Flow based modules for grid generation in two and three dimensions

Castellini, A.; Edwards, Michael G.; Durlofsky, Louis J.

doi:10.3997/2214-4609.201406120

Cited by 47 publications

(14 citation statements)

References 0 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

“…For such situations, well pseudo-functions to account for the pressure changes were suggested by Chappelear and Hirasaki (1976) and King et al (1991). Durlofsky et al (2000) developed a method for calculating the transmissibility and well index for single-phase flow based on the solution to the local well-driven flow. Grid selection methods that rely on dynamic responses, such as streamline simulation, in order to identify the locations of the grid blocks in the GM through which most of the fluids pass, were also proposed by Verma and Aziz (1996) and Castellini et al (2000).…”

Section: Introductionmentioning

confidence: 99%

“…Durlofsky et al (2000) developed a method for calculating the transmissibility and well index for single-phase flow based on the solution to the local well-driven flow. Grid selection methods that rely on dynamic responses, such as streamline simulation, in order to identify the locations of the grid blocks in the GM through which most of the fluids pass, were also proposed by Verma and Aziz (1996) and Castellini et al (2000). Static methods, suggested by Garcia et al (1992), Li and Beckner (2000), and Caers (2001, 2002), that rely on the spatial distribution of the permeability for developing upscaled grids, are also robust.…”

Section: Introductionmentioning

confidence: 99%

Upscaling and Simulation of Waterflooding in Heterogeneous Reservoirs Using Wavelet Transformations: Application to the SPE-10 Model

Rasaei

Sahimi

2007

Transp Porous Med

View full text Add to dashboard Cite

We have developed an accurate and highly efficient method for upscaling and simulation of immiscible displacements in three-dimensional (3D) heterogeneous reservoirs, which is an extension of the technique that we developed previously for 2D systems. The method utilizes wavelet transformations (WTs) to upscale the geological model of a reservoir, based on the spatial distribution of the single-phase permeabilities and the locations of the wells in the reservoir. It generates a non-uniform grid in which the resolved structure of the fine grid around the wells, as well as in the high-permeability sectors, are preserved, but the rest of the grid is upscaled. A robust uplayering procedure is used to reduce the number of the layers, and the WTs are used to upscale each layer areally. To demonstrate the method's accuracy and efficiency, we have applied it to the geological model of a highly heterogeneous reservoir put forward in the tenth Society of Petroleum Engineers comparative solution project (the SPE-10 model), and carried out simulation of waterflooding in the upscaled model. Various upscaling scenarios were examined, and although some of them resulted in efficient simulations and accurate predictions, the results when non-uniform upscaling is used based on the WT technique are in excellent agreement with the solution of the same problem in the fine grid of the SPE-10 model. Most importantly, the speed-up factors that we obtain are several orders of magnitude. Hence, the method renders it unnecessary to use massively parallel computations for such problems.

show abstract

“…Thus, numerous techniques have also been developed for upscaling of the GM. Some of such methods rely on the dynamic response of the reservoir, in order to identify the sectors in the grid in which a relatively resolved structure must be used, while the rest of the GM is upscaled and is represented by coarsened (enlarged) grid blocks (see, for e.g., Verma and Aziz 1997;Durlofsky et al 1997;Edwards et al 1998;Wallstorm et al 1999;Portella and Hewett 2000;Castellini et al 2000). Such dynamics-based upscaling methods are effective in accurately preserving the flow response of the fine-scale regions in the cases in which the boundary conditions remain relatively constant.…”

Section: Introductionmentioning

confidence: 99%

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

Flow based modules for grid generation in two and three dimensions

Cited by 47 publications

References 0 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

Upscaling and Simulation of Waterflooding in Heterogeneous Reservoirs Using Wavelet Transformations: Application to the SPE-10 Model

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

Contact Info

Product

Resources

About