Hydrogeomechanical modeling of reservoir by external coupling of specialized computational software and universal CAE Fidesys

A. V. Vershinin ; D. I. Sabitov ; S. Y. Ishbulatov ; A. V. Myasnikov

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 154-187.

Résumé

We study several algorithms for solving the coupled problem of hydrogeomechanical modeling of fluid filtration in a deformed fractured rock, allowing to describe the mutual influence of filtration and rock deformation processes on the dynamic parameters of the medium: porosity, permeability, rock stiffness and fracture extensions. These algorithms allow solving the problems of choosing the location and drilling trajectory of a well either wellbore stability, ensuring high productivity of the formation due to optimization of the design of hydraulic fracturing and sand control. Together with seismic and reservoir testing data, coupled hydrogeomechanical modeling allows optimizing the tactics and strategy of reservoir development. The disturbance of formation stress-strain state in the near-well zone leads to the development of deformation processes and fracture zones, as well as changes in pore pressure and filtration properties in the reservoir. At the first stage, we verify external and internal iterative external coupling procedures. The specially developed research code was used for internal coupling procedure. For external coupling, a finite element simulator FIDESYS was used which solves numerically the problems of geomechanical stresses and deformation distributions in the rock. We developed the control module to organize the iterative process of geomechanical and hydrodynamic simulators, including reading special simulation data formats, unit conversion, as well as the value fields projection on different model grids. In this paper, we present the modeling for several problems and discuss the computation results. Effective elastic-strength properties are determined numerically at every mesh node as a result of solving the time consuming spatial elastoplastic problem. Therefore, the reduction in the frequency of data exchange is important in this approach. One of the goals of this numerical study, related to the above methodology, is to determine the effect of the coupling frequency on the solution. Based on the computation results for the example of the cyclic CO2 injection procedure in the Bazhenov Formation formation (Palyanovo section), only the local production characteristics are sensitive to the coupling frequency. The results obtained in this paper allow us to conclude that the role of geomechanical effects of fractured rock deformations saturated with a fluid is significant for modeling the formation processes.

Détail

Keywords: geomechanics, effective properties, fractured media, numerical modeling, finite element method, coupling.

Bibliographie

[1] Vavakin L. S., Salganik R.L., “Ob effektivnyh harakteristikah neodnorodnyh sred s izolirovannymi neodnorodnostyami”, Izv. AN SSSR. Mekhanika tverdogo tela, 1975, no. 3, 65–75

[2] Zingerman K.M., Levin V.A., “Pereraspredelenie konechnyh uprugih deformacii posle obrazovaniya vklyuchenij. Priblizhennoe analiticheskoe reshenie”, Prikladnaya matematika i mekhanika, 73:6 (2009), 983–1001 | Zbl

[3] Konovalenko Ig.S., Smolin A.Yu., Nikonov A.Yu., Psakhier S.G., “Multilevel modeling of deformation and destruction of brittle porous materials based on the method of mobile cellular automata”, Physical mesomechanics, 12:5 (2009)

[4] Christensen R., Introduction to Composite Mechanics, Mir, 1982

[5] Levin V.A., Zingerman K.M., Vershinin A.V., “Geomechanical modeling of crack growth for finite deformations. Zones of pre-destruction”, Technologies of seismic prospecting, 2014, no. 4, 34–39

[6] Levin V.A., Kalinin V.V., Zingerman K.M., Vershinin A.V., Development of defects in finite deformations. Computer and physical modeling, Fizmatlit, 2007, 392 pp.

[7] Levin V.A., “O koncentracii napryazhenij vblizi otverstiya, obrazovannogo v predvaritel'no napryazhennom tele iz vyazkouprugogo materiala”, DAN SSSR, 299:5 (1988)

[8] Levin V.A., Zingerman K.M., “O postroenii ehffektivnyh opredelyayushchih sootnoshenij dlya poristyh uprugih materialov pri konechnyh deformaciyah i ih nalozhenii”, Reports of the Russian Academy of Sciences, 382:4 (2002), 482–487

[9] Levin V.A., Vershinin A.V., Numerical methods. Parallel computing, Computational structural mechanics, 2, Fizmatlit, M., 2015, 544

[10] Levin V.A., Lokhin V.V., Zingerman K.M., “Ob ocenke ehffektivnyh harakteristik poristyh materialov pri bolshih deformaciyah”, Vestnik MGU, 1996, no. 6, 48–50

[11] Levin V.A., Mnogokratnoe nalozhenie bol'shih deformacij v uprugih i vyazkouprugih telah, Nauka. Fizmatlit, 1999, 224 pp.

[12] Levin V.A., Lokhin V.V., Zingerman K.M., “Ob odnom sposobe ocenki ehffektivnyh harakteristik poristyh tel pri konechnyh deformaciyah”, Izvestiya RAN Mekhanika tverdogo tela, 1997, no. 4, 45–50

[13] Lurie A.I., Nonlinear theory of elasticity, Nauka, M., 1980, 512 pp.

[14] Methods of computational mathematics, Nauka, M., 1977

[15] Miftakhov R.F., Myasnikov A.V., Vershinin A.V., Chugunov S.S., Zingerman K.M., “On the construction of hydrogeomechanical models of shale formations”, Technologies of seismic prospecting, 2015, no. 4, 97–108

[16] Morozov E.M., Levin V.A., Vershinin A.V., Strength analysis. Fidesys in the hands of an engineer, URSS, 2015, 408

[17] Myasnikov A.V., Stefanov Yu.P., Stenin V.P., Beck D.D., Akhtyamova A.I., “O vozmozhnom reshenii zadachi dizajna mnogostadijnogo GRP v bazhenovskih formaciyah”, Nedropolzovanie, XXI:6 (2016), 62–79

[18] Pobedrya B.E., Mekhanika kompozicionnyh materialov, Izd-vo MGU, M., 1984, 336 pp.

[19] Pobedrya B.E., Chislennye metody v teorii uprugosti i plastichnosti, Publishing house of Moscow University, 1995

[20] Vvedenie v mekhaniku sploshnoj sredy, Fizmatgiz, M., 1962, 284 pp.

[21] Sedov L.I., Mekhanika sploshnoj sredy, v. 2, Nauka, M., 1994, 560 pp.

[22] Sonnov M., Vershinin A., Zhukov V., Ovcharenko Y., Lukin S., Glazyrina A., “Geomechanical modeling of the near wellbore zone”, Oil Journal Russia, 2017, no. 1-2(112), 72–76

[23] Filshtinskij L.A., “Napryazheniya i smeshcheniya v uprugoj ploskosti, oslablennoj dvoyakoperiodicheskoj sistemoj odinakovyh kruglyh otverstij”, Prikl. matem. i mekh., 28:3 (1964), 430–441

[24] Khakimova L.A., Myasnikov A.V., Bondarenko T.M., Popov E.Yu., Cheremisin A.N., Karpov I.A., “Validaciya chislennoj modeli processa zakachki vozduha vysokogo davleniya na mestorozhdenii bazhenovskoj svity na osnove rezul'tatov fizicheskogo modelirovaniya”, Neftyanoe hozyajstvo, 2017, no. 4, 85–89

[25] Aboudi J., “Micromechanics-based thermoviscoelastic constitutive equations for rubber-like matrix composites at finite strains”, International Journal of Solids and Structures, 41 (2004), 5611–5629 | DOI | Zbl

[26] “Amadei B., Goodman R.E.”, Proceedings of the International Symposium on the Mechanical Behavior of Structured Media (Ottawa, 1981), 249–268

[27] Andersen M. A., Petroleum Research in North Sea Chalk, RF-Rogaland Research, No 142, Stavanger, Norway, 1995

[28] Bagheri M., Modeling geomechanical effects on the flow properties of fractured reservoirs, Ph.D thesis, University of Calgary, Calgary, Alta, 2006

[29] Bagheri M., Settari A., “Modeling of Geomechanics in Naturally Fractured Reservoirs”, SPE Reservoir Simulation Symposium (Houston, USA, 2005), SPE-93083-MS

[30] Bagheri M., Settari A., “Effects of fractures on reservoir deformation and flow modeling”, Can. Geotech. J., 43 (2006), 574–586 | DOI

[31] Bagheri M., Settari A., “Modeling Coupled Fluid Flow and Deformation of Fractured Reservoirs Using Full Tensor Permeability”, Europec/EAGE Conference and Exhibition (9–12 June 2008, Rome, Italy), SPE paper 113319 | DOI

[32] Bandis S.C., Lumsden A.C., Barton N.R., “Fundamentals of rock joint deformation”, International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, 20 (1983), 249–268 | DOI

[33] Barton N.R., Choubey V., “The shear strength of rock joints in theory and practice”, Rock Mechanics, 10 (1977), 1–54 | DOI

[34] Bruhns O. T., Schiesse P., “A continuum model of elastic-plastic materials with anisotropic damage by oriented microvoids”, European Journal of Mechanics A: Solids, 15:3 (1996), 367–396 | Zbl

[35] Chen H.-Y., Teufel L.W., Coupling Fluid-Flow and Geomechanics in Dual-Porosity Modeling of Naturally Fractured Reservoirs, SPE-38884-MS, Society of Petroleum Engineers, 1997, January 1 | DOI

[36] Costa A., “Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption”, Geophysical Research Letters, 33:2 (2006) | DOI | Zbl

[37] Daim F., Eymard R., Hilhorst D., Mainguy M., Masson R., “A Preconditional Conjugate Gradient Based Algorithm for Coupling Geomechanical-Reservoir Simulations”, Rev. IFP, 57 (2002), 515–524

[38] Firoozabadi A., Thomas L.K., “Sixth Comparative Solution Project: Dual Porosity Simulators”, Journal of Petroleum Technology, 42 (1990), 710–715 | DOI

[39] Fish J., Fan R., “Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading”, International Journal for Numerical Methods in Engineering, 76 (2008), 1044–1064 | DOI | MR | Zbl

[40] Fish J., “Multiscale Modeling and Simulation of Composite Materials and Structures”, Lecture Notes in Applied and Computational Mechanics, 55, 2011, 215–231 | DOI | Zbl

[41] Goodman R.E., Methods of geological engineering in discontinuous rocks, West Publication Company, 1976

[42] Hashin Z., Shtrikman S., “On some variational principles in anisotropic and nonhomogeneous elasticity”, Journal of the Mechanics and Physics of Solids, 10 (1962), 335–342 | DOI | MR

[43] Hashin Z., Shtrikman S., “A variational approach to the theory of the elastic behavior of multiscale materials”, Journal of the Mechanics and Physics of Solids, 11 (1963), 127–140 | DOI | MR | Zbl

[44] Hashin Z., “The elastic moduli of heterogeneous materials”, J. Appl. Mech., 29 (1962), 143 | DOI | MR | Zbl

[45] Hernandez I., Numerical Reservoir Simulation Coupled with Geomechanics, SPE-152364-STU, 2011

[46] Hill R., “Elastic properties of reinforced solids: some theoretical principles”, Journal of the Mechanics and Physics of Solids, 11 (1963), 357–372 | DOI | Zbl

[47] Hohe J., Becker W., “A probabilistic approach to the numerical homogenization of irregular solid foams in the finite strain regime”, International Journal of Solids and Structures, 42 (2005), 3549–3569 | DOI | Zbl

[48] Huang T.H., Chan C.H., Yang Z.Y., “Elastic Moduli for Fractured Rock Mass”, Rock Mechanics and Rock Engineering, 28:3 (1995), 135–144 | DOI

[49] Jalali M., Dusseault M., Coupled Fluid-Flow and Geomechanics in Naturally Fractured Reservoirs, ISRM-ARMS5-2008-153

[50] Kachanov M., Sevostianov I., “On quantitative characterization of microstructures and effective properties”, International Journal of Solids and Structures, 42 (2005), 309–336 | DOI | MR | Zbl

[51] Kachanov M., Tsukrov I., Shafiro B., “Effective moduli of a solid with holes and cavities of various shapes”, Appl. Mech. Reviews, 47:1-2 (1994), S151–S174 | DOI

[52] Khalili N., Valliapan S., “Unified theory of flow and deformation in double porous media”, European Journal of Mechanics, 15:2 (1996), 321–336 | Zbl

[53] Levin V. A., Zingerman K. M., “Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains”, Trans. ASME. Journal of Applied Mechanics, 70:6 (2003), 809–816 | DOI | Zbl

[54] Levin V. A., Lokhin V. V., Zingerman K. M., “Effective elastic properties of porous materials with randomly dispersed pores. Finite deformation”, Trans. ASME. Journal of Applied Mechanics, 67:4 (2000), 667–670 | DOI | Zbl

[55] Lewis R.W., Ghafouri H.R., “A novel FE DP model for multiphase flow through deformable fractured porous media”, Int. J. for Numerical and Analytical Methods in Geomechanics, 21 (1997), 789–816 | 3.0.CO;2-C class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[56] Lewis R.W., Pao W.K.S., “Numerical simulation of Three-Phase Flow in Deformning Fractured Reservoir”, Oil Gas Science and Technology, 57:5 (2002), 499–514 | DOI

[57] Mauge C., Kachanov M., “Effective elastic properties of an anisotropic material with arbitrary oriented interacting cracks”, J. Mech. Phys. Solids, 42:4 (1994), 561–584 | DOI | Zbl

[58] Mercier S., Molinari A., Berbenni S., Berveiller M., “Comparison of different homogenization approaches for elastic-viscoplastic materials”, Modeling and Simulation in Material Science and Engineering, 20 (2012), 024004 | DOI

[59] Mori T., Tanaka K., “Average stress in matrix and average energy of materials with misfitting inclusions”, Acta Metallurgica, 21 (1973), 571–574 | DOI

[60] Myasnikov A.V., Vershinin A.V., Sboychakov A.M., “A generalization of geomechanical model for naturally fractured reservoirs”, Proceedings - SPE Russian Petroleum Technology Conference and Exhibition (24–26 October 2016, Moscow, Russia), v. 2, M., 2016, 1050–1092

[61] Popov E., Myasnikov A., Cheremisin A., Miftakhov R., Stukachev V., Mukhametdinova A., “Experimental and computational complex for determination of the effectiveness of cyclic carbon dioxide injection for tight oil reservoirs”, Proceedings - SPE Russian Petroleum Technology Conference and Exhibition (24–26 October 2016, Moscow, Russia), v. 2, M., 2016, 811–830

[62] Samier P., DeGennaro S., Practical iterative coupling of GeoMechanics with reservoir simulation, SPE 106188, 2007

[63] Smit R. J. M., Brekelmans W. A. M., Meijer H. E. H., “Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling”, Computer Methods in Applied Mechanics and Engineering, 155:1–2 (1998), 181–192 | DOI | Zbl

[64] Stefanov Y. P., Myasnikov A. V., “Modeling of inelastic deformation around vertical and horizontal wells”, AIP Conference Proceedings, 1683, 2015, 020221, 4 pp. | DOI

[65] Talbot D. R. S., Willis J. R., “Bounds for the effective constitutive relation of a nonlinear composite”, Proceedings of the Royal Society A, 460 (2004), 2705–2723 | DOI | MR | Zbl

[66] Tsukrov I., Kachanov M., “Effective Moduli of an Anisotropic Material with Elliptical Holes of Arbitrary Orientational Distribution”, International Journal of Solids and Structures, 37 (2000), 5919–5941 | DOI | MR | Zbl

[67] Tsukrov I., Novak J., “Effective Elastic Properties of Solids with Defects of Irregular Shapes”, International Journal of Solids and Structures, 39 (2002), 1539–1555 | DOI | Zbl

[68] Vershinin A. V., Levin V. A., Zingerman K. M., Sboychakov A. M., Yakovlev M. Ya., “Software for estimation of second order effective material properties of porous samples with geometrical and physical nonlinearity accounted for”, Adv. Eng. Softw., 86 (2015), 80–84 | DOI

[69] Wilmanski K., Continuum Thermodynamics, v. I, Foundations, Wold Scientific, Singapore, 2008 | MR

[70] Yarushina V. M., Bercovici D., Oristaglio M. L., “Rock deformation models and fluid leak-off in hydraulic fracturing”, Geophysical Journal International, 194:3 (2013), 1514–1526 | DOI

[71] Yarushina V. M., Y. Y. Podladchikov, “(De)compaction of porous viscoelastoplastic media: Model formulation”, J. Geophys. Res. Solid Earth, 120 (2015) | DOI

[72] Youshinaka R., Yamabe T., “Joint stiffness and the deformation behavior of discontinuous rock”, International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, 23:1 (1986), 19–28 | DOI

[73] Zienkiewicz O.C., Taylor R.L., The finite element method, v. 1, The basis, Butterworth-Heinemann, Oxford, United Kingdom, 2000, 707 pp. | MR | Zbl

[74] Zienkiewicz O.C., Taylor R.L., The finite element method, v. 2, Solid mechanics, Butterworth-Heinemann, Oxford, United Kingdom, 2000, 479 pp. | MR | Zbl

[75] Fidesys LLC official website