrated in Figure 4. 

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