Statistical simulation technique for deformation band spatial distribution in the fault damage zone

D. R. Kolyukhin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 465-479.

Résumé

The paper presents two methods for statistical simulation of deformation bands distribution for reservoir modelling purposes based on analysis of field data. The proposed algorithms reproduce spatial density distribution and clustering of deformation bands observed in fault damage zones. Application and precision of the algorithms for different parameter values have been checked numerically.

Détail

Keywords: statistical simulation, fault damage zone, deformation bands, fractals and multifractals
Mots-clés : correlation dimension.

Bibliographie

[1] Antonellini M., Cilona A., Tondi E., Zambrano M., Agosta F., “Fluid flow numerical experiments of faulted porous carbonates, Northwest Sicily (Italy)”, Marine and Petrol. Geol., 55 (2014), 186–201 | DOI

[2] Belfield W. C., “Incorporating spatial distribution into stochastic modelling of fractures: multifractals and Levy-stable statistics”, J. Struct. Geol., 20 (1998), 473–486 | DOI

[3] Bonnet E., Bour O., Odling N. E., Davy P., Main I., Cowie P., Berkowitz B., “Scaling of fracture systems in geological media”, Rev. Geophys., 39:3 (2001), 347–383 | DOI | MR

[4] Bour O., Davy P., Darcel C., “A statistical scaling model for fracture network geometry, with validation on multiscale mapping of a joint network (Hornelen Basin, Norway)”, J. Geophys. Res., 107:B6 (2002) | DOI

[5] Braathen A., Tveranger J., Fossen H., Skar T., Cardozo N., Semshaug S. E., Bastesen E., Sverdrup E., “Fault facies and its application to sandstone reservoirs”, AAPG Bulletin, 93 (2009), 891–917 | DOI

[6] Clauset A., Shalizi C. R., Newman M. E. J., “Power-law distributions in empirical data”, SIAM Review, 51:4 (2009), 661–703 doi:10.1137/070710111. | DOI | MR | Zbl

[7] Darcel C., Bour O., Davy P., de Dreuzy J. R., “Connectivity properties of two-dimensional fracture network with stochastic fractal correlation”, Water Resources Res., 39:10 (2003), 1272 | DOI

[8] Dowd P. A., Xu C., Mardia K. V., Fowell R. J., “A Comparison of Method for the Stochastic Simulation of Rock Fractures”, Math. Geol., 39 (2007), 697–714 | DOI | Zbl

[9] Du Bernard X., Labaume P., Darcel C., Davy P., Bour O., “Cataclastic slip band distribution in normal fault damage zones, Nubian sandstones, Suez rift”, J. Geophys. Res., 107:B7 (2002) | DOI | MR | Zbl

[10] Fachri M., Tveranger J., Braathen A., Schueller S., “Sensitivity of fluid flow to deformation-band damage zone heterogeneities: A study using fault facies and truncated Gaussian simulation”, J. Struct. Geol., 52 (2013), 60–79 | DOI

[11] Fossen H., Bale A., “Deformation bands and their influence on fluid flow”, AAPG Bulletin, 91:12 (2007), 1685–1700 | DOI

[12] Fossen H., Schultz R. A., Shipton Z. K., Mair K., “Deformation bands in sandstone: a review”, J. Geol. Soc., London, 164 (2007), 755–769 | DOI

[13] Gelman A., “Commentary: P Values and Statistical Practice”, Epidemiology, 24:1 (2013), 69–72 | DOI

[14] Grassberger P., Procaccia I., “Measuring the strangeness of strange attractors”, Physica D: Nonlinear Phenomena, 9:1–2 (1983), 189–208 | DOI | MR | Zbl

[15] Harris S. D., McAllister E., Knipe R. J., Odling N. E., “Predicting the three-dimensional population characteristics of fault zones: a study using stochastic models”, J. Struct. Geol., 25:8 (2003), 1281–1299 | DOI

[16] Kolyukhin D., Schueller S., Espedal M., Fossen H., “Deformation band populations in fault damage zone — impact on fluid flow”, Computational Geosciences, 14:2 (2010), 231–248 | DOI | Zbl

[17] Odling N. E., Gillespie P. A., Bourgine B., Castaing C., Chiles J. P., Christiansen N. P., Fillion E., Genter A., Olsen C., Thrane L., Trice R., Aarseth E., Walsh J. J., Watterson J., “Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs”, Petrol. Geosci., 5 (1999), 373–384 | DOI

[18] Odling N. E., “The scaling of hydrailic connectivity of in rock fracture zones”, Geophys. Res. Lett., 28:15 (2001), 3019–3022 | DOI

[19] Ouillon G., Sornette D., “Unbiased multifractal analysis: Application to fault patterns”, Geophys. Res. Lett., 23:23 (2001), 3409–3412 | DOI

[20] Qu D., Roe P., Tveranger J., “A method for generating volumetric fault zone grids for pillar gridded reservoir models”, Computers and Geosciences, 81 (2015), 28–37 | DOI

[21] Rotevatn A., Sandve T. H., Keilegavlen E., Kolyukhin D., Fossen H., “Deformation bands and their impact on fluid flow in sandstone reservoirs: the role of natural thickness variations”, Geofuids, 13:3 (2013), 359–371 | DOI

[22] Schueller S., Braathen A., Fossen H., Tveranger J., “Spatial distribution of deformation bands in damage zones of extensional faults in porous sandstones: Statistical analysis of field data”, J. Struct. Geol., 52 (2013), 148–162 | DOI

[23] Tran N. H., “Simulated annealing technique in discrete fracture network inversion: optimizing the optimization”, Computational Geosciences, 11 (2007), 249–260 | DOI | Zbl

[24] Tveranger J., Skar T., Braathen A., “Incorporation of fault zones as volumes in reservoir models”, Bolletino di Geofisica Teorica e Applicata, 45:1 (2004), 316–318

[25] Xie H., Wang J. A., Kwasniewski M. A., “Multifractal characterization of rock fracture surfaces”, Int. J. Rock. Mech. Min. Sci., 36 (1999), 19–27 | DOI