The DuMux Simulation Software and - uni-stuttgart.de · Simulation Software and its Applicability...
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Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The DuMux Simulation Software and its Applicability to CO2 Reservoir
Simulation
Bernd FlemischHolger Class, Melanie Darcis, Rainer Helmig,
Johannes Hommel, Alexander Kissinger, Lena Walter
PANACEA – Third consortium meetingParis, September 17, 2013
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Requirements on Modelling Tools for CO2 Storage
• hydraulic• compositional• thermal• geomechanical• geochemical
Complex processes: Different time scales:
Different length scales
Sco2 [-]
Δp [bar]
F. Schäfer & L. Walter, 2011
IPCC, 2007
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Outline
MotivationOverview of DuMux
ApplicationsSetting up an application
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
DuMux: DUNE for Multi-{Phase, Component, Scale, Physics, ...} Flow and Transport in Porous Media
Goals and Features• Sustainable and consistent framework for the implementation and
application of model concepts and constitutive relations• Free and open source• Modular structure
Developed by more than 15 PhD students and post docs at LH2• 1/2007: development starts• 17/1/2013: SVN revision 10,000• More than 500 “real'' release downloads dumux.org
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Some Example Applications
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Modular Design of DuMux
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
DUNE: Distributed and Unified Numerics Environment
• Developed by groups in Heidelberg (P. Bastian), Freiburg (D. Kröner), Aachen (O. Sander), Boulder (R. Klöfkorn), Münster (M. Ohlberger), Warwick (A. Dedner)
• Separation of data structures and algorithms by abstract interfaces• Efficient implementation using generic programming techniques• Reuse of existing FE packages with a large body of functionality• Current stable release: 2.2 (June 2012)
Core Modules• dune-common: basic classes• dune-geometry: geometrical entities• dune-grid: abstract grid/mesh interface• dune-istl: iterative solver template library• dune-localfunctions: finite element shape functions
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
DUNE: Distributed and Unified Numerics Environment
dune-istl: iterative solver template library
Direct solvers:
– SuperLU– Pardiso
Iterative solvers:
– BiCGSTAB– AMG– and many more see dune-project.org
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Modular Design of DuMux
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Available Models
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Mass balances for brine and CO2 component:
Optional: energy balance:
Primary variables:
We assume local mechanical, thermal and chemical equilibrium
Mathematical Model co2 and co2ni
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Modular Design of DuMux
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Numerical scheme for fully implicit models
Temporal discretization:Fully implicit backward Euler method
Spatial discretization:BOX method – node centred finite volume method on a finite
element grid (Helmig, 1997)Applicable for structured and unstructured grids (tetrahedron)Requires conforming grid
Cell centred finite volume methodApplicable for structured gridCurrently requires conforming grid
Solution method for non-linear PDEs:Newton Raphson method
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Modular Design of DuMux
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Simulation Control
For the fully-implicit models, the time-step size is based on the number of Newton iterations
Maximum time-step size can be set
Definition of episodes is possible
Choice of different direct and iterative linear solvers
Default settings for linear and non-linear solver can be changed at the application level
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Modular Design of DuMux
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
Application
SpatialParameterse.g. Porosity, permeability etc
Comp1
Model Concept
Constraint SolverCalculates phase composition
…
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Material System
Application Model Concept
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Fluid System
Interface for the constitutive relationships for a mixture of components
TwoPImmiscible
H2OAir
BrineCO2
H2OAirMesitylene
Spe5: gas, oil and water phase with seven components water, Methane(C1), Propane (C3), Pentane (C5), Heptane (C7), Decane (C10), Pentadecane (C15) and Icosane (C20)
Selected Available Implementations
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The CO2 – Brine Fluid System
Binary diffusion: diffusion of water in the CO2 phaseBin Xu et al., Diffusion of Water in Liquid and Supercritical Carbon DioxideNMR Study, 2002
Phase composition: depending on temperature and pressureSpycher and Pruess 2005, Duan and Sun 2003, Spycher, Pruess and Ennis-King 2003
Phase density, viscosity, … depending on temperature, pressure, and phase composition called from the components.
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Material System
Application Model Concept
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Component
Thermodynamic relations of a single chemical species or a fixed mixture of speciesProvide a convenient way to access these quantities from fluid systems Not supposed to be used by models directly
H20
Brine
CO2
Air, CH4, DNAPL, H2, LNAPL, Mesitylene, N2, O2, Xylene
Selected Available Implementations
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Component CO2
Vapor pressure depending on temperature, density and enthalpydepending on temperature and pressureR. Span and W. Wagner, 1996
Viscosity depending on temperature and pressureVesovic et al. 1990, and Fenhour et al. 1998.
Density, enthalpy and viscosity can be calculated for the gaseous, liquid and supercritical state of CO2 but the phase change across the vapor pressure line is not accounted forNegligence mobility issues in the three phase zone
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Component Brine
Based on a component H2O: different choices possible, most accurate IAPWS: Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam
Globally fixed salinity value, to be chosen dependend on the problem
Liquid density and viscosity depending on temperature and pressureBatzle and Wang 1992, cited by: Adams and Bachu in Geofluids, 2002
Liquid enthalpy depending on temperature and pressurePalliser and McKibbin 1997, Michaelides 1981, Daubert and Danner 1989
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Material System
Application Model Concept
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Constraint Solver
Calculates the phase composition
Connects the thermodynamic relations expressed by fluid systems with the thermodynamic quantities stored by fluid states
Takes all component fugacities, the temperature and pressure of a phase as input and calculates the phase composition. Thermodynamic constraints are:
Fugacity/activity coefficients for the CO2/Brine system calculated according to Spycher and Pruess 2005
Selected Available Implementations
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Material System
Application Model Concept
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Fluid State
Stores the complete thermodynamic configuration of a system at a given spatial and temporal position.
Provides access methods to all thermodynamic quantities
CompositionalFluidState: assumes thermodynamic equilibrium, only a single temperature needs to be stored
Selected Available Implementations
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Material System
Application Model Concept
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Fluid-Matrix Interaction
Parameters that depend on fluid properties and the porous medium, i.e. capillarity and relative permeability, heat conductivity
Through modular adapters, regularization schemes can be imposed for extreme values
Uses a set of parameters of type MaterialLawParams, which may depend on the location inside the domain
LinearMaterial
VanGenuchten
BrooksCorey
Selected Available Implementations
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Material System
Fluid SystemInterface for components
Fluid StateContainer for primary and secondary variables
Compn
Fluid – Matrix interactionsRelative perm., cap. Pressure etc.
SpatialParameterse.g. Porosity, permeability etc
Comp1
Constraint SolverCalculates phase composition
…
Material System
Application Model Concept
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
The Material System: Spatial Parameters
Collects all parameters that may vary depending on the location within the porous medium
Local assignment of intrinsic properties like porosity, permeability, heat capacity, or material law parameters
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Outline
MotivationOverview of DuMux
ApplicationsSetting up an application
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Problem Oriented Benchmarks
1. Injection into saline formations including well leakage andlarge-scale computation in a heterogeneous formationNordbotten et al., 2005, Class et al., 2009
2. 3D, reservoir-scale problemsClass et al., 2009
3. Long term problem: furthest updip extent of CO2 plumeNordbotten et al., 2012
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Problem 1
Leakage scenario as described in J.M. Nordbotten et al., 2005
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Problem 1: Comparison
Results of Simulator comparison, given in Class et al., 2009
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Problem 3: Setup Johansen Formation
• Injection of CO2at 15 kg/s for 25 years
• Total simulation time: 50 years
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Problem 3: Solution Snapshot
Plume shape after 50 years as given in Class et al., 2009
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Geomechanics and CO2 storage
Vertical displacement rate of the term from 2004/7/31 to 2008/5/31 due to CO2 injection at In Salah, Algeria (Onuma and Ohkawa, Energy Procedia, 2008).
CO2 injection causes large overpressures resulting in: • deformations of rock matrix• change of effectiveparameters (porosity,permeability)
• feedback on pressurebuild-up
• enlargement of faults,generation of fractures
Need for geomechanicalmodel
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
First Application Example: Wagrien Formation
Subdomain of linear-elastic, fully coupled geomechanicalmodel includes over- and underburden
Outer subdomainrepresenting hydraulic model is restricted to reservoir layer
15 km
3 km
Injection rate: 1 Mt/yVertical extent inner subdomain: 1 kmVertical extent reservoir: 30 m
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Results: Application Example
Results after 1.5 years of CO2 injection, shown are vertical cuts through the injection well:
CO2 saturationdisribution
Pressuredisribution
Changes in effective stress σzz Solid displacement uy
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Outline
MotivationOverview of DuMux
ApplicationsSetting up an application
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an application: Prerequisites
Download Dumux from dumux.org or use svn repositories
Dumux has been successfully installed on different Linux distributions (SUSE, Ubuntu) and on Mac
Detailed installation instructions as well as the required packages for Dune and Dumux are given in the handbook (download from dumux.org)
Subscribe to the Dumux mailing list to post messages to the community
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an application: Prerequisites
Some basic knowledge of the Linux command line is required
C++ knowledge is indispensable
Get to know the handbook
Perform the tutorial given in the handbook
Each model has a test application, get to know the ones relevant for your problem
They can be modified to fit for your purpose, do not start from scratch!
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an Application
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an Application
The most important files in your application folder are:
yourproblem.hh
– Choose the model you use– Choose the FluidSystem and components– Set global properties (e.g. gravity, Newton thresholds,
2d/3d, linear solver to use, etc.)– Set initial and boundary conditions– Set output file frequency– etc.
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an Application
yourspatialparameters.hh
– Set the spatial distribution of permeability and porosity– For multi-phase flow set fluid-matrix interaction relationship
like Van Genuchten or Brooks and Corey relationship
yourparameterfile.input
– Set run-time parameters like start and end time, the grid file to use, the name of your output files
– You can make most parameters used in yourproblem.hhor in yourspatialparameters.hh into a run-time parameter
– Advantage: changing run-time parameters does not require recompilation of your problem!
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Setting up an Application
yourgrid.dgf
– Grids for Dumux require the DUNE Grid Format (*.dgf), see dune-project.org
– For simple grids (structured) the cubegridcreator.hh or simplexgridcreator.hh can be used which do not require an extra grid file (see tutorial)
– For complex geological models node- or element-specific parameters can be imported from the dgf gridfile
– Cornerpoint grids can be imported but they require the installation of additional modules and without manual effort they will fail if the grid is non-conforming
No “easy” interface, best to convert grid into dgf format
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Output
Output files are binary or Ascii in the *.vtu format
vtu-files can be visualised using Paraview, see http://www.paraview.org/
Number of output files and parameters therein can be specified in yourproblemfile.hh or yourinputfile.input
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
Thank youfor your attention!
dumux.org
Universität Stuttgart Department of Hydromechanics and Modelling of Hydrosystems
References
Baber, K., Mosthaf, K., Flemsich, B., Helmig, R., Müthing, Wohlmuth, B.I., 2011, Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow. Accepted in IMA Juarnal of Applied Mathematics.
M. Batzle and Z. Wang. Seismic properties of pore fluids. Geophysics, 57(11):1396–1408, 1992.Class, H., Ebigbo, A., Helmig, R., Dahle, H.K., Nordbotten, J.M., Celia, M.A., Audigane, P.,
Darcis, M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S.E., Jin, M., Krug, S., Labregere, D., Naderi Beni, A., Pawar, R.J., Sbai, A., Thomas, S.G., Trenty, L. and L. Wie: A benchmarkstudy on problems related to CO2 storage in geologic formations: Summary and discussion of theresults. Computational Geosciences 13,4 (2009) 409-434.
A. Fenghour, W. A. Wakeham, and V. Vesovic. The viscosity of carbon dioxide. Journal of Physical and Chemical Reference Data Reprints , 27:31–44, 1998.
B. Flemisch, M. Darcis, K. Erbertseder, B. Faigle, A. Lauser K. Mosthaf, S. Müthing, P. Nuske, A. Tatomir, M. Wolf, and R. Helmig. Dumux: Dune for multi-phase, component, scale, physics,... flow and transport in porous media. Advances in Water Resources, 2010.
R. Span and W. Wagner: A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple‐Point Temperature to 1100 K at Pressures up to 800 MPa. Journal of Physical and Chemical Reference Data, 25 (6), pp. 1509-1596, 1996.
N. Spycher and K. Pruess. Co2-h2o mixtures in the geological sequestration of co2. ii. partitioning in chloride brines at 12-100c and up to 600 bar. Geochimica et Cosmochimica Acta, 69(13):3309 –3320, 2005
B. Xu, K. Nagashima, J.M. DeSimone, and C.S. Johnson Jr. Diffusion of water in liquid and supercritical carbon dioxide: An nmr study. The Journal of Physical Chemistry A, 107(1):1–3, 2003