Systematic bias in pro rata allocation schemes

Misallocation due to allocation uncertainty may result in increased exposure to economic risk for owners or stakeholders in hydrocarbon fields. It is often assumed that allocation errors are random and that they will “even out” over time, irrespective of the system setup and allocation uncertainty. In this paper, we show that this is normally not the case, even for simple allocation systems using standard pro rata allocation. For instance, a two-field pro rata allocation setup with a high measurement uncertainty for one of the meters compared to the other, causes the field with the highest allocation uncertainty to be systematically under-allocated. We show that this misallocation is inherent to the allocation system, and will occur even without any systematic measurement error present.

Systematic bias in pro rata allocation schemes

Since pro rata allocation systems are widely used, either as general allocation principle or as part in a multi-tier allocation, this inherent misallocation should be of particular interest to the industry.  The financial loss associated with systematic misallocation can only be evaluated based on a correct quantification of the misallocation. Therefore, it is important to be aware of how systematic misallocation may be a direct consequence of the setup of a pro rata allocation system and the maintenance scheme of the different metering stations.

The objective of our work is to quantify the systematic misallocation in pro rata allocation setups, and identify in which cases this effect is economically significant. Furthermore, the aim is to establish some useful “rules of thumb” that may be used to evaluate if an allocation setup is subject to systematic misallocation.

We explain the mechanisms behind systematic misallocation, illustrating the effect with a few simple examples. Then we analytically show how the statistical expected value in pro rata allocation differs from the actual production rate. As it may be practically unmanageable to express the systematic misallocation analytically for more complex systems, we show how this can be done using numerical methods instead.

Finally, we demonstrate the calculation of systematic misallocation for a realistic measurement setup and allocation scenario in a multi-field setting based on experience from industrial projects.

Our work shows that the pro rata allocation principle inherently leads to systematic misallocation, particularly in cases where there is a significant difference between the uncertainties of the allocated fields. This misallocation is systematic and does not cancel out over time. Therefore, pro rata allocation systems should always be evaluated for any inherent systematic misallocation.