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					     Computational Framework for
       Subsurface Energy and
     Environmental Modeling and
             Simulation
     Mary Fanett Wheeler, Sunil Thomas




           Center for Subsurface Modeling
Institute for Computation Engineering and Sciences
          The University of Texas at Austin
                    Acknowledge
   Collaborators:
    • Algorithms: UT-Austin (T. Arbogast, M. Balhoff, M.
       Delshad, E. Gildin, G. Pencheva, S. Thomas, T. Wildey): Pitt
       (I. Yotov); ConocoPhillips (H. Klie)

    • Parallel Computation: IBM (K. Jordan, A. Zekulin, J.
       Sexton); Rutgers (M. Parashar)

    • Closed Loop Optimization: NI (Igor Alvarado, Darren
       Schmidt)


   Support of Projects:         NSF, DOE, and Industrial
    Affiliates (Aramco, BP, Chevron, ConocoPhillips,
    ExxonMobil, IBM, KAUST)
                     Outline
   Introduction
   General Parallel Framework for Modeling Flow,
    Chemistry, and Mechanics (IPARS)
     • Solvers
     • Discretizations
     • Multiscale and Uncertainty Quantification
     • Closed Loop Optimization
   Formulations (IPARS-C02)
     • Compositional and Thermal
   Computational Results
     • Validation and Benchmark Problems
   Current and Future Work
 Societal Needs in Relation to Geological Systems

Resources Recovery
                                                    Site Restoration
• Petroleum and natural gas recovery from
                                                    • Aquifer remediation
           conventional/unconventional reservoirs
                                                    • Acid-rock drainage
• In situ mining
• Hot dry rock/enhanced geothermal systems
• Potable water supply
• Mining hydrology
 Waste Containment/Disposal
• Deep waste injection
• Nuclear waste disposal
• CO2 sequestration
• Cryogenic storage/petroleum/gas
Underground Construction
• Civil infrastructure
• Underground space
• Secure structures
                                      Highly Integrated
                         Multidisciplinary, Multiscale, Multiprocess

                                                                  Exploration
                                         Physics                  Characterization
     Exploration                       Mathematics   Geophysics   Diagnostics
                       Geological
   Characterization      Eng.
                        Geology                                          Earth Stresses
                                                                          Mechanical
  Fluid Flow                                                 Geomechanics Rock/Soil
    Waste                                                                  Behavior
   isolation
             GeoHydrology
                                                                             Hydrocarbon
                                                                  Petroleum Recovery
Construction                                                      Engineering Simulation
 Soil Mech.      Civil
Rock Mech.
              Engineering
Struct. Anal.

                                                             Geochemistry
  Mining Design/    Mining                                                 Waste isolation
   Stab, Waste,
                  Engineering                        Computer
 Land Reclamation                      Mechanical
                                       Engineering   Sciences
                      Drilling & Excav.,                      Code Development,
                      Support, Instruments                    Software Engineering
             Long Range Vision: Characterization
           And Management of Diverse Geosystems


                            Sensor Data
      Uncertainty           Management        Characterization
      Assessment                                & Imaging

3D Visualization                                   Sensor Placement
& Interpretation
                         Complex
                        Geosystem                        Optimization
   Data                 Management                       and Control
Management

  Geophysical                                        Multiscale
 Interpretation                                      Simulation

                    Petrophysical         Multiphysics
                    Interpretation        Simulation


    A Powerful Problem Solving Environment
         Framework Components
   High fidelity algorithms for treating relevant physics:
    • Locally Conservative discretizations (e.g. mixed finite element
      and DG)
    • Multiscale (spatial & temporal multiple scales)
    • Multiphysics (Darcy flow, biogeochemistry, geomechanics)
    • Complex Nonlinear Systems (coupled near hyperbolic &
      parabolic/ elliptic systems with possible discrete models)
    • Robust Efficient Physics-based Solvers (ESSENTIAL)
    • A Posteriori Error Estimators

   Closed loop optimization and parameter estimation
    • Parameter Estimoation (history matching) and uncertainty
      quantification

   Computationally intense:
    • Distributed computing
    • Dynamic steering
The Instrumented Oil Field




   Detect and track changes in data during production.
           Invert data for reservoir properties.
           Detect and track reservoir changes.

       Assimilate data & reservoir properties into
               the evolving reservoir model.
Use simulation and optimization to guide future production.
IPARS: Integrated Parallel and
 Accurate Reservoir Simulator
                 PHYSICS BASED SOLVERS
                              Fractures      K Tensor


              Heterogeneity                              Flow Regimes          Reinforced
                                                                                Learning
                                                                             Random Graph
           Multiple Physics          Physics             Well Operations        Theory
                                                                             Multiresolution
                                                                                Analysis
               Numerical                                                       Randomized
             representation                             Insights                Algorithms

           FDM                                                     AMG
     MFE                                                                     AML

CVM
                                                                                DD

DG                                                        Physics-based
       Discretization                                        Solvers                        HPC
                                      Numerical              Solvers
MPFA                                   Solution                               Krylov

 Mortar                                                                    LU/ILU
                      Why Multiscale?
   Subsurface properties vary on the
    scale of millimeters
   Computational grids can be refined
    to the scale of meters or
    kilometers
   Multiscale methods are designed to
    allow fine scale features to impact
    a coarse scale solution
    • Variational multiscale finite
       elements
        Hughes et al 1998
                                          Upscale
        Hou, Wu 1997

        Efendiev, Hou, Ginting et al
          2004
    • Mixed multiscale finite elements
        Arbogast 2002

        Aarnes 2004
    • Mortar multiscale finite elements
        Arbogast, Pencheva, Wheeler,
          Yotov 2004
        Yotov, Ganis 2008
Basic Idea of the Multiscale Mixed Mortar Method
Multiscale Mortar Mixed Finite Element Method
          Domain Decomposition and Multiscale
        Domain Decomposition                            Multiscale Approach
       For each stochastic realization,                For each stochastic realization,
         time step and linearization                     time step and linearization


Subdomain            Compute data for           Subdomain            Compute data for
  solves             interface problem            solves             interface problem


                                                  Multiple
    Apply             Precondition               subdomain
                                                                      Compute multiscale
   precond.               data                                       basis for coarse scale
                                                   solves

  Multiple
 subdomain
   solves                                     Multiple linear
                         Solve the            combinations
                                                                         Solve the
                     interface problem          of basis             interface problem
  Multiple
 precond.
applications

Subdomain            Solve local problems       Subdomain            Solve local problems
  solves             given interface values       solves             given interface values
Domain Decomposition and Multiscale
           Multiple                Compute the multiscale
       subdomain solves          basis for a training operator


                   For each stochastic realization,
                     time step and linearization


             Subdomain           Compute data for
               solves            interface problem


               Apply
              Multiscale         Precondition
              precond.               data

         Fixed number
     of subdomain solves
                                     Solve the
                                 interface problem
      Fixed number of
     multiscale precond.
         applications

             Subdomain           Solve local problems
               solves            given interface values
    Example: Uncertainty Quantification

   360x360 grid
   25 subdomains of equal size
   129,600 degrees of freedom
   Continuous quadratic
    mortars
   Karhunen-Loéve expansion
    of the permeability truncated      Mean Permeability
                                    Number of Interface Iterations
    at 9 terms
   Second order stochastic
    collocation
   512 realizations
   Training operator based on
    mean permeability



                                          Mean Pressure
                                        Interface Solver Time
    Example: IMPES for Two Phase Flow

   360x360 grid
   25 subdomains of equal
    size
   129,600 degrees of
    freedom
   Continuous quadratic
    mortars                      Absolute Permeability
                              Number of Interface Iterations
   50 implicit pressure
    solves
   100 explicit saturation
    time steps per pressure
    solve
   Training operator based
    on initial saturation

                                    Initial Solver Time
                                 Interface Saturation
Finite Element Oxbow Problem
FD & FEM Couplings: 3 Blocks with Fault
Solution
Continuous Measurement and Data
  Analysis for Reservoir Model
           Estimation




                       Source: E. Gildin, CSM, UT-Austin
  Continuous Measurement and Data
    Analysis for Reservoir Model
             Estimation
                      Optimization &                       Field
                       Supervisory                      Controller(s)
                         Control



IPARS                                                                               Reservoir
  Dynamic
    I/F
                                   Online Analysis
        Data Assimilation              (Data Fusion,   Data Acquisition
             (EnKF)                     Denoising,     (Sensors + DAQ)
                                       Resampling…)



                                                              Source: I. Alvarado and D. Schmidt, NI
Parameter Estimation Using SPSA
               Key Issues in C02 Storage
   What is the likelihood and magnitude of CO2 leakage and
    what are the environmental impacts?

   How effective are different CO2 trapping mechanisms?

   What physical, geochemical, and geomechanical
    processes are important for the next few centuries and
    how these processes impact the storage efficacy and
    security?

   What are the necessary models and modeling capabilities
    to assess the fate of injected CO2?
                                                                   drinking-water
                                                     groundwater       aquifer
   What are the computational needs and   capabilities to
                                                         flow
    address these issues?
                                                                    CO2 leakage
   How these tools can be made useful
                                                             deep brine aquifer
    and accessible to regulators and industry?
Global Experience in CO2 Injection




                      From Peter Cook, CO2CRC
CO2 Sequestration Modeling Approach
   Numerical simulation
     Characterization (fault, fractures)
     Appropriate gridding
     Compositional EOS
     Parallel computing capability
   Key processes
     CO2/brine mass transfer
     Multiphase flow
           During injection (pressure driven)
           After injection (gravity driven)
     Geochemical reactions
     Geomechanical modeling
                IPARS-COMP

                   Gridding

                   Parallel

                   Solvers

EOS Comp.        Geomechanics     Geochemical
                                   Reaction
                   Thermal
 2-P Flash
                                Graphics

Physical Prop
                     Numerics
       IPARS-COMP Flow Equations
Mass Balance Equation


         Ni                                 
                    .    i u   S Di i   qi
          t                                       

Pressure Equation




Solution Method
      Iteratively coupled until a volume balance convergence
       criterion is met or a maximum number of iterations
       exceeded.
   Thermal & Chemistry Equations
Energy Balance
  Solved using a time-split             MT T                             
   scheme (operator splitting)                     .    Cp u  T  T   q H
                                           t                               
  Higher-order Godunov for            Internal energy : MT
   advection                           MT  1    s Cvs    CvS
  Fully implicit/explicit in time and                          
   Mixed FEM in space for thermal
   conduction


Chemistry
  System of (non-linear) ODEs
  Solved using a higher order
   integration schemes such as
   Runge-Kutta methods
Coupled Flow-Thermal-Chemistry Algorithm
CO2 EOR Simulations
                         Validation

SPE5 -- A quarter of 5 spot benchmark WAG problem
3-phase, 6 components C1, C3, C6, C10, C15, C20


  IPARS-CO2 vs CMG-GEM
       Cum. oil produced                  Cum. gas
                                                       Inj




                                                Prod
                      Validation
CO2 pattern flood injection
3-phase, 10 components CO2, N2, C1, C3, C4, C5, C6, C15, C20


IPARS-CO2 vs CMG-GEM
        Cum. gas                                CO2 conc.


                Inj




                         Prod.
               Parallel Simulations

Modified SPE5 WAG injection
 Permeability from SPE10

 160x160x40 (1,024,000 cells)

 32, 64, 128, 256, 512 processors




Oil pressure and water saturation    Gas saturation and propane conc.
             @ 3 yrs                              @ 3 yrs
                                     Parallel Scalability
                                                 Hardware
                                      Lonestar: Linux    Blue GeneP: CNK
                                      cluster system     system, Linux I/O
                                      1,300 Nodes /      262,144 Nodes /
                                       5,200 cores       1,048,576 cores
                                      Processor Arch:     Processor Arch:
                                      2.66GHz, Dual          850MHz,
                                      core, Intel Xeon
                                      5100, Peak: 55     IBM CU-08, Peak:
                                         TFlops/s           ~1 PFlop/s
Texas Advanced Computing Center
 The University of Texas at Austin      8 GB/node           2 GB/node
                                          Network:          Network:
                                     InfiniBand, 1GB/s   10Gb Eth,1.7GB/s

                                                    Software
                                        GMRES, BCGS, LSOR, Multigrid.
                                        MPI: MVAPICH2 library for parallel
                                                communication
Scalability On Ranger (TACC) & Blue Gene P

     GMRES solver with Multigrid Preconditioner
     3500ft, 3500 ft, 100ft reservoir
     40x160x160=1,024,000 elements
     CPUs: 32, 64, 128, 256, 512, 1024

  Ranger (TACC)              Blue Gene P
CO2 Storage Benchmark Problems

A Benchmark-Study on Problems Related to CO2 Storage in
Geological formations, Summary and Discussion of the Results
   H. Class, A. Ebigbo, R. Helming et al., 2008
            Benchmark Problem 1.1
      CO2 Plume Evolution and Leakage via
               Abandoned Well

Objective
Quantification of leakage rate in    K = 20 md
deep aquifer @2840-3000 m


Output
1- Leakage rate = %CO2 mass
flux/injection rate                  =0.15
2- Max. leakage value
3- Leakage value at 1000 d
                                       P = 3.08x104 KPa
              Benchmark Problem 1.1
               Leakage Rate of CO2




CO2 BT: 10 days
Peak Leakage value: 0.23%
Final leakage value: 0.11%
Agrees with semi-analytic
solution (Nordbotten et al.)
Comparison with Published Results
           at 80 days
     IPARS-COMP      Ebigbo et al., 2007

   Gas Saturation




    Pressure
Frio Brine CO2 Injection Pilot




                Bureau of Economic Geology
                Jackson School Of Geosciences
                The University of Texas at Austin
                Funded by DOE NETL
                     Frio Brine Pilot Site
                    Injection interval: 24-m-thick,
                     mineralogically complex fluvial
                     sandstone, porosity 24%,
                     Permeability 2.5 D
                    Unusually homogeneous
                    Steeply dipping 16 degrees
                    7m perforated zone
                    Seals  numerous thick shales,
                     small fault block
   Injection        Depth 1,500 m
                    Brine-rock, no hydrocarbons
   interval         150 bar, 53 C, supercritical CO2


Oil production

                                  From Ian Duncan
                Frio Modeling Effort
   Stair stepped approximation on a 50x100x100 grid (~70,000
    active elements) has been generated from the given data.
    Figure shows porosity in the given and approximated data.
                    Solution profiles
   Pressure and close-up of top-view of gas (CO2) saturation at t=33
    days. Simulations on bevo2 cluster at CSM, ICES on 24
    processors.
               CO2 Plume Transport
   CO2 saturation as seen below the shale barrier at t=2 and 33 days.
    Breakthrough time is observed to be close to 2 days.
   Current Research Activities at CSM
Model CO2 injection either in deep saline aquifers or
depleted oil and gas reservoirs using compositional
and parallel reservoir simulator (IPARS-CO2)
   Large scale parallel computing
   Efficiency with different solvers
   Couple IPARS-CO2 with geochemistry
   Couple IPARS with geomechanics
   Enhance EOS model and physical property
     models (effect of salt, hysteresis, etc)
   Data sources, field sites, practical applications
     (in collaboration with Duncan from BEG at UT)
   Gridding and a posteriori error estimators
   Optimization
   Risk and uncertainty analysis

				
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