Modeling subsurface flow in three-dimensional (3D) discrete fracture networks (DFN) is of interest of many engineering problems, such as CO2 sequestration, natural gas production and geothermal energy extractions. However, the recent grid-based models describing flow behaviors in 3D DFN are still suffering from the complex gridding issue and high computational burden. In this work, a meshless approach is presented for the steady-state flow in DFNs with arbitrary geometries and penetrated wellbores.
A DFN consists of planar polygonal fractures with random orientation, size and flow transmissivity. Based on a parallel BEM approach, the flow solution of a large DFN can be decomposed into a series of sub-domains by the domain decomposition method (DDM). The problem on each sub-domain can be solved independently from each other, and iterations are performed until the continuities of pressure and flux balance are satisfied at fracture intersections. Additionally, BEM solution of each planar fracture only requires the discretization along fracture edges, and penetrated wellbores are simulated by only adding point source nodes instead of the local grid refinement as in conventional grid-based methods. Thus the presented parallel BEM approach significantly reduces the overall storage and computational burden.
The presented method is verified against a commercial finite element method (FEM) simulator on several synthetic examples from simple to complex fracture network geometries. The resultant pressure field shows a good agreement with the fine grid FEM models. The method shows nearly a linear CPU-time scaling dependency to the number of fractures. The performance of the presented method is also investigated in terms of convergence properties and accuracy with respect to several fracture parameters, such as the number of fractures, fracture flow transmissivity, penetrated wellbores and mesh density.
The method has potentials to provide an efficient, accurate and parallel framework to account for large and complex DFNs with numerous penetrated wellbores.
Source code of PyDFN3D will be provided .
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