Quasi K-Orthogonal Streamline Grids: Gridding and Discretization

Edwards, Michael G.; Elf, Regis Agut; Aziz, Khalid

doi:10.2118/49072-ms

Cited by 19 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As shown in the figure, curvilinear lines derived from constant ψ in the Φ-domain are tangent to flow streamlines, and curvilinear lines derived from constant φ are perpendicular to the direction of flow of information. At the end, it is worth to mention that various numerical techniques for structured flow-based gridding have been proposed both within Cartesian and curvilinear grid frameworks [27][28][29]. These techniques are based on the use of streamlines computed from a single-phase flow problem.…”

Section: Boundary-fitted Flow-based Griddingmentioning

confidence: 99%

Topology control in large-scale wireless sensor networks: Between information source and sink

2013

View full text Add to dashboard Cite

With non-uniform traffic patterns in wireless sensor networks due to the manyto-one nature of communications, the traditional definition of connectivity in graph theory does not seem to be sufficient to satisfy the requirements of sensor networks. In this work, a new notion of connectivity (called pathimplementability) is defined which represents the ability of sensor nodes to relay traffic along a given direction field (referred to as information flow vector field) D. The magnitude of information flow is proportional to the traffic flux (per unit length) passing through any point in the network, and its direction is toward the flow of traffic. The flow field may be obtained from engineering knowledge or as a solution to an optimization problem. In either case, information flow flux lines are abstract paths that are assumed to represent desired paths for flow of traffic. In a sensor network with a given flow field D(x, y), we show that a density of n(x, y) = O(| D(x, y)| 2 ) sensor nodes is not sufficient to implement the flow field. On the other hand, by increasing the density of wireless nodes to n(x, y) = O(| D(x, y)| 2 log | D(x, y)|), the flow field becomes path-implementable. Path-implementability requires more nodes than simple connectivity. However, it guarantees existence of enough paths connecting the information source to the sink so that all the traffic can be transmitted to the sink. We also propose a joint MAC and routing protocol to forward traffic along the flow field; the proposed tier-based scheme can be further exploited to build lightweight protocol stacks which meet the specific requirements of dense sensor networks.

show abstract

Section: Boundary-fitted Flow-based Griddingmentioning

confidence: 99%

Topology control in large-scale wireless sensor networks: Between information source and sink

2013

View full text Add to dashboard Cite

show abstract

Upscaled Unstructured Computational Grids for Efficient Simulation of Flow in Fractured Porous Media

et al. 2009

View full text Add to dashboard Cite

Discrete fracture modeling (DFM) is currently the most promising approach for modeling of naturally fractured reservoirs and simulation of multiphase fluid flow therein. In contrast with the classical double-porosity/double permeability models, in the DFM approach all the interactions and fluid flow in and between the fractures and within the matrix are modeled in a unified manner, using the same computational grid. There is no need for computing the shape factors, which are crucial to the accuracy of the double-porosity models. We have exploited this concept in order to develop a new method for the generation of unstructured computational grids. In the new approach the geological model (GM) of the reservoir is first generated, using square or cubic grid blocks. The GM is then upscaled using a method based on the multiresolution wavelet transformations that we recently developed. The upscaled grid contains a distribution of the square or cubic blocks of various sizes. A map of the blocks' centers is then used with an optimized Delauney triangulation method and the advancingfront technique, in order to generate the final unstructured triangulated grid suitable for use in any general reservoir simulator with any number of fluid phases. The new method also includes an algorithm for generating fractures that, contrary to the previous methods, does not require modifying their paths due to the complexities that may arise in spatial distribution of the grid blocks. It also includes an effective partitioning of the simulation domain that results in large savings in the computation times. The speed-up in the computations with the new upscaled unstructured grid is about three orders of magnitude over that for the initial GM. Simulation of waterflooding indicates that the agreement between the results obtained with the GM and the upscaled unstructured grid is excellent. The method is equally 123 196 M. Sahimi et al. applicable to the simulations of multiphase flow in unfractured, but highly heterogeneous, reservoirs.

show abstract

Upscaling of Geological Models of Oil Reservoirs with Unstructured Grids Using Lifting-Based Graph Wavelet Transforms

2018

View full text Add to dashboard Cite

Quasi K-Orthogonal Streamline Grids: Gridding and Discretization

Cited by 19 publications

References 7 publications

Topology control in large-scale wireless sensor networks: Between information source and sink

Topology control in large-scale wireless sensor networks: Between information source and sink

Upscaled Unstructured Computational Grids for Efficient Simulation of Flow in Fractured Porous Media

Upscaling of Geological Models of Oil Reservoirs with Unstructured Grids Using Lifting-Based Graph Wavelet Transforms

Contact Info

Product

Resources

About