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    Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity

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    Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity.pdf
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    2.429Mb
    Format:
    PDF
    Description:
    Accepted manuscript
    Embargo End Date:
    2022-05-29
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    Type
    Article
    Authors
    Yang, Haijian
    Li, Yiteng cc
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    BAS/1/1351-01
    REP/1/2879-01
    Date
    2020-05-29
    Online Publication Date
    2020-05-29
    Print Publication Date
    2020-08
    Embargo End Date
    2022-05-29
    Submitted Date
    2019-12-09
    Permanent link to this record
    http://hdl.handle.net/10754/662982
    
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    Abstract
    The multiphase flow model has been extensively used to describe complicated flow behaviors in subsurface formations, together with sophisticated reservoir models and well-defined fluid property. In this study, the fully implicit method, as one of most promising schemes for subsurface flow modeling, is employed to solve multiphase flow problems. In contrast to the conventional approach where mathematical models often include a pressure equation, the multiphase flow problems are modeled by up to three continuity equations so that mass conservation holds for all present phases. Another challenge that frequently shows up is the computed solution may sit outside its physically meaningful range, thereby leading to inaccurate predictions or even a failure of the simulation process. A simple remedy is to apply a cutting-off operation to the out-of-bound solution but such an action could ruin both local and global mass conservation. Instead, we replace the original model by a variational inequality formulation with box inequality constraints to protect the boundedness requirement on pressure and saturations from being violated. The variational inequality problem is then solved by a well-designed nonlinear solver consisting of the active-set reduced-space method and the nonlinear elimination preconditioning technique. A number of examples are presented to demonstrate that the proposed formulation is bound-preserving and mass-conservative for each of the present phases/components.
    Citation
    Yang, H., Li, Y., & Sun, S. (2020). Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity. Computer Methods in Applied Mechanics and Engineering, 367, 113140. doi:10.1016/j.cma.2020.113140
    Sponsors
    The authors would like to express their appreciations to the anonymous reviewer for the invaluable comments that have greatly improved the quality of the manuscript. This work is partially supported by the National Natural Science Foundation of China (No. 11971006, 11871069 and 51874262). The authors also greatly thank for the support from King Abdullah University of Science and Technology (KAUST), Saudi Arabia through the grants BAS/1/1351-01, REP/1/2879-01, and URF/1/3769-01. The first author was also supported in part by the PetroChina Innovation Foundation (2019D-5007-0213).
    Publisher
    Elsevier BV
    Journal
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2020.113140
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S004578252030325X
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cma.2020.113140
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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