Inspecting flow rate measurement accuracy with cumulative performance plots

For those out there working with multiphase flow meters (MPFMs) or virtual flow meters (VFMs), the cumulative performance plot may be an easyread plot. Yet, when first introduced to the plot, it can confuse the best of us. Let us deep-dive into it.

The cumulative performance plot can be used to evaluate the accuracy of any measurement device. It shows the percentage of test points that falls within a certain percentage deviation or less from a reference value (Corneliussen 2005). Clear and understandable? No? Let us explain in more detail. Imagine that you have a set of measurements and their corresponding reference values. For each measurement point, we may calculate the error, or deviation, between the measurement and the reference value. This error can also be given as a percentage deviation from the reference value. For instance, let us assume that you measure the volumetric flow rate from a petroleum well to be 105m3/h, however, the reference value is 100m3/h. The percentage deviation of the measurement from the reference is then 5%. Now, if we calculate the percentage deviation for all our measurement points, we can count the number of times the deviation is below a certain level (e.g. 5%) or less. This is called the cumulative performance.

Figure 1 shows a typical cumulative performance plot. This figure in particular is based on the aggregated performance of flow rate measurements (MPFM or VFMs), from multiple assets around the world during real operations. We use the latest well test results (which are considered to be of high precision) as the reference values. To read the figure, start by picking a target deviation on the X-axis, e.g. 20%. From here, move in a vertical line upwards until the plotted line is reached. Thereafter, move in a horizontal line towards the Y-axis and read off the cumulative performance. If we look at e.g. 20% deviation, the cumulative performance is about 42%. This means that 42% of all the test points that have been evaluated obtained an error of 20% or less from their respective reference value. In this figure in particular, this means that the MPFM or VFM values deviated at most 20% from the (true) well test value in 42% of all the points in time where we did this performance test. The steeper this curve is and the sooner it reaches 100% on the Y-axis, the better the performance.

The results shown in Figure 1 are noteworthy for several reasons. First of all, the “industry standard” way of reporting accuracy and errors with a simple percentage value tells only a fraction of the story. For instance, reporting a 5-10% error is not enough information to evaluate model performance in operations. When evaluating such numbers, the alert production engineer should also question the uncertainty in the reported results and ask what fraction of time or instances such results are actually achieved in operations.

Secondly, for a company like ours that develops data-driven solutions, the fact that many of the flow rate measurements out there are highly inaccurate gives us a real headache. Since our overarching goal is real-time production optimization, you can imagine how a potential 2-5% improvement in production throughput will drown in well rate inaccuracies of 20%. In fact, Solution Seeker has been compelled to think outside the box and create additional services that may aid in information gathering and high accuracy measurement acquisition. Examples are our well test optimization and scheduling applications. We are also the first company to offer the market commercial data-driven VFMs. Our goal is to predict flow rates with less than 5% error, on 90% of the wells, 90% of the time with 90% less effort than traditional solutions.


  • Corneliussen, S., Couput, J.P., Dahl, E., Dykesteen, E., Frøysa, K.E., Malde, E., Moestue, H., Moksnes, P.O., Scheers, L., Tunheim, H., 2005. Handbook of multiphase flow metering. The Norwegian Society for Oil and Gas Measurements