A multiple-point geostatistical method based on geological vector information

The reproduction of the non-stationary distribution and detailed characteristics of geological bodies is the main difficulty of reservoir modeling. Recently developed multiple-point geostatistics can represent a stationary geological body more effectively than traditional methods. When restricted to a stationary hypothesis, multiple-point geostatistical methods cannot simulate a non-stationary geological body effectively, especially when using non-stationary training images (TIs). According to geologic principles, the non-stationary distribution of geological bodies is controlled by a sedimentary model. Therefore, in this paper, we propose auxiliary variables based on the sedimentary model, namely geological vector information (GVI). GVI can characterize the non-stationary distribution of TIs and simulation domains before sequential simulation, and the precision of data event statistics will be enhanced by the sequential simulation’s data event search area limitations under the guidance of GVI. Consequently, the reproduction of non-stationary geological bodies will be improved. The key features of this method are as follows: (1) obtain TIs and geological vector information for simulated areas restricted by sedimentary models; (2) truncate TIs into a number of sub-TIs using a set of cut-off values such that each sub-TI is stationary and the adjacent sub-TIs have a certain similarity; (3) truncate the simulation domain into a number of sub-regions with the same cut-off values used in TI truncation, so that each sub-region corresponds to a number of sub-TIs; (4) use an improved method to scan the TI or TIs and construct a single search tree to restore replicates of data events located in different sub-TIs; and (5) use an improved conditional probability distribution function to perform sequential simulation. A FORTRAN program is implemented based on the SNESIM.

[1]  Alexandre Boucher,et al.  Considering complex training images with search tree partitioning , 2009, Comput. Geosci..

[2]  G. Mariéthoz,et al.  Modeling complex geological structures with elementary training images and transform‐invariant distances , 2011 .

[3]  Alexandre Boucher,et al.  A SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM , 2008, Comput. Geosci..

[4]  Yuhong Liu,et al.  Using the Snesim program for multiple-point statistical simulation , 2006, Comput. Geosci..

[5]  J. Vargas-Guzmán.  Transitive Geostatistics for Stepwise Modeling Across Boundaries between Rock Regions , 2008 .

[6]  Jef Caers,et al.  Multiple-point Geostatistics: A Quantitative Vehicle for Integrating Geologic Analogs into Multiple Reservoir Models , 2004 .

[7]  Jacques Rivoirard,et al.  Process‐Based Stochastic Modelling: Meandering Channelized Reservoirs , 2009 .

[8]  G. Mariéthoz,et al.  An Improved Parallel Multiple-point Algorithm Using a List Approach , 2011 .

[9]  G. Mariéthoz,et al.  Reconstruction of Incomplete Data Sets or Images Using Direct Sampling , 2010 .

[10]  Gregoire Mariethoz,et al.  The Direct Sampling method to perform multiple‐point geostatistical simulations , 2010 .

[11]  Jef Caers,et al.  Direct Pattern-Based Simulation of Non-stationary Geostatistical Models , 2012, Mathematical Geosciences.

[12]  Sebastien Strebelle,et al.  Non-Stationary Multiple-point Geostatistical Models , 2005 .

[13]  Jose A. Vargas-Guzman.  Unified Principles for Nonlinear Nonstationary Random Fields in Stochastic Geosciences , 2014 .

[14]  Jesús Carrera,et al.  Application of Multiple Point Geostatistics to Non-stationary Images , 2008 .

[15]  Hongmei Li,et al.  Direct Modeling of Reservoirs through Forward Process-based Models: Can We Get There? , 2008 .

[16]  J. Vargas-Guzmán,et al.  The Kappa model of probability and higher-order rock sequences , 2011 .

[17]  A. Dassargues,et al.  Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium) , 2009 .

[18]  S. Hashemi,et al.  Two-point versus multiple-point geostatistics: the ability of geostatistical methods to capture complex geobodies and?their facies associations?an application to a channelized carbonate reservoir, southwest Iran , 2014 .

[19]  L. Hu,et al.  Multiple-Point Simulations Constrained by Continuous Auxiliary Data , 2008 .

[20]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[21]  L. Y. Hu,et al.  Multiple-Point Simulation with an Existing Reservoir Model as Training Image , 2014, Mathematical Geosciences.

[22]  Alain Dassargues,et al.  Using Multiple-Point Geostatistics for Tracer Test Modeling in a Clay-Drape Environment with Spatially Variable Conductivity and Sorption Coefficient , 2013, Mathematical Geosciences.

[23]  Sebastien Strebelle,et al.  Event-Based Geostatistical Modeling: Application to Deep-Water Systems , 2006 .

[24]  P. Renard,et al.  Three-dimensional high resolution fluvio-glacial aquifer analog - Part 2: Geostatistical modeling , 2011 .

[25]  Gregoire Mariethoz,et al.  Nonstationary Modeling with Training Images , 2014 .

[26]  Omid Asghari,et al.  Multiple-point geostatistical simulation of dykes: application at Sungun porphyry copper system, Iran , 2014, Stochastic Environmental Research and Risk Assessment.

[27]  Clayton V. Deutsch,et al.  Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances , 2009 .

[28]  Omid Asghari,et al.  Multiple-point geostatistical simulation using the bunch-pasting direct sampling method , 2013, Comput. Geosci..

[29]  Yan Sheng-ke,et al.  Architectural units and heterogeneity of channel reservoirs in the Karamay Formation, outcrop area of Karamay oil field, Junggar basin, northwest China , 2005 .

[30]  G. Mariéthoz,et al.  Multiple-point Geostatistics: Stochastic Modeling with Training Images , 2014 .

[31]  J. Caers,et al.  Conditional Simulation with Patterns , 2007 .