Hydrostatic pressure sensors may be used to detect the level of a liquid-liquid interface, if and only if the total height of liquid sensed by the instrument is fixed. A single hydrostatic-based level instrument cannot discriminate between a changing interface level and a changing total level, so the latter must be fixed to measure the former.
One way of fixing total liquid height is to equip the vessel with an overflow pipe and ensure that drain flow is always less than incoming flow (forcing some flow to always go through the overflow pipe). This strategy naturally lends itself to separation processes, where a mixture of light and heavy liquids is separated by their differing densities:
Here we see a practical application for liquid-liquid interface level measurement. If the goal is to separate two liquids of differing densities from one another, we need only the light liquid to exit out the overflow pipe and only the heavy liquid to exit out the drainpipe. This means we must control the interface level to stay between those two piping points on the vessel. If the interface drifts too far up, the heavy liquid will be carried out the overflow pipe; and if we let the interface drift too far down, the light liquid will flow out of the drainpipe. The first step in controlling any process variable is to measure that variable, and so here we are faced with the necessity of measuring the interface point between the light and heavy liquids.Another
way of fixing the total height seen by the transmitter is to use a compensating
leg located at a point on the vessel always lower than the total liquid height.
In this example, a transmitter with remote seals is used:
(γ1h1
+ γ2h2 + γ2h3) − (γ4h4 + γ2h3)
γ1h1 +
γ2h2 + γ2h3 − γ4h4 − γ2h3
γ1h1 +
γ2h2 − γ4h4
The
hydrostatic pressure in the compensating leg is constant (γ4h4 = Constant),
since the fill fluid never changes density and the height never changes. This
means the transmitter’s sensed pressure will differ from that of an
uncompensated transmitter merely by a constant offset, which may be “calibrated
out” to have no impact on the measurement:
γ1h1 +
γ2h2 – Constant
At the first, it may seem as though determining the calibration points (lower- and
upper-range values: LRV and URV) for a hydrostatic interface level transmitter
is impossibly daunting given all the different pressures involved. A recommended
problem-solving technique to apply here is that of a thought experiment, where
we imagine what the process will “look like” at lower-range value condition and
at the upper-range value condition, drawing two separate illustrations:
We
know from our previous exploration of this setup that any hydrostatic pressure
resulting from the liquid level above the top remote seal location is irrelevant to
the transmitter since it is “seen” on both sides of the transmitter and thus
cancels out. All we must do, then, is calculate hydrostatic pressures as though
the total liquid level stopped at that upper diaphragm connection point.
First,
calculating the hydrostatic pressure “seen” at the high port of the
transmitter:
P high
= 4.5 feet of heavy liquid + 4.5 feet of light liquid
P high
= 54 inches of heavy liquid + 54 inches of light liquid
P high
”W.C. = (54 inches of heavy liquid )(1.1) + (54 inches of light liquid )(0.78)
P high
”W.C. = 59.4 ”W.C. + 42.12 ”W.C.
P high
= 101.52 ”W.C.
Next,
calculate the hydrostatic pressure “seen” at the low port of the transmitter:
P low
= 9 feet of fill fluid
P low
= 108 inches of fill fluid
P low
”W.C. = (108 inches of fill fluid )(1.09)
P low
= 117.72 ”W.C.
The
differential pressure applied to the transmitter in this condition is the
difference between the high and low port pressures, which becomes the lower
range value (LRV) for calibration:
P LRV
= 101.52 ”W.C. − 117.72 ”W.C. = − 16.2 ”W.C.
As the
second step in our “thought experiment,” we imagine what the process would look
like with the interface at the URV level, calculating hydrostatic pressures
seen at each side of the transmitter:
P high
= 90 inches of heavy liquid + 18 inches of light liquid
P high
”W.C. = (90 inches of heavy liquid )(1.1) + (18 inches of light liquid )(0.78)
P high
”W.C. = 99 ”W.C. + 14.04 ”W.C.
P high
= 113.04 ”W.C.
The
hydrostatic pressure of the compensating leg is exactly the same as it was
before: 9 feet of fill fluid having a specific gravity of 1.09, which means there
is no need to calculate it again. It will still be 117.72 inches from the water
column. Thus, the differential pressure at the URV point is:
P URV
= 113.04 ”W.C. − 117.72 ”W.C. = − 4.68 ”W.C.
Using
these two pressure values and some interpolation, we may generate a 5-point
calibration table (assuming a 4-20 mA transmitter output signal range) for this
interface level measurement system:
Interface Level (ft) |
Percentage of Range (%) |
Differential Pressure at Transmitter (“WC) |
Transmitter Output (mA) |
4.5 |
0 |
-16.2 |
4 |
5.25 |
25 |
-13.32 |
8 |
6.0 |
50 |
-10.44 |
12 |
6.75 |
75 |
-7.56 |
16 |
7.5 |
100 |
-4.68 |
20 |
When the time comes to bench-calibrate this instrument in the shop, the easiest way to do so will be to set the two remote diaphragms on the workbench (at the same level), then apply 16.2 to 4.68 inches of water column pressure to the low remote seal diaphragm with the other diaphragm at atmospheric pressure to simulate the desired range of negative differential pressures.
The
more mathematically inclined reader will notice that the span of this
instrument (URV − LRV) is equal to the span of the interface level (3 feet, or
36 inches) multiplied by the difference in specific gravities (1.1 − 0.78):
Span
in ”W.C. = (36 inches)(1.1 − 0.78)
Span =
11.52 ”W.C.
Looking
at our two “thought experiment” illustrations, we see that the only difference
between the two scenarios is the type of liquid filling that 3-foot region
between the LRV and URV marks.
Therefore,
the only difference between the transmitter’s pressures in those two conditions
will be the difference in height multiplied by the difference in density. Not
only is this an easy way for us to quickly calculate the necessary transmitter
span, but it also is a way for us to check our previous work: we see that the
difference between the LRV and URV pressures is indeed a difference of 11.52 inches of water column just as this method predicts.
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