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dc.contributor.authorKou, Jisheng
dc.contributor.authorSun, Shuyu
dc.contributor.authorWu, Yuanqing
dc.date.accessioned2018-09-26T13:27:40Z
dc.date.available2018-09-26T13:27:40Z
dc.date.issued2018-09-12
dc.identifier.citationKou J, Sun S, Wu Y (2019) A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer model. Journal of Computational and Applied Mathematics 348: 401–420. Available: http://dx.doi.org/10.1016/j.cam.2018.08.055.
dc.identifier.issn0377-0427
dc.identifier.doi10.1016/j.cam.2018.08.055
dc.identifier.urihttp://hdl.handle.net/10754/628763
dc.description.abstractIn this paper, we consider numerical simulation of wormhole propagation with the Darcy-Brinkman-Forchheimer model. Matrix acidization in carbonate reservoirs is a widely practiced technique in the product enhancement of the oil and gas reservoir. A wormhole, i.e. a flow channel with high porosity, is generated during reactive dissolution of carbonates by the action of the injected acid. In the wormhole forming process, the porosity changes non-uniformly in space, and it even becomes close to unity in the central regions of a wormhole. The Darcy-Brinkman-Forchheimer model accounts for both the porous media and clear fluid area, so it can be used to model wormhole propagation perfectly. This model, however, strongly depends on porosity. Therefore, the time schemes for solving the evolutionary equation of porosity have a significant effect on accuracy and stability of the numerical simulation for wormhole propagation. We propose a semi-analytic time scheme, which solves the porosity equation analytically at each time step for given acid concentration. The proposed numerical method can improve the accuracy and stability of numerical simulation significantly. For theoretical analysis of the proposed time scheme for the wormhole simulation, we first reconstruct the analytical functions of porosity to analyze the time error of the porosity, and on the basis of error estimates of porosity, we employ a coupled analysis approach to achieve the estimates of pressure, velocity and solute concentration. The time error estimates for velocity, pressure, concentration and porosity are obtained in different norms. Finally, numerical results are provided to verify the effectiveness of the proposed scheme.
dc.description.sponsorshipNational Natural Science Foundation of China[11601345]
dc.description.sponsorshipNatural Science Foundation of SZU[2017059]
dc.description.sponsorshipPeacock Plan Foundation of Shenzhen[000255]
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042718305429
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. 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 Journal of Computational and Applied Mathematics, [, , (2018-09-12)] DOI: 10.1016/j.cam.2018.08.055 . © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectWormhole
dc.subjectDarcy-Brinkman-Forchheimer model
dc.subjectTime scheme
dc.subjectError estimate
dc.titleA semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy-Brinkman-Forchheimer model
dc.typeArticle
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.eprint.versionPost-print
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China
dc.contributor.institutionCollege of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China
kaust.personSun, Shuyu
refterms.dateFOA2018-09-27T08:24:04Z
dc.date.published-online2018-09-12
dc.date.published-print2019-03


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