Slide 1

Some problems of computational geophysicsYu.M. Laevsky, B.G. Mikhaylenko, G.V. ReshetovaInstitute of Computational Mathematics and Mathematical Geophysics SB RASV.A. TcheverdaInstitute of Petroleum Geology and Geophysics SB RAS Moscow 2013(simulation of oil exploration and production)

11Outline:1. Preliminaries and motivation 2. Oil exploration: seismic waves propagation in multiscale media3. Oil production: filtration of two-phase fluid in inhomogeneous media 4. Parallel implementation5. Outlook223

1. Preliminaries and motivation Fracture corridors41. Preliminaries and motivation Fracture corridors

Samples from cavernous/fractured reservoirs1. Preliminaries and motivation

Subvertical fractures(main streamlines)Caverns along the fractures (reservoir capacitive properties) Impermeable rock matrix5

Fracture corridors1. Preliminaries and motivation 6

FC fracture corridorsBFC bed controlled fractureMBF multibed fracturesHPF highly persistent fractures

7Fractures variety of carbonate collectors (J.-P.Petit, L.Bazalgette Fracture corridors: What they are?)1. Preliminaries and motivation 81. Preliminaries and motivation Scattered waves are one of the main indicator in seismic exploration of fractured structure of oil reservoir

Scattered waves1/2l1/4l1/8lOne needs to take into accountmacro- and microheterogeneities!Solution:usage a coarse mesh for smooth background, and a fine mesh for the microscale description 1. Preliminaries and motivation

Fractured/porous media two-porous homogenization FracturesPorous blocks9Injection wellProduction wellOilWaterOil production

1. Preliminaries and motivation 10 . . . - 20-30 . 500-4000 . , , - . .

: , . - . . , .

- . . , , , . , .

: , , , , . 102.1. Mathematical model 2.2. Numerical algorithm2.3. Seismic waves propagation 2. Oil exploration: seismic waves propagation in multiscale media112.1. Mathematical model 12

Fluid (oil): stress tensor Skeleton (carbonate): velocity

2.2. Numerical algorithm13Main requirements: The algorithm must take 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 implementation2.2. Numerical algorithm14

spacetimeSimultaneous time-space refinementDisplacement Stress2.3. Seismic waves propagation 15

Microscale (scattered waves) within realistic environment

2.3. Seismic waves propagation 16

Vp in XZ plane at Y=1100m Vp in YZ plane at X=1100m 2.3. Seismic waves propagation 17

Vp in XY plane at Z=1650m 2.3. Seismic waves propagation 18

Azimuthal distribution of scattered energy3. Oil production: filtration of two-phase fluid in inhomogeneous media 3.1. Mathematical models3.2. Numerical algorithms3.3. 2D examples3.4. 3D examples3.5. Fractured/porous media examples 193.1. Mathematical models202-velocity 2-pase model filtration of incompressible fluid (Masket-Leverett model):

conservation law (separately in fractures and porous blocks)

Darcy law

capillary pressure;

partial pressure;

mass exchange;3.2. Numerical algorithms21

Spatial approximation: MFEM3.2. Numerical algorithms22

.

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

5-point location3.3. 2D examples23 . . 10^-3 m2/c. . .

. , . .

, , .23

7-point location3.3. 2D examples24 . . 10^-3 m2/c. . .

. , . .

, , .24

9-point location3.3. 2D examples25 . . 10^-3 m2/c. . .

. , . .

, , .25

9-point location(5+4)-point location3.3. 2D examplesControl of wells: oil recovery optimization 263.4. 3D examples27

Water saturation near production wells at different porosity28

Fractures with small porosity Fractures with increased permeability3.5. Fractured/porous media examples4. Parallel implementation 4.1. Parallelization for the problem of seismic waves propagation4.2. Parallelization for the problem of two-phase filtration294.1. Parallelization for the problem of seismic waves propagation

Domain Decomposition (separately for the coarse and fine meshes) 304.1. Parallelization for the problem of seismic waves propagationDimensional Domain Decomposition

3D2D 1DModel volume31

4.1. Parallelization for the problem of seismic waves propagationTheoretical acceleration via DD1D2D 3D32

4.2. Parallelization for the problem of two-phase filtrationDistribution of memory33

.

. , . , . , -, .

: , - : 3.

: - , , .. .334.2. Parallelization for the problem of two-phase filtration

2D 3D 345. Outlook 35Implementation of the approach for elastic media with attenuation and anisotropyJoint simulation of oil exploration and production with taking into account movement of oil-water interface Further development of the software and access to petaflops massive computing with the assessment of the performance of exaflops computer systems

At the moment, the grant for 32 million cores-hours in HRLS is received from the Partnership for Advanced Computing in EuropeHRLS: Hermit Cray XE6, University of Stuttgart, No. 26 in Top 500 November 2012Acknowledgments

Russian Foundation for Basic Research:12-05-00943 13-01-00019 13-05-12051 36

Partnership for Advanced Computing in Europe !Thank you for attention!Q & A37