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Journal ArticleDOI

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

25 Jan 2018-Fluid Phase Equilibria (Elsevier)-Vol. 456, pp 7-24
TL;DR: In this paper, a phase equilibrium calculation at specified moles, volume and temperature is proposed to simulate phase properties and flow of liquid-gas fluids in porous media, and a dynamical model is developed for the first time by using the laws of thermodynamics and Onsager's reciprocal principle.
About: This article is published in Fluid Phase Equilibria.The article was published on 2018-01-25 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Thermodynamic equilibrium & Helmholtz free energy.

Summary (1 min read)

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

  • In the phase equilibrium calculation, the selection of specified thermodynamical variables largely depends on the practical problems to be solved.
  • The authors consider the phase equilibrium calculation incorporating capillarity at specified specified moles, volume and temperature (i.e. NVT conditions).
  • Different from the dynamical model in [14] , the proposed model in this work is that capillarity effect is included in the NVT flash.
  • 3. Thermodynamical stability of the numerical scheme.
  • As shown in [36] , Fig. 5 .5(a) depicts that the gas-phase saturation pressure can be reduced by capillarity effect, while Fig. 5 .5(b) shows that the capillary pressure becomes weaker as the temperature increases.

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  • When the entropy attains its maximum, the system reaches the equilibrium state.
  • Phase stability analysis with capillarity and initial conditions.
  • The appropriate initial conditions, including initial values of moles and volumes, are required for the proposed dynamical model.
  • The authors use the method of selecting a reference component [23] to specify the phase identification, which is based on the fact that the reference component has the larger molar density in the liquid phase than in the gas phase.

6. Conclusions.

  • A dynamical model for phase equilibria involving capillary pressure at specified moles, volume and temperature is derived by using the laws of thermodynamics and Onsager's reciprocal principle.
  • This model has a set of unified formulations for both pure substances and multi-component mixtures, which describe the evolutionary process from a non-equilibrium state to an equilibrium state.
  • Based on the convex-concave splitting of the total Helmholtz energy, an efficient, thermodynamically stable numerical algorithm is developed to simulate the dynamical model.
  • The authors derive a phase stability condition in the presence of capillarity effect at the NVT condition, and moreover, they propose a stable numerical algorithm for the phase stability testing, which can provide the feasible initial conditions.

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Citations
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Book ChapterDOI
01 Jan 2014
TL;DR: In this article, the authors studied systems at equilibrium, i.e., systems that do not change or evolve over time, and showed that these systems do not evolve at all.
Abstract: In the preceding chapters with few exceptions we studied systems at equilibrium. This means that the systems do not change or evolve over time.

504 citations

Journal ArticleDOI
TL;DR: This paper proposes two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state and proves that the methods preserve the unconditional energy-dissipation feature.
Abstract: In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multicomponent two-phase compressible flow with a realistic equation of state (e.g., Peng--Ro...

67 citations


Cites methods from "A stable algorithm for calculating ..."

  • ...The diffusion flux has a form [5,17] as Ji = −ii RT ∇μi....

    [...]

  • ...The energy-stable numerical scheme based on the convex splitting method have also been developed and analyzed for the diffuse-interface models with Peng-Robinson equation of state [9,17,20,21,31,32]....

    [...]

Posted Content
TL;DR: In this article, a general diffuse interface model with a realistic equation of state (e.g., Peng-Robinson equation) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework.
Abstract: 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.

43 citations

Journal ArticleDOI
TL;DR: In this article, a general diffuse interface model with a realistic equation of state (e.g., Peng-Robinson equation) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework.

41 citations

Journal ArticleDOI
TL;DR: The Peng-Robinson equation of state (EoS) has become one of the most extensively applied equations of state in chemical engineering and the petroleum industry due to its excellent accuracy in p...
Abstract: The Peng--Robinson equation of state (PR-EoS) has become one of the most extensively applied equations of state in chemical engineering and the petroleum industry due to its excellent accuracy in p...

33 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the attractive pressure term of the semi-empirical van der Waals equation has been modified for predicting the vapor pressure and volumetric behavior of singie-component systems.
Abstract: The development of a new two-constant equation of state in which the attractive pressure term of the semiempirical van der Waals equation has been modified is outlined. Examples of the use of the equation for predicting the vapor pressure and volumetric behavior of singie-component systems, and the phase behavior and volumetric behavior of binary, ternary, and multicomponent systems are given. The proposed equation combines simplicity and accuracy. It performs as well as or better than the Soave-Redlich-Kwong equation in all cases tested and shows its greatest advantages in the prediction of liquid phase densities.

10,520 citations


"A stable algorithm for calculating ..." refers background in this paper

  • ...The Peng-Robinson equation of state (PR-EOS) [27] has the following form:...

    [...]

  • ...The Peng-Robinson equation of state (PR-EOS) [27] has the following form: p = RT v − b − a(T ) v(v + b) + b(v − b) , where p is the pressure and v is the molar volume....

    [...]

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01 Jan 1962

6,437 citations

Journal ArticleDOI
TL;DR: In this article, a number of numerical methods for stability analysis based on Gibbs' tangent plane criterion are described, which are applicable for both single phase and multiphase systems, mainly for Equation of State calculations using a single model for all fluid phases.

991 citations

Book
01 Apr 2006
TL;DR: The Black Oil model is applied as a guide for welling modeling of fractured porous media and nonisothermal flow as well as for solution of linear systems.
Abstract: Preface 1. Introduction 2. Flow and transport equations 3. Rock and fluid properties 4. Numerical methods 5. Solution of linear systems 6. Single phase flow 7. Two-phase flow 8. The Black Oil model 9. The Compositional model 10. Nonisothermal flow 11. Chemical flooding 12. Flows in fractured porous media 13. Welling modeling 14. Special topics 15. Nomenclature 16. Units Bibliography Index.

790 citations

Journal ArticleDOI
TL;DR: In this paper, an algorithm for calculation of multiphase equilibrium at given temperature and pressure using a single Equation of State as the thermodynamic model is described, and the use of stability analysis to generate initial estimates and of second order convergence methods lead to rapid solution even in the immediate vicinity of critical points.

657 citations


"A stable algorithm for calculating ..." refers background in this paper

  • ...NPT-flash accounts for the condition at specified pressure, temperature, and chemical composition [17, 18, 20]....

    [...]

Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model" ?

In this paper, capillarity is incorporated into the phase equilibrium calculation at specified moles, volume and temperature. To simulate the proposed dynamical model efficiently, the authors adopt the convex-concave splitting of the total Helmholtz energy, and propose a thermodynamically stable numerical algorithm, which is proved to preserve the second law of thermodynamics at the discrete level. Moreover, the authors propose a stable numerical algorithm for the phase stability testing, which can provide the feasible initial conditions.