Difference between revisions of "Model concepts"
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== Model concepts == | == Model concepts == | ||
| − | + | Model concepts of different complexity have been developed and are used for the modeling of flow and transport in fractured porous media. Here is an overview of the major groups. | |
=== Equivalent porous-medium model (EPM) === | === Equivalent porous-medium model (EPM) === | ||
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However, the numerical efforts are also highest for this model, especially for complex fracture networks with many fractures. | However, the numerical efforts are also highest for this model, especially for complex fracture networks with many fractures. | ||
For good simulation results, a very fine grid resolution at the fracture-matrix interface is required. | For good simulation results, a very fine grid resolution at the fracture-matrix interface is required. | ||
| − | [[File:DFM.png|Discrete-fracture approach.|x200px|none|thumb|Discrete-fracture approach.]] | + | <!--[[File:DFM.png|Discrete-fracture approach.|x200px|none|thumb|Discrete-fracture approach.]]--> |
| − | [[File:Plume DFM 8yrs highKcontrast-50ug.png|x200px|none|thumb|Example of a DFM simulation.]] | + | <!--[[File:Plume DFM 8yrs highKcontrast-50ug.png|x200px|none|thumb|Example of a DFM simulation.]]--> |
| + | |||
| + | <gallery widths=180px heights=200px> | ||
| + | File:DFM.png|Discrete-fracture approach. | ||
| + | File:Plume DFM 8yrs highKcontrast-50ug.png|Example of a DFM simulation. | ||
| + | </gallery> | ||
=== Random-walk methods === | === Random-walk methods === | ||
Revision as of 09:16, 12 January 2017
Contents
Model concepts
Model concepts of different complexity have been developed and are used for the modeling of flow and transport in fractured porous media. Here is an overview of the major groups.
Equivalent porous-medium model (EPM)
The equivalent porous medium model is a standard model concept for porous media with parameters averaged over control volumes. Usually, a flow model and a transport model are solved. Darcy's law is usually used to compute flow in the porous media. Contaminant transport can be modeled with the advection-dispersion equation, where different processes like sorption and degradation can be included.
Due to its simplicity and its low computational effort, the EPM model is widely used, also for fractured geologies. However, fractures are not explicitly modeled. Instead, a bulk or average hydraulic conductivity and effective diffusion or dispersion coefficients are used. This has as consequence that flow and transport in fractures and the exchange with the matrix cannot be correctly reproduced, leading to poor predictions for dual-continuum aquifers.
Dual-continuum model
The dual-continuum model, often also called dual-porosity model, uses two continua, the matrix and the fracture continuum. Balance equations for flow and transport are formulated for each continuum. The basic concept is described in Gerke and Van Genuchten (1993). Different parameters are used in the continua, f.e. porosities and conductivities specific for the fractures and for the matrix. The continua are coupled via exchange fluxes using the source and sink terms in the balance equations, allowing for exchange of water and substances between fractures and matrix. For that purpose, the exchange fluxes and exchange coefficient have to be defined and the choice is not clear. The exchange coefficients are usually used as fitting parameters. Concepts with more than two continua (f.e. Multiple INteracting Continua approach, MINC) have also been developed.
Discrete-fracture model (DFM)
The discrete-fracture model (DFM) is the most detailed approach for fracture flow and transport modeling. The (major) fractures are explicitly discretized and embedded in the porous matrix. Usually, the fractures are resolved with one dimension less than the matrix (e.g. matrix in 3D, fractures in 2D). The fractures have to be characterized by properties like aperture, length, spacing, main orientation. Fractures and matrix are usually coupled at the fracture-matrix interface by flux continuity and continuity of the primary variables (hydraulic head, concentration). This is the most physically-based approach and the exchange between fractures and matrix happens naturally. However, the numerical efforts are also highest for this model, especially for complex fracture networks with many fractures. For good simulation results, a very fine grid resolution at the fracture-matrix interface is required.
Discrete-fracture approach.
Example of a DFM simulation.
Random-walk methods
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