Analytical Probabilistic Reserve Estimation by Volumetric Method and Aggregation of Resources

In oil and natural gas production projects, many investment and development plans are based on oil and gas reserve estimates. There is a large uncertainty in the calculation of hydrocarbon reserves because the input variables always contain uncertainties to some degree that propagate into reserve estimates. From the view point of a field investment, an accurate assessment of uncertainty in reserves is crucial for making decisions that will create value and/or mitigate loss in value. Therefore, to make good decisions, one must be able to accurately assess and manage the uncertainties and risks. In this study, we present an analytical uncertainty propagation method (AUPM) for modeling of uncertainties on volumetric reserve estimations. Analytical uncertainty propagation equations (AUPEs) are derived based on a Taylor-series expansion around the mean values of the input variables. The AUPEs are general in that correlation among the input variables, if it exists, can also be accounted for on the resulting uncertainty. Comparative studies that we have conducted show that the AUPM is as accurate as the Monte Carlo method (MCM). The AUPM provides a fast alternative to Monte Carlo simulation for accurately characterizing uncertainty markers such as variance, P90, P50, and P10. In addition, we present uncertainty percentage coefficient for simulating uncertainty contribution of each parameter and correlated parameter pairs to the total uncertainty in volumetric calculations.
We also discuss the problem of probabilistic aggregation of reserves for projects involving more than one reservoir or field. We provide a general analytical formulation for estimating the values of mean, variance, P10, P50 and P90 for aggregated estimates. Probabilistic aggregation requires the knowledge of pair-wise correlation of the fields. In this study, we propose uncertainty sorting method (USM) to determine pair-wise correlation coefficients for multiple resources. The method provides a simple and fast analytical approach based on uncertainty percentage coefficient of individual field parameters. Proposed analytical models can be used as a fast tool eliminating the need for MCM.