Scaling-Up Fine Grid Models Using Pseudo Functions in Heterogeneous Porous Media

2004 ◽  
Author(s):  
Y. Azoug ◽  
D. Tiab
Keyword(s):  
Porous Media ◽  
Scaling Up ◽  
Heterogeneous Porous Media ◽  
Fine Grid

scholarly journals Complexity Reduction of Multiphase Flows in Heterogeneous Porous Media

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 144-151 ◽  
Author(s):  
Mehdi Ghommem ◽  
Eduardo Gildin ◽  
Mohammadreza Ghasemi
Keyword(s):  
Porous Media ◽  
Model Reduction ◽  
Flow Behavior ◽  
Computational Cost ◽  
Heterogeneous Porous Media ◽  
Production Optimization ◽  
Dynamic Mode ◽  
Two Phase ◽  
Fine Grid ◽  
Mode Decomposition

Summary In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in heterogeneous porous media. We propose intrusive and nonintrusive model-reduction approaches that enable a significant reduction in the size of the subsurface flow problem while capturing the behavior of the fully resolved solutions. In one approach, we use the dynamic mode decomposition. This approach does not require any modification of the reservoir simulation code but rather post-processes a set of global snapshots to identify the dynamically relevant structures associated with the flow behavior. In the second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper-orthogonal-decomposition modes. Furthermore, we use the discrete empirical interpolation method to approximate the mobility-related term in the global-system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE-10 benchmark permeability field, and present a numerical example in two-phase flow. One can efficiently use the proposed model-reduction methods in the context of uncertainty quantification and production optimization.

scholarly journals Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 904
Author(s):  
Denis Spiridonov ◽  
Maria Vasilyeva ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Raghavendra Jana
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Surface Topography ◽  
Rough Surface ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Basis Functions ◽  
Richards Equation ◽  
Small Scale ◽  
Fine Grid

In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions.

scholarly journals Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Li ◽  
Donald Brown
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Effective Permeability ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Force Model ◽  
Fine Grid ◽  
Reduced Order ◽  
Boltzmann Method

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.

The Convergence Rate of Iterative Procedures for Elliptic Problems in Heterogeneous Media

2014 ◽  
Vol 353 ◽  
pp. 298-305
Author(s):  
Alexandre Sant Francisco ◽  
Helio Pedro Amaral Souto ◽  
Thiago Jordem Pereira
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Heterogeneous Media ◽  
Heterogeneous Porous Media ◽  
Computational Effort ◽  
Fine Grid ◽  
Hybrid Finite Element Method ◽  
State Diffusion ◽  
Media Flows ◽  
Iterative Procedures

We investigate the convergence rate of two iterative procedures that approximate the solutionof fluid flow problems in heterogeneous porous media. Porous media flows at large scales arecomplex problems, which require fine grid solutions to provide accurate results. Pressures and velocitiesassociated to these problems are governed by second order elliptic equations. We discretizesuch equations by a mixed and hybrid finite element method, combined with domain-decompositioniterative procedures. In order to minimize the computational effort involved in the numerical approximation,we have presented an iterative procedure to accelerate the convergence rate in the approximation.In this paper, we perform numerical experiments to compare iterative procedures in order tocheck which one provides the best convergence rate. We believe that steady-state diffusion problemscan be solved efficient and accurately by the most robust procedure.

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