A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

doi:https://doi.org/10.1016/J.JCP.2016.10.061

Title: A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

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Abstract

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.

Authors:

Liao, Qinzhuo ^[1]; Zhang, Dongxiao ^[1]; Tchelepi, Hamdi ^[2]

ERE & BIC-ESAT, College of Engineering, Peking University, Beijing (China)
Department of Energy Resources Engineering, Stanford University, Stanford, CA (United States)

Publication Date:: 2017-02-01

OSTI Identifier:: 22622250

Resource Type:: Journal Article

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ACCURACY; COMPUTERIZED SIMULATION; EFFICIENCY; INTERPOLATION; MULTIPHASE FLOW; PERMEABILITY; POROUS MATERIALS; QUADRATURES; RANDOMNESS; SATURATION; STOCHASTIC PROCESSES; VELOCITY

Citation Formats


                    Liao, Qinzhuo, Zhang, Dongxiao, and Tchelepi, Hamdi. A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media.  United States: N. p., 2017. 
        Web.  doi:10.1016/J.JCP.2016.10.061.

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                    Liao, Qinzhuo, Zhang, Dongxiao, & Tchelepi, Hamdi. A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media.  United States.  https://doi.org/10.1016/J.JCP.2016.10.061

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                    Liao, Qinzhuo, Zhang, Dongxiao, and Tchelepi, Hamdi. Wed .  
        "A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media".  United States.  https://doi.org/10.1016/J.JCP.2016.10.061.

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@article{osti_22622250,

  title        = {A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media},

  author       = {Liao, Qinzhuo and Zhang, Dongxiao and Tchelepi, Hamdi},

  abstractNote = {A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.},

  doi          = {10.1016/J.JCP.2016.10.061},

  url          = {https://www.osti.gov/biblio/22622250},
  journal      = {Journal of Computational Physics},

  issn         = {0021-9991},

  number       = ,

  volume       = 330,

  place        = {United States},

  year         = {2017},

  month        = {2}

}

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