• A Preliminary Study of Enhanced Predictability of Non-Parametric Geostatistical Simulation through History Matching Technique
  • Jeong, Jina;Paudyal, Pradeep;Park, Eungyu;
  • Department of Geology, Kyungpook National University;Department of Geology, Kyungpook National University;Department of Geology, Kyungpook National University;
  • 히스토리매칭 기법을 이용한 비모수 지구통계 모사 예측성능 향상 예비연구
  • 정진아;프라딥 포디얄;박은규;
  • 경북대학교 지질학과;경북대학교 지질학과;경북대학교 지질학과;
Abstract
In the present study, an enhanced subsurface prediction algorithm based on a non-parametric geostatistical model and a history matching technique through Gibbs sampler is developed and the iterative prediction improvement procedure is proposed. The developed model is applied to a simple two-dimensional synthetic case where domain is composed of three different hydrogeologic media with $500m{\times}40m$ scale. In the application, it is assumed that there are 4 independent pumping tests performed at different vertical interval and the history curves are acquired through numerical modeling. With two hypothetical borehole information and pumping test data, the proposed prediction model is applied iteratively and continuous improvements of the predictions with reduced uncertainties of the media distribution are observed. From the results and the qualitative/quantitative analysis, it is concluded that the proposed model is good for the subsurface prediction improvements where the history data is available as a supportive information. Once the proposed model be a matured technique, it is believed that the model can be applied to many groundwater, geothermal, gas and oil problems with conventional fluid flow simulators. However, the overall development is still in its preliminary step and further considerations needs to be incorporated to be a viable and practical prediction technique including multi-dimensional verifications, global optimization, etc. which have not been resolved in the present study.

Keywords: Geostatistical simulation;History matching;Groundwater;Subsurface prediction;Gibbs sampler;

References
  • 1. Bear, J., 1972, Dynamics of fluids in porous media, American Elsevier Pub. Co., New York, 764p.
  •  
  • 2. Besag, J., 1986, On the Statistical analysis of dirty pictures, J. R. Statist. Soc., 48(3), 259-302.
  •  
  • 3. Carle, S.F. and Fogg, G.E., 1996, Transition probability-based indicator geostatistics, Math. Geol., 28, 453-477.
  •  
  • 4. Daily, W., Ramirez, A., LaBrecque, D. et al, 1992, Electrical resistivity tomography of vadose water movement, Water Resour. Res., 28(5), 1429-1992.
  •  
  • 5. Day-Lewis, F.D., 2000, Identifying fracture-zone geometry using simulated annealing and hydraulic-connection data, Water Resour. Res., 36(7), 1707-1721.
  •  
  • 6. Deutsch, C.V. and Journel, A.G., 1998, GSLIB: Geostatistical Software Library and User's Guide, 2nd edn., Oxford University Press., New York, 369 p.
  •  
  • 7. Doyen, P.M., 1988, Porosity from seismic data: A geostatistical Approach, Geophys., 53(10), 1263-1275.
  •  
  • 8. Doyen, P.M., Pasaila, D.E., and Strandenes, S., 1994, Bayesian sequential indicator simulation of channel sands form 3-D seismic data in the Oseberg field, Norwegian North Sea, SPE 69th Annual Technical Conference and Exhibition, SPE, New Orleans, 25-28.
  •  
  • 9. Ezzedine, S., Rubin, Y., and Chen, J., 1999, Bayesian method for hydrogeological site characterization using borehole and geophysical survey data: Theory and application to the Lawrence Livermore National Laboratory Superfund site, Water Resour. Res., 35(9), 2671-2683.
  •  
  • 10. Geman, S. and Geman, D., 1984, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
  •  
  • 11. Han, Y., Park, C., and Kang, J., 2010, Multi-objective History Matching for Estimating the Individualized Performance of Multiple Production Wells, The Korean society for geosystem engineering, 47(5), 660-667.
  •  
  • 12. Heath, R.C., 1983, Basic Ground-Water Hydrology, U.S. Geological Survey, Reston, Virginia, 81p.
  •  
  • 13. Hill, M.C., Harbaugh, A.W., Banta, E.R., McDonald, M.G., MODFLOW-2000, 2000, The U.S. geological survey modular ground-water model-user guide to modularization concepts and the ground-water flow process, U.S. Geological Survey, Reston, Virginia, 113p.
  •  
  • 14. Hyndman, D.W., Harris, J.M., and Gorelick, S.M., 1994, Coupled seismic and tracer test inversion for aquifer property characterization, Water Resour. Res., 30(7), 1965-1977.
  •  
  • 15. Jung, S. and Choe, J., 2009, Improvement of Numerical Stability in History-matching Using Streamline Assisted Ensemble Kalman Filter, The Korean society for geosystem engineering, 46(4), 453-465.
  •  
  • 16. Kitanidis, P.K., 1995, Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31(10), 2411-2419.
  •  
  • 17. Konikow L.F. and Bredehoeft, J.D., 1992, Ground-water models cannot be validated, Adv. Water Resour. Res., 15, 75-83.
  •  
  • 18. Mariethoz, G., Renard, P., and Caers, J., 2010, Bayesian inverse problem and optimization with iterative spatial resampling, Water Resour. Res., 46, W11530, doi:10.1029/2010WR009274.
  •  
  • 19. McKenna, S.A. and Poeter, E.P., 1995, Feild example of data fusion in site characterization, Water Resour. Res., 31(12), 3229- 3240.
  •  
  • 20. Park, E., 2010, A multidimensional generalized coupled Markov chain model for surface and subsurface characterization, Water Resour. Res., 46, W11509, doi:10.1029/2009WR008355.
  •  
  • 21. Pesti, G., Bogardi, I., Kelly, W.E. et al., 1993, Cokriging of geoelectric and well data to define aquifer properties, Groundwater, 31(6), 905-912.
  •  
  • 22. Sheng, Q., Moreau, Y., and De Moor, B., 2003, Biclustering microarray data by Gibbs sampling, Bioformatics, 19, 196-205, doi:10.1093/bioinformatics/btg1078
  •  
  • 23. Rogers, L., 1992, History matching to determine the retardation of PCE in ground water, Ground Water, 30(1), 50-60.
  •  
  • 24. Yeh, T.-C.J., Jin, M., and Hanna, S., 1996, An iterative stochastic inverse method: conditional effective transmissivity and hydraulic head fields, Water Resour. Res., 32(1), 85-92.
  •  

This Article

  • 2012; 17(5): 56-67

    Published on Oct 31, 2012

  • 10.7857/JSGE.2012.17.5.056
  • Received on Jul 27, 2012
  • Revised on Sep 3, 2012
  • Accepted on Sep 3, 2012