Core Concepts
A simple yet effective extension of the Box-DFM method to include low-permeable barriers, requiring only minimal additional degrees of freedom and maintaining the symmetric positive-definite property of the stiffness matrix.
Abstract
The paper presents an extension of the Box-DFM (Discrete Fracture Model) method to include the effects of low-permeable barriers in fractured porous media. The key highlights are:
The extended Box-DFM method remains identical to the traditional Box-DFM in the absence of barriers, requiring only minimal additional degrees of freedom to accommodate pressure discontinuities across barriers.
The method adopts a broken Lagrange finite element space as the trial functions and uses the low-dimensional Darcy's law to compute the flux across cell interfaces aligned with low-permeable barriers.
The resulting stiffness matrix of the extended Box-DFM is proven to be symmetric positive-definite, inheriting the favorable properties of the original Box-DFM.
Extensive numerical tests on published benchmark problems demonstrate the validity and performance of the extended method, with comparisons to existing finite volume discrete fracture models.
The range of validity is also studied, showing the method performs well when the tangential permeability of barriers is no greater than the porous matrix, but may not be suitable for barriers with high tangential permeability.
Stats
The permeability tensor of the porous matrix is denoted as Km.
The permeability of high-permeable fractures is denoted as kf.
The permeability of low-permeable barriers is denoted as kb.
The aperture of fractures and barriers is denoted as a.
Quotes
"The box method discrete fracture model (Box-DFM) is an important finite volume-based discrete fracture model (DFM) to simulate flows in fractured porous media."
"The inclusion of barriers requires only minimal additional degrees of freedom to accommodate pressure discontinuities and necessitates minor modifications to the original coding framework of the Box-DFM."
"We use extensive numerical tests on published benchmark problems and comparison with existing finite volume DFMs to demonstrate the validity and performance of the method."