The Matlab Reservoir Simulation Toolbox (MRST)

The Matlab Reservoir Simulation Toolbox (MRST)
Knut–Andreas Lie, SINTEF, Oslo, Norway
Edinburgh, 8th January 2014
Overview of lectures
Lectures today:
1
Overview of MRST (this talk)
2
Getting started
3
Grids and petrophysical properties
4
Discretization on polyhedral grids
5
Fully implicit simulators using automatic differentiation
On Friday:
Fast simulation of large-scale CO2 storage: spill-point analysis
and vertical-equilibrium models
1 / 21
The MATLAB Reservoir Simulation Toolbox (MRST)
Open-source framework for rapid prototyping of new models and computational
methods written in Matlab:
I
grid structure and grid factory routines
I
petrophysical data and incompressible fluid models
I
physical units and conversion routines between SI
and common field units
I
routines for setting and manipulating boundary
conditions, sources/sinks, and well models
I
reservoir state (pressure, fluxes, saturations,. . . )
I
visualisation routines for cell and face data
Light weight/
special purpose
Black box/
general purpose
physical/computational complexity
2 / 21
Why in MATLAB?
Prototyping in a scripting language is much less time-consuming than in
traditional compiled languages (C, C++, Fortran, . . . )
Explore alternative algorithms/implementations close to mathematics
Gradually replace individual (or bottleneck) operations with
accelerated editions callable from Matlab
Direct access to Matlab environment and prototype whilst developing
replacement components
More experienced in Matlab/Octave than in e.g., Python
If we were to start all over, we would probably have chosen Phyton
3 / 21
Why free and open source?
Research strategy:
Support reproducible research and promote replicability
Preserve know-how and simplify reuse of results from previous research
Accelerate relevant research by students and our peers
Benchmarking: simplify comparison of different methods on standard test
problems
Marked strategy:
Accelerate time-to-market for new technology
Combined with publications: an efficient means to disseminate results
while protecting IP rights
In addition: research funded by the Research Council of Norway should be
freely available
4 / 21
Two open-source initiatives
Open Porous Media Initiative
Matlab Reservoir Simulation Toolbox
Initiated by Statoil Research Center
Developed by SINTEF ICT for rapid prototyping
Academic partners in Norway and Germany
Add-on modules by others . . .
Developed mainly in C++
MRST 2013a: 1000+ downloads since Apr 18th
So far: special-purpose tools mostly
MRST 2013b: 360+ downloads since Oct 18th
General-purpose functionality in progress
Industry use increasing
http://www.opm-project.org
http://www.sintef.no/MRST
5 / 21
How is MRST designed?
6 / 21
Grids and petrophysical properties
The fundamental object in MRST is the grid:
All grids are assumed to be unstructured
Data structure for geometry and topology
Several grid factory routines
Input of industry-standard formats
Physical quantities defined as dynamic objects in Matlab:
Properties of medium: φ, K, net-to-gross, . . .
Reservoir fluids: ρ, µ, kr , PVT, . . .
Driving forces: wells, boundary conditions, sources
Reservoir state: pressure, fluxes, saturations, . . .
MRST operations accept, manipulate, and produce these objects
Physical quantities are assumed to be in SI units (e.g., [K] = m2 ,
[µ] = Pa · s, . . . ).
7 / 21
Modules in MRST
8 / 21
Modules: mimetic and MPFA methods
Consistent discretization methods capable of handling
general polyhedral grids
TPFA
MFD
MPFA
Example: anisotropy ratio 1 : 1000, π/6 angle with grid directions
→ TPFA: montone, but qualitatively incorrect
→ mimetic/MPFA: nonmonotone, but qualitatively correct.
9 / 21
Modules: C-acceleration via mex interface
Sequential solvers:
Geometry calculation: threaded implementation in C
Pressure: TPFA method in Matlab
with AGMG linear solver
120
Transport: reorder method in C, cellwise solver with local control over iterations
Transmissibility
Solver
Transport
TOF
Geometry
100
Time-of-flight: mldivide in Matlab
seconds
80
60
Computer
Dell Precision T5500
40
24 GiB memory, DIMM DDR3 1333 MHz
20
Intel Xeon X5690 @ 3.47 GHz, 6 cores
Cache: 384 KiB (L1), 1536 KiB (L2), 12
MiB (L3)
0
0
2
4
6
8
10
Million cells
12
14
16
18
Example: Cartesian grid, heavy-oil fluid model, two
saturation regions
10 / 21
Modules: fully-implicit simulators
New feature in 2012b release:
I
fully implicit method as in commercial
simulators
I
reads industry standard input decks
I
based on automatic differentiation
I
calculation of adjoints is greatly simplified
I
easy to extend to new models – you
basically write the equations!
I
POD methods supported
SPE1 benchmark
11 / 21
Modules: interactive visualization
Features:
Script-based visualization in core
Visualization GUI in separate module
plotGrid / plotCellData
time steps and complex data sets
plotFaces / plotFaceData
dynamic histogram filtering
plotWell / plotFaults
filtering and logical indices
...
geometric slicing
12 / 21
Modules: interactive visualization
Features:
Script-based visualization in core
Visualization GUI in separate module
plotGrid / plotCellData
time steps and complex data sets
plotFaces / plotFaceData
dynamic histogram filtering
plotWell / plotFaults
filtering and logical indices
...
geometric slicing
12 / 21
Modules: interactive visualization
Features:
Script-based visualization in core
Visualization GUI in separate module
plotGrid / plotCellData
time steps and complex data sets
plotFaces / plotFaceData
dynamic histogram filtering
plotWell / plotFaults
filtering and logical indices
...
geometric slicing
12 / 21
Modules: flow diagnostics
Numerical methods for probing the
reservoir:
I time-of-flight (time lines in reservoir)
I
I
Volumes per well pair
tracer-partitions: drainage regions,
swept regions, well-pair connections,
well allocation factors, . . .
heterogeneity measures:
flow-capacity/storage-capacity, sweep
efficiency, Lorenz coefficient, . . .
1%
20%
29%
I1, P1
I2, P1
1%
I1, P2
I2, P2
I1, P3
I2, P3
I1, P4
I2, P4
6%
19%
10%
13%
13 / 21
Modules: flow diagnostics
Numerical methods for probing the
reservoir:
I time-of-flight (time lines in reservoir)
I
I
tracer-partitions: drainage regions,
swept regions, well-pair connections,
well allocation factors, . . .
heterogeneity measures:
flow-capacity/storage-capacity, sweep
efficiency, Lorenz coefficient, . . .
Allocation factors
I1
I2
50
50
40
40
30
30
20
20
P1
P1
P2
10
P2
10
P3
P3
P4
0
0.5
P4
1
0
P1
0.5
1
P2
50
50
40
40
30
30
20
20
I1
I1
10
10
I2
0
0.5
I2
1
0
P3
0.5
1
P4
50
50
40
40
30
30
20
20
I1
I1
10
10
I2
0
0.5
I2
1
0
0.5
1
13 / 21
Modules: flow diagnostics
Numerical methods for probing the
reservoir:
I time-of-flight (time lines in reservoir)
I
tracer-partitions: drainage regions,
swept regions, well-pair connections,
well allocation factors, . . .
I
heterogeneity measures:
flow-capacity/storage-capacity, sweep
efficiency, Lorenz coefficient, . . .
Quality of upscaling methods
13 / 21
Modules: coarsening by amalgamation
Adapting to flow
Different partitioning
Dynamic coarsening
Adapting to geology
14 / 21
Modules: upscaling
Several upscaling methods:
Analytical methods: geometric,
harmonic, arithmetic
Flow-based single-phase upscaling
Steady-state upscaling
capillary limit
viscous limit
general steady-state
In-house: various experimental
15 / 21
Modules: multiscale methods
Conservative fine-scale approximation at the cost of solving a coarse-scale
problem (upscaling and downscaling in one step)
Key idea of multiscale methods
Local decomposition
Multiscale basis functions:
p = Φpc + p̃
v = Ψvc + ṽ
homogeneous (RT0 )
heterogeneous
16 / 21
Modules: multiscale methods
Multiscale mixed FEM:
Multiscale finite-volume:
Very flexible wrt fine/coarse grids
Well developed wrt flow physics
Automated coarsening demonstrated
for structured and unstructured grids
Primal/dual makes coarsening
challenging
Mixed formulation complicates
physics
Prototype of coarsening algorithms
demonstrated
16 / 21
Modules: numerical CO2 laboratory
Example: structural trapping in the Johansen formation (model from CO2 atlas)
Features:
scripts to download and process public
data
CO2 atlas
Sleipner, Johansen
IGEMS, ..
simulation of basic trapping mechanisms
structural
residual
solubility
with detailed volumetric inventory
interactive visualization of traps and spill
point paths
vertical-equilibrium simulation
3D simulations
17 / 21
Modules: numerical CO2 laboratory
Example: migration in the uppermost geological layer of Sleipner (model from ieaghg.org)
Features:
scripts to download and process public
data
CO2 atlas
Sleipner, Johansen
IGEMS, ..
simulation of basic trapping mechanisms
structural
residual
solubility
with detailed volumetric inventory
interactive visualization of traps and spill
point paths
vertical-equilibrium simulation
3D simulations
17 / 21
Simple access to public data sets
Simplified access to open data sets is one of our goals with MRST. To
this end, we offer a large number of scripts and utility routines, including
support of Eclipse input decks.
SPE10
SAIGUP
Johansen
Model 2 from the 10th SPE Comparative
Solution Project
Realistic model of shallow-marine clastic
reservoir
Real models of North Sea aquifer, candidate for large-scale CO2 sequestration
60 × 220 × 85 Cartesian
40 × 120 × 20 corner-point model
149 × 189 × 16 corner-point
Strongly heterogeneous
Faults, erosions, inactive cells, . . .
100 × 100 × n for n = 11, 16, 21
http://www.spe.org/web/csp/
http://www.sintef.no/MRST
http://www.sintef.no/MatMorA/
18 / 21
Simple access to public data sets
SPE1
SPE9
The ’Egg’ model
10 × 10 × 10 Cartesian
9000 cell corner-point, 26 wells
Benchmark by TU Delft
Three-phase, gas injection
Three-phase black oil
Compare with Eclipse, GPRS, MoReS
CO2 atlas: surfaces
CO2 Storage Atlas: Norwegian North Sea
depth and thickness maps
CO2 atlas: sand volumes
14 volumetric models reconstructed from
the CO2 atlas
IGEMS
15 structural/stratigraphic scenarios
14 × 100 surface realizations
19 / 21
Third-party modules
Ensemble Kalman Filter (EnKF)
Discrete Fracture Matrix (DFM)
Developed by Olwijn Leeuwenburgh (TNO).
Includes:
Developed by Eirik Keilegavlen and Tor Harald
Sandve (University of Bergen) Includes:
EnKF and EnRML schemes,
triangularization routines
localization, inflation, asynchronous data,
TPFA discretization
production and seismic (saturation) data
MPFA-O discretization
conventional and structural parameters
Implicit/explicit transport solvers
We also know of other developments (e.g., exponential integrators from Heriot–Watt,
a geothermal module from Univ. Bergen, etc).
New contributions are most welcome!
20 / 21
Examples of in-house prototypes
Multiscale TPFA
Implicit higher-order
Best properties of MsMFE and MsFV
Here: viscous fingering in moving reference
frame. Comparison of fully implicit single-point
upwind and ’TVD type’ schemes
Thermal effects
Geochemistry
Experimental, 3D unstructured
Experimental, 3D unstructured
21 / 21