A preliminary computational investigation of a macro-model for vuggy porous media

Arbogast, Todd; Brunson, Dana; Bryant, Steven L.; Jennings, James W.

doi:10.1016/s0167-5648(04)80056-x

Cited by 33 publications

(29 citation statements)

References 7 publications

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“…A continuous Darcy velocity would therefore be desirable. These spaces have been exploited in [1,2,3]. Current mixed methods achieve (i) at the expense of (ii).…”

Section: Introductionmentioning

confidence: 99%

A Family of Rectangular Mixed Elements with a Continuous Flux for Second Order Elliptic Problems

Arbogast¹,

Wheeler²

2005

SIAM J. Numer. Anal.

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Abstract. We present a family of mixed finite element spaces for second order elliptic equations in two and three space dimensions. Our spaces approximate the vector flux by a continuous function. Our spaces generalize certain spaces used for approximation of Stokes problems. The finite element method incorporates projections of the Dirichlet data and certain low order terms. The method is locally conservative on the average. Suboptimal convergence is proven and demonstrated numerically. The key result is to construct a flux π-projection operator that is bounded in the Sobolev space H 1 , preserves a projection of the divergence, and approximates optimally. Moreover, the corresponding Raviart-Thomas flux preserving π-projection operator is an L 2 -projection when restricted to this family of spaces.

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“…A continuous Darcy velocity would therefore be desirable. These spaces have been exploited in [1,2,3]. Current mixed methods achieve (i) at the expense of (ii).…”

Section: Introductionmentioning

confidence: 99%

A Family of Rectangular Mixed Elements with a Continuous Flux for Second Order Elliptic Problems

Arbogast¹,

Wheeler²

2005

SIAM J. Numer. Anal.

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“…Additional numerical examples related to simulation of flow in vuggy porous media can be found in [1]. For simplicity, in all our examples, is the unit square and α = μ = K = 1.…”

Section: Some Numerical Resultsmentioning

confidence: 99%

“…Here d represents a Darcy element, s is a Stokes element, unspecified is either, and a heavy line is a part of . For x 1 velocity components, a quarter circle in an element indicates that the corner basis function is present over the element 1,2]. Note that in the most reduced case, the element becomes the lowest order space due to Raviart and Thomas [20].…”

Section: The Finite Element Spacementioning

confidence: 99%

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

2007

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We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers-Joseph-Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy-Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L 2 convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses RaviartThomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.

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“…The effective permeability of the entire system can be calculated using the macro-model. Computation studies were performed on this macro-model [1].…”

Section: A Previous Flow Modelingmentioning

confidence: 99%

The Effect of Vug Density on Fluid Flow

Zhan-guo

2009

2009 International Conference on Computational Intelligence and Software Engineering

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Abstract-Fractured vuggy reservoirs have long been observed. A thorough understanding of the variability and fluid flow in fractured vuggy carbonates is lacking. Classical theories of fluid flow are not applicable for highly heterogeneous carbonates. Therefore, it is necessary to conduct research on this type of carbonate which is found in many petroleum reservoirs. Singlephase flow in fractured vuggy media is studied by finite element method. The purpose of this study is to obtain phenomenological data (streamlines, velocity and pressure) during flow in a fractured vuggy media to better understand the effect of vug density on flow. Numerical simulation on fractured vuggy model with different vug density are suggested that gravitational impact on flow is more significant in vugs; in identical horizontal plane, velocity in vug is less than velocity in fracture; pressure drop between the both sides of model with bigger vug density is less.

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A preliminary computational investigation of a macro-model for vuggy porous media

Cited by 33 publications

References 7 publications

A Family of Rectangular Mixed Elements with a Continuous Flux for Second Order Elliptic Problems

A Family of Rectangular Mixed Elements with a Continuous Flux for Second Order Elliptic Problems

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

The Effect of Vug Density on Fluid Flow

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