Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Geologic CO2 sequestration in deep saline aquifers is a promising technique to mitigate the effect of greenhouse gas emissions. Designing optimal CO2 injection strategy becomes a challenging problem in the presence of geological uncertainty. We propose a surrogate assisted optimisation technique for robust optimisation of CO2 injection strategies. The surrogate is built using Adaptive Sparse Grid Interpolation (ASGI) to accelerate the optimisation of CO2 injection rates. The surrogate model is adaptively built with different numbers of evaluation points (simulation runs) in different dimensions to allow automatic refinement in the dimension where added resolution is needed. This technique is referred to as dimensional adaptivity and provides a good balance between the accuracy of the surrogate model and the number of simulation runs to save computational costs. For a robust design, we propose a utility function which comprises the statistical moment of the objective function. Numerical testing of the proposed approach applied to benchmark functions and reservoir models shows the efficiency of the method for the robust optimisation of CO2 injection strategies under geological uncertainty.

[1]  Erich Novak,et al.  High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..

[2]  Behnam Jafarpour,et al.  Controlled CO2 injection into heterogeneous geologic formations for improved solubility and residual trapping , 2012 .

[3]  Sergey Kazakov,et al.  Modeling Spatial Uncertainty for Locally Uncertain Data , 2010 .

[4]  K. Ritter,et al.  High dimensional integration of smooth functions over cubes , 1996 .

[5]  Dennis Denney.  Fast and Efficient Numerical-Simulation Method for Supersonic-Gas Processing , 2010 .

[6]  G. Gary Wang,et al.  Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions , 2010 .

[7]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[8]  B. Metz.  IPCC special report on carbon dioxide capture and storage , 2005 .

[9]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[10]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[11]  John S. Kimball,et al.  Projected climate change impacts on the hydrology and temperature of Pacific Northwest rivers , 2012 .

[12]  Barbara I. Wohlmuth,et al.  Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB , 2005, TOMS.

[13]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[14]  M. E. Johnson,et al.  Generalized simulated annealing for function optimization , 1986 .

[15]  Jason E. Heath,et al.  Geologic Heterogeneity and Economic Uncertainty of Subsurface Carbon Dioxide Storage , 2012 .

[16]  Bruce Frederick Kohse,et al.  Simulation and Optimization of Trapping Processes for CO2 Storage in Saline Aquifers , 2010 .

[17]  Albert C. Reynolds,et al.  Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management , 2012 .

[18]  C. Tsang,et al.  Large-scale impact of CO2 storage in deep saline aquifers: A sensitivity study on pressure response in stratified systems , 2009 .

[19]  Robert J. Rosenbauer,et al.  Carbon dioxide (CO2) sequestration in deep saline aquifers and formations , 2010 .

[20]  Alexandre M. Baptista,et al.  Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis , 2002 .

[21]  Barbara I. Wohlmuth,et al.  Uncertainty Modeling Using Fuzzy Arithmetic Based On Sparse Grids: Applications To Dynamic Systems , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  L. Durlofsky,et al.  Optimization of well placement, CO2 injection rates, and brine cycling for geological carbon sequestration , 2012 .

[23]  Dennis Denney.  Modeling CO 2 Storage in Aquifers: Assessing Key Contributors to Uncertainty , 2010 .

[24]  M. Hegland.  Adaptive sparse grids , 2003 .

[25]  Bruce Frederick Kohse,et al.  Optimization of Residual Gas and Solubility Trapping for CO2 Sequestration in Saline Aquifers , 2009 .

[26]  Gijs van Essen,et al.  Robust Waterflooding Optimization of Multiple Geological Scenarios , 2006 .

[27]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[28]  A. R. Syversveen,et al.  Methods for quantifying the uncertainty of production forecasts: a comparative study , 2001, Petroleum Geoscience.

[29]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[30]  Jan M. Nordbotten,et al.  Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation , 2011 .

[31]  Franklin M. Orr,et al.  Storage of CO2 in saline aquifers: Effects of gravity, viscous, and capillary forces on amount and timing of trapping , 2007 .

[32]  David A. Jones,et al.  Prediction uncertainty in a median‐based index flood method using L moments , 2006 .

[33]  Michael Kühn,et al.  The impact of heterogeneity on the distribution of CO2: Numerical simulation of CO2 storage at Ketzin , 2010 .

[34]  Slawomir Koziel,et al.  Computational Optimization, Methods and Algorithms , 2016, Computational Optimization, Methods and Algorithms.

[35]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[36]  Dongxiao Zhang,et al.  Ensemble based co-optimization of carbon dioxide sequestration and enhanced oil recovery , 2012 .

[37]  Nikita Chugunov,et al.  CO2 Injection in a Saline Formation: How Do Additional Data Change Uncertainties in Our Reservoir Simulation Predictions? , 2012 .

[38]  Ahmed H. Alhuthali.  Optimal Waterflood Management Under Geologic Uncertainty Using Rate Control: Theory and Field Applications , 2009 .

[39]  Dongxiao Zhang,et al.  Optimization of the Net Present Value of Carbon Dioxide Sequestration and Enhanced Oil Recovery , 2011 .

[40]  John E. Mottershead,et al.  A review of robust optimal design and its application in dynamics , 2005 .

[41]  Sandro Gronchi,et al.  On Investment Criteria Based on the Internal Rate of Return , 1986 .

[42]  Leifur Leifsson,et al.  Surrogate-Based Methods , 2011, Computational Optimization, Methods and Algorithms.

[43]  Bruce Frederick Kohse,et al.  Risk mitigation through the optimization of residual gas and solubility trapping for CO2 storage in saline aquifers , 2009 .

[44]  Thomas Gerstner,et al.  Dimension–Adaptive Tensor–Product Quadrature , 2003, Computing.

[45]  Wei Chen,et al.  Quality utility : a Compromise Programming approach to robust design , 1999 .

[46]  John Killough,et al.  Reservoir Simulation With History-Dependent Saturation Functions , 1976 .

[47]  Ruben Juanes,et al.  Impact of relative permeability hysteresis on geological CO2 storage , 2006 .

[48]  Martin J. Blunt,et al.  Modeling CO2 Storage in Aquifers : Assessing the key contributors to uncertainty , 2009 .

[49]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.