Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State

Handle URI:
http://hdl.handle.net/10754/575703
Title:
Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State
Authors:
Qiao, Zhonghua; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory of thermodynamics and variational calculus to derive a generalized chemical equilibrium equation, which is mathematically a second-order elliptic partial differential equation (PDE) in molar density with a strongly nonlinear source term. To solve this PDE, we convert it to a time-dependent parabolic PDE with the main interest in its final steady state solution. A Lagrange multiplier is used to enforce mass conservation. The parabolic PDE is then solved by mixed finite element methods with a semi-implicit time marching scheme. Convex splitting of the energy functional is proposed to construct this time marching scheme, where the volume exclusion effect of an EOS is treated implicitly while the pairwise attraction effect of EOS is calculated explicitly. This scheme is proved to be unconditionally energy stable. Our proposed algorithm is able to solve successfully the spatially heterogeneous two-phase systems with the Peng-Robinson EOS in multiple spatial dimensions, the first time in the literature. Numerical examples are provided with realistic hydrocarbon components to illustrate the theory. Furthermore, our computational results are compared with laboratory experimental data and verified with the Young-Laplace equation with good agreement. This work sets the stage for a broad extension of efficient convex-splitting semi-implicit schemes for numerical simulation of phase field models with a realistic EOS in complex geometries of multiple spatial dimensions.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Science and Engineering Program; Computational Transport Phenomena Lab
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2014
DOI:
10.1137/130933745
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author's work was partially supported by Hong Kong Research Council GRF grant PolyU 2021/12P and NSFC/RGC Joint Research Scheme N_HKBU204/12.This author's work was supported in part by the project entitled "Simulation of Subsurface Geochemical Transport and Carbon Sequestration," funded by the GRP-AEA Program at King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Science and Engineering Program; Computational Transport Phenomena Lab; Environmental Science and Engineering Program; Earth Science and Engineering Program; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorQiao, Zhonghuaen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-08-24T08:36:10Zen
dc.date.available2015-08-24T08:36:10Zen
dc.date.issued2014-01en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/130933745en
dc.identifier.urihttp://hdl.handle.net/10754/575703en
dc.description.abstractIn this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory of thermodynamics and variational calculus to derive a generalized chemical equilibrium equation, which is mathematically a second-order elliptic partial differential equation (PDE) in molar density with a strongly nonlinear source term. To solve this PDE, we convert it to a time-dependent parabolic PDE with the main interest in its final steady state solution. A Lagrange multiplier is used to enforce mass conservation. The parabolic PDE is then solved by mixed finite element methods with a semi-implicit time marching scheme. Convex splitting of the energy functional is proposed to construct this time marching scheme, where the volume exclusion effect of an EOS is treated implicitly while the pairwise attraction effect of EOS is calculated explicitly. This scheme is proved to be unconditionally energy stable. Our proposed algorithm is able to solve successfully the spatially heterogeneous two-phase systems with the Peng-Robinson EOS in multiple spatial dimensions, the first time in the literature. Numerical examples are provided with realistic hydrocarbon components to illustrate the theory. Furthermore, our computational results are compared with laboratory experimental data and verified with the Young-Laplace equation with good agreement. This work sets the stage for a broad extension of efficient convex-splitting semi-implicit schemes for numerical simulation of phase field models with a realistic EOS in complex geometries of multiple spatial dimensions.en
dc.description.sponsorshipThis author's work was partially supported by Hong Kong Research Council GRF grant PolyU 2021/12P and NSFC/RGC Joint Research Scheme N_HKBU204/12.This author's work was supported in part by the project entitled "Simulation of Subsurface Geochemical Transport and Carbon Sequestration," funded by the GRP-AEA Program at King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.titleTwo-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of Stateen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionHong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R Chinaen
kaust.authorSun, Shuyuen
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