Modeling epistemic subsurface reservoir uncertainty using a reverse Wiener jump–diffusion process

This paper develops a mathematical model of how subsurface reservoir uncertainty, in particular estimated ultimate recovery (EUR), can evolve over time. The model assumes that epistemic uncertainty reduces over time as information from seismic surveys, appraisal wells and production logs is used to improve EUR estimates. A reverse Wiener diffusion process with superimposed jumps is developed to capture the exponential decrease in estimate volatility due to learning but also the existence of sudden jumps in estimates due to unexpected discoveries such as reservoir fault lines or aquifer support. The model can be applied to quantify the evolution of reservoir uncertainty over time during appraisal and planning of new oil and gas development projects. Appreciation Factor data from 34 North Sea fields is used to calibrate and validate the model showing that the evolution of EUR estimates is predicted with 82.4% of validation data points within the simulated P10 and P90 uncertainty envelope, which should theoretically cover 80% of data points if there is no model error. The key parameters in the model are the initial EUR distribution, as well as the exponential decay rates for EUR volatility and the likelihood of occurrence of discrete jumps.