Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

By J. Monteagudo, Abbas Firoozabadi. 2004

215 citations recorded by the source corpus.

We provide a numerical procedure for the simulation of two‐phase immiscible and incompressible flow in two‐ and three‐dimensional discrete‐fractured media. The concept of cross‐flow equilibrium is used to reduce the fracture dimension from n to (n‐1) in the calculation of flow in the fractures. This concept, which is often referred to as the discrete‐fracture model, has a significant effect on the reduction of computational time. The spatial discretization is performed with the control‐volume method. This method is locally conservative and allows the use of unstructured grids to represent complex geometries, such as discrete‐fracture configurations. The relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes, which is consistent with the physics of fluid flow. The system of partial differential equations is decoupled and solved using the implicit‐pressure, explicit‐saturation (IMPES) approach. The algorithm has been successfully tested in two‐ and three‐dimensional numerical simulations of wetting phase fluid injection (such as water) in discrete‐fractured media saturated by a nonwetting phase (such as nonaqueous phase liquid or oil) with mild to high nonlinearity in relative permeability and capillary pressure. To the best of our knowledge, results for simulations of two‐phase immiscible and incompressible flow in three‐dimensional discrete‐fractured media, including capillary and gravity effects, are the first to appear in the literature.

Subfields: Computational Mechanics, Environmental Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/57f69880861c26749aee5fc25ea3daf450d9e8e1

How researchers see this paper

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In Computational Mechanics

1. Abbas Firoozabadi
2. H. Hoteit
3. Ali Zidane
4. Jisheng Kou
5. Shuyu Sun
6. Matthew W. Farthing
7. Fred L. Ogden

In Environmental Engineering

1. H. Hoteit
2. Abbas Firoozabadi
3. Ali Zidane
4. Fred L. Ogden
5. Matthew W. Farthing

In Mechanical Engineering

1. H. Hoteit
2. Abbas Firoozabadi
3. Ali Zidane

Citations in the corpus

• Numerical Modeling of Diffusion in Fractured Media for Gas-Injection and -Recycling Schemes (2009, methodology): “…work, we use the discrete-fracture model, where fractures in an n-dimensional space are simplified to elements in an (n-1)-dimensional space by integrating along the fracture aperture (Bastian et al. 2000; Bogdanov et al. 2003; Karimi-Fard and Firoozabadi 2003; Monteagudo and Firoozabadi 2004).”
• Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures (2008, unknown): “(4), we get the following expression of the capillary potential, Uc [84]: Uc 1⁄4 Un Uw 1⁄4 pc þ ðqn qwÞgz: ð6Þ”
• Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media (2005, methodology): “Unlike the methods of the first category [Bastian et al., 2000; Karimi-Fard and Firoozabadi, 2003; Monteagudo and Firoozabadi, 2004], all methods in the W11412 HOTEIT AND FIROOZABADI: MULTICOMPONENT FLUID FLOW IN FRACTURED MEDIA 5 of 15 W11412 second category face difficulties and therefore need…”