# Numerical modeling of two-phase binary fluid mixing using mixed finite elements

Handle URI:
http://hdl.handle.net/10754/562248
Title:
Numerical modeling of two-phase binary fluid mixing using mixed finite elements
Authors:
Sun, Shuyu ( 0000-0002-3078-864X ) ; Firoozabadi, Abbas; Kou, Jisheng
Abstract:
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy's law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Springer Verlag
Journal:
Computational Geosciences
Issue Date:
27-Jul-2012
DOI:
10.1007/s10596-012-9306-2
Type:
Article
ISSN:
14200597
Sponsors:
This work was supported by the member companies of the Reservoir Engineering Research Institute. Their support is greatly appreciated. The authors also cheerfully appreciate the generous support of the university research fund to the Computational Transport Phenomena Laboratory at KAUST. This work is partly support by Key Project of Chinese Ministry of Education (No. 212109).
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

# Full metadata record

DC FieldValue Language
dc.contributor.authorSun, Shuyuen
dc.contributor.authorFiroozabadi, Abbasen
dc.contributor.authorKou, Jishengen
dc.date.accessioned2015-08-03T09:57:57Zen
dc.date.available2015-08-03T09:57:57Zen
dc.date.issued2012-07-27en
dc.identifier.issn14200597en
dc.identifier.doi10.1007/s10596-012-9306-2en
dc.identifier.urihttp://hdl.handle.net/10754/562248en
dc.description.abstractDiffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy's law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.en
dc.description.sponsorshipThis work was supported by the member companies of the Reservoir Engineering Research Institute. Their support is greatly appreciated. The authors also cheerfully appreciate the generous support of the university research fund to the Computational Transport Phenomena Laboratory at KAUST. This work is partly support by Key Project of Chinese Ministry of Education (No. 212109).en
dc.publisherSpringer Verlagen
dc.subjectBinary mixingen
dc.subjectConservation lawen
dc.subjectMixed finite element methodsen
dc.subjectMulticomponent transporten
dc.subjectTwo-phase flowen
dc.titleNumerical modeling of two-phase binary fluid mixing using mixed finite elementsen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputational Geosciencesen
dc.contributor.institutionReservoir Engineering Research Institute, Palo Alto, CA, United Statesen
dc.contributor.institutionChemical and Environmental Engineering Department, Mason Laboratory, Yale University, New Haven, CT 06520, United Statesen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432100 Hubei, Chinaen
kaust.authorSun, Shuyuen
kaust.authorKou, Jishengen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.