Proposal

Petroleum field decision-making process is associated to high risks due to geological, economic and technological uncertainties, and high investments, mainly in the appraisal and development phases of petroleum fields. In these phases, it is necessary to model the recovery process with higher precision increasing the computation time to represent all possible scenarios. The necessity to speedup the process demands simplification of the process. The use of Monte Carlo technique, for instance, is normally not viable when numerical flow simulation is used to model the recovery process due to the high number of simulations required. The use of the derivative tree technique can be an alternative in such a case but it also yields a high number of simulations when several attributes have to be considered. An alternative, in such cases, is to use fewer attributes or to use a lower number of discretization levels. Another alternative is to simplify the reservoir modeling process with faster models. Several works are being presented recently about these techniques but normally they show applications but not a comparison among alternatives. The objective of this work is to compare these techniques taking into account the reliability and precision of the results and speed up of the process due to the simplifications. Monte Carlo and derivative tree techniques are compared using reservoir simulation, sensitivity analysis, experimental design and response surface method as supporting tools. These techniques are applied to an offshore field to quantify the risk in economic and technical parameters. The results show that it is possible to reduce significantly the number of flow simulation runs maintaining the precision of the results.

Introduction

A petroleum field is always associated to uncertainties, whose importance varies during its life. In the exploration stage, for example, uncertainties in volumes in place and recovery factors are sufficient in risk analysis and a probabilistic recovery factor combined with Monte Carlo technique may be sufficient to reach the required precision (Garb, 1988; Newendorp and Schuyler, 2000; Rose, 2001).

In the development phase, the importance of uncertainties with impact on recovery factor increases significantly and the economic impact of decisions requires detailed information about the resevoir performance prediction, such as oil, water and gas production, amount of fluid to be injected and speed of recovery. The presence of uncertainties also requires a probabilistic procedure to evaluate risk (Schiozer et al., 2004).

Numerical flow simulation is a reliable manner to predict the reservoir performance. However, reservoir simulation associated to Monte Carlo technique may not be viable due to the high number of simulations needed, when the number of uncertain attribuites is elevated. An alternative is to use the derivative tree technique, which is based on simulation of various reservoir models through the combination of the uncertain attributes (Loschiavo et al., 2000; Stegall and Schiozer, 2001). The disadvantages of this methodology are large computational effort and total time of process. It is possible to reduce the computational effort and time, without significant loss of precision, through some simplifications:

  1. use of fewer levels of uncertainties for attributes that are not critical and aggregation of several attributes that are not critical (Costa and Schiozer, 2002 and 2003),

  2. use of simpler simulation models, for example, streamline model or fewer blocks (Ligero et al., 2003(b) and Subbey and Christie, 2003) and

  3. automation of the process and parallel computing (Ligero and Schiozer, 2002 and Costa and Schiozer, 2004).

An important and exclusive advantage of the derivative tree technique is the possibility to obtain the geological representative models (GRM) that are used to integrate geological uncertainties to economic and technological uncertainties and to production strategy definition (Ligero et al., 2003(a); Santos and Schiozer (2003) and Schiozer et al., 2004)

In spite of these simplifications, if the number of uncertain attributes is elevated, the derivative tree technique could become unfeasible due to the high number of reservoir models to be simulated. In such cases, it is possible to use the experimental design and surface response method to substitute the reservoir simulator in risk analysis. Mosf of published works (Damsleth et al., 1991; Dejean and Blanc, 1999; Manceu et al., 2001; Friedmann et al., 2001; Narahara et al., 2004 and Yeten et al., 2005) consider the use of experimental design and response surface associated to Monte Carlo technique.

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