Oil companies use statistical decision-making techniques, like portfolio analysis, to make more informed decisions and estimate resource volumes more accurately. In general companies using these techniques are more successful. Probabilistic aggregation and dependency estimation are essential in portfolio methods and resource estimation. However, current methods have some very real limitations.

Probabilistic aggregation and dependency estimation are recognised in the SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) for multi-field integrated projects. However, Section 4.2.1 of the PRMS recommends that "results reporting beyond this (field, property, or project) level should use arithmetic summation by category but should caution that the aggregate Proved may be a very conservative estimate and aggregate 3P may be very optimistic depending on the number of items in the aggregate"

Arithmetic summation understates the true value of the resource estimates within a portfolio. Potentially, this could result in deferral of a project, or loss of lucrative business and commercial opportunities, such as project investment, facility-sizing decisions or incremental gas supply commitments.

Statistically-robust tools that appropriately use expert opinion are essential for aggregation of resource estimates. Using two integrated project examples we will demonstrate methods for:

1. probabilistic aggregation of the resource estimates for multiple fields; and

2. estimating a measure of dependency between the resource estimates of individual fields.

The methods reviewed for probabilistic aggregation include both Monte-Carlo simulation and analytical methods. We present a new analytical method based on multivariate skew-normal distributions. These can model a wide range of skewness through a shape parameter and are used heavily in financial and actuarial applications. This method will allow a wide range of skewness to be incorporated in the probabilistic aggregation of resource estimates for multiple fields.

This paper presents methods for evaluating measures of dependency between the resource estimates from a portfolio of fields. In cases where the multiple realizations approach is used as a basis for the uncertainty framework for the individual fields, tornado diagrams are generated. These describe the dependence of the individual field estimates on reservoir parameters. When experimental design and response surface methods are used, a surrogate model for estimates based on a response surface will be available.

Incorporating the expertise and knowledge of oil and gas professionals is a critical step, allowing the uncertainties and dependencies to be identified and quantified.

These methodologies for probabilistic aggregation and estimating dependencies were developed within the context of the oil industry. However, their use is not limited to the oil industry. They are general and can be used in any situation where there is a probabilistic aggregation problem.

The techniques require limited time and effort, compared to individual field studies and can have a profound impact on the total P90 reserves for the project.

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