scholarly journals Study of compositional multiphase flow formulation using complementarity conditions

2019 ◽  
Vol 74 ◽  
pp. 43 ◽  
Author(s):  
Ibtihel Ben Gharbia ◽  
Eric Flauraud
Keyword(s):  
Phase Transitions ◽  
Multiphase Flow ◽  
Reservoir Simulation ◽  
Flow Problem ◽  
Equations Of State ◽  
Reservoir Engineering ◽  
Petroleum Reservoir ◽  
Complementarity Conditions ◽  
Engineering Problems ◽  
Natural Variable

In this article, two formulations of multiphase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so-called natural variable formulation commonly used in reservoir simulation, the second has been introduced by Lauseret al.and uses the phase pressures, saturations and component fugacities as main unknowns. We will discuss how the Coats and the Lauser approaches can be used to solve a compositional multiphase flow problem with cubic equations of state of Peng and Robinson. Then, we will study the results of several synthetic cases that are representative of petroleum reservoir engineering problems and we will compare their numerical behavior.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

High-pressure phase transitions and the equations of state of BaS and BaO

1986 ◽  
Vol 33 (6) ◽  
pp. 4221-4226 ◽  
Author(s):  
Samuel T. Weir ◽  
Yogesh K. Vohra ◽  
Arthur L. Ruoff
Keyword(s):  
High Pressure ◽  
Phase Transitions ◽  
Equations Of State ◽  
High Pressure Phase ◽  
Pressure Phase

scholarly journals Prediction of 10-fold coordinated TiO2 and SiO2 structures at multimegabar pressures

2015 ◽  
Vol 112 (22) ◽  
pp. 6898-6901 ◽  
Author(s):  
Matthew J. Lyle ◽  
Chris J. Pickard ◽  
Richard J. Needs
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Electronic Properties ◽  
First Principles ◽  
Pressure Range ◽  
Extrasolar Planets ◽  
Equations Of State ◽  
Space Group ◽  
P Type ◽  
Pressure Phase

We predict by first-principles methods a phase transition in TiO2 at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated structure with space group I4/mmm. This is the first report, to our knowledge, of the pressure-induced phase transition to the I4/mmm structure among all dioxide compounds. The I4/mmm structure was found to be up to 3.3% denser across all pressures investigated. Significant differences were found in the electronic properties of the two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implications of our findings were extended to SiO2, and an analogous Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, which are well-established models for the phase transitions in other AX2 compounds, including SiO2. As in TiO2, the transition to I4/mmm corresponds to the metallization of SiO2. This transformation is in the pressure range reached in the interiors of recently discovered extrasolar planets and calls for a reformulation of the equations of state used to model them.

Phase Transitions

2019 ◽  
pp. 205-222
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Van Der Waals ◽  
Ideal Gas ◽  
Phase Rule ◽  
Clapeyron Equation ◽  
Maxwell Construction

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, and an instability leads to a liquid-gas phase transition. The Maxwell construction for the pressure at which a phase transition occurs is derived. The effect of phase transition on the Gibbs free energy and Helmholtz free energy is shown. Latent heat is defined, and the Clausius–Clapeyron equation is derived. Gibbs' phase rule is derived and illustrated.

A Comparison Study on Algorithms in Reservoir Automatic History Matching

2012 ◽  
Vol 518-523 ◽  
pp. 4376-4379
Author(s):  
Bao Yi Jiang ◽  
Zhi Ping Li
Keyword(s):  
Objective Function ◽  
Reservoir Simulation ◽  
History Matching ◽  
Optimization Algorithms ◽  
Reservoir Engineering ◽  
Comparison Study ◽  
Automatic History Matching ◽  
Numerical Reservoir Simulation ◽  
Computational Capability ◽  
Matching Procedure

With the increase in computational capability, numerical reservoir simulation has become an essential tool for reservoir engineering. To minimize the objective function involved in the history matching procedure, we need to apply the optimization algorithms. This paper is based on the optimization algorithms used in automatic history matching.

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