Application of Multiple Point Geostatistics to Non-stationary Images

Simulation of flow and solute transport through aquifers or oil reservoirs requires a precise representation of subsurface heterogeneity that can be achieved by stochastic simulation approaches. Traditional geostatistical methods based on variograms, such as truncated Gaussian simulation or sequential indicator simulation, may fail to generate the complex, curvilinear, continuous and interconnected facies distributions that are often encountered in real geological media, due to their reliance on two-point statistics. Multiple Point Geostatistics (MPG) overcomes this constraint by using more complex point configurations whose statistics are retrieved from training images. Obtaining representative statistics requires stationary training images, but geological understanding often suggests a priori facies variability patterns. This research aims at extending MPG to non-stationary facies distributions. The proposed method subdivides the training images into different areas. The statistics for each area are stored in separate frequency search trees. Several training images are used to ensure that the obtained statistics are representative. The facies probability distribution for each cell during simulation is calculated by weighting the probabilities from the frequency trees. The method is tested on two different object-based training image sets. Results show that non-stationary training images can be used to generate suitable non-stationary facies distributions.

[1]  John W. Harbaugh,et al.  Simulating Clastic Sedimentation , 1989 .

[2]  Andre G. Journel,et al.  The deterministic side of geostatistics , 1985 .

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

[4]  S. Strebelle.  Sequential Simulation for Modeling Geological Structures from Training Images , 2006 .

[5]  Michael J. King,et al.  Flow Simulation of Geologic Models , 1999 .

[6]  Jesús Carrera,et al.  On the relationship between indicators of geostatistical, flow and transport connectivity , 2005 .

[7]  Eulogio Pardo-Igúzquiza,et al.  CONNEC3D: a computer program for connectivity analysis of 3D random set models☆ , 2003 .

[8]  Alain Galli,et al.  The Pros and Cons of the Truncated Gaussian Method , 1994 .

[9]  W. Pryor.  Permeability-Porosity Patterns and Variations in Some Holocene Sand Bodies , 1973 .

[10]  Gaisheng Liu,et al.  Limits of applicability of the advection‐dispersion model in aquifers containing connected high‐conductivity channels , 2004 .

[11]  H. Haldorsen,et al.  Stochastic Modeling (includes associated papers 21255 and 21299 ) , 1990 .

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

[13]  A. Journel,et al.  Entropy and spatial disorder , 1993 .

[14]  R. M. Srivastava,et al.  Multivariate Geostatistics: Beyond Bivariate Moments , 1993 .

[15]  Wenlong Xu,et al.  Conditional curvilinear stochastic simulation using pixel-based algorithms , 1996 .

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

[17]  Eulogio Pardo-Igúzquiza,et al.  Plurigau: a computer program for simulating spatial facies using the truncated Plurigaussian method , 2003 .

[18]  J. Carrera.  An overview of uncertainties in modelling groundwater solute transport , 1993 .

[19]  Clayton V. Deutsch,et al.  Challenges in reservoir forecasting , 1996 .

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

[21]  Jef Caers,et al.  Modeling of a Deepwater Turbidite Reservoir Conditional to Seismic Data Using Multiple-Point Geostatistics , 2002 .

[22]  Yuhong Liu,et al.  Multiple-point simulation integrating wells, three-dimensional seismic data, and geology , 2004 .

[23]  S. Gorelick,et al.  Heterogeneity in Sedimentary Deposits: A Review of Structure‐Imitating, Process‐Imitating, and Descriptive Approaches , 1996 .

[24]  Andre G. Journel,et al.  Conditional Indicator Simulation: Application to a Saskatchewan uranium deposit , 1984 .

[25]  G. Marsily,et al.  Some current methods to represent the heterogeneity of natural media in hydrogeology , 1998 .

[26]  Andrew Richard Gardiner,et al.  Best practice stochastic facies modeling from a channel-fill turbidite sandstone analog (the Quarry outcrop, Eocene Ainsa basin, northeast Spain) , 2006 .

[27]  Jef Caers,et al.  Geostatistical Reservoir Modelling using Statistical Pattern Recognition , 2001 .

[28]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[29]  J. Muñoz,et al.  Statistical grid-based facies reconstruction and modelling for sedimentary bodies. Alluvial-palustrine and turbiditic examples , 2007 .