Reserves estimation is crucial to the petroleum business as it involves all financial aspects of the petroleum companies. Among reserves classification, proved reserves always capture the most attention because most value is attached to it. By the SPE definition, proved reserves must be estimated by reliable methods that have a high-at least a 90% probability (P90) - that the actual quantities recovered will equal or exceed the estimate.
Decline curve analysis (DCA) is one of the most commonly used methods for proved reserves estimation throughout the industry. Through the DCA, a production history is fitted with a trend line, then the line will be extrapolated to an economic limit for the reserves estimation. If linear regression is used, the line is the "best estimate" that represents the performance, which corresponds to the 50th percentile value (P50). This practice, therefore, conflicts with the proved reserves definition.
In this paper a method is derived to estimate the variation of the reserves spread (the difference between P50 and P90). Compared to Monte Carlo, the method gives good results. The analytical solution is then used to study the sensitivity analysis of the spread and a field application. The study covers all decline models (exponential, hyperbolic and harmonic models) and both cases where the decline exponent is known and unknown.