General algorithm for multiphase equilibria calculation at given volume, temperature, and moles

Jindrová, Tereza; Mikyška, Jiří

doi:10.1016/j.fluid.2015.02.013

Cited by 68 publications

(46 citation statements)

References 28 publications

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“…Compared to the well-known Van der Waals equation of state, PR-EoS can provide more reasonable accuracy in predicting the properties of a wide variety of materials, such as N 2 , CO 2 and hydrocarbons. PR-EoS has been extensively applied for simulation of many important problems in petroleum and chemical engineering, for instance, phase equilibria calculations [7][8][9]13,[21][22][23]25] and prediction of surface tension between gas and liquid [7,10,11,24]. Modeling and simulation of compressible multi-component two-phase flows with partial miscibility and realistic equations of state (e.g.…”

mentioning

confidence: 99%

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Kou¹,

Sun²,

Wang³

2020

SIAM J. Sci. Comput.

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The Peng-Robinson equation of state (PR-EoS) has become one of the most extensively applied equations of state in chemical engineering and petroleum industry due to its excellent accuracy in predicting the thermodynamic properties of a wide variety of materials, especially hydrocarbons. Although great efforts have been made to construct efficient numerical methods for the diffuse interface models with PR-EoS, there is still not a linear numerical scheme that can be proved to preserve the original energy dissipation law. In order to pursue such a numerical scheme, we propose a novel energy factorization (EF) approach, which first factorizes an energy function into a product of several factors and then treats the factors using their properties to obtain the semiimplicit linear schemes. We apply the EF approach to deal with the Helmholtz free energy density determined by PR-EoS, and then propose a linear semi-implicit numerical scheme that inherits the original energy dissipation law. Moreover, the proposed scheme is proved to satisfy the maximum principle in both the time semi-discrete form and the cell-centered finite difference fully discrete form under certain conditions. Numerical results are presented to demonstrate the stability and efficiency of the proposed scheme.

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confidence: 99%

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Kou¹,

Sun²,

Wang³

2020

SIAM J. Sci. Comput.

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“…This leads to the complication of constructing the pressure evolution equation for application of the NPT-based framework [25].In order to resolve the issues of the NPT-based framework, an alternative framework [19] has been developed, and it uses the moles, volume, and temperature (the so-called NVT-based framework) as the primal state variables. The NVT-based framework is initially applied to the phase-split computations of multi-component fluids at the constant moles, volume and temperature (also called NVT flash computation) in [19], and for the subsequent research progress of the NVT flash computation, we refer to [10,11,15,20]. Recently, the NVT-based framework has been successfully applied in the numerical simulation of compositional two-phase flow in porous media [25].…”

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confidence: 99%

“…This framework has been extensively used in many applications [4,8,17,22]. However, the NPT-based framework has some essential limitations [10,11,19,20,25]. First, a realistic equation of state (e.g.…”

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confidence: 99%

Thermodynamically consistent modeling and simulation of multi-component two-phase flow with partial miscibility

Kou

Sun

2018

Computer Methods in Applied Mechanics and Engineering

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A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a latest alternative over the NPT-based framework to model the realistic fluids. The proposed model uses the Helmholtz free energy rather than Gibbs free energy in the NPT-based framework. Different from the classical routines, we combine the first law of thermodynamics and related thermodynamical relations to derive the entropy balance equation, and then we derive a transport equation of the Helmholtz free energy density. Furthermore, by using the second law of thermodynamics, we derive a set of unified equations for both interfaces and bulk phases that can describe the partial miscibility of two fluids. A relation between the pressure gradient and chemical potential gradients is established, and this relation leads to a new formulation of the momentum balance equation, which demonstrates that chemical potential gradients become the primary driving force of fluid motion. Moreover, we prove that the proposed model satisfies the total (free) energy dissipation with time. For numerical simulation of the proposed model, the key difficulties result from the strong nonlinearity of Helmholtz free energy density and tight coupling relations between molar densities and velocity. To resolve these problems, we propose a novel convex-concave splitting of Helmholtz free energy density and deal well with the coupling relations between molar densities and velocity through very careful physical observations with a mathematical rigor. We prove that the proposed numerical scheme can preserve the discrete (free) energy dissipation. Numerical tests are carried out to verify the effectiveness of the proposed method. specification of pressure, temperature, and mole fractions does not always determine the equilibrium state of the system uniquely. In addition, in compositional fluid simulation, the pressure is not known a-priori and there exists no intrinsic equation for the pressure. This leads to the complication of constructing the pressure evolution equation for application of the NPT-based framework [25].In order to resolve the issues of the NPT-based framework, an alternative framework [19] has been developed, and it uses the moles, volume, and temperature (the so-called NVT-based framework) as the primal state variables. The NVT-based framework is initially applied to the phase-split computations of multi-component fluids at the constant moles, volume and temperature (also called NVT flash computation) in [19], and for the subsequent research progress of the NVT flash computation, we refer to [10,11,15,20]. Recently, the NVT-based framework has been successfully applied in the numerical simulation of compositional two-phase flow in porous media [25]. Very recently, in [16], we have extended the NVT-based framework to the pore scale and developed a diffuse interface model to simulate multi-component t...

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“…Peng-Robinson equation of state [54]) are intensively studied in recent years [19,31,32,35,39,55,57]. The multicomponent models with realistic equations of state are traditionally applied for simulation of many problems in chemical and petroleum engineering, for example, the phase equilibria calculations [20,26,27,33,36,45,46,49] and prediction of surface tension [20,30,38,47], but the fluid motion is never considered in these applications. The models of compositional fluid flows in porous media, for example, [25,44,48,56], describe the fluid motion through Darcy's law, but using the sharp interface.…”

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confidence: 99%

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

Kou

Sun

2018

Computer Methods in Applied Mechanics and Engineering

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In this paper, we consider mathematical modeling and numerical simulation of nonisothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

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General algorithm for multiphase equilibria calculation at given volume, temperature, and moles

Cited by 68 publications

References 28 publications

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Thermodynamically consistent modeling and simulation of multi-component two-phase flow with partial miscibility

Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

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