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Evaluating Long Term CO 2 Storage in Saline Aquifers Mary Fanett Wheeler Center for Subsurface Modeling The University of Texas at Austin

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Acknowledge Collaborators: Algorithms: UT-Austin ( B. Ganis, G. Pencheva, G.. Xue, H. Florez, B. Wang, R. Tavakoli) ; Pitt (I. Yotov); Paris VI (V. Girault, M. Vohralik); Lyon (A. Mikelic) Parallel Computation: IBM (K. Jordan), Rutgers (M. Parashar) Phase Behaviour and Compositional Modeling : UT-Austin ( M. Delshad, X. Kong); Chevron (S. Thomas) Support of Projects : NSF, DOE (DE-FG02-04ER25617 and EFRC-DE-SC ), CSM Industrial Affiliates

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Outline Motivation Why Carbon Capture and Storage (CCS)? Mechanisms, Questions Needing Answers Mathematical and Computational Models Benchmarks Investigate applicability of existing oil/water/gas models to supercritical C02/water strategy Calibrate and history match demonstration sites Mathematical and Computational Challenges Discretizations and Solvers Multiscale, Multiphysics, Multinumerics & Data Assimilation Conclusions

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Mtoe Other renewables Hydro Nuclear Biomass Gas Coal Oil World energy demand expands by 45% between now and 2030 – an average rate of increase of 1.6% per year – with coal accounting for more than a third of the overall rise World Primary Energy Demand From: Joan MacNaughton (Alstom Power Company)

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Units:1 Gt = 10 ^12 kg 1 Source: IEA/OECD (200) Year Total: 26,6 Gt in 2005 Source: Alstom, adapted from CDIAC 2004 Coal generates 70% of the CO 2 emissions from power generation % 22 % Power Industry Transport 16 % Others World CO 2 fossil emissions GtCO 2 by sector Gton of CO 2 70 % 8 % 3 % Coal Gas Oil Power by fuel From: Joan MacNaughton (Alstom Power Company) CO 2 from Fossil Fuel Combustion

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Center for Frontiers of Subsurface Energy Security The University of Texas Summary statement: Our goal is scientific understanding of subsurface physical, chemical and biological processes from the very small scale to the very large scale so that we can predict the behavior of CO 2 and other byproducts of energy production that may need to be stored in the subsurface. RESEARCH PLAN AND DIRECTIONS Challenges and approaches: Integrate and expand our knowledge of subsurface phenomena across scientific disciplines using both experimental and modeling approaches to better understand and quantify behavior far from equilibrium. Unique aspects: The uncertainty and complexity of fluids in geologic media from the molecular scale to the basin scale. Outcome: Predict long term behavior of subsurface storage.

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Multi-Scale Investigation Dissolved CO 2 Aquifer Brine SC-CO 2

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Geographical location of Denbury Resources, Incorporated’s Cranfield Unit east of Natchez, Mississippi Gulf Coast Stacked Storage Project (SECARB)

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? How can we represent the essential features of large-scale behavior that emerge from small-scale phenomena? Can we engineer solutions to mitigate contaminant leakage pathways? What are the relevant physics, biology, and chemistry of CO 2 transport in the subsurface? How does supercritical CO 2 behave in the subsurface?

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Goal of CO 2 Geological Sequestration Permanently store CO 2 in deep saline aquifers by different trapping mechanism: Residual Dissolution Mineral Structural Precipitated Carbonate Minerals Confining Layer(s) Injection Well Supercritical CO 2 Dissolved CO 2 Celia et al., 2002

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Modeling CO 2 Storage Accurate prediction of the CO 2 fate is a challenge CO 2 injection in subsurface brings a weighty list of variables, parameters, and potential outcomes CO 2 properties of density, viscosity, solubility depend on pressure, temperature, and water salinity Relative permeabilities are functions of rock properties such as wettability and permeability Relative permeability and capillary pressure are hysteretic Relative permeability and capillary pressure are influenced by pressure, interfacial tension, and flow rate

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Forces Controlling the Movement of CO 2 Pressure Gradient (Driving Force) Buoyancy Force (Driving or Trapping Force) Capillary Pressure (Trapping Force) Mobilization Condition of Trapped CO 2 Globule

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Compositional Modeling

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Compositional Flow and Thermal Formulation

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IPARS-COMP Flow Equations Mass Balance Equation Pressure Equation Solution Method Iteratively coupled until a volume balance convergence criterion is met or a maximum number of iterations exceeded.

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Thermal & Chemistry Equations Energy Balance Solved using a time-split scheme (operator splitting) Higher-order Godunov for advection 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

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EOS Model CO 2 Properties Fugacity (T, P) Density (T, P) Viscosity (T, P) Aqueous Solution Properties CO 2 Solubility (T, P) Aqueous Density (T, P) Effect of salinity Peng-Robinson EOS

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Parallel Subsurface Compositional Framework Thermal 2 or 4- P Flash Geomechanics Numerics Visualization EOSComp EOS Comp. Geochemical Reaction Gridding Solvers Physical Prop

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EOS Compositional Flow Simulations 6 Component Compositional Benchmark Large Scale CO 2 Simulation Calibration: Resid. Sat & Trapping Core Studies and Scaling Preliminary – Matching Cranfield Field Studies M. Delshad, X. Kong, and W

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EOS Compositional Simulations Modified SPE5 WAG injection, 6 non-aqueous components-solved using EOS compositional model SPE10 permeability distribution 50x480x480 cells (~11 million) Linear Solver: BiCGS or GMRES + MG preconditioner. Water Saturation Gas SaturationPropane Concentration After Three Years Permeability Oil Pressure

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Texas Advanced Computing Center The University of Texas at Austin Parallel Scalability

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Large-Scale High Resolution Simulation million cells CO2 Injection wells Permeability, md CO2 saturation after 2 years Permeability and well locationsVertical cross section

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Case 1: 3.34 million grids, 3 leaky points Aquifer size, L, W, H5304 ft × 6581 ft × 1080 ft Mesh3,342,336 (128 × 256 × 102), (40ft x25ft x15 ft) Dip, Depth (top corner)0 degree, 3000 ft Residual gas and water in aquifer0.103, Initial pressure1800 psi at injection layer Aquifer temperature43 C (110 F) Well positionfour wells in the center of bottom aquifer Vertical well perforated length240 ft, bottom half depth of bottom aquifer Injection rate7000 mscfd each well Aquifer permeabilityheterogeneous with average 96 md Leaky points2 ft x 2 ft Shale permeability md permeability at leaky paths3000 md injection time2 years

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Residual Saturation vs. Trapping Number Residual Saturation vs. Trapping Number Points: data from Bennion and Bachu Line: Model

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Generate heterogeneous permeability and porosity data with FFTSIM (geostatistics software) Permeability and porosity are highly heterogeneous with a Dykstra- Parson coefficient of 0.6 Honor average permeability and porosity of experimental data (Ref. SPE ) Isotropic permeability IPARS Coreflood Simulation Permeability along the core Permeability in a cross section

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T ( o C)50CO2 dissolution (mass fraction) Pressure (MPa)12.41CO2 density (kg/m^3) Salinity (ppm)6500CO2 viscosity (cp)0.06 Porosity0.185Brine Density (kg/m^3) Permeability (md)85Interfacial tension (N/m) Core length (cm)20Injection rate (ml/min)3 Core Diameter (cm)4.064Total pore volume injection7 Residual saturation Of both water and CO2 0.2Final average gas saturation0.54 Simulation Data Set up simulation model with same parameters as the experiment (SPE )

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Relative permeability and capillary pressure used in simulation Core is initially saturated with 100% water, residual of both CO 2 and water is assumed to be 0.2 Relative Permeability and Capillary Pressure Drainage relative permeability Drainage capillary pressure

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Numerical Experiment Total injection: 7 pore volumes Fine mesh cylindrical case, required very small time steps Coarse grids used for testing purpose Gas Saturation at 0.3 Pore Volume with Mesh (32x32x64)

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Cube and Coarse Grid Comparison Cases Permeability for coarse case Porosity for coarse case Cube and coarse grid was used to test sensitivity of simulation to model parameters. Grid : 8x8x32

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CO2 narrowly distributed and uniform Case 1… Without P c Scaling

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CO2 histogram shows log normal distribution Case 2… With P c Scaling Using J-Leverret

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Summary 1 Experimental histogram indicates very low and high values of gas saturation Simulation results show relatively narrow distribution. This is due to setting a residual saturation for both CO 2 and water to be 0.2, and employing a grid that is not fine enough to capture the pore scale flow statistics. Compared with zero capillary pressure scaling, capillary pressure based on J-Leverret function produces results that better match experimental results. Gas saturation distribution is more widely distributed and matches experimental distribution for case with J-Leverret function based capillary pressure.

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Summary For case without J-Leverret capillary pressure, CO2 saturation is more uniform and continuously distributed than that of experiment‘ Locally non-uniform distribution of CO2 is shown in Case 2 Final gas saturation with Pc scaling is close to experimental results of 0.54 (ref. Paper ). Results indicate that J-Leverret function based capillary pressure is important for core flood simulation.

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MFMFE for General Hexahededra and Simplices Formulation: W, Xue and Yotov Solvers: Siefert, Tuminaro (Sandia), Pencheva (UT Austin - EFRC)

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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 Depth 1,500 m Brine-rock, no hydrocarbons 150 bar, 53 C, supercritical CO 2 Injection interval Oil production From Ian Duncan

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Corner Point Grid for Frio Pilot Test Permeability

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Multipoint Flux Mixed Finite Element BDM1 Space on reference element:

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Multipoint Flux Mixed Finite Element (MFMFE) on General Hexahedra

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Convergence Test for MFMFE on General Hexahedra

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Solver Performances for SPE 10 Benchmark Problems SPE 10 permeability on 220 x 65 x 50 highly perturbed hexahedral mesh Model 1: Symmetric multipoint flux Model 2: Non-symmetric multipoint flux AMG solvers: HYPRE (developed by researchers at LLNL) SAMG (developed by the group of K. Stüben) FASP (developed by the group of J. Xu from Penn State) ML in Trilinos (developed by researchers at Sandia) (tested in a different code) Stopping criteria: relative residual less than ML ML

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Parallel Non-Overlapping DD for MFMFE Using ML (Trilinos) Smoothed Aggregation (SA) with standard SA dropping Symmetric Gauss-Seidel for pre- and post-smoother within the W cycle Drop tolerance discourages aggregates that traverse large material jumps - give a sense for both total storage and total cost per iteration Increasing the drop tolerance tends to reduce iterations but increases complexity

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Parallel EnKF for Reservoir History Matching G. Pencheva, R. Tavakoli, W, K. Jordan, M. Parashar

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Continuous Measurement and Data Analysis for Reservoir Model Estimation Source: E. Gildin, CSM, UT-Austin

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Recent Award 1st Place, IEEE SCALE 2011 Challenge, “A Scalable Ensemble- based Oil-Reservoir Simulations using Blue Gene/P-as-a- Service”, with Rutgers and IBM.

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Ensemble Kalman Filter (EnKF) Monte Carlo approach for recursively updating the model parameters (as well as primary variables) based on an ensemble of prior realizations and observation data. The EnKF consists of two steps: 1)Forecast step: running a set of reservoir simulations (IPARS) to predict data at the next update step 2)Update step: computing Kalman gain matrix and updating state vectors m timet0t0 t1t1 t2t2 t3t3 True Model Production prediction

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Serial vs. Parallel EnKF Sequentially run each of the realizations one after another for j=1, 2, …, N e Run N e realizations simultaneously where each simulation run is performed in parallel

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Linear and Nonlinear Solvers Reservoir simulation application uses models for multiphase flow in porous media: time- dependent, highly nonlinear, conserve mass. We would like each realization to run efficiently (parallel scalable), so must utilize good solvers and preconditioners. Moreover, need to synchronize multiple simulation runs during the EnKF process. (The update step is a barrier).

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Solver with Preconditioning In IPARS, linear system is solved using preconditioned generalized minimum residual (GMRES). Two-stage preconditioning: decoupling preconditioner stage: allows us to precondition the diagonal pressure block of the Jacobian independently of the saturation blocks At the second stage, the pressure block is preconditioned

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GMRES preconditioner in IPARS GMRES- PREC DESCRIPTION 3Block Gauss-Siedel (GS) 4LSOR with N_GS_STEP iterations 5Truncated NS + CG inner iterations 6Truncated NS + BCGstab inner iterations 7Truncated NS + GMRES inner iterations 8Un-accelerated truncated NS 11Two-stage: SEP-PREC + LSOR smoother 13Multilevel incomplete LU (MLILU) 14Two-stage: MLILU + LSOR smoother 15Algebraic Multigrid (AMG) 16Two-stage: AMG+LSOR 17 SPARSE FACTORIZATION

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Dynamic Tolerance In addition to proper choice of a preconditioner in solving a Jacobian equation (AX=B), the problem of an adequate tolerance in the linear solver appears. The forcing term technique is used in IPARS to dynamically adjust the tolerance in the course of the Newton process (start with loose tolerance and tighten the condition as we proceed for further iterations) The optimal choice of forcing factor has appeared to be 0.1 (FORCING=0.1)

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Results: EnKF Observation data: oil flow rate, water oil ratio (WOR), bottom hole pressure (BHP) Assimilate time: 1550 days (with variable assimilation interval) followed with prediction phase till 2800 days Uncertain Model parameters: Horizontal permeability and porosity. Ensemble size: 100 realizations

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Computational Results Example: water saturation distribution after 1550 days 3D reservoir, 80x60x5 gridblocks, two-phase (oil-water) 4 inverted five-spot patterns 9 production wells with liquid rate constraint of 4000 STB/day 4 injection wells with constant water injection rate of 8000 STB/day Horizontal permeability and porosity are uncertain model parameters 3D ViewLayer # 4

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Results: EnKF True porosity Final average porosity

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Results: EnKF True horizontal log-permeability Final average horizontal log-permeability

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Results: EnKF Cumulative wall-clock computational time (sec) for EnKF run with 100 ensemble members on ICES-BVO2 cluster Number of Simulation Run at a Time (NRun) Number of Processors per Each Simulation (NpSim) 163,38132,10216,43313,2817,0693, ,29823,99812,40610,0205,3973, ,77218,2239,4697,6734,1812, ,42516,5358,6467,0193,8822,272 Total Computational Time: Total Sim. Time (forecast step) + EnKF update steps Time The total time of update steps is less than 4% of the total.

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Results: EnKF As we increase Nrun>10, the efficiency gets far from the ideal Two main reasons are; 1) additional waiting time due to the slowest simulation run, 2) the update step is done in a serial mode

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Summary Calibration of the linear and nonlinear solvers help to reduce and synchronize the simulation times of each forward run. We employ two levels of parallelism in EnKF: Multiple processors per ensemble member Multiple concurrent ensemble members. The EnKF algorithm helps to reduce uncertainty in reservoir simulation by assimilating production data. The combination of parallelizing the EnKF algorithm with an efficient choice of solver gives over 40% parallel efficiency.

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On Prediction of Realistic CO 2 Tests Fluid properties as a function of pressure, temperature, composition Viscosity, density, interfacial tension, phase behavior Viscosity, density, interfacial tension, phase behavior Rock dependent relative permeability and capillary pressure as a function of Saturation, composition, saturation history (hysteresis), IFT Saturation, composition, saturation history (hysteresis), IFT Rock reaction to pressure changes and subsequent impact on pore volumes and permeability (geomechanics) Reactions of rock minerals and injected CO 2 (geochemistry) Model estimators that include upscaling and downscaling for property manipulations for coarse/fine grid Upscale strategy for CO 2 storage (if needed) Increase grid resolution to improve the quality of model results Increase CPU and memory requirements Increase CPU and memory requirements Faster numerical methods – dynamic grid refinement based on a posteriori error estimators that include upscaling and down scaling, efficient solvers Faster numerical methods – dynamic grid refinement based on a posteriori error estimators that include upscaling and down scaling, efficient solvers Efficient parallelization methods Efficient parallelization methods Optimization and Uncertainty analysis Optimization and Uncertainty analysis

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Summary Renewables all have major problems – cost, energy efficiency, reliable, location, …. CCS May Be Best Hope for Handling Greenhouse Gases Until Solar Becomes Economically Feasible-- Buys Time Conclusions

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