A Quantitative and Qualitative Comparison of Coarse Grid Generation Techniques for Numerical Simulation of Flow in Heterogeneous Porous Media

2009 ◽  
Author(s):  
Peyman Mostaghimi Qomi ◽  
Hassan Mahani ◽  
Bahar Firoozabadi
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Grid Generation ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Qualitative Comparison

A Quantitative and Qualitative Comparison of Coarse-Grid-Generation Techniques for Modeling Fluid Displacement in Heterogeneous Porous Media

2010 ◽  
Vol 13 (01) ◽  
pp. 24-36 ◽  
Author(s):  
P.. Mostaghimi ◽  
H.. Mahani
Keyword(s):  
Performance Indicator ◽  
Fluid Velocity ◽  
Grid Generation ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Two Phase ◽  
Qualitative Comparison ◽  
Fluid Displacement ◽  
Local Results ◽  
Global And Local

Summary To apply upscaling techniques is an undeniable demand in reservoir simulation, when one considers the difference between the level of detail in a geological model and the level of details that can be handled by a reservoir simulator. Upscaling the reservoir model involves first constructing a coarse grid by using gridding algorithms and then computing average properties for coarse gridblocks. Although various techniques have been proposed for each of these steps, one needs to be aware of strengths and weaknesses of each technique before attempting to apply them. In this paper, we focus on different gridding methods and evaluate their performances. Three main grid-generation techniques are considered: permeability-based (PB), flow-based (FB), and vorticity-based (VB) methods. We apply all three methods to a number of 2D heterogeneous models and simulate two-phase flow on the constructed grids. Then we compare their obtained global and local results. Fluid cuts at the producer is employed as the global performance indicator and saturation-distribution error as the local indicator. We show that FB and VB gridding, which are dynamic methods, are superior to PB gridding, which is a static method. On the basis of this analysis, we then concentrate on FB and VB gridding and investigate their performance in greater detail. While FB gridding uses fluid velocity as gridblock density indicator, VB gridding combines velocity and permeability variation in gridding according to its definition and takes advantage of both. Therefore, although performance of FB and VB gridding is comparable in many cases, VB has the benefit of producing coarse gridblocks with more-uniform permeability and fluid-properties distribution. This in turn yields more-accurate global and local results and reduces application of sophisticated upscaling techniques and fulltensor permeability upscaling.

scholarly journals Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

2012 ◽  
Vol 95 (1) ◽  
pp. 25-54 ◽  
Author(s):  
Panneerselvam Ranganathan ◽  
Rouhollah Farajzadeh ◽  
Hans Bruining ◽  
Pacelli L. J. Zitha
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Natural Convection ◽  
Heterogeneous Porous Media ◽  
Geological Storage ◽  
Co2 Geological Storage

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.

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