Unstructured-Coarse-Grid Generation Using Background-Grid Approach

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 326-340 ◽  
Author(s):  
M.. Evazi ◽  
H.. Mahani
Keyword(s):  
Source Term ◽  
Local Density ◽  
Fluid Velocity ◽  
Flow Simulation ◽  
Grid Generation ◽  
Coarse Grid ◽  
Optimization Techniques ◽  
Fine Grid ◽  
Background Grid ◽  
Coarse Grids

Summary Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized gridpoint density and a minimized number of gridblocks, especially for coarse-grid generation from a fine-grid geological model. In any coarse-grid generation, proper distribution of gridpoints, which form the basis of numerical gridblocks, is a challenging task. We show that this can be achieved effectively by a novel grid-generation approach based on a background grid that stores gridpoint spacing parameters. Spacing parameter (L) can be described by Poisson's equation (∇2L = G), where the local density of gridpoints is controlled by a variable source term (G); see Eq. 1. This source term can be based on different gridpoint density indicators, such as permeability variations, fluid velocity, or their combination (e.g., vorticity) where they can be extracted from the reference fine grid. Once a background grid is generated, advancing-front triangulation (AFT) and then Delaunay tessellation are invoked to form the final (coarse) gridblocks. The algorithm produces grids varying smoothly from high- to low-density gridpoints, thus minimizing use of grid-smoothing and -optimization techniques. This algorithm is quite flexible, allowing choice of the gridding indicator, hence providing the possibility of comparing the grids generated with different indicators and selecting the best. In this paper, the capabilities of approach in generation of unstructured coarse grids from fine geological models are illustrated using 2D highly heterogeneous test cases. Flexibility of algorithm to gridding indicator is demonstrated using vorticity, permeability variation, and velocity. Quality of the coarse grids is evaluated by comparing their two-phase-flow simulation results to those of fine grid and uniform coarse grid. Results demonstrate the robustness and attractiveness of the approach, as well as relative quality/performance of grids generated by using different indicators.

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.

A Methodology for Simulations of Complex Turbulent Flows

2002 ◽  
Vol 124 (4) ◽  
pp. 933-942 ◽  
Author(s):  
H. F. Fasel ◽  
J. Seidel ◽  
S. Wernz
Keyword(s):  
Turbulent Flows ◽  
Flow Simulation ◽  
Turbulence Models ◽  
Grid Size ◽  
Coarse Grid ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Fine Grid ◽  
Subgrid Scales ◽  
Grid Points

A new flow simulation methodology (FSM) for computing turbulent shear flows is presented. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The centerpiece of FSM is a strategy to provide the proper amount of modeling of the subgrid scales. The strategy is implemented by use of a “contribution function” which is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is obtained during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that the computation approaches a direct numerical simulation in the fine grid limit, or provides modeling of all scales in the coarse grid limit and thus approaches an unsteady RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in traditional large-eddy simulations (LES). However, a LES that is based on the present strategy is distinctly different from traditional LES in that the required amount of modeling is determined by physical considerations, and that state-of-the-art turbulence models (as developed for Reynolds-averaged Navier-Stokes) can be employed for modeling of the unresolved scales. Thus, in contrast to traditional LES based on the Smagorinsky model, with FSM a consistent approach (in the local sense) to the coarse grid and fine grid limits is possible. As a consequence of this, FSM should require much fewer grid points for a given calculation than traditional LES or, for a given grid size, should allow computations for larger Reynolds numbers. In the present paper, the fundamental aspects of FSM are presented and discussed. Several examples are provided. The examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating complex wall bounded flows, and on the other hand demonstrate the potential of the FSM approach.

scholarly journals Flow Simulation Using Local Grid Refinements to Model Laminated Reservoirs

2018 ◽  
Vol 73 ◽  
pp. 5 ◽  
Author(s):  
Manuel Gomes Correia ◽  
Célio Maschio ◽  
Denis José Schiozer
Keyword(s):  
Simulation Model ◽  
Dynamic Properties ◽  
Flow Behavior ◽  
Flow Simulation ◽  
Coarse Grid ◽  
Thin Layers ◽  
Static Properties ◽  
Dynamic Representation ◽  
Medium Flow ◽  
Local Grid

Super-giant carbonate fields, such as Ghawar, in Saudi Arabia, and Lula, at the Brazilian pre-salt, show highly heterogeneous behavior that is linked to high permeability intervals in thin layers. This article applies Local Grid Refinements (LGR) integrated with upscaling procedures to improve the representation of highly laminated reservoirs in flow simulation by preserving the static properties and dynamic trends from geological model. This work was developed in five main steps: (1) define a conventional coarse grid, (2) define LGR in the conventional coarse grid according to super-k and well locations, (3) apply an upscaling procedure for all scenarios, (4) define LGR directly in the simulation model, without integrate geological trends in LGR and (5) compare the dynamic response for all cases. To check results and compare upscaling matches, was used the benchmark model UNISIM-II-R, a refined model based on a combination of Brazilian Pre-salt and Ghawar field information. The main results show that the upscaling of geological models for coarse grid with LGR in highly permeable thin layers provides a close dynamic representation of geological characterization compared to conventional coarse grid and LGR only near-wells. Pseudo-relative permeability curves should be considered for (a) conventional coarse grid or (b) LGR scenarios under dual-medium flow simulations as the upscaling of discrete fracture networks and dual-medium flow models presents several limitations. The conventional approach of LGR directly in simulation model, presents worse results than LGR integrated with upscaling procedures as the extrapolation of dynamic properties to the coarse block mismatch the dynamic behavior from geological characterization. This work suggests further improvements for results for upscaling procedures that mask the flow behavior in highly laminated reservoirs.

A Combined Global Coarsening Method for 3D Multigrid Applications

2012 ◽  
Vol 236-237 ◽  
pp. 1049-1053
Author(s):  
Zong Zhe Li ◽  
Zheng Hua Wang ◽  
Lu Yao ◽  
Wei Cao
Keyword(s):  
Aspect Ratio ◽  
Present Method ◽  
Unstructured Grid ◽  
Unstructured Grids ◽  
Coarse Grid ◽  
3D Flow ◽  
High Quality ◽  
Coarse Grids

An automatic agglomeration methodology to generate coarse grids for 3D flow solutions on anisotropic unstructured grids has been introduced in this paper. The algorithm combines isotropic octree based coarsening and anisotropic directional agglomeration to yield a desired coarsening ratio and high quality of coarse grids, which developed for cell-centered multigrid applications. This coarsening strategy developed is presented on an unstructured grid over 3D ONERA M6 wing. It is shown that the present method provides suitable coarsening ratio and well defined aspect ratio cells at all coarse grid levels.

A modified-boundary condition algorithm for efficient 3D forward modeling of CSEM data

2021 ◽  
Author(s):  
Rahul Dehiya
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Source Term ◽  
Forward Modeling ◽  
Field Vector ◽  
Fine Grid ◽  
Boundary Field ◽  
Radiation Boundary ◽  
3D Forward Modeling ◽  
Modeling Algorithm

<p>I present a newly developed 3D forward modeling algorithm for controlled-source electromagnetic data. The algorithm is based on the finite-difference method, where the source term vector is redefined by combining a modified boundary condition vector and source term vector. The forward modeling scheme includes a two-step modeling approach that exploits the smoothness of the electromagnetic field. The first step involves a coarse grid finite-difference modeling and the computation of a modified boundary field vector called radiation boundary field vector. In the second step, a relatively fine grid modeling is performed using radiation boundary conditions. The fine grid discretization does not include stretched grid and air medium. The proposed algorithm derives computational efficiency from a stretch-free discretization, air-free computational domain, and a better initial guess for an iterative solver. The numerical accuracy and efficiency of the algorithm are demonstrated using synthetic experiments. Numerical tests indicate that the developed algorithm is one order faster than the finite-difference modeling algorithm in most of the cases analyzed during the study. The radiation boundary method concept is very general; hence, it can be implemented in other numerical schemes such as finite-element algorithms.</p>

Sensitivity-Coefficient Based Inverse Heat Conduction Method for Identifying Hot Spots in Electronics Packages: A Comparison of Grid-Refinement Methods

2021 ◽  
Author(s):  
Patrick Krane ◽  
David Gonzalez Cuadrado ◽  
Francisco Lozano ◽  
Guillermo Paniagua ◽  
Amy Marconnet
Keyword(s):  
Heat Conduction ◽  
Hot Spots ◽  
Computation Time ◽  
Grid Method ◽  
Sensitivity Coefficient ◽  
Coarse Grid ◽  
Inverse Heat Conduction ◽  
Fine Grid ◽  
Temperature Maps ◽  
Electronics Packages

Abstract Estimating the distribution and magnitude of heat generation within electronics packages is pivotal for thermal packaging design and active thermal management systems. Inverse heat conduction methods can provide estimates using measured temperature profiles acquired using infrared imaging or discrete temperature sensors. However, if the heater locations are unknown, applying a fine grid of potential heater locations across the surface where heat generation is expected can result in prohibitively-large computation times. In contrast, using a more computationally-efficient coarse grid can reduce the accuracy of heat flux estimations. This paper evaluates two methods for reducing computation time using a sensitivity-coefficient method for solving the inverse heat conduction problem. One strategy uses a coarse grid that is refined near the hot spots, while the other uses a fine grid of potential heaters only near the hot spots. These grid-refinement methods are compared using both input temperature maps acquired from a "numerical experiment" (where the outputs of a 3D steady-state thermal model in FloTHERM are used for input temperatures) and temperature maps procured using infrared microscopy on a real electronics package. Compared to the coarse-grid method, the fine-grid method reduces computation time without significantly reducing accuracy, making it more convenient for designing and testing electronics packages. It also avoids the problem of "false hot spots" that occurs with the coarse-grid method. Overall, this approach provides a mechanism to predict hot spot locations during design and testing and a tool for active thermal management.

scholarly journals An Integrally Embedded Discrete Fracture Model for Flow Simulation in Anisotropic Formations

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3070
Author(s):  
Renjie Shao ◽  
Yuan Di ◽  
Dawei Wu ◽  
Yu-Shu Wu
Keyword(s):  
Flow Simulation ◽  
Fracture Model ◽  
Fluid Exchange ◽  
Two Phase ◽  
Fine Grid ◽  
Discrete Fracture Model ◽  
Matrix Fracture ◽  
Discrete Fracture ◽  
The Matrix ◽  
Anisotropic Formation

The embedded discrete fracture model (EDFM), among different flow simulation models, achieves a good balance between efficiency and accuracy. In the EDFM, micro-scale fractures that cannot be characterized individually need to be homogenized into the matrix, which may bring anisotropy into the matrix. However, the simplified matrix–fracture fluid exchange assumption makes it difficult for EDFM to address the anisotropic flow. In this paper, an integrally embedded discrete fracture model (iEDFM) suitable for anisotropic formations is proposed. Structured mesh is employed for the anisotropic matrix, and the fracture element, which consists of a group of connected fractures, is integrally embedded in the matrix grid. An analytic pressure distribution is derived for the point source in anisotropic formation expressed by permeability tensor, and applied to the matrix–fracture transmissibility calculation. Two case studies were conducted and compared with the analytic solution or fine grid result to demonstrate the advantage and applicability of iEDFM to address anisotropic formation. In addition, a two-phase flow example with a reported dataset was studied to analyze the effect of the matrix anisotropy on the simulation result, which also showed the feasibility of iEDFM to address anisotropic formation with complex fracture networks.

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