Disproving Equation 3
Figure 4. If Golden Rule isn’t satisfied, equalization shown isn’t possible.
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 [email protected] and [email protected].
REFERENCE
1. Martyn, K., "Level Measurement in Bridles," Process West, p. 50, April 2006.