For multiple well drilling and completion campaigns, cost and schedule performance tend to improve over time. This trend in improvement is commonly referred to as a "learning curve." When a learning curve is assumed, the campaign cost and schedule estimates may be reduced dramatically (relative to an assumption of constant performance). Many operators consider the use of learning curves a best practice, and provide procedures for estimation and implementation in their cost estimating guidelines.

This paper investigates methods for systematic integration of learning curves in probabilistic estimates. Brief reviews of probabilistic estimating methods and learning curves are provided. A general method and specific procedures for integrating learning curves in probabilistic estimates are then provided. For each method, the key assumptions are itemized and discussed and a demonstration is provided. While no single procedure will fit every situation, it is concluded that the general method is straightforward, transparent, and can be implemented using off-the-shelf spreadsheet software. The proposed procedures generate results that provide engineers and decision-makers with a refined representation of uncertainty, and can improve capital investment valuation and decision-making.

Probabilistic Analysis

The drilling engineering community is familiar with probabilistic analysis in well construction estimating, and in some drilling organizations, probabilistic estimating is a required practice. There are numerous papers on the subject. Murtha (1997), Williamson, Sawaryn, and Morrison (2004), and Akins, Abell, and Diggins (2005), focus on theory, methods, and implementation. Examples of empirical investigations can be found in Peterson, Murtha, and Schneider (1993), Peterson, Murtha, and Roberts (1995), Kitchel et al. (1997), Zoller, Graulier, and Paterson (2003), Hariharan, Judge, and Nguyen (2006), and Adams, Gibson, and Smith (2009).

Conventional Methods.

The conventional approach for probabilistic analysis is to first define a dependent variable of interest (typically a cost or time metric). The dependent variable is specified based on the purpose of the estimate, and estimates can be made for specific well activities, for an entire well interval, or for a whole well. Second, independent variables are specified as random variables based on an analysis of past performance. Third, the independent variables are sampled in a repetitive fashion and then used to develop simulated observations on the dependent variable. For example, the engineer may specify the rate of penetration (ROP) as a random variable, and then use a simulated result for ROP and the footage for a specific interval to compute interval drilling time. The procedure yields a simulated distribution of possible outcomes. The distribution of outcomes provides the engineer and other decision-makers with information not available from a deterministic estimate. In some decision settings, the range of outcomes can be more important than the expected value of the distribution.

The main challenges in implementing probabilistic analysis are data collection and specification of the independent variable probability distributions (shapes and parameters). Several of the aforementioned papers address this issue and provide guidance. There are also other hurdles to implementation of probabilistic analysis. A survey of the global drilling community conducted in 2004 and summarized in Hariharan, Judge, and Nguyen (2006) indicated that a large majority of respondents believed that probabilistic analysis has value. But the survey also revealed that respondents felt the analysis took more time, that support tools were lacking, and that additional training was required. If the use of probabilistic analysis is to increase, it is important that workflows and methods remain simple in structure, easy to use, and transparent regarding the assumptions. One means to address these concerns is to perform the analysis using desktop spreadsheet tools. The advantage of this approach is that all of the assumptions and computations are transparent and subject to review and discussion.

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