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