1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
  5. Conference paper

Abstract

Summary

Reservoirs result from complex and intricate natural formation processes, and are therefore very heterogeneous at multiple scales. As fluid displacements are very sensitive to heterogeneity, it is crucial to understand and characterize how petrophysical properties vary in space to be able to predict oil production.

Multiple point statistics has become a common tool to build models representing geological formations comprising objects characterized by complex geometries such as curvilinear shapes. The idea consists in referring to a training image depicting the expected geological structures, and then in generating images reproducing the multiple point statistics inferred from the training image.

We investigate a substitute to the commonly referenced multiple-point methodologies that was initially developed in computer graphics: it is called texture synthesis. We modify the way it works so that it can handle reservoir simulation issues. Additionally, we focus on its multiscale variant to make it more efficient.

Within this multiscale context, the basic training image is used to create a set of images with decreasing resolutions that are all viewed as training images. Then, a realization is simulated one scale at a time, starting from the level of lowest resolution. When simulating the realization at a given scale, the selection of the value to be assigned to a grid block involves various levels of comparison. We still compare the neighbors of the grid block under consideration with the events extracted from the training image corresponding to the same level of resolution as done for multipoint simulation. In addition, we compare its ancestors with the events extracted from the coarser training images. The ancestors are the values already simulated to populate the coarser grids. In such conditions, the first realization generated at the coarsest scale is able to capture the largest geological objects or heterogeneities. Then, it is used as a constraint that is propagated scale by scale towards the finest resolution grid. This makes it possible to use small size neighborhoods. A few improvements are then suggested to make the algorithm more efficient without deteriorating the simulated images. Last, we present numerical tests performed with complex training images.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141871
2014-09-08
2024-04-25

  • From This Site

    /content/papers/10.3997/2214-4609.20141871
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Arpat, G.B. and Caers, J.
    [2007] Conditional simulation with patterns. Mathematical Geology, 39(2), 177–203.
     [Google Scholar]
  2. Boisvert, J.B., Leuangthong, O., Ortiz, J.M., Deutsch, C.V.
    [2008] A methodology to construct training images for vein-type deposits. Computers and Geosciences, 34, 502–.
     [Google Scholar]
  3. Efros, A.A., Leung, T.K.
    [1999] Texture synthesis by non-parametric sampling. IEEE International Conference on Computer Vision, Corfu, Greece.
     [Google Scholar]
  4. Efros, A.A. and Freeman, W.T.
    [2001] Image quilting for texture synthesis and transfer. Proceedings of 28th ACM SIGGRAPH Conference on computer graphics and interactive techniques, 341–346.
     [Google Scholar]
  5. Gloaguen, E. and Dimitrakopoulos, R.
    [2009] Two dimensional conditional simulation based on the wavelet decomposition of training images. Mathematical Geosciences, 41, 701–.
     [Google Scholar]
  6. Hertzman, A., Jacobs, C.E., Olivier, N., Curless, B. and Salesin, D.H.
    [2001] Image analogies. SIGGRAPH 2001, 327–340.
     [Google Scholar]
  7. Hewett, T.A.
    [1986] Fractal Distributions of Reservoir Heterogeneity and their Influence on Fluid Transport. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana.
     [Google Scholar]
  8. Honarkhah, M. and Caers, J.
    [2010] Stochastic simulation of patterns using distance-based pattern modeling. Mathematical Geosciences, 42, 517–.
     [Google Scholar]
  9. Hu, L.Y., Liu, Y., Scheepens, C., Shultz, A.W. and Thompson, R.D.
    [2014] Multiple-point simulation with existing reservoir model as training image. Mathematical Geosciences, 46, 240–.
     [Google Scholar]
  10. Li, H. and Caers, J.
    [2011] Geological modelling and history matching of multi-scale flow barriers in channelized reservoirs: methodology and application. Petroleum Geoscience, 17, 34–.
     [Google Scholar]
  11. Mahmud, K., Mariethoz, G., Caers, J., Tahmasebi, P. and Baker, A.
    [2014] Simulation of Earth textures by conditional image quilting. Water Resources Research, Accepted Article, doi: 10.1002/2013WR015069.
     https://doi.org/10.1002/2013WR015069 [Google Scholar]
  12. Mariethoz, G., Renard, P. and Straubhaar, J.
    [2010] The direct sampling method to perform multiple-point geostatistical simulations. Water Resources Research, 46, W11536.
     [Google Scholar]
  13. Mariethoz, G. and Lefebvre, S.
    [2014] Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future search. Computers & Geosciences, http://dx.doi.org/10.1016/j.cageo.2014.01.001.
     [Google Scholar]
  14. Strebelle, S.
    [2000] Sequential simulation drawing structures from training images. Ph.D. thesis, Stanford University, CA, USA.
     [Google Scholar]
  15. [2002] Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Mathematical Geology, 34(1), 1–21.
     [Google Scholar]
  16. Tahmasebi, P., Sahimi, M. and Caers, J.
    [2014] MC-CCSIM: accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Computers & Geosciences, http://dx.doi.org/10.1016Zj.cageo.2014.03.009.
     [Google Scholar]
  17. Wei, L. and Levoy, M.
    [2000] Fast texture synthesis using tree-structured vector quantization. Proceedings of SIGGRAPH 2000.
     [Google Scholar]
  18. Zelinka, S. and Garland, M.
    [2004] Jump map-based interactive texture synthesis. ACM Trans. Graph., 23(4), 930–962.
     [Google Scholar]
  19. Zhang, T., Switzer, P. and Journel, A.G.
    [2006] Filter-based classification of training image patterns for spatial simulation. Mathematical Geology, 38(1), 63–80.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141871
Loading
Multiscale Multiple Point Simulation Based on Texture Synthesis
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141871
/content/papers/10.3997/2214-4609.20141871
/content/papers/10.3997/2214-4609.20141871
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error