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International Journal for Uncertainty Quantification

Impact factor: 0.967

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003480
pages 323-339


Richard Booth
Schlumberger BRGC, Rio de Janeiro, Brazil
Kirsty Morton
Schlumberger BRGC, Rio de Janeiro, Brazil
Mustafa Onur
Technical University of Istanbul, Istanbul, Turkey
Fikri Kuchuk
Schlumberger Ribould Product Centre, Clamart, France


In any subsurface exploration and development, indirect information and measurements, such as detailed geological description, outcrop studies, and direct measurements (such as seismic, cores, logs, and fluid samples), provide useful data and information for static reservoir characterization, simulation, and forecasting. However, core and log data delineate rock properties only in the vicinity of the wellbore, while geological and seismic data are usually not directly related to formation permeability. Pressure transient test (PTT) data provide dynamic information about the reservoir and can be used to estimate rock properties, fluid samples for well productivity, and dynamic reservoir description. Therefore, PTT data are essential in the industry for the general purposes of production and reservoir engineering as well as commonly used for exploration environments. With the need for improved spatial resolution of the reservoir parameters, grid-based techniques have been developed in which the reservoir properties are discretized over a fine grid and characterization of the probable state of the reservoir is sought using the Bayesian framework. Unfortunately, for the exploration of hydrocarbon-bearing formations, the available prior information is often limited: in particular, unexpected geological features, such as fracture and faults, may be present. There are two groups of recent methods for dynamic characterization of the reservoir: (i) data assimilation techniques, e.g., ensemble Kalman filter (EnKF) and (ii) maximum-likelihood techniques, such as gradient-based methods. The EnKF is designed to produce a set of realizations of the reservoir properties that fit the PTT data; however, the method often fails to honor the data when unexpected features are not captured by the prior model. The alternative gradient-based methods do provide a good fit to the PTT data. They can also be made efficient for high-dimensional problems by using an adjoint scheme for determining the gradient of the log-likelihood function. However, as a maximum likelihood technique, this method only yields a single realization of the reservoir. It is important to maintain a model of the uncertainty of the reservoir characterization after PTT data assimilation, so that the risk associated with future decisions is understood. We therefore present and investigate a stochastic, gradient-based method that allows for proper sampling of realizations of the reservoir parameters that preserve the fit with the PTT data. The results indicate that our proposed method is quite encouraging for efficiently generating realizations of rock property distributions conditioned to PTT data sets and a given prior geostatistical model.