An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature

Handle URI:
http://hdl.handle.net/10754/621656
Title:
An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X ) ; Wang, Xiuhua
Abstract:
In this paper, we propose an energy-stable evolution method for the calculation of the phase equilibria under given volume, temperature, and moles (VT-flash). An evolution model for describing the dynamics of two-phase fluid system is based on Fick’s law of diffusion for multi-component fluids and the Peng-Robinson equation of state. The mobility is obtained from diffusion coefficients by relating the gradient of chemical potential to the gradient of molar density. The evolution equation for moles of each component is derived using the discretization of diffusion equations, while the volume evolution equation is constructed based on the mechanical mechanism and the Peng-Robinson equation of state. It is proven that the proposed evolution system can well model the VT-flash problem, and moreover, it possesses the property of total energy decay. By using the Euler time scheme to discretize this evolution system, we develop an energy stable algorithm with an adaptive choice strategy of time steps, which allows us to calculate the suitable time step size to guarantee the physical properties of moles and volumes, including positivity, maximum limits, and correct definition of the Helmhotz free energy function. The proposed evolution method is also proven to be energy-stable under the proposed time step choice. Numerical examples are tested to demonstrate efficiency and robustness of the proposed method.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
Citation:
Kou J, Sun S, Wang X (2016) An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature. Computational Geosciences 20: 283–295. Available: http://dx.doi.org/10.1007/s10596-016-9564-5.
Publisher:
Springer Science + Business Media
Journal:
Computational Geosciences
Issue Date:
25-Feb-2016
DOI:
10.1007/s10596-016-9564-5
Type:
Article
ISSN:
1420-0597; 1573-1499
Sponsors:
This work is supported by National Natural Science Foundation of China (No. 11301163). The authors cheerfully appreciate the generous support of the university research fund to the Computational Transport Phenomena Laboratory at KAUST.
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.authorWang, Xiuhuaen
dc.date.accessioned2016-11-03T13:22:01Z-
dc.date.available2016-11-03T13:22:01Z-
dc.date.issued2016-02-25en
dc.identifier.citationKou J, Sun S, Wang X (2016) An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperature. Computational Geosciences 20: 283–295. Available: http://dx.doi.org/10.1007/s10596-016-9564-5.en
dc.identifier.issn1420-0597en
dc.identifier.issn1573-1499en
dc.identifier.doi10.1007/s10596-016-9564-5en
dc.identifier.urihttp://hdl.handle.net/10754/621656-
dc.description.abstractIn this paper, we propose an energy-stable evolution method for the calculation of the phase equilibria under given volume, temperature, and moles (VT-flash). An evolution model for describing the dynamics of two-phase fluid system is based on Fick’s law of diffusion for multi-component fluids and the Peng-Robinson equation of state. The mobility is obtained from diffusion coefficients by relating the gradient of chemical potential to the gradient of molar density. The evolution equation for moles of each component is derived using the discretization of diffusion equations, while the volume evolution equation is constructed based on the mechanical mechanism and the Peng-Robinson equation of state. It is proven that the proposed evolution system can well model the VT-flash problem, and moreover, it possesses the property of total energy decay. By using the Euler time scheme to discretize this evolution system, we develop an energy stable algorithm with an adaptive choice strategy of time steps, which allows us to calculate the suitable time step size to guarantee the physical properties of moles and volumes, including positivity, maximum limits, and correct definition of the Helmhotz free energy function. The proposed evolution method is also proven to be energy-stable under the proposed time step choice. Numerical examples are tested to demonstrate efficiency and robustness of the proposed method.en
dc.description.sponsorshipThis work is supported by National Natural Science Foundation of China (No. 11301163). The authors cheerfully appreciate the generous support of the university research fund to the Computational Transport Phenomena Laboratory at KAUST.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectAdaptive time stepsen
dc.subjectEnergy stableen
dc.subjectMobilityen
dc.subjectMulti-component fluiden
dc.subjectPhase equilibriaen
dc.subjectVT flashen
dc.titleAn energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles, volume and temperatureen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalComputational Geosciencesen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei, Chinaen
dc.contributor.institutionSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Chinaen
kaust.authorSun, Shuyuen
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