Numerical modeling of isothermal compositional grading by convex splitting methods

Handle URI:
http://hdl.handle.net/10754/623875
Title:
Numerical modeling of isothermal compositional grading by convex splitting methods
Authors:
Li, Yiteng; Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X )
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.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
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.
Publisher:
Elsevier BV
Journal:
Journal of Natural Gas Science and Engineering
KAUST Grant Number:
BAS/1/1351-01-01
Issue Date:
9-Apr-2017
DOI:
10.1016/j.jngse.2017.03.019
Type:
Article
ISSN:
1875-5100
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.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S1875510017301397
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Yitengen
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2017-05-31T11:23:11Z-
dc.date.available2017-05-31T11:23:11Z-
dc.date.issued2017-04-09en
dc.identifier.citationLi 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.en
dc.identifier.issn1875-5100en
dc.identifier.doi10.1016/j.jngse.2017.03.019en
dc.identifier.urihttp://hdl.handle.net/10754/623875-
dc.description.abstractIn 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.en
dc.description.sponsorshipThis 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.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S1875510017301397en
dc.subjectConvex splitting methoden
dc.subjectHelmholtz free energyen
dc.subjectIsothermal compositional gradingen
dc.subjectSemi-implicit schemeen
dc.titleNumerical modeling of isothermal compositional grading by convex splitting methodsen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of Natural Gas Science and Engineeringen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, , Chinaen
kaust.authorLi, Yitengen
kaust.authorSun, Shuyuen
kaust.grant.numberBAS/1/1351-01-01en
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