Orifice flow meters are one of the most commonly used flow measurement devices used in the industry. Flow measurement by orifice not only needs compensation for temperature and pressure but also correction for inaccurate calculations which can lead to errors as high as 20%. This article will simplify those calculation into a ready to use formula.

1. Orifice Flows Can Lie
Orifice flow measurement not only needs compensation for
temperature and pressure but also correction for inaccurate
calculations. This article will simplify those calculation into a
ready to use formula.
Orifice flow meters are one of the most commonly used flow
measurement devices used in the industry. They are cheap,
easy to maintain, easily replaceable and generic. Typically the
accuracy of these meters is within +/- 2% of measured value
which is mostly acceptable to clients. But this accuracy is
contingent on the calculation behind flow measurement using
orifice, specifically flow correction for temperature and
pressure changes. A flow meter reading can be completely off
if wrong compensations are used.
Let’s understand how flow is measured by an orifice. Orifice is
simply a flow restriction with known behavior i.e. the
performance or orifice w.r.t. flow can be defined quantitatively
by using empirically established equations. Certain flow causes
certain delta P under given conditions. In practical
applications, the delta P produced across the orifice due to
flow through it is used to estimate the flow. These calculations
require temperature, pressure and density amongst other
parameters and constants.
The transmitters in plant uses design values of T, P and density
(rho) to do these calculations whereas, in actual, the flowing
conditions are often different. It is important to know how to
correct the flow displayed on control board/DCS. This is what
the article will talk about in a practical perspective.
An abridged version of orifice equation goes like,
(1)
For gasses, we can write
(2)
(3)
Where,
V = Actual volumetric flow (Am3/hr)
Rho = flowing density (kg/m3)
Remember, the delta P measured by transmitter remains fixed
for a given flow and conditions, it’s just the conversion of delta
P to flow using equations that can be done differently to arrive
at correct or incorrect values. The flow transmitter does these
calculations by using the values fed into it, which are the
design values. The required correction is to change the T, P,
rho used in these calculations from design to flowing values.
Since delta P is same, the uncorrected and corrected flows are
related. Using previous equation, we get
(4)
Rearranging, we get
(5)
Where, subscript “old” refers to the design value being used in
calculations and “f” means the properties at actual flowing
conditions.
Also, from ideal gas equation, we know
(6)
Where again, subscript “d” stands for design conditions
(considered in orifice and flow meter datasheet).
Using the two previous equations, the observed reading can
be corrected to get actual reading. This is commonly done by
a flow compensation feature in modern digital systems in DCS.
The values of T and P needs to be imported to the calculation
block configured in DCS and the flow value shown on control
board/panel is then the compensated value.
F
Flow
Compensation
PT TTFT
Flow Orifice
Delta P based flow
transmitter
Pressure and
Temperature
transmitter
Fig. 1: T and P compensation in Flow Transmitters
Tushar Goel
Chemical Engineer
IIT (BHU), Varanasi

2. Above shown configuration is one of the most commonly used
flow compensation system at the battery limit flows of plant
for accurate measurement of import and export streams.
Actual volumetric flow vs Normal volumetric flow
But this is just the beginning of corrections and
compensations. Many clients prefer their flow measurements
represented on a standard or normal conditions for easy
comparison. This makes it easy to communicate the flow
values by eliminating the need to tell P and T every time the
flow value is reported. Typically the normal conditions are 0
deg C and 1 atm i.e. the flow reported in Nm3/hr is always at
273.15 K and 1.033 kg/cm2a.
where, Flowing Pressure (Pf) and Flowing Temperature (Tf) are
expressed in units of kg/cm2 (g) and °C.
As one can see, once again the use of T, P arises to covert the
flows from actual to normal conditions. If flowing conditions
(Tf, Pf) are not provided to the calculation block, design
conditions will be used by default, which is again bound to give
wrong flow values.
Correcting the uncorrected flows represented at normal
conditions (Nm3/hr)
One of the tedious tasks for a process engineer is to correct
the uncompensated and uncorrected DCS reading into correct
flow measurements. The calculation to convert Am3/hr to
Nm3/hr was done by DCS by using design T and P while actually
the flowing T and P are different. This needs to be corrected.
Below flowchart explain the process of doing the calculations.
Let us consider an example:
Td = 10 deg C
Pd = 2.2 kg/cm2g
Rhod = 3.8597 kg/m3
MWd = 28.03
Tf = 20 deg C (measured by instrument)
Pf = 2.7 kg/cm2g (measured by instrument)
MWf = 22.8 (as provided by laboratory sample analysis)
Flow as shown on DCS screen = 4000 Nm3/hr which is
uncorrected and uncompensated.
Converting the Nm3/hr to Am3/hr (uncorrected)
= 4000 ∗ (
1.033
1.033+2.2
) ∗ (
10+273.15
273.15
)
= 1324.86 Am3/hr (uncorrected)
Now, we know
(7)
𝑟ℎ𝑜_𝑜𝑙𝑑
𝑟ℎ𝑜_𝑛𝑒𝑤
=
(2.2 + 1.033)
2.7 + 1.033
∗
20 + 273.15
10 + 273.15
∗ (
28.03
22.8
)
So we get, rhoold/rhonew = 1.104717
Now using the correction formula from eq. (5)
And finally converting the Am3/hr to Nm3/hr based on actual
flowing conditions, we get
The correct flow is 4688.83 vs 4000 Nm3/hr as shown on DCS
screen which equals to 17% error in measurement. The above
calculations are summarized in the following single formula for
correction of gas flows reported in Nm3/hr:
Convert the measured Nm3/hr
to Am3/hr based on Design
conditions
The DCS system has
incorporated a calculation which
converts the Am3/hr to Nm3/hr
based on DESIGN
CONDITIONS. But the conditions
have changed to FLOWING
CONDITIONS, so you would like
to undo those calculations.
Correct this Am3/hr by using
the orifice correlation.
Convert the Corrected
Am3/hr back to Nm3/hr based
on actual flowing conditions
The Am3/hr that we got in
previous step was calculated
based on ΔP observed across
orifice.
The conversion of ΔP to Am3/hr
also involves T & P and Mol. Wt.
Since these values have
changed, we need to correct this
conversion of ΔP to flow.
Once the corrected Am3/hr
based on actual MW, T and P is
obtained, we need to convert it
to Nm3/hr.
This conversion has to be done
based on FLOWING
CONDITIONS and not the
design conditions.