Abstract
An upscaled Lattice Boltzmann Method (LBM) for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution) and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.
Highlights
Detailed flow simulations in porous media are often modeled using the Darcy or Brinkman approximations. Effective parameters, such as absolute and relative permeabilities, depend on the pore-scale geometry. To compute these effective parameters, pore-scale simulations accounting for relevant geometric features in a Representative Elementary Volume (REV) are commonly used as in [1]
In [9, 10], an external body force, which increases with decreasing permeability, is employed to represent the resistance effect of the porous media to the fluid, where Lattice Boltzmann Method (LBM) is considered as a unified framework for simulations at all scales
Pore-scale flows are routinely modeled by the LBM simulations due to their ability to handle complex geometries and physics
Summary
Detailed flow simulations in porous media are often modeled using the Darcy or Brinkman approximations In these models, effective parameters, such as absolute and relative permeabilities, depend on the pore-scale geometry. In [9, 10], an external body force, which increases with decreasing permeability, is employed to represent the resistance effect of the porous media to the fluid, where LBM is considered as a unified framework for simulations at all scales. These simulations require significant computational resources to converge since the permeability distribution usually has drastic changes in space, which requires a very fine grid for high spatial resolution. The upscaled LBM approach is applied to single-phase flows; this approach can be used for modeling multiphase flow phenomena
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