HYDROGEOMECHANICAL MODELING OF RESERVOIR BY EXTERNAL COUPLING OF SPECIALIZED COMPUTATIONAL SOFTWARE AND UNIVERSAL CAE FIDESYS

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.

1. Aboudi, J. 2004, “Micromechanics-based thermoviscoelastic constitutive equations for rubber-like matrix composites at finite strains” International Journal of Solids and Structures. Vol. 41, pp. 5611–5629

2. Amadei, B., Goodman, R.E. 1981, “A 3-D constitutive relation for fractured rock masses”. In Proceedings of the International Symposium on the Mechanical Behavior of Structured Media, Ottawa. pp. 249–268

3. Andersen, M.A. 1995, “Petroleum Research in North Sea Chalk”.Rogaland Research, Stavanger, Norway. RF, pp. 142

4. Bagheri, M. 2006, “Modeling geomechanical effects on the flow properties of fractured reservoirs”.Ph.D thesis, University of Calgary, Calgary, Alta.

5. Bagheri, M., Settari, A. 2005, “Modeling of Geomechanics in Naturally Fractured Reservoirs”,In: SPE Reservoir Simulation Symposium, Houston, USA, SPE-93083-MS

6. Bagheri, M., Settari, A. 2006, “Effects of fractures on reservoir deformation and flow modeling”, Can. Geotech. J, no. 43, pp. 574–586. doi:10.1139/T06-024

7. Bagheri, M., Settari, A. 2008, “Modeling Coupled Fluid Flow and Deformation of Fractured Reservoirs Using Full Tensor Permeability”, In: EAGE Conference and Exhibition, Rome, Italy, SPE paper 113319

8. Bandis, S.C., Lumsden, A.C., and Barton, N.R. 1983. “Fundamentals of rock joint deformation”. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, no. 20, pp. 249–268

9. Barton, N.R. & Choubey, V. 1977. “The shear strength of rock joints in theory and practice”. Rock Mechanics, no. 10, pp. 1–54

10. Bruhns, O.T., Schiesse P. 1996, “A continuum model of elastic-plastic materials with anisotropic damage by oriented microvoids”, European Journal of Mechanics A: Solids. no.3, Vol. 15, pp. 367–396

11. Chen, H.-Y. & Teufel, L. W. 1997, “Coupling Fluid-Flow and Geomechanics in Dual- Porosity Modeling of Naturally Fractured Reservoirs”. Society of Petroleum Engineers. doi:10.2118/38884-MS

12. Christensen, R. 1982, Introduction to Composite Mechanics, Mir 13. Costa, A. 2006, “Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption”, Geophysical Research Letters, no. 2, Vol. 33

13. Daim, F., Eymard R., Hilhorst D., Mainguy M., Masson R. 2002, A preconditional Conjugate Gradient Based Algorithm for Coupling Geomechanical-Reservoir Simulations Rev, IFP, Vol. 57, pp. 515-524

14. Filshtinskij, L.A. 1964, “Napryazheniya i smeshcheniya v uprugoj ploskosti, oslablennoj dvoyakoperiodicheskoj sistemoj odinakovyh kruglyh otverstij”, Prikl. matem. i mekh., no.3, Vol. 28, pp. 430-441

15. Firoozabadi, A., Thomas, L. K. 1990, “Sixth Comparative Solution Project: Dual Porosity Simulators”, Journal of Petroleum Technology, no. 42, pp. 710 – 715

16. Fish, J. 2011, “Multiscale Modeling and Simulation of Composite Materials and Structures”, Lecture Notes in Applied and Computational Mechanics,. Vol. 55, pp. 215-231

17. Fish, J., Fan, R. 2008, “Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading”, International Journal for Numerical Methods in Engineering. Vol. 76, pp. 1044–1064

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

19. Hashin, Z. 1962, “The elastic moduli of heterogeneous materials”, J. Appl. Mech., Vol. 29, pp. 143

20. Hashin, Z., Shtrikman, S. 1962, “On some variational principles in anisotropic and nonhomogeneous elasticity”, Journal of the Mechanics and Physics of Solids. Vol. 10, pp. 335–342

21. Hashin, Z., Shtrikman, S. 1963, “A variational approach to the theory of the elastic behavior of multiscale materials”, Journal of the Mechanics and Physics of Solids, Vol. 11, pp. 127–140

22. Hernandez, I. 2011, “Numerical Reservoir Simulation Coupled with Geomechanics”. SPE-152364-STU

23. Hill, R. 1963, “Elastic properties of reinforced solids: some theoretical principles”, Journal of the Mechanics and Physics of Solids, Vol. 11, pp. 357–372

24. Hohe, J., Becker, W. 2005, “A probabilistic approach to the numerical homogenization of irregular solid foams in the finite strain regime”, International Journal of Solids and Structures, Vol. 42, pp. 3549–3569

25. Huang, T. H., Chan, C. H., Yang, Z. Y 1995, “Elastic Moduli for Fractured Rock Mass Rock”, Mechanics and Rock Engineering, Vol. 28, no. 3, pp. 135–144

26. Jalali, M., Dusseault, M.2008, “Coupled Fluid-Flow and Geomechanics In Naturally Fractured Reservoirs” . ISRM-ARMS5-2008-153.

27. Kachanov, M., Sevostianov I. 2005, “On quantitative characterization of microstructures and effective properties”, International Journal of Solids and Structures,Vol. 42, pp. 309-336

28. Kachanov, M., Tsukrov, I., Shafiro, B 1994, “Effective moduli of a solid with holes and cavities of various shapes”, Appl. Mech. Reviews, Vol. 47, no. 1, issue 2, pp 151-174

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

30. Khalili, N., Valliapan, S. 1996, “Unified theory of flow and deformation in double porous media”, European Journal of Mechanics, Vol. 15, no 2, pp. 321–336.

31. Konovalenko, Ig.S., Smolin, A.Yu., Nikonov, A.Yu., Psakhier, S.G. 2009, “Multilevel modeling of deformation and destruction of brittle porous materials based on the method of mobile cellular automata”. Physical mesomechanics. No. 5, Vol. 12

32. 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. 2003. Vol. 70, No. 6. – P. 809–816.

33. Levin, V.A. & Vershinin, A.V. 2015, “Nelinejnaja vychislitel’naja mehanika prochnosti. V 5 tomah. Tom 2. Chislennye metody. Parallel’nye vychislenija na JeVM” [“Computational structural mechanics. Volume 2. Numerical methods. Parallel computing”], FIZMATLIT Moskva

34. Levin, V.A. 1988, “O koncentracii napryazhenij vblizi otverstiya, obrazovannogo v predvaritel’no napryazhennom tele iz vyazkouprugogo materiala”, DAN SSSR. Vol. 299, no. 5

35. Levin, V.A. 1999, “Mnogokratnoe nalozhenie bol’shih deformacij v uprugih i vyazkouprugih telah” , Nauka, Fizmatlit, pp. 224

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

37. Levin, V.A., Lokhin, V.V., Zingerman, K.M. 1996, “Ob ocenke ehffektivnyh harakteristik poristyh materialov pri bolshih deformaciyah” , Vestnik MGU, 1996, no. 6, Vol. 48-50

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

39. Levin, V.A., Lokhin, V.V., Zingerman, K.M. 2000, “Effective elastic properties of porous materials with randomly dispersed pores. Finite deformation”, Trans. ASME. Journal of Applied Mechanics, Vol. 67, no. 4, pp. 667-670

40. Levin, V.A., Zingerman, K.M. 2002, “O postroenii ehffektivnyh opredelyayushchih sootnoshenij dlya poristyh uprugih materialov pri konechnyh deformaciyah i ih nalozhenii”, Reports of the Russian Academy of Sciences, Vol. 382, no. 4, pp. 482-487

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

42. Lewis, R.W., Ghafouri, H.R. 1997, “A novel FE DP model for multiphase flow through deformable fractured porous media”, Int. J. for Numerical and Analytical Methods in Geomechanics, Vol. 21, pp. 789–816

43. Lewis, R.W., Pao, W.K. 2002, “Numerical simulation of Three-Phase Flow in Deforming”, Fractured Reservoir Oil & Gas Science and Technology, Vol. 57, no. 5, pp. 499–514

44. Lurie, A.I. 1980, Nonlinear theory of elasticity, Nauka, Moscow, pp. 512

45. Marchuk, G.I. 1977, Methods of computational mathematics, Nauka, no.1, pp. 456

46. Mauge, C., Kachanov, M., “Effective elastic properties of an anisotropic material with arbitrary oriented interacting cracks”, J. Mech. Phys. Solids, Vol. 42, no. 4, pp. 561-584

47. Mercier, S., Molinari, A., Berbenni, S., Berveiller, M. 2012, “Comparison of different homogenization approaches for elastic–viscoplastic materials”, Modeling and Simulation in Material Science and Engineering, Vol. 20.

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

49. Mori, T., Tanaka, K. 1973, “Average stress in matrix and average energy of materials with misfitting inclusions”, Acta Metallurgica, Vol. 21, pp. 571-574

50. Morozov, E.M., Levin, V.A. & Vershinin, A.V. 2015 “Prochnostnoj analiz. Fidesys v rukah inzhenera” [“Strength analysis. Fidesys in the hands of an engineer”]. URSS, p. 408

51. Myasnikov, A.V., Stefanov, Yu.P., Stenin, V.P., Beck, D.D., Akhtyamova, A.I. 2016, “O vozmozhnom reshenii zadachi dizajna mnogostadijnogo GRP v bazhenovskih formaciyah”, Nedropolzovanie XXI, no. 6, pp. 62-79

52. Myasnikov, A.V., Vershinin, A.V., Sboychakov, A. M 2016, “A generalization of geomechanical model for naturally fractured reservoirs”, In: SPE Russian Petroleum Technology Conference and Exhibition, Moscow, Vol. 2, pp. 1050–1092

53. Pobedrya, B.E. 1984, “Mekhanika kompozicionnyh materialov”, Izd-vo MGU, Moscow, pp. 336

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

55. Popov, E, Myasnikov, A., Cheremisin, A., Miftakhov, R., Stukachev, V., Mukhametdinova, A. 2016, “Experimental and computational complex for determination of the effectiveness of cyclic carbon dioxide injection for tight oil reservoirs”, In: SPE Russian Petroleum Technology Conference and Exhibition, Moscow, Vol.2., pp. 811-830

56. Samier, P., DeGennaro, S. 2007, “Practical iterative coupling of GeoMechanics with reservoir simulation” . SPE 106188

57. Sedov, L.I. 1962, Vvedenie v mekhaniku sploshnoj sredy, Fizmatgiz, Moscow, pp. 284

58. Sedov, L.I. 1994, Mekhanika sploshnoj sredy, Nauka, Moscow, Vol. 2, pp. 560.

59. Smit, R.J.M., Brekelmans, W.A.M., Meijer, H.E.H 1998, “Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling”, Computer Methods in Applied Mechanics and Engineering, Vol. 155, pp. 181-192

60. Sonnov, M., Vershinin, A., Zhukov, V., Ovcharenko, Y., Lukin, S., Glazyrina, A. 2017, “Geomechanical modeling of the near wellbore zone”, Oil & Gas Journal Russia, no. 1-2, Vol. 112, pp. 72-76.

61. Stefanov, Y.P., Myasnikov, A.V. 2015, “Modeling of inelastic deformation around vertical and horizontal wells”, AIP Conference Proceedings, Vol. 1683.pp. 020221-1–4

62. Talbot, D.R.S., Willis, J. R. 2004, “Bounds for the effective constitutive relation of a nonlinear composite”, Proceedings of the Royal Society A, Vol. 460, pp. 2705-2723

63. Tsukrov, I., Kachanov, M 2000, “Effective Moduli of an Anisotropic Material with Elliptical Holes of Arbitrary Orientational Distribution”, International Journal of Solids and Structures, Vol.37, pp. 5919-5941

64. Tsukrov, I., Novak, J. 2002, “Effective Elastic Properties of Solids with Defects of Irregular Shapes”, International Journal of Solids and Structures, Vol. 39, pp. 1539-1555

65. Vavakin, LS, Salganik, R.L. 1975, “Ob effektivnyh harakteristikah neodnorodnyh sred s izolirovannymi neodnorodnostyami”, Izv. AN SSSR. Mekhanika tverdogo tela, no. 3, pp. 65-75

66. Vershinin, A.V., Levin, V.A., Zingerman, K.M., Sboychakov, A.M., Yakovlev, M.Ya 2015, “Software for estimation of second order effective material properties of porous samples with geometrical and physical nonlinearity accounted for”, Adv. Eng. Softw., Vol. 86, pp. 80-84

67. Wilmanski, K. 2008, Continuum Thermodynamics, Part I: Foundations,Wold Scientific, Singapore, ISBN 978-981-283-556-7

68. Yarushina, V.M. & Podladchikov, Y. Y. (2015), “(De)compaction of porous viscoelastoplastic media: Model formulation”, J. Geophys. Res. Solid Earth, pp. 120. doi:10.1002/2014JB011258

69. Yarushina, V.M., Bercovici, D., Oristaglio, M. L. 2013, “Rock deformation models and fluid leak-off in hydraulic fracturing”, Geophysical Journal International, Vol. 194, issue 3, pp. 1514-1526. doi: 10.1093/gji/ggt199

70. Youshinaka, R. & Yamabe, T. 1986, “Joint stiffness and the deformation behavior of discontinuous rock”, International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, Vol. 23(1), pp. 19–28.

71. Zienkiewicz, O.C., Taylor, R.L 2000, The finite element method, Solid mechanics. Butterworth-Heinemann: Oxford, United Kingdom, Vol. 2, pp. 479.

72. Zienkiewicz, O.C., Taylor, R.L 2000, The finite element method, The basis. Butterworth-Heinemann: Oxford, United Kingdom, Vol. 1, pp. 707.

73. Zingerman, K.M., Levin, V.A. 2009, “Pereraspredelenie konechnyh uprugih deformacii posle obrazovaniya vklyuchenij. Priblizhennoe analiticheskoe reshenie”, Prikladnaya matematika i mekhanika, Vol. 73, no 6., pp. 983-1001

74. Fidesys LLC official website http://www.cae-fidesys.com