Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)

Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)

Hosseinimehr, S.M. (TU Delft Numerical Analysis)
Cusini, M. (TU Delft Reservoir Engineering)
Vuik, Cornelis (TU Delft Numerical Analysis)
Hajibeygi, H. (TU Delft Reservoir Engineering)

2018

We present an algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM), where fractures are resolved at fine scale with an embedded discrete modelling approach. This fine-scale discrete system employs independent fine-scale computational grids for heterogeneous matrix and discrete fractures, which results in linear system sizes out of the scope of the classical simulation approaches. To reduce the computational costs, yet provide accurate solutions, on this highly resolved fine-scale mesh, F-ADM imposes independent dynamic multilevel coarse grids for both matrix and lower-dimensional discrete fractures. The fully-implicit discrete system is then mapped into this adaptive dynamic multilevel resolution for all unknowns (i.e., pressure and phase saturation). The dynamic resolution aims for resolving sharp fronts for the transport unknowns, thus constant interpolators are used to map the saturation from coarse to fine grids both in matrix and fractures. However, due to the global nature of the pressure unknowns, local multilevel basis functions for both matrix and fractures with flexible matrix-fracture coupling treatment are introduced for the pressure. The assembly of the full sets of basis functions allows for mapping the solutions up and down between any resolutions. Due to its adaptive multilevel resolution, F-ADM develops an automatic integrated framework to homogenise or explicitly represent a fracture network at a coarser level by selection of the multilevel coarse nodes in each sub-domain. Various test cases, including multiphase flow in 2D and 3D media, are studied, where only a fraction of the fine-scale grids is employed to obtain accurate nonlinear multiphase solutions. F-ADM casts a promising approach for large-scale simulation of multiphase flow in fractured media.

Adaptive mesh refinement
Algebraic multiscale method
Flow in porous media
Fractured porous media
Multilevel multiscale method
Multiscale basis functions
Scalable physics-based nonlinear simulation

http://resolver.tudelft.nl/uuid:e3f5a9df-2c73-40fd-a51b-d4ba6469c9e6

https://doi.org/10.1016/j.jcp.2018.06.075

0021-9991

Journal of Computational Physics, 373, 324-345

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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© 2018 S.M. Hosseinimehr, M. Cusini, Cornelis Vuik, H. Hajibeygi