Hybrid Parameterization for Robust History Matching

Abstract

Summary Identification of reservoir connectivity is critical for reliable production predictions and field-development planning. Field-scale connectivity is particularly important at early stages when costly development decisions are made. However, in developing fields, knowledge about reservoir flow-property distribution is subject to significant uncertainty. In addition, initial measurements of the dynamic response of the reservoir are too limited to resolve reservoir properties at a high-enough resolution. Therefore, reservoir identification problems must account for the limited data resolution and significant geologic uncertainty, and emphasize the importance of field-scale reservoir connectivity estimation. Under such conditions, parameterization of reservoir properties should primarily describe the large-scale flow connectivity. Parameterization techniques that are derived from prior information, such as the principal component analysis (PCA) or Karhunen-Loeve transform (KLT), can be biased by errors in the prior knowledge, whereas prior-independent methods such as the Wavelet or Fourier-based image-compression techniques are robust but do not take advantage of prior knowledge. We propose an effective approach for describing reservoir continuity by combining prior-dependent and prior-independent parameterizations to form a hybrid technique that possesses the advantages of both methods. We introduce a robust hybrid parameterization approach that is less sensitive to possible errors in the prior model and yet quite effective in reproducing geologic features if the prior knowledge is reliable. We apply the new method with conventional parameter reduction and sparse history-matching methods and show that the proposed method can identify reservoir continuity from available dynamic data under both correct and incorrect prior knowledge. In identification of reservoir continuity from limited (low-resolution) available data (particularly at early stages of development), accounting for geologic uncertainty becomes imperative. Hybrid parameterization offers a robust parameterization option that incorporates the prior knowledge about reservoir connectivity when it is reliable and reduces the degrading effect of prior information when the prior model is incorrect.

A Sparse Bayesian Imaging Technique for Efficient Recovery of Reservoir Channels With Time-Lapse Seismic Measurements

“…Selection of a suitable sparse domain that incorporates and preserves structural information in the estimation process can further help in recovering subsurface geological structures [3,17,18,16].…”

“…However, these basis functions only help achieving performances comparable to a standard spatial domain EnKF, while improving the illposedness of the problem [19,20]. Principal Component Analysis (PCA) based geologic basis functions were also investigated in [18] under a hybrid parametrization framework. However, the PCA basis functions did not prove useful for recovering complex geological structures, such as meandering flow channels [18].…”

“…Principal Component Analysis (PCA) based geologic basis functions were also investigated in [18] under a hybrid parametrization framework. However, the PCA basis functions did not prove useful for recovering complex geological structures, such as meandering flow channels [18]. A sparse Bayesian estimation approach was presented in [21], where the Gaussian prior for the gradient is replaced by a Laplace prior and is combined with DCT transform domain parameterization.…”

“…These can potentially lead to enhanced recovery of complex geological structures. However these, as well as those in [11,18,16], require implementing the adjoint model for efficient computation of the gradients of the objective function. This can be a particularly challenging and demanding process, especially when dealing with realistic large scale reservoir simulations.…”

Reconstruction of channelized geological facies based on RIPless compressed sensing

“…This work departs from the problem of image recovery based on reproducing patterns of a training image (Ortiz and Deutsch, 2004;Tahmasebi et al, 2014;Mariethoz and Renard, 2010;Mariethoz and Lefebvre, 2014), and treats the image recovery as a generalized sampling problem (Vetterli and Kovacevic, 1995;Donoho et al, 1998;Mallat, 2009). We follow the essential idea proposed by , 2010, Jafarpour (2011) in the context of subsurface flow model characterization from nonlinear measurements (Khaninezhad et al, 2012;Elsheikh et al, 2013;Khaninezhad and Jafarpour, 2014), which considers that subsurface facies images have a common structure that can be efficiently represented in a transform domain. Then, our conjecture is that this signal structure is information that can be used to recover the missing pixels directly from the partial measurements.…”