Consider the liquid storage system shown in Fig.10.5. A high-level alarm is used to prevent tank overflow. After a high alarm sounds, the operator has 10 minutes to respond before the ESD system turns off the pumps on the inlet streams. The tank is 6 ft in diameter, 8 ft tall, and half full at the

Question

Consider the liquid storage system shown in Figure below. A high-level alarm is used to prevent tank overflow. After a high alarm sounds, the operator has 10 minutes to respond before the ESD system turns off the pumps on the inlet streams. The tank is 6 ft in diameter, 8 ft tall, and half full at the nominal conditions. The density of the liquid is constant. The nominal values and ranges of the flow rates are as follows:

Flow rate	Nominal Value (ft³/min)	Range (ft³/min)
q1	10	8–12
q2	5	4–6
q	15	13–17

(a) Assuming that the pumps are operating properly, determine an appropriate set-point value for the high-level alarm, that is, the numerical value of liquid level h that triggers the alarm.
(b) What additional safety features are required to handle unanticipated pump shutdowns?

Accepted Answer

(a) For constant liquid density, the mass balance for the liquid in the tank is
[latex]\rho A\frac{dh}{dt}=\rho (q_{1}+q_{2} -q) [/latex]
In order to specify the high alarm limit, consider the worst-case conditions that result in the largest rate of change, dh/dt. This situation occurs when the inlet flow rates are at their maximum values and the exit flow rate is a minimum.
Substituting [latex]q_{1} = 12 ft^{3}/min,q_{2} = 6 ft^{3}/min, \space and \space q = 13 ft^{3}/min [/latex] gives:

[latex]\frac{dh}{dt}=\frac{5ft^{3}/min}{\pi (3ft)^{2}}=0.176ft/min [/latex]
Consequently, the maximum increase in liquid level that can occur during any 10-min period is,
[latex]Δh_{\max} = (10 min) (0.176 ft∕min) = 1.76 ft[/latex]
Thus, the alarm limit should be at least 1.76 ft below the tank height. As a safety margin, choose 2 ft and set the high alarm limit at 6 ft.

(b) A pump failure could result in tank overflow or a tank level so low that the exit pump could be damaged. Thus, high and low level alarms should be connected to interlocks on the inlet and exit pumps, respectively.

Question 10.1: Consider the liquid storage system shown in Fig.10.5. A high...

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