Inferential Measurement Uncertainty Of Two Flow Meters


Thread Starter


I have a case of one water injection header with 3 water injection riser / pipes attaced to it.

We have a flowmeter before the header, so we know the total flowrate. Assume the flowmeter is at 5% uncertainty.

Two of the risers/pipes has flow meters attached to it. Assume that each flow meter is at 5% uncertainty.

The third riser/pipes flow rate is gained by inferential methods, i.e.,

3rd Riser Flow rate = Total Flow rate - (Summation of flow rate on the other two pipes/risers)

May question is, what is the uncertainty of the measurement for this 3rd riser? How do we do it?

Does the 3rd riser measurement uncertainty = 5% + 5% + 5% = 15%?

Looking forward for your answers & thanks in advance,

Rohit Chandak

It is very difficult to confirm the uncertainity of the third meter especially when the flow through this third line is estimated by cancelling the volume flown through 1st & 2nd line from the volume flown through master meter. If you can get the total consumption through process guys you can come close to the uncertainity of the third meter else it is very difficult without a flow meter. The other approach would be to install the meter on the main header (before branching) & install it on the third line, in that case you know individual line accuracy as well as could know the total flow by adding all the values from this three meters.

The best way to avoid any debate would be to install another meter on the third line. When comparison are made within meters (which are not calibrated often) try to use single make & same technology meter.
Thanks Rohit,

The discussion actually starts there. The project is evaluating either we need to add flow meter at the 3rd line or not. Instrumentation wise, it's better to have one.

Due to the fact that the installation will be done offshore, the project is trying to avoid any not necessary instrument. Or we need to make process shutdown.
You can estimate the inferential flow uncertainty using the root sum of square method (RSS) as follows:

Uncertainty = squareroot of the sum of the [squares of flowmeter uncertainties + square of the error of the device that will be doing the math]

= square root of Meter1E2 + Meter2E2 + Meter3E2 + eE2

where e = the error of the calculating device.

All uncertainties must have the same units.

William (Bill) L. Mostia, Jr. PE
Sr. Consultant
SIS-Tech Solutions



2. "How Accurate is Accurate? Part 2", William Mostia, CONTROL, July 1996

3. "The Application of Statistical Methods in Evaluation of the Accuracy of Analog Instruments and Systems," C.S. Zalkind & F.G. Shinskey, Foxoboro Company

Rohit Chandak

Use a portable ultrasonic to check the uncertainity on periodic basis or use multichannel ultrasonic flow meter which can do mathematical calculation to know individual volume as well as total etc. By this you don't have to shut the process as well as do any mechnical work on off shore.

Just a thought but I know off-shore applications are challenging & the people who work on such platforms can only take better decision.