Mathematical Modification to the Classical Volumetric Method for Estimating Oil Reserves

Using fuzzy logic technique, this work proposes a mathematical adjustment to the classical volumetric method for estimating oil reserves to manage the level of uncertainty associated with oil reserves estimation. This technique introduces a risk factor (α) into the volumetric method equation to account for the uncertainty associated with estimating the parameters that are used in the volumetric method equation. Risk types that may affect oil reserves estimation can be considered using the risk factor (α) in the modified equation. Results showed that the amount of proven oil reserves decreases exponentially as the value of risk factor (α) increases. It also showed that the ratio of the expected proven oil reserves with respect to proven oil reserves (N*/N) goes to zero when the value of risk factor (α) reaches a value of (5). Three cases were proposed to categorize uncertainty in proven oil reserves estimation: high risk estimate, middle risk estimate and risk-free estimate. Results showed that, for the case of high-risk estimate, expected proven oil reserves (N*) was appreciably lower than the proven oil reserves (N) due to the inclusion of risk. Sources of risk may include, but not limited to, lack of expertise of the evaluator, level of integrity of the evaluator, engineering errors during measurement and calculation and governmental laws. Results also showed that the calculated amount of proven oil reserves (N*), for the middle risk estimate case, is much higher than that for high risk estimate case. As for the riskfree estimate case, the calculated proven oil reserves (N*) using the modified formula equals to the proven oil reserves (N) calculated by the classical volumetric formula. This case reflects 100% confidence and reliability in the parameters’ estimation which also places great trust in the evaluator’s integrity and expertise.