Structural adjustment for accurate conditioning in large-scale subsurface systems

Most of the current subsurface simulation approaches consider a priority list for honoring the well and any other auxiliary data, and eventually adopt a middle ground between the quality of the model and conditioning it to hard data. However, as the number of datasets increases, such methods often produce undesirable features in the subsurface model. Due to their high flexibility, subsurface modeling based on training images ( TI s) is becoming popular. Providing comprehensive TI s remains, however, an outstanding problem. In addition, identifying a pattern similar to those in the TI that honors the well and other conditioning data is often difficult. Moreover, the current subsurface modeling approaches do not account for small perturbations that may occur in a subsurface system. Such perturbations are active in most of the depositional systems. In this paper, a new methodology is presented that is based on an irregular gridding scheme that accounts for incomplete TI s and minor offsets. Use of the methodology enables one to use a small or incomplete TI and adaptively change the patterns in the simulation grid in order to simultaneously honor the well data and take into account the effect of the local offsets. Furthermore, the proposed method was used on various complex process-based models and their structures are deformed for matching with the conditioning point data. The accuracy and robustness of the proposed algorithm are successfully demonstrated by applying it to models of several complex examples. © 2017 Elsevier Ltd. All rights reserved. t ( l g s p 2 s e ( T t s d t S s m p M e Introduction Development of realistic geostatistical approaches for simulating large-scale subsurface systems has been motivated in part by the need to include complex patterns and data in geological models. Most geostatistical models of the past relied on traditional two-point geostatistics, which have been demonstrated to be inadequate descriptors of structures containing complex features and variability ( Strebelle, 2002; Journel, 2005; Arpat, 2005; Zhang et al., 2006; Tahmasebi et al., 2012 ). Therefore, multiple-point statistical (MPS) simulation that relies on higher-order statistics was developed to address the limitations of the traditional methods. The MPS methods are partly based on use of a training image ( TI ) that represents a conceptual framework for the most important features of a subsurface system and the prior geological information available for it, and is constructed without using any conditional data (e.g. secondary and well data). The MPS was first introduced nearly three decades ago ( Journel, 1992; Guardiano and Srivastava, 1993 ). The original method was not, however, computationally feasible. The first practicable method, single-normal equation simulation (SNESIM) algorithm E-mail address: [email protected] f w http://dx.doi.org/10.1016/j.advwatres.2017.01.009 0309-1708/© 2017 Elsevier Ltd. All rights reserved. hat used a search tree structure, was introduced by Strebelle 2002) . The computational time of the SNESIM is dramatically ower than the original MPS algorithm, hence helping to investiate further applications of the MPS to practical problems. Ever ince that breakthrough, several other MPS algorithms were also roposed (for a comprehensive review, see Tahmasebi et al., 2012, 014 ). For example, Arpat (2005) introduced the pattern-based imulation (SIMPAT) algorithm that is based on the patterns of hetrogeneities and a distance function that measures the differences i.e. distance ) and similarities between the model and the data. he proposed method requires, however, highly intensive compuations. For this reason, Zhang et al. (2006) proposed a method, imulation of patterns using filters (FILTERSIM) that uses some preefined filters, fast searching, and a classification method to reduce he patterns’ dimension. Later, Honarkhah (2011) improved FILTERIM by transferring the original patterns into a multi-dimensional caling space and using a kernel space to reduce the dimensions ore effectively. All such techniques suffer, however, from extreme attern reduction, which is referred here as “pattern smoothing.” eanwhile, a direct sampling algorithm was introduced ( Mariethoz t al., 2010 ) that was essentially identical to SIMPAT, with the diferences that it did not require extensive scanning of the TI , and as based on adding one pixel at a time to the model, instead of P. Tahmasebi / Advances in Water Resources 101 (2017) 60–74 61