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| David W. Spitzer, P.E.
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A flow control loop consisting of a flowmeter, controller, and control
valve is used to control the flow of a gas to a process. Measurements
from a pressure transmitter installed some time ago indicate the
incoming air pressure is typically two bar, but that it can vary from
one to 2.5 bar due to process upsets that occur upstream. How will
these pressure variations affect the flow measurement assuming the
flowmeter is calibrated to operate at a typical pressure of two bar?
Commentary
First, it is the absolute pressure of the gas that is important when
measuring flow. The pressure of a standard atmosphere is 1.01325 bar
absolute, but to make the mathematics simpler here, we will approximate
an atmosphere to be one bar absolute. Making this approximation, the
typical operating pressure is three bar absolute with variations that
can reach from two to 3.5 bar absolute.
Second, many gas flow measurements are inferential
mass measurements in units expressed as a standard cubic volume per
unit time. However, regardless of the gas pressure, raw flowmeter
measurements reflect the mass, volume, velocity, or velocity head of
the gas.
With regard to how these pressure variations affect
the flow measurement — it depends. If the flowmeter measures mass flow,
there will (in theory) be no effect on the flow measurement. That is, a
mass flowmeter should not be affected by process pressure variations.
However, if the flowmeter measures volume or
velocity, the effects are inversely proportional to the variation in
absolute pressure. For example, if the gas were operating at a pressure
of 3.5 bar absolute, its volume would be approximately 3/3.5, or 85.7
percent of what it would be if the operating pressure were three bar
absolute. As a result, the flowmeter would measure approximately 14.3
percent lower than it would if the same mass of gas were flowing at
three bar absolute.
The output of flowmeters that infer mass flow by
measuring the differential pressure across a restriction — such as an
orifice plate, Venturi, flow nozzle, and the like — is also inversely
affected by variations in operating pressure. However, the relationship
is not 1-to-1 as in the case of flowmeters that measure volume or
velocity, but rather approximately 0.5-to-1. In the above example, the
effect of operating at 3.5 bar absolute is approximately 0.5*14.3, or
7.2 percent. A more accurate approximation can be calculated as
one-sqrt (3/3.5), or 7.4 percent.
Additional Complicating Factors
Not only is the flow measurement affected by the type of flowmeter
used, but also by pressure effects on the raw flow measurement. For
example, varying the static operating pressure on a
differential-pressure transmitter can cause a calibration shift of as
much as 0.01 percent of the upper-range limit (URL) of the transmitter
per bar. This may not seem like much, but let’s assume the transmitter
is not zeroed at operating pressure, its set span is 50 percent of URL,
and the differential pressure is 10 percent of the set span. At a
pressure of 3.5 bar absolute, the effect could be as much as
approximately (3.5-1)*0.01/(0.5*0.1), or 0.5 percent of the
differential-pressure measurement. The effect of this shift on the flow
measurement will be approximately 1.6 percent of flowrate after taking
the square root relationship of the flowmeter into account.
David W. Spitzer, P.E., is a regular contributor to Flow Control. He
has more than 30 years of experience in specifying, building,
installing, startup, and troubleshooting process control
instrumentation. He has developed and taught seminars for over 20 years
and is a member of ISA and belongs to the ASME MFC and ISO TC30
committees. Mr. Spitzer has written a number of books concerning the
application and use of fluid handling technology, including the popular
“Consumer Guide” series, which compares flowmeters by supplier. Mr.
Spitzer is currently a principal in Spitzer and Boyes LLC, offering
engineering, product development, marketing, and distribution
consulting for manufacturing and automation companies. He can be
reached 845 623-1830.
www.spitzerandboyes.com
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