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Assessing multiple-point statistical facies simulation behavior for effective conditioning on probabilistic data. (English) Zbl 1428.86026
Summary: Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relation between flow responses and facies distribution. One way to incorporate feedback from the flow data into MPS simulation is by constructing (and updating) facies probability maps (soft data) and using the results to constrain the MPS simulation outputs, for example, through Single Normal Equation SIMulation (SNESIM) algorithm and the \(\tau \)-model. The pattern-imitating behavior of MPS simulation (specifically, the SNESIM) has been shown to result in a sizable fraction of facies models that fail to effectively capture the correct location and spatial connectivity represented by the facies probability map. This paper presents two key observations that explains this behavior/outcome: (1) the facies patterns resulting from the SNESIM are primarily controlled by the outcome of the first few grid cells along the corresponding random path (early stages of the simulation); and (2) the facies outcomes in the remaining grid cells are dominated by extremely confident conditional probabilities extracted from the TI to generate the encoded connectivity patterns in the TI. Hence, the contribution of facies probability map become increasingly inconsequential as the simulation proceeds. This intrinsic property must be accounted for in developing data conditioning methods, especially when training images with large-scale connectivity patterns are considered. Two approaches for addressing this issue include adapting the random path at early stages to the key information in the probability map to properly reflect its impact, or treating high-probability events from the probability map as hard data. Examples are presented to illustrate this behavior, followed by a simple method to improve the effectiveness of integrating facies probability maps (and flow response data) into SNESIM.
86A32 Geostatistics
62M40 Random fields; image analysis
Full Text: DOI
[1] Alcolea, A.; Carrera, J.; Medina, A., Pilot points method incorporating prior information for solving the groundwater flow inverse problem, Adv Water Resour, 29, 1678-1689 (2006)
[2] Allard, D.; Comunian, A.; Renard, P., Probability aggregation methods in geoscience, Math. Geosci., 44, 545-581 (2012) · Zbl 1256.86006
[3] Caers, J., Geostatistical reservoir modelling using statistical pattern recognition, J Petrol Sci Eng, 29, 177-188 (2001)
[4] Caers, J.; Hoffman, T., The probability perturbation method: a new look at Bayesian inverse modeling, Math Geol, 38, 81-100 (2006) · Zbl 1119.86312
[5] Caers J, Zhang T (2004) Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models. In: Grammer GM, Harris PM, Eberli GP (eds) Integration of outcrop and modern analogs in reservoir modeling, vol 80. American Association of Petroleum Geologists, Memoirs, pp 383-394
[6] Carle, SF; Fogg, GE, Modeling spatial variability with one and multidimensional continuous-lag Markov chains, Math Geol, 29, 891-918 (1997)
[7] Carle, SF; Labolle, EM; Weissmann, GS; etal., Conditional simulation of hydrofacies architecture: a transition probability/Markov approach, Hydrogeol Models Sediment Aquifers Concepts Hydrogeol Environ Geol, 1, 147-170 (1998)
[8] Chiles JP, Delfiner P (2009) Geostatistics: modeling spatial uncertainty, vol 497. Wiley, Hoboken (Reprint) · Zbl 0922.62098
[9] Chiu SN, Stoyan D, Kendall WS et al (2013) Stochastic geometry and its applications. Wiley, Hoboken (Reprint)
[10] Marsily, GH; Delay, F.; Gonçalvès, J.; etal., Dealing with spatial heterogeneity, Hydrogeol J, 13, 161-183 (2005)
[11] Deutsch, CV; Journel, AG, Geostatistical software library and user’s guide, New York, 119, 147 (1992)
[12] Deutsch, CV; Wang, L., Hierarchical object-based stochastic modeling of fluvial reservoirs, Math Geol, 28, 857-880 (1996)
[13] Evensen, G., Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics (1978-2012), J Geophys Res Oceans, 99, 10143-10162 (1994)
[14] Evensen, G., Sampling strategies and square root analysis schemes for the EnKF, Ocean Dyn, 54, 539-560 (2004)
[15] Falivene, O.; Cabrera, L.; Muñoz, JA; etal., Statistical grid-based facies reconstruction and modelling for sedimentary bodies Alluvial-palustrine and turbiditic examples, Geol Acta, 5, 199-230 (2007)
[16] Gómez-Hernández, JJ; Srivastava, RM, ISIM3D: an ANSI-C three-dimensional multiple indicator conditional simulation program, Comput Geosci, 16, 395-440 (1990)
[17] Gómez-Hernández, JJ; Wen, XH, To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology, Adv Water Resour, 21, 47-61 (1998)
[18] Gómez-Hernánez, JJ; Sahuquillo, A.; Capilla, JE, Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—1. Theory, J Hydrol, 203, 167-174 (1997)
[19] Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press on Demand, Oxford (Reprint)
[20] Gu, Y.; Oliver, DS, History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter, SPE J, 10, 217-224 (2005)
[21] Guardiano FB, Srivastava RM (1993) Multivariate geostatistics: beyond bivariate moments. In: Geostatistics Troia’92. Springer, pp. 133-144
[22] Haldorsen HH, Lake LW (1982) A new approach to shale management in field scale simulation models. University of Texas, Austin
[23] Haldorsen, HH; Lake, LW, A new approach to shale management in field-scale models, Soc Petrol Eng J, 24, 447-457 (1984)
[24] Holden, L.; Hauge, R.; Skare, Ø.; etal., Modeling of fluvial reservoirs with object models, Math Geol, 30, 473-496 (1998)
[25] Hu, LY; Chugunova, T., Multiple-point geostatistics for modeling subsurface heterogeneity: a comprehensive review, Water Resour Res, 44, 1-14 (2008)
[26] Isaaks EH (1991) The application of Monte Carlo methods to the analysis of spatially correlated data, Stanford University Dissertation
[27] Jafarpour, B.; Khodabakhshi, M., A probability conditioning method (PCM) for nonlinear flow data integration into multipoint statistical facies simulation, Math Geosci, 43, 133-164 (2011) · Zbl 1207.86010
[28] Journel, AG, Nonparametric estimation of spatial distributions, Math Geol, 15, 445-468 (1983)
[29] Journel, AG, Combining knowledge from diverse sources: an alternative to traditional data independence hypotheses, Math Geol, 34, 573-596 (2002) · Zbl 1032.86005
[30] Kerrou, J.; Renard, P.; Hendricks Franssen, HJ; etal., Issues in characterizing heterogeneity and connectivity in non-multiGaussian media, Adv Water Resour, 31, 147-159 (2008)
[31] Kowalsky, MB; Finsterle, S.; Rubin, Y., Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements during transient flow in the vadose zone, Adv Water Resour, 27, 583-599 (2004)
[32] Law, J., A statistical approach to the interstitial heterogeneity of sand reservoirs, Trans AIME, 155, 202-222 (1944)
[33] Le, LG; Galli, A., Truncated plurigaussian method: theoretical and practical points of view, Geostat Wollongong, 96, 211-222 (1997)
[34] Le DH, Younis R, Reynolds AC (2015) A history matching procedure for non-Gaussian facies based on ES-MDA. In: Society of Petroleum Engineers Paper SPE-173233-MS, SPE Reservoir Simulation Symposium, 23-25 February, Houston
[35] Liu, N.; Oliver, DS, Automatic history matching of geologic facies, SPE J, 9, 429-436 (2004)
[36] Ma, W.; Jafarpour, B., Pilot points method for conditioning multiple-point statistical facies simulation on flow data, Adv Water Resour, 115, 219-233 (2018)
[37] Ma, W.; Jafarpour, B., Integration of soft data into multiple-point statistical simulation: re-assessing the probability conditioning method for facies model calibration, Comput Geosci (2019) · Zbl 1421.86027
[38] Mariethoz, G.; Renard, P.; Straubhaar, J., The Direct Sampling method to perform multiple-point geostatistical simulations, Water Resour. Res., 46, w11536 (2010)
[39] Oliver, DS; Chen, Y., Recent progress on reservoir history matching: a review (in English), Comput Geosci, 15, 185-221 (2011) · Zbl 1209.86001
[40] Remy N, Boucher A, Wu J (2009) Applied geostatistics with SGeMS: A user’s guide. Cambridge University Press, Cambridge (Reprint)
[41] Rollins, JB; Holditch, SA; Lee, WJ, Characterizing average permeability in oil and gas formations (includes associated papers 25286 and 25293), SPE Form Eval, 7, 99-105 (1992)
[42] Skjervheim JA, Evensen G (2011) An ensemble smoother for assisted history matching. In: Society of Petroleum Engineers Paper # SPE-14929-MS, SPE Reservoir Simulation Symposium, 21-23 February, The Woodlands
[43] Skjervheim, J.; Evensen, G.; Aanonsen, SI; etal., Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter, SPE J Richardson, 12, 282 (2007)
[44] Straubhaar, J.; Renard, P.; Mariethoz, G.; etal., An Improved parallel multiple-point algorithm using a list approach, Math Geosci, 43: 305.https, //doi.org/10.1007/s11004-011-9328-7 (2011)
[45] Strebelle, S., Conditional simulation of complex geological structures using multiple-point statistics, Math Geol, 34, 1-21 (2002) · Zbl 1036.86013
[46] Leeuwen, PJ; Evensen, G., Data assimilation and inverse methods in terms of a probabilistic formulation, Mon Weather Rev, 124, 2898-2913 (1996)
[47] Wen, XH; Deutsch, CV; Cullick, AS, Construction of geostatistical aquifer models integrating dynamic flow and tracer data using inverse technique, J Hydrol, 255, 151-168 (2002)
[48] Western, AW; Blöschl, G.; Grayson, RB, Toward capturing hydrologically significant connectivity in spatial patterns, Water Resour Res, 37, 83-97 (2001)
[49] Zinn, B.; Harvey, CF, When good statistical models of aquifer heterogeneity go bad: a comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields, Water Resour Res, 39, 19 (2003)
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