Modelling the Water Level in a Tank

Consider the task of developing models for the water level in the four tanks shown in Fig. 6.8. In this system, there are two inputs, and U2, which represent the flow rate delivered by the two pumps. Each input is split into two and enters a bottom 

The objective of this experiment is to determine an appropriate model for the water level in Tank 1 assuming that the splits are fixed, but the flow rate from the two pumps can vary. Design an appropriate experiment and analyse the results. Perform both linear and nonlinear system identification and compare the resulting models. Which one would be preferred  

The design of the experiment can be split into two parts preliminary identification using step tests and final identification using a random binary signal. 

6 Modelling Dynamic Processes Using Systean Identification Methods 

In preliminary identification, the objective is to obtain a rough idea of how the system behaves under different conditions. In order to achieve this, a series of step tests will be performed on the system. Each pump will be tested separately at this point in order to make the computations easier. For each pump, a step increase of +2 cm /s will be made. The resulting changes in the Tank 1 level are shown in Fig. 6.9. Table 6.2 shows the values obtained and the computatimi of the required time constants. 

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The inside surface should be 316L electro-polished (Ra < 0.8 p) the tank must be totally drainable. Storage tanks must be equipped with a spray ball on the circulation return line to sanitize all internal parts of the tank and to assure that the tank interior surfaces above the water level are continuously flushed. Tanks must be equipped with a vent hlter (0.2 pm hydrophobic) installed in such a way as to prevent condensate from being trapped. The technical services manager and QA manager must approve the model. 

A simplified model was built of the onshore facilities. This model represents the main pieces of onshore equipment and represents all important throughput and capacity constraints. Constraints modelled are slug catcher level, slug catcher pressure, condensate separator level, pressure in condensate separators, product gas demand, coalescer interface level, level in storage tanks for condensate, produced water, MEG and the unseparated MEG-water mixture and the capacity in MEG separation and condensate stabilisation. 

It will be appreciated that our description of the plant is, in reality, only an approximation covering as few features as we can get away with, while still capturing the essential behaviour of the plant. For instance, in the example above of the tank liquid level, no mention was made of liquid temperature, entailing an implicit assumption that temperature variations would be small over the period of interest. If it had been necessary to allow for temperature effects, perhaps because of fear of excessive evaporation or because of environmental temperature limits set for a waste water stream, then liquid temperature would have had to be included as an additional state variable, and the dimension or order of the plant as we modelled it would go up from 4 to 5. If we had needed to make an allowance for the temperature of the metal in the tank. 

Level II Model The added refinement involves accounting for losses from compartments either by advection or reaction. A steady state is achieved where input is balanced by the loss from the system, but the compartments remain at equilibrium as indicated by the fluid height in the tank analogy (Fig. 10.9). Quantities defining the loss of 1,2,3-trichlorobenzene from the system by advection and reaction are compiled in Table 10.8. Photochemical reactions would be the most likely processes involved in air and water, while microbial degradation would be active in soil and bottom sediments, and the use of first-order rate constants (h ) is an appropriate approximation. 

The measurement of drag on a surface vessel in a towing tank is another problem that is difficult to model exactly. For surface vessels which operate at a water-air interface, the acceleration due to gravity (g) must be included in a dimensional analysis for drag, since water is lifted vertically from the level surface against gravitational attraction during the formation of a bow wave. The variables of importance in this case are ... 

The model shown in Figure 3-6 depicts a model that constructs a tank to which water is added or drained (=flow) according to the level of water (= level). Until the level of water falls to a defined limit liquid is drained by a constant rate (= constant). If the level lls below the limit water is tapped by a calculated rate (= auxiliary). 

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