I didn't think I could solve the problem. I had to specify the level settings for a flanged and dished tank divided into three compartments with a bottom head as the third tank. It was a challenge but I met it. What do you know — integral calculus is actually good for something!
In a typical level problem, you must set high-high (HH), high (H), low (L) and low-low (LL), based on percent, for a standard two-element (wet, dry) differential pressure (dP) transmitter. Don't forget about full (100%) and empty (0%). All measurements normally are to centerline unless otherwise noted.
For a dP level transmitter, the upper range value (URV) and lower range value (LRV) are defined as:
URV = liquid specific gravity (SG) × the distance between 100% and 0% (h100%) + LRV; and
LRV = capillary fill SG × distance between the elements or pancakes × -1. The LRV distance should comfortably exceed the URV span.
The HH setting usually is at the lip of the overflow but sometimes is lower if process constraints dictate. Equating that with 100% full can cause problems. You may want to measure above HH in case the overflow fails. "Cameron Hydraulic Data" recommends a minimum spacing between settings of 3 in. or 2 min.
Establishing LL is simple for a cylindrical shape. Cameron suggests 1-ft submergence for every ft/sec velocity for the pump suction. So, for a 2-ft/sec velocity and a 6-in. nozzle, LL should be: 6/2 + 2×12 = 27 in. above the pump suction nozzle centerline. For saturated (boiling) liquids, use a safety factor or company standard.
The setting for H depends on the maximum fill rate. The material balance may be helpful. The L setting depends on the maximum withdrawal rate. It may make sense to set HH and H for the light liquid and LL and L for the dense liquid. However, here's where the calculation gets complicated.
To calculate a setting for a cylinder, first calculate the volume per inch. For a 10-ft-dia. tank this is 4.9 gal/in. If the fill rate were 50 gal/min, then for 2-min. minimum spacing the gap between HH and H would be 50×2/4.9 = 20 in. If the total span between 100% and 0% were 450 in. and HH were set at 95%, then H would be at (427.5 – 20) /450 = 91%. Change any gap less than 3 in. to 3 in. If you wanted H at 85%, the time between H and HH would be 4.4 min.
With other shapes such as cones and vessels where most of the volume is in the head, the calculation is more difficult. I've found it best to use the actual volume rather than the column change. In one vessel only 30% of the volume was in the cone. I've set LL based on liquid holdup and recirculation rate for such tanks. Also, you may want to confirm LL against Cameron's submergence recommendation.
Calibration introduces new problems. The density of ambient water used in testing probably won't match that of your process liquid. There's a simple correction. If water temperature during testing is 75°F, SG is 0.997. If process fluid at process temperature has an SG of 0.880, correct via a ratio. For example, if an H of 90% were desirable, then during calibration, the setting should be: 90% × 0.997/0.880 = 102%. The total inches of water column is the same but the height of the liquid is less for the heavier test water.
While geometry makes life difficult, SG causes real problems in dP level measurement. Sometimes a vessel contains more than one liquid, sometimes it changes during the process. Usually, it's best to set HH and H using the lighter liquid but not if the density ratio is more than about 1.2:1. Otherwise, your HH and LL alarms would be separated by only 20–40%, which is unworkable.
When this occurs, it's still possible to use a dP — but not alone. Consider a density measurement; a nuclear or dP cell in a still well may work. Calculate a new URV from the density: URVnew = SGnew×h100% + LRV. Now, determine the true level: % level = (dPnew - LRV)/(URVnew - LRV). In this way, URV and span are variables.
(For more on level measurement options, see "Select the Right Liquid Level Sensor")
DIRK WILLARD is a Chemical Processing Contributing Editor. You can e-mail him at firstname.lastname@example.org