Multi-Start Method for Reservoir Model Uncertainty Quantification with Application to Robust Decision-Making
Authors: Basu Saurav , Das Ananda , Paola Giorgio De , Ciaurri David Echeverría , Droz Sonia Embid , Llano Cristina Ibanez , Ocheltree Kenneth B. , Torrado Rubén Rodríguez 
Published: November 2016

Abstract
In this work we present an approach to determine geologically plausible reservoir models that are consistent with well-log data and multimodal observations (e.g., production and seismic data). The methodology is based on optimization techniques that are not invasive to the simulators used to reproduce observations. The geologically plausible reservoir models obtained facilitate reliable probabilistic production forecasts and lead to more robust optimization and decision-making support tools.
The methodology approaches model inversion as an optimization problem where the cost function is a measure of the discrepancy between simulated responses and measurement data. Reservoir model uncertainty quantification is addressed by means of multi-start optimization, i.e., the use of local optimization methods with multiple initial guesses. Parameter reduction techniques allow a more effective and efficient global exploration of the optimization space. Geological realism is incorporated in the approach through multiple-point statistics. The set of reservoir models, determined as the output of the multi-start optimization, is thereafter included in a framework for robust optimization under uncertainty (e.g., to determine the drilling location of a new well). The optimization algorithms used are noninvasive with respect to the simulators used in the workflow and are implemented on a distributed- computing cluster.
Different aspects of this approach are illustrated by means of a comprehensive case example that uses well-log and production data. It is important to note that the use of simulator-noninvasive (black box, derivative-free) optimization algorithms reduces significantly the dependence of the methodology on the simulators. The optimization methods tested include Generalized Pattern Search, Mesh Adaptive Direct Search, Sequential Quadratic Programming (with numerical derivatives) and Particle Swarm Optimization, a population-based procedure. These algorithms may yield efficient performance in terms of wall-clock time when they are combined with parameter reduction techniques and distributed computing (as is the case in this work). When parallel computing resources are scarce or nonexistent one may resort to methods suited to serial implementations (examples of these simulator-noninvasive algorithms are Hooke-Jeeves Direct Search and model-based approaches). The parameter reduction techniques studied here are based on Principal Component Analysis. In particular, the recently introduced Optimization-based Principal Component Analysis has been observed to deal with complex geological models satisfactorily. Uncertainty in future production is then incorporated in the robust optimization of well placement and of reactive well controls.
The Ensemble Kalman Filter is widely used in industry for reservoir model uncertainty quantification. This method fails in some occasions (e.g., the ensemble collapses) for reasons that are not yet well understood. The multistart methodology proposed in this work can be an alternative to the Ensemble Kalman Filter in these problematic situations. Seismic data could be included in this methodology to mitigate uncertainty in probabilistic forecasts.