Population-Based Optimization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3
Authors: Denney Dennis 
Published: February 2015

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 136861, ’Comparative Study of Novel Population-Based Op timization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3 Revisited,’ by Yasin Hajizadeh, SPE, Mike Christie, SPE, and Vasily Demyanov, Institute of Petroleum En gineering, Heriot-Watt University, prepared for the 2010 Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 1-4 November. The paper has not been peer reviewed.
Multiple history-matched models are essential for a realistic uncertainty estimate of the field’s future behavior. This study compared application of ant-colony optimization (ACO), differential evolution (DE), and neighborhood algorithms (NAs) for history matching and uncertainty quantification of the PUNQ-S3 reservoir, a synthetic benchmark case with challenging parameterization, history-matching, and uncertainty-quantification steps.
Introduction
History matching of reservoir models and uncertainty quantification of the predictions are two important steps in any field-management process. In the history-matching phase, simulation models are calibrated on the basis of the observed production history of the reservoir. Parameters of the reservoir model are perturbed, and the model’s output is compared with available fluid-production rates or pressure measurements. This procedure is repeated with new parameter values until good agreement is obtained between output of the simulation and observations. History matching is an inverse problem with nonunique solutions. Multiple combinations of reservoir properties can provide a good match to observed field behavior. To quantify the uncertainty of predictions realistically, multiple history-matched reservoir models are required. Diverse models are likely to show different production behavior in the future because of different reservoir parameters.
Recently, ACO and DE algorithms have been applied to history matching of a simple reservoir model with a small number of unknowns (eight). The subject methods for history matching were applied to a more-complex reservoir with 45 uncertain parameters, and the results were compared to those from NA. Originally, ACO was proposed for problems with discrete parameter space, and it later was adopted to handle continuous-optimization problems.
DE is a powerful global-optimization algorithm that is a parallel-population-based search algorithm. The NA is a recent stochastic-optimization method that uses simple geometrical constructs called Voronoi cells to find good-fitting regions of the search space. Voronoi cell is a method to decompose the search space into n cells around n points by centering on the generated points. Each of these cells is the nearest neighborhood region of the points.
Case Study
The PUNQ-S3 reservoir-simulation model is a five-layer model. The top depth of PUNQ-S3 reservoir is 2430 m. It has a 1.5° dip angle and is bounded by faults to the east and south. A relatively strong aquifer on the north and west provides pressure support. Because of this pressure support, no injection wells have been drilled in this reservoir. There also is a small gas cap in the reservoir in Layer 1, and no wells are completed in this layer because of the effect of free-gas production on recovery from the reservoir. There are six production wells, all near the initial gas/oil contact. Three producers are perforated in Layers 4 and 5. Two producers are completed in Layers 3 and 4, and one producer is perforated only in Layer 4. One of the producers is completed near the aquifer, and water breakthrough was observed in the seventh year. Free-gas production starts in Years 4 and 5 in two of the producers. There also are positions for five infill wells.