Mixed finite element-based fully conservative methods for simulating wormhole propagation

Handle URI:
http://hdl.handle.net/10754/581349
Title:
Mixed finite element-based fully conservative methods for simulating wormhole propagation
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X ) ; Wu, Yuanqing ( 0000-0002-8286-8078 )
Abstract:
Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy–Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy–Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab
Citation:
Mixed finite element-based fully conservative methods for simulating wormhole propagation 2015 Computer Methods in Applied Mechanics and Engineering
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
11-Oct-2015
DOI:
10.1016/j.cma.2015.09.015
Type:
Article
ISSN:
00457825
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0045782515003096
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.contributor.authorWu, Yuanqingen
dc.date.accessioned2015-10-28T13:44:55Zen
dc.date.available2015-10-28T13:44:55Zen
dc.date.issued2015-10-11en
dc.identifier.citationMixed finite element-based fully conservative methods for simulating wormhole propagation 2015 Computer Methods in Applied Mechanics and Engineeringen
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2015.09.015en
dc.identifier.urihttp://hdl.handle.net/10754/581349en
dc.description.abstractWormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy–Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy–Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0045782515003096en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 11 October 2015. DOI: 10.1016/j.cma.2015.09.015en
dc.subjectMixed finite element methodsen
dc.subjectWormholeen
dc.subjectError estimateen
dc.subjectDarcy–Forchheimer modelen
dc.titleMixed finite element-based fully conservative methods for simulating wormhole propagationen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.eprint.versionPost-printen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, Chinaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorSun, Shuyuen
kaust.authorWu, Yuanqingen
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