Some problems of computational geophysics

1. Some problems of computational geophysics (simulation of oil exploration and production) Yu.M. Laevsky, B.G. Mikhaylenko, G.V. Reshetova Institute of Computational Mathematics and Mathematical Geophysics SB RAS V.A. Tcheverda Institute of Petroleum Geology and Geophysics SB RAS Moscow 2013

2. Outline: 1. Preliminaries and motivation 2. Oil exploration: seismic waves propagation in multiscale media 3. Oil production: filtration of two-phase fluid in inhomogeneous media 4. Parallel implementation 5. Outlook

3. 1. Preliminaries and motivation Fracture corridors

4. 1. Preliminaries and motivation Fracture corridors

5. 1. Preliminaries and motivation Samples from cavernous/fractured reservoirs Subvertical fractures (main streamlines) Caverns along the fractures (reservoir capacitive properties) Impermeable rock matrix

6. 1. Preliminaries and motivation Fracture corridors

7. 1. Preliminaries and motivation Fractures variety of carbonate collectors (J.-P.Petit, L.Bazalgette “Fracture corridors: What they are?”) FC – fracture corridors BFC – bed controlledfracture MBF – multibed fractures HPF – highly persistent fractures

8. 1/2l Scattered waves 1/4l 1/8l 1. Preliminaries and motivation Scattered waves are one of the main indicator in seismic exploration of fractured structure of oil reservoir One needs to take into account macro- and microheterogeneities! Solution: usage a coarse mesh for smooth background, and a fine mesh for the microscale description

9. 1. Preliminaries and motivation Fractured/porous media two-porous homogenization Fractures Porous blocks

10. 1. Preliminaries and motivation Oil production Injection well Production well Oil Water

11. 2. Oil exploration: seismic waves propagation in multiscale media 2.1. Mathematical model 2.2. Numerical algorithm 2.3. Seismic waves propagation

12. 2.1. Mathematical model – velocity – stress tensor Skeleton (carbonate): Fluid (oil):

13. 2.2. Numerical algorithm Main requirements: • The algorithm musttake into account macro- and microheterogeneities to describe the scattered waves • Algorithmic artificial reflections must be small in comparison with the scattered waves • The algorithm must have feasibility of parallel implementation

14. time space 2.2. Numerical algorithm Simultaneous time-space refinement Displacement Stress

15. 2.3. Seismic waves propagation Microscale (scattered waves) within realistic environment

16. 2.3. Seismic waves propagation Vpin XZ plane at Y=1100m Vpin YZ plane at X=1100m

17. 2.3. Seismic waves propagation Vpin XY plane at Z=1650m

18. 2.3. Seismic waves propagation Azimuthal distribution of scattered energy

19. 3. Oil production: filtration of two-phase fluid in inhomogeneous media 3.1. Mathematical models 3.2. Numerical algorithms 3.3. 2D examples 3.4. 3D examples 3.5. Fractured/porous media examples

20. 3.1. Mathematical models 2-velocity 2-pase model filtration of incompressible fluid (Masket-Leverett model): conservation law (separately in fractures and porous blocks) Darcy law – partial pressure; – capillary pressure; – mass exchange;

21. 3.2. Numerical algorithms Spatial approximation: MFEM

22. 3.2. Numerical algorithms Integration in time: IMPES-like algorithm 2nd order of accuracy predictor-corrector with only one calculation of r.h.s. in time step ……………………….

23. 3.3. 2D examples 5-point location

24. 3.3. 2D examples 7-point location

25. 3.3. 2D examples 9-point location

26. 3.3. 2D examples Control of wells: oil recovery optimization 9-point location (5+4)-point location

27. 3.4. 3D examples Water saturation near production wells at different porosity

28. 3.5. Fractured/porous media examples Fractures with small porosity Fractures with increased permeability

29. 4. Parallel implementation 4.1. Parallelization for the problem of seismic waves propagation 4.2. Parallelization for the problem of two-phase filtration

30. 4.1. Parallelization for the problem of seismic waves propagation Domain Decomposition (separately for the coarse and fine meshes)

31. 4.1. Parallelization for the problem of seismic waves propagation “Dimensional” Domain Decomposition 1D 2D Model volume 3D

32. 4.1. Parallelization for the problem of seismic waves propagation Theoretical acceleration via DD 3D 2D 1D

33. 4.2. Parallelization for the problem of two-phase filtration Distribution of memory

34. 4.2. Parallelization for the problem of two-phase filtration 2D 3D

35. 5. Outlook • Implementation of the approach for elastic media with attenuation and anisotropy • Joint simulation of oil exploration and production with taking into account movement of oil-water interface • Further development of the software and access to petaflopsmassive computing with the assessment of the performance of exaflopscomputer systems At the moment, the grant for 32 million cores-hours in HRLSis received from the Partnership for Advanced Computing in Europe HRLS: Hermit Cray XE6, University of Stuttgart, No. 26 inTop 500 November 2012

36. Acknowledgments Russian Foundation for Basic Research: 12-05-0094313-01-00019 13-05-12051 Partnership for Advanced Computing in Europe

37. Thank you for attention! 感 谢 您 的 关 注！ Спасибо за внимание! Q & A