Probabilistic Reserves Estimation Using Decline Curve Analysis with the Bootstrap Method
Authors: Jochen V.A. , Spivey J.P. 
Published: December 2007

Abstract
The bootstrap method of Monte Carlo analysis has been applied to the production performance data of two fields to obtain probabilistic distribution of reserves estimates. This method does not require a prior knowledge of the underlying parameter distributions. For the fields discussed, the deterministic reserves estimates using constant percent decline obtained are comparable to the P90 method from the bootstrap method.

Introduction
The value of the successful oil and gas producing company is determined by the company's hydrocarbon reserves and producing capacity. While production is easily measured, reserves must be estimated and categorized based on definitions such as those of the Securities and Exchange Commission (SEC), Society of Petroleum Engineers (SPE), Society of Petroleum Evaluation Engineers (SPEE) or the World Petroleum Congress (WPC). An important reserve category for an oil and gas producing company is the proved category. Production decline curve analysis of production rate versus time plots is an industry accepted method of predicting proved developed producing reserves and yields a deterministic reserves estimate. The 1983 WPC report referred to probabilistic reserve estimation methods. However, the 1987 SPEE definitions recognize deterministic reserve methods, without mentioning probabilistic reserves. The SPE, SPEE and WPC are currently working to develop a clearer, more consistent set of reserve classifications based on current industry practice. These definitions will allow for both probabilistic and deterministic methods and should give oil companies a better estimate of the ultimate potential recovery of their oil fields than can be given by the terms 'proven', 'probable', and 'possible'. These terms currently indicate increasing uncertainty without quantification of this uncertainty.
The concept of probabilistic reserve estimation is simply a measure of confidence that is assigned to both production performance and volumetric estimation. The purpose of this work is to provide a basis for making a probabilistic link between production performance and reserve estimates in the form of decline curve estimates. The bootstrap method described in this paper provides an objective method for probabilistic reserves estimates from the decline curve equations. It is readily extended to obtaining reserve estimates from automatic history matching with either analytical or numerical models.

Background
The current reserve status categories of proved, probable and possible are defined using words like 'reasonable certainty' 'more likely', and 'less certain' to assign the proper category for an individual reserve determination. A clearer, more consistent reserve classification system is necessary for estimators to communicate intelligibly. This classification system must include an indication of what level of confidence the estimator has in the estimate. Reserve estimates based on extrapolation of areas with established performance trends are considered the estimates of highest confidence, but do not indicate a specific certainty.
The 1983 WPC discussed probabilistic methods in reserve estimation and suggested the use of probability curves for the estimation of the ultimate potential recovery of discovered fields. The WPC identified specific points on the probability curve with certain reserve categories: a maximum at 90% (proved), a middle value at 50% (proved + probable), and a minimum at 10% (proved + probable + possible). The Monte Carlo method can be used to get these confidence levels when using probabilistic determination methods. For consistency in estimation it would be desirable to also have a clear method to identify these confidence levels when using performance analysis or decline curves.
Decline Curve Analysis. Decline curve analysis is a common method used for analyzing oil reserves in areas with established performance trends. Beninger and Caldwell attributed the following description of decline curve analysis to Steve Holditch: "The estimator will then pick up his pencil and straight-edge, squint through one eye, stick his tongue out the corner of his mouth, and rely on his experience to make a reasonable pick of the decline." P. 589