Modeling Channel Forms and Related Sedimentary Objects Using a Boundary Representation Based on Non-uniform Rational B-Splines

Mathematical Geosciences - Tập 48 - Trang 259-284 - 2015
Jeremy Ruiu1, Guillaume Caumon1, Sophie Viseur2
1Georessources, Université de Lorraine-ENSG, CNRS, GREGU, Vandoeuvre-Lès-Nancy, France
2CEREGE (UMR 7330), Aix Marseille University, Marseille Cedex 03, France

Tóm tắt

This paper aims at providing a flexible and compact volumetric object model capable of representing many sedimentary structures at different scales. Geobodies are defined by a boundary representation; each bounding surface is constructed as a parametric deformable surface. A three-dimensional sedimentary object with a compact parametrization which allows for representing various geometries and provides a curvilinear framework for modeling internal heterogeneities is proposed. This representation is based on non-uniform rational basis splineswhich smoothly interpolate between a set of points. The three-dimensional models of geobodies are generated using a small number of parameters, and hence can be easily modified. This can be done by a point and click user interaction for manual editing or by a Monte-Carlo sampling for stochastic simulation. Each elementary shape is controlled by deformation rules and has connection constraints with associated objects to maintain geometric consistency through editing. The boundary representations of the different sedimentary structures are used to construct hexahedral conformal grids to perform petrophysical property simulations following the particular three-dimensional parametric space of each object. Finally these properties can be upscaled, according to erosion rules, to a global grid that represents the global depositional environment.

Tài liệu tham khảo

Abrahamsen P, Fjellvoll B, Hauge R (2007) Process based stochastic modelling of deep marine reservoirs. In: EAGE petroleum geostatistics Abreu V, Sullivan M, Pirmez C, Mohrig D (2003) Lateral accretion packages (laps): an important reservoir element in deep water sinuous channels. Mar Pet Geol 20(6):631–648 Allen JR (1963) The classification of cross-stratified units. With notes on their origin. Sedimentology 2(2):93–114 Alpak FO, Barton MD, Naruk SJ (2013) The impact of fine-scale turbidite channel architecture on deep-water reservoir performance. AAPG Bull 97(2):251–284. doi:10.1306/04021211067 Arnott R (2010) Deep-marine sediments and sedimentary systems. In: James N, Dalrymple R (eds) Facies model 4. St. John’s: Geological Association of Canada, pp 295–322 Bertoncello A, Caers JK, Biver P, Caumon G (2008) Geostatistics on stratigraphic grids. In: Ortiz J, Emery X (eds) Proc. eighth geostatistical geostatistics congress, vol 2. Gecamin ltd, pp 677–686 Bertoncello A, Sun T, Li H, Mariethoz G, Caers J (2013) Conditioning surface-based geological models to well and thickness data. Math Geosci 45(7):873–893 Bhattacharya J (2010) Deltas. In: James N, Dalrymple R (eds) Facies model 4. St. John’s: Geological Association of Canada, pp 233–264 Boisvert JB, Pyrcz MJ, Deutsch CV (2007) Multiple-point statistics for training image selection. Nat Resour Res 16(4):313–321 Comunian A, Jha SK, Giambastiani BM, Mariethoz G, Kelly BF (2014) Training images from process-imitating methods. Math Geosci 46(2):241–260 Desbarats A (1987) Numerical estimation of effective permeability in sand–shale formations. Water Resour Res 23(2):273–286 Deutsch CV, Wang L (1996) Hierarchical object-based stochastic modeling of fluvial reservoirs. Math Geol 28(7):857–880 Deutsch C, Tran T (2002) Fluvsim: a program for object-based stochastic modeling of fluvial depositional systems. Comput Geosci 28(4):525–535 Deutsch C, Tran T (2004) Simulation of deepwater lobe geometries with object based modelling: Lobesim. Tech. rep., Tech. rep., University of Alberta. http://www.uofaweb.ualberta.ca/ccg//pdfs/1999%2004-LobeModeling1.pdf. Accessed 7 Dec 2015 Durlofsky LJ (2005) Upscaling and gridding of fine scale geological models for flow simulation. In: 8th international forum on reservoir simulation, Borromees Island, pp 20–24 Fisher T, Wales R (1992) Rational splines and multidimensional geologic modeling. In: Pflug R, Harbaugh J (eds) Computer graphics in geology, vol 41., Lecture notes in earth sciencesSpringer, Berlin, pp 17–28 Gai X, Wu Xh, Branets L, Sementelli K, Robertson G (2012) Concept-based geologic modeling using function form representation. In: Abu Dhabi international petroleum conference and exhibition Google Earth (2012) Atchafalaya delta 29\(^\circ \)O Graham GH, Jackson MD, Hampson GJ (2015) Three-dimensional modeling of clinoforms in shallow-marine reservoirs: part 1. Concepts and application. AAPG Bull 99(06):1013–1047. doi:10.1306/01191513190 Haldorsen H, Lake L (1984) A new approach to shale management in field-scale models. Old SPE J 24(4):447–457 Hassanpour MM, Pyrcz MJ, Deutsch CV (2013) Improved geostatistical models of inclined heterolithic strata for McMurray formation, Alberta, Canada. AAPG Bull 97(7):1209–1224. doi:10.1306/01021312054 Holden L, Hauge R, Skare Ø, Skorstad A (1998) Modeling of fluvial reservoirs with object models. Math Geol 30(5):473–496 Howard A (1996) Modelling channel evolution and floodplain morphology. In: Floodplain processes, pp 15–62 Howard A, Knutson T (1984) Sufficient conditions for river meandering: a simulation approach. Wat Resour Res 20(11):1659–1667 Issautier B, Fillacier S, Gallo YL, Audigane P, Chiaberge C, Viseur S (2013) Modelling of \({\rm CO}_2\) storage capacity and performance. Energy Procedia 37:5181–5190 Jackson M, Muggeridge A (2000) Effect of discontinuous shales on reservoir performance during horizontal waterflooding. SPE J 5(4):446–455 Jackson MD, Hampson GJ, Sech RP (2009) Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: part 2. Geologic controls on fluid flow and hydrocarbon recovery. AAPG Bull 93(9):1183–1208. doi:10.1306/05110908145 Journel A (1996) Conditional simulation of geologically averaged block permeabilities. J Hydrol 183(1): 23–35 Journel A, Gundeso R, Gringarten E, Yao T (1998) Stochastic modelling of a fluvial reservoir: a comparative review of algorithms. J Pet Sci Eng 21(1):95–121 Knighton D (2014) Fluvial forms and processes: a new perspective, 2nd edn. Routledge, New York Li H, Caers J (2011) Geological modelling and history matching of multi-scale flow barriers in channelized reservoirs: methodology and application. Pet Geosci 17(1):17–34. doi:10.1144/1354-079309-825 Lopez S (2003) Modélisation de réservoirs chenalisés méandriformes: une approche génétique et stochastique. PhD thesis, Mines Paris Tech Manchuk JG, Deutsch CV (2012) Implementation aspects of sequential gaussian simulation on irregular points. Comput Geosci 16(3):625–637 Manchuk J, Leuangthong O, Deutsch CV (2005) Direct geostatistical simulation on unstructured grids. In: Geostatistics Banff 2004. Springer, New York, pp 85–94 Mariethoz G, Caers J (2014) Multiple-point geostatistics: stochastic modeling with training images. Wiley-Blackwell, New York Mariethoz G, Comunian A, Irarrazaval I, Renard P (2014) Analog-based meandering channel simulation. Water Resour Res 50(2):836–854. doi:10.1002/2013WR013730 McKee ED (1957) Flume experiments on the production of stratification and cross-stratification. J Sediment Res 27(2):129–134. doi:10.1306/74D70678-2B21-11D7-8648000102C1865D Miall A (1985) Architectural-element analysis: a new method of facies analysis applied to fluvial deposits. Earth-Sci Rev 22(4):261–308 Miall A (1996) Geology of fluvial deposits: sedimentary facies. Springer, New York Miall A (2010) Alluvial deposits. In: James N, Dalrymple R (eds) Facies model 4. St. John’s: Geological Association of Canada, pp 105–138 Mirowski PW, Tetzlaff DM, Davies RC, McCormick DS, Williams N, Signer C (2009) Stationarity scores on training images for multipoint geostatistics. Math Geosci 41(4):447–474 Nordahl K, Ringrose PS, Wen R (2005) Petrophysical characterization of a heterolithic tidal reservoir interval using a process-based modelling tool. Pet Geosci 11(1):17–28 Novakovic D, White C, Corbeanu R, Hammon Iii W, Bhattacharya J, McMechan G (2002) Hydraulic effects of shales in fluvial–deltaic deposits: Ground-penetrating radar, outcrop observations, geostatistics, and three-dimensional flow modeling for the Ferron sandstone, Utah. Math Geol 34(7):857–893 Piegl L, Tiller W (1995) The NURBS book. Springer, London Pyrcz MJ, Catuneanu O, Deutsch CV (2005) Stochastic surface-based modeling of turbidite lobes. AAPG Bull 89(2):177–191. doi:10.1306/09220403112 Pyrcz M, Boisvert J, Deutsch C (2009) Alluvsim: a program for event-based stochastic modeling of fluvial depositional systems. Comput Geosci 35(8):1671–1685. doi:10.1016/j.cageo.2008.09.012 Reineck HE, Singh IB (1980) Depositional sedimentary environments. Springer, Berlin Renard P, Mariethoz G (2014) Special issue on 20 years of multiple-point statistics: part 1. Math Geosci 46(2):129–131 Rongier G, Collon P, Renard P, Ruiu J (2015) Channel simulation using L-system, potential fields and NURBS. In: Petroleum geostatistics 2015, EAGE. doi:10.3997/2214-4609.201413604 Ruiu J, Caumon G, Viseur S, Antoine C (2014) Modeling channel forms using a boundary representation based on non-uniform rational b-splines. In: Mathematics of planet earth. Springer, New York, pp 581–584 Ruiu J, Caumon G, Viseur S (2015) Semiautomatic interpretation of 3D sedimentological structures on geologic images: an object-based approach. Interpretation 3(3):SX63–SX74 Sech RP, Jackson MD, Hampson GJ (2009) Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: part 1. Surface-based modeling to capture high-resolution facies architecture. AAPG Bull 93(9):1155–1181. doi:10.1306/05110908144 Shtuka A, Samson P, Mallet JL (1996) Petrophysical simulation within an object-based reservoir model. In: Proc. European 3D reservoir modelling conference (SPE 35480) Viseur S (2004) Turbidite reservoir characterization: object-based stochastic simulation meandering channels. Bull Soc Geol Fr 175(1):11–20. doi:10.2113/175.1.11 Wen R, Martinius A, Næss A, Ringrose P (1998) Three-dimensional simulation of small-scale heterogeneity in tidal deposits—a process-based stochastic simulation method. In: Proceedings of the 4th annual conference of the international association of mathematical geology (IAMG). De Frede editore, Ischia, pp 129–134