Probabilistic Field Development in Presence of Uncertainty
Authors: Passone Sara , McRae Gregory J. 
Published: February 2016

Abstract
Field developments are characterized by high levels of uncertainty and dynamic interconnected decisions with a complex value description. Typical decisions to be made within the context of field development include duration of each development phase, allocation of resources, data acquisition, the use of expensive novel technologies and project impact on the overall company portfolio. The present paper introduces a unified fully bayesian design optimization methodology that helps with the complexity of decision-making in field development. The proposed scheme can be easily customized with respect to the decision components: the metrics chosen, objective function and associated uncertainties. Its generality permits to overcome the theoretical limitations of popular specific decision-making tools that too often compromise the validity of their results. It allowes the treatment of uncertainty in the objective function, in the physics of the system domain as well as problem constraints. The obtained results are proved to be probabilistically meaningful and can be used to fully support decision-making and generation of project options. The computation solution of the proposed framework is carried out using a modified Markov Chain Monte Carlo scheme that is three to four orders of magnitude faster than traditional Monte Carlo based sampling methodologies. The framework is illustrated with an example drawn from smart well deployment in water flooding operations in presence of geological uncertainty. The proposed methodology results to be consistent with the probabilistic assumptions of the example. The results are also compared to those obtained for the same problem description using deterministic optimization technique coupled with an uncertainty analysis. A key advantage of the new approach is that it is now possible to identify robust value control strategies that can increase reservoir yields, particularly when considered in conjuction with the emergence of increasingly more sophisticated sensing technologies and down-hole flow control systems.

Introduction
Various methods are currently used in decision-making in the oil industry. Some of them are: Worst Case/Best Case Scenario, Tornado Plots, Boston Grid, Expected Net Present Value, Decision Trees, Monte Carlo Simulation and Real Options. These methods are characterized by different degrees of complexity and specific theoretical assumptions ([1], [2], [3], [4]). For instance the decision tree technique is a standard tool in decision-making [2]. However, it is affected by some important limitations. The number of decisions considered complicates the tree very quickly, especially when the decision tree is used to represent the whole project design over time. Furthermore, because decision trees only provide the maximum of the expected Net Present Value of a project, they do not offer any mean for quantifying the volatility that comes with the estimate.
Some of the decision-making methods only partially model the decision process involved. Monte Carlo Simulation is an example. Its use is very well-established and wide spread. Monte Carlo is a formal probabilistic technique through which different types of knowledge can be combined and uncertainty is propagated [3]. However, various problems characterize the application of Monte Carlo. For instance, correlation between uncertain variables can be modeled via Monte Carlo but through complicated mathematical algorithms. Furthermore, Monte Carlo is not suitable for incorporating management flexibility or analyzing the value added by new available information.