Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Juanes, Ruben; Patzek, Tadeusz W

doi:10.1023/b:tipm.0000038251.10002.5e

Cited by 46 publications

(72 citation statements)

References 69 publications

(98 reference statements)

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“…Under a (linear) change of variables, the water and gas saturations may be understood as normalized saturations, rather than actual saturations [43]. In what follows we shall understand that this change of variables has been employed, so that the three-phase flow region -the range of saturations where relative permeabilities are strictly positivecovers the entire saturation triangle:…”

Section: Remarksmentioning

confidence: 99%

“…The character of the system (34) depends on the eigenvalues and eigenvectors of the Jacobian matrix f . In [43] we argue that this matrix must have real and distinct eigenvalues for the solution to be physically plausible, and we derive conditions on the relative permeability functions so that this requirement is satisfied. Here, we further assume that the capillary diffusion tensor is positive semi-definite.…”

Section: Remarksmentioning

confidence: 99%

“…Strictly speaking, relative permeabilities should depend not only on the fluid saturations, but also on the saturation history, wettability characteristics, gravity effects, and fluid viscosities [43,44]. Thus, they should be properly called functionals, rather than functions.…”

Section: Relative Permeabilities and Capillary Pressuresmentioning

confidence: 99%

“…The saturation triangle is usually represented as a ternary diagram [43], in which the pair (S w , S g ) corresponds to the triple (S w , S g , S o ), where Figure 1). …”

Section: Remarksmentioning

confidence: 99%

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Stabilized numerical solutions of three-phase porous media flow using a multiscale finite element formulation

Juanes¹,

Patzek²

2003

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We present a multiscale formulation for the numerical solution of one-dimensional three-phase flow through porous media. In the case of vanishing capillarity effects, the system of equations describing three-phase flow becomes almost hyperbolic, and the solution develops shocks and boundary layers. Under these conditions, classical numerical methods produce a solution that is either unstable or excessively diffusive. The key idea of the proposed formulation, originally presented by Hughes [Comput. Methods Appl. Mech. Engrg., 127:387-401 (1995)], is a multiple-scale decomposition into resolved -grid-scales and unresolved -subgrid-scales. Incorporating the effect of the subgrid scales onto the coarse scale problem results in a finite element method with enhanced stability properties, capable of accurately representing the sharp features of the solution. In the formulation developed herein, the multiscale split is invoked prior to any linearization of the equations. Special attention is given to the choice of the matrix of stabilizing coefficients, and a novel discontinuity-capturing technique is proposed and compared with existing formulations.The methodology is applied to the simulation of two problems of great practical interest: oil filtration in the vadose zone, and watergas injection in a hydrocarbon reservoir. These numerical simulations clearly show the potential and applicability of the formulation for solving the highly nonlinear, nearly hyperbolic system of threephase porous media flow on very coarse grids.

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Section: Remarksmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

Section: Relative Permeabilities and Capillary Pressuresmentioning

confidence: 99%

“…The saturation triangle is usually represented as a ternary diagram [43], in which the pair (S w , S g ) corresponds to the triple (S w , S g , S o ), where Figure 1). …”

Section: Remarksmentioning

confidence: 99%

See 2 more Smart Citations

Stabilized numerical solutions of three-phase porous media flow using a multiscale finite element formulation

Juanes¹,

Patzek²

2003

Self Cite

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“…See [6] for some experimental evidence of the occurrence of transitional shock waves. Following [16], any choice…”

Section: Numerical Experimentsmentioning

confidence: 99%

Numerical Simulation of Three-Phase Flow in Heterogeneous Porous Media

Abreu

Furtado

Pereira

Lecture Notes in Computer Science

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Abstract. We describe an efficient numerical simulator, based on an operator splitting technique, for three-phase flow in heterogeneous porous media that takes into account capillary forces, general relations for the relative permeability functions and variable porosity and permeability fields. Our numerical procedure combines a non-oscillatory, second order, conservative central difference scheme for the system of hyperbolic conservation laws modeling the convective transport of the fluid phases with locally conservative mixed finite elements for the approximation of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity calculation. This numerical procedure has been used to investigate the existence and stability of nonclassical waves (also called transitional or undercompressive waves) in heterogeneous two-dimensional flows, thereby extending previous results for one-dimensional problems.

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Comparative assessment of three‐phase oil relative permeability models

Ranaee

Riva

Porta

et al. 2016

Water Resources Research

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We assess the ability of 11 models to reproduce three‐phase oil relative permeability ( kro) laboratory data obtained in a water‐wet sandstone sample. We do so by considering model performance when (i) solely two‐phase data are employed to render predictions of kro and (ii) two and three‐phase data are jointly used for model calibration. In the latter case, a Maximum Likelihood (ML) approach is used to estimate model parameters. The tested models are selected among (i) classical models routinely employed in practical applications and implemented in commercial reservoir software and (ii) relatively recent models which are considered to allow overcoming some drawbacks of the classical formulations. Among others, the latter set of models includes the formulation recently proposed by Ranaee et al. (), which has been shown to embed the critical effects of hysteresis, including the reproduction of oil remobilization induced by gas injection in water‐wet media. We employ formal model discrimination criteria to rank models according to their skill to reproduce the observed data and use ML Bayesian model averaging to provide model‐averaged estimates (and associated uncertainty bounds) of kro by taking advantage of the diverse interpretive abilities of all models analyzed. The occurrence of elliptic regions is also analyzed for selected models in the framework of the classical fractional flow theory of displacement. Our study confirms that model outcomes based on channel flow theory and classical saturation‐weighted interpolation models do not generally yield accurate reproduction of kro data, especially in the regime associated with low oil saturations, where water alternating gas injection (WAG) techniques are usually employed for enhanced oil recovery. This negative feature is not observed in the model of Ranaee et al. (2015) due to its ability to embed key effects of pore‐scale phase distributions, such as hysteresis effects and cycle dependency, for modeling kro observed during WAG.

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Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Cited by 46 publications

References 69 publications

Stabilized numerical solutions of three-phase porous media flow using a multiscale finite element formulation

Stabilized numerical solutions of three-phase porous media flow using a multiscale finite element formulation

Numerical Simulation of Three-Phase Flow in Heterogeneous Porous Media

Comparative assessment of three‐phase oil relative permeability models

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