Jointly updating the mean size and spatial distribution of facies in reservoir history matching

详细信息    查看全文

• 作者：Haibin Chang ; Dongxiao Zhang
• 关键词：Reservoir history matching ; Facies distribution ; Facies mean size ; KL expansion ; LM_EnRML
• 刊名：Computational Geosciences
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：19
• 期：4
• 页码：727-746
• 全文大小：2,365 KB
• 参考文献：1.Aanonsen, S.I., Naevdal, G., Oliver, D.S., Reynolds, A.C., Valles, B.: The ensemble Kalman filter in reservoir engineering—a review. SPE J. 14(3), 393-12 (2009)CrossRef
  2.Agbalaka, C.C., Oliver, D.S.: Application of the EnKF and localization to automatic history matching of facies distribution and production data. Math. Geosci. 40(4), 353-74 (2008)CrossRef
  3.Agbalaka, C.C., Oliver, D.S.: Joint updating of petrophysical properties and discrete facies variables from assimilating production data using the EnKF. SPE J. 16(2), 318-30 (2011)CrossRef
  4.Berre, I., Lien, M., Mannseth, T.: A level-set corrector to an adaptive multiscale permeability prediction. Comput. Geosci. 11(1), 27-2 (2007)CrossRef
  5.Bocquet, M., Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems. Nonlinear Process. Geophys. 19(3), 383-99 (2012)CrossRef
  6.Carle, S., Fogg, G.: Transition probability-based indicator geostatistics. Math. Geol. 28(4), 453-76 (1996)CrossRef
  7.Carle, S., Fogg, G.: Modeling spatial variability with one and multidimensional continuous-lag Markov chains. Math. Geol. 29(7), 891-18 (1997)CrossRef
  8.Chang, H., Zhang, D.: History matching of statistically anisotropic fields using the Karhunen-Loeve expansion-based global parameterization technique. Comput. Geosci. 18(2), 265-82 (2014)CrossRef
  9.Chang, H., Zhang, D.: History matching of facies distribution with varying mean lengths or different principle correlation orientations. J. Pet. Sci. Eng. 124, 275-92 (2014)CrossRef
  10.Chang, H., Zhang, D., Lu, Z.: History matching of facies distribution with the EnKF and level set parameterization. J. Comput. Phys. 229(20), 8011-030 (2010)CrossRef
  11.Chen, Y., Oliver, D.: Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Comput. Geosci. 17(4), 689-03 (2013)CrossRef
  12.Dorn, O., Villegas, R.: History matching of petroleum reservoirs using a level set technique. Inverse Prob. 24(3), 035015 (2008)CrossRef
  13.Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99(C5), 10143-0162 (1994)CrossRef
  14.Galli, A., Beucher, H., Le Loc’h, G., Doligez, B., Heresim Group: The pros and cons of the truncated Gaussian method. In: Armstrong, M., Dowd, P.A. (eds.) Geostatistical Simulations, pp. 217-33. Kluwer Academic, Dordrecht (1994)CrossRef
  15.Ghanem, R., Spanos, P.: Stochastic Finite Element: a Spectral Approach. Springer, New York (1991)CrossRef
  16.Gu, Y., Oliver, D.S.: An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. SPE J. 12(4), 438-46 (2007)CrossRef
  17.Haugen, V., Naevdal, G., Natvik, L.J., Evensen, G., Berg, A.M., Flornes, K.M.: History matching using the ensemble Kalman filter on a North Sea field case. SPE J. 13(4), 382-91 (2008)CrossRef
  18.Jafarpour, B., McLaughlin, D.B.: History matching with an ensemble Kalman filter and discrete cosine parameterization. Comput. Geosci. 12(2), 227-44 (2008)CrossRef
  19.Karhunen, K.: Uber lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fen. Ser. A. I. Math. Phys. 37, 1-9 (1947)
  20.Le Loc’h, G., Galli, A.: Truncated plurigaussian method: theoretical and practical points of view. In: Baafi, E.Y., Schofiled, N.A. (eds.) Geostatistics Wollongong -6, vol. 1, pp. 211-22. Kluwer Academic, Dordrecht (1997)
  21.Li, G., Reynolds, A.C.: An iterative ensemble Kalman filter for data assimilation. In Proceedings of SPE Annual Technical Conference and Exhibition, Anaheim, California (2007)
  22.Li, R., Reynolds, A.C., Oliver, D.S.: History matching of three phase flow production data. SPE J. 8(4), 328-40 (2003)CrossRef
  23.Liu, N., Oliver, D.S.: Ensemble Kalman filter for automatic history matching of geologic facies. J. Pet. Sci. Eng. 47(3-4), 147-61 (2005)CrossRef
  24.Loeve, M.: Fonctions aleatoires de second order. In: Levy, P. (ed.) Processus Stochastiques et Movement Brownien. Hermann, Paris (1948)
  25.Lorentzen, R.J., Flornes, K.M., N?vdal, G.: History matching channelized reservoirs using the ensemble Kalman filter. SPE J. 17(1), 137-51 (2012)CrossRef
  26.Lorentzen, R., N?vdal, G., Shafieirad, A.: Estimating facies fields by use of the ensemble Kalman filter and distance functions—applied to shallow-marine environments. SPE J. 3(1), 146-58 (2013)CrossRef
  27.Lu, Z., Zhang, D.: On stochastic modeling of flow in multimodal heterogeneous formations. Water Resour. Res. 38(10), 1190 (2002). doi:10.-029/-001WR001026
  28.Lu, Z., Zhang, D.: Conditional simulations of flow in randomly heterogeneous porous media using the KL-based moment-equation approach. Adv. Water Resour. 27(9), 859-71 (2004)CrossRef
  29.Mannseth, T.: Relation between level set and truncated plurigaussian methodologies for facies representation. Math.
• 作者单位：Haibin Chang (1)
  Dongxiao Zhang (1)
  
  1. ERE and LTCS, College of Engineering, Peking University, Beijing, 100871, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Geotechnical Engineering
  Hydrogeology
  Soil Science and Conservation
  
• 出版者：Springer Netherlands
• ISSN：1573-1499

文摘

There exist several methods for history matching of reservoir facies distribution. When using these methods, the facies mean size is usually supposed to be prior information known without uncertainty. However, in reality, it is often difficult to acquire an accurate estimation of the facies mean size due to limited measurement data. Thus, it is more reasonable to treat the facies mean size as an uncertain model parameter for updating. In this work, we propose a methodology to jointly update the mean size and spatial distribution of facies in reservoir history matching. In the parameterization step, we utilize a Gaussian random field and a level set algorithm to parameterize each facies. The range of the Gaussian field controls the facies mean size of the generated facies distribution realizations. To accomplish jointly updating the mean size and spatial distribution of facies, the Gaussian random field is further parameterized by the Karhunen–Loeve (KL) expansion. We choose the range of the Gaussian field and the independent Gaussian random variables in the KL expansion as model parameters. After model parameterization, we use the Levenberg–Marquardt ensemble randomized maximum likelihood filter (LM_EnRML) to perform history matching. Three synthetic cases are set up to test the performance of the proposed method. Numerical results show that for estimating the facies field, the mean size and spatial distribution of facies can be jointly updated to match the reference distribution using the proposed method. Keywords Reservoir history matching Facies distribution Facies mean size KL expansion LM_EnRML