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    Numerical modeling of isothermal compositional grading by convex splitting methods

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    Type
    Article
    Authors
    Li, Yiteng cc
    Kou, Jisheng 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/1/1351-01-01
    Date
    2017-04-09
    Online Publication Date
    2017-04-09
    Print Publication Date
    2017-07
    Permanent link to this record
    http://hdl.handle.net/10754/623875
    
    Metadata
    Show full item record
    Abstract
    In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.
    Citation
    Li Y, Kou J, Sun S (2017) Numerical modeling of isothermal compositional grading by convex splitting methods. Journal of Natural Gas Science and Engineering 43: 207–221. Available: http://dx.doi.org/10.1016/j.jngse.2017.03.019.
    Sponsors
    This work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the grant BAS/1/1351-01-01.
    Publisher
    Elsevier BV
    Journal
    Journal of Natural Gas Science and Engineering
    DOI
    10.1016/j.jngse.2017.03.019
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S1875510017301397
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jngse.2017.03.019
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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