In practice it can be difficult to locate nozzles to satisfy the Golden Rule under all operating conditions. If a vessel may contain widely varying levels of liquid inventories, then it's worth considering multiple nozzle locations. Select nozzle positioning and spacing to minimize the chance that one no longer is connected to a liquid phase. It's possible for light liquid to become trapped in the gauge, causing an error when the light liquid inventory no longer is connected to a nozzle (Figure 3). This could occur, for example, when the heavy liquid level drops and too large a nozzle spacing was used.
Considerations other than nozzle locations can affect the accuracy of the level measurement. It's well known that temperature differences between the fluid in the gauge and the vessel can lead to erroneous readings.
AVOID NOZZLE PLACEMENT ERRORS
Adhering to our simple Golden Rule will ensure the liquid/liquid interface in the gauge matches the interface level in the vessel. If you can't manage liquid inventories to satisfy the rule then errors may arise in the measurement.
TEST THE NOZZLE PLACEMENT RULE
In Figure 4 assume the Golden Rule is satisfied -- i.e., each liquid phase in the vessel is connected to the gauge by a nozzle. At equilibrium the pressures at the middle and bottom nozzles are balanced via Eqs.1 and 2, respectively:
Pv + ρoil g H1 + ρwater g H2 = Pv + ρoil g H1* (1)
Pv + ρoil g H1 + ρwater g (H2 + Htap) = Pv + ρoil g ( H1* + H2*) + ρwater g Hwater (2)
where Pv is the vessel vapor pressure, ρoil is the oil density, ρwater is the water density, and g is gravitational acceleration. Substitution and algebraic rearrangement yields:
ρoil H2* = ρwater H2* (3)
Because the densities of the oil and water phases aren’t equal and H2*≠ 0 (remember we assumed that the Golden Rule is satisfied), then Equation 3 is a contradiction and can’t be true. Therefore, the equalization shown in Figure 4 isn’t possible. You can examine different equalizations, all of which will result in contradictions unless the gauge interface and vessel interface levels are equal.
JONATHAN WEBBER is a process engineer for Fluor Canada, Saint John, NB. PATRICK RICHARDS is an independent instrumentation consultant at Irving Oil, Saint John, NB. E-mail them at Jonathan.Webber@fluor.com and Patrick.Richards@irvingoil.com.
1. Martyn, K., "Level Measurement in Bridles," Process West, p. 50, April 2006.