Upscaling, Gridding, and Simulation Using Streamtubes

Portella, Ricardo Cunha Mattos; Hewett, Thomas T.

doi:10.2523/49071-ms

Cited by 5 publications

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“…They are usually nonzero for only a few values of i. Press et al (1992) list values of h k for many wavelets. Based on our previous simulations and experience, we utilized the DB4 wavelet in order to compute the results, for which,…”

Section: The Wavelet Functionsmentioning

confidence: 99%

“…The scale and wavelet functions are interrelated (Daubechies 1988(Daubechies , 1992Press et al 1992). …”

Section: Generation Of the Initial Upscaled Gridmentioning

confidence: 99%

“…In some sense, the WT method, which has been developed by our group over the past few years (Mehrabi and Sahimi 1997;Ebrahimi and Sahimi 2002Sahimi 2008, 2009a,b), is also based on the minimization of the local variations in the permeabilities. The WTs represent relatively recent developments in mathematics (Daubechies 1988(Daubechies , 1992Press et al 1992), which have found a broad and diverse set of applications, including data processing, reservoir engineering and simulations, and upscaling (Sahimi 2003).…”

Section: Introductionmentioning

confidence: 99%

“…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%

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

et al. 2009

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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.

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Section: The Wavelet Functionsmentioning

confidence: 99%

“…The scale and wavelet functions are interrelated (Daubechies 1988(Daubechies , 1992Press et al 1992). …”

Section: Generation Of the Initial Upscaled Gridmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2009

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“…However, it is limited because the coarser grid is constrained to be aligned with the fine grid. Other researchers (Verma and Aziz 1997;Edwards 2002;Portella and Hewett 2000;Castellini et al 2000;Castellini 2001;He 2004) presented techniques based on the use of streamlines computed from a single phase flow solution of the fine scale problem. Alternate gridding procedures based on the grouping of cells of similar permeability were suggested by Garcia et al (1992) and Ebrahimi and Sahimi (2004).…”

mentioning

confidence: 98%

Flexible Unstructured Gridding for 2D Reservoir Coarse Scale Modeling using Fine Scale Permeability Filtering

Hesami

Dabir

2011

Transp Porous Med

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Accurate up-scaling is an essential part of creating a valid reservoir coarse scale dynamic model. In this article, unstructured discretization of spatial domain is accompanied by numerical permeability up-scaling in order to construct an accurate coarse scale model. A new technique for generating a course scale triangular mesh is presented in which the density of elements in key flow regions is kept high to capture accuracy. The fine scale permeability map is investigated using image processing techniques, especially steerable filters, and the results are converted into a high-resolution element size map. This element size map will be refined by the integration of other important factors such as well-position effects and used to construct a coarse triangular mesh. The combination of flux-continuous pressure approximation and mass conservative, total variation diminishing finite volume schemes have been considered to solve two phase flow equations on the control volume finite element mesh. Fine scale simulations results are compared with the coarse scale ones for a series of water flooding examples to investigate the efficiency and accuracy of the presented gridding methodology. This method is developed for 2D cases, but can be easily extended to 3D problems.

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A Streamtube Approach for Modeling Mass and Heat Migration for Thermal Recovery Methods

Usman¹,

Arihara

2002

SPE Asia Pacific Oil and Gas Conference and Exhibition

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This paper presents a new reservoir simulator for mass and heat migrationbased on the streamtube technique. The current version of the program focuseson characterizing migration of the injected fluid. The method is heavily basedon the distribution of the pore volume along each streamtube calculated byusing the Time-of-Flight method. This information and the 1D solution of massand energy equations are used to determine thermal migration as well astemperature changes at production wells. The streamtubes are derived from anunderlying velocity field, which is obtained from the solution of the pressureequation under the assumption of incompressibility. The compressibility effectsare accounted for in the 1D solutions along periodically changingstreamtubes. Simulations are carried out for a five-spot well pattern in 2D areal domainswith various types of heterogeneity under different injection scenarios. Weconfirmed that the results from the streamtube approach had a reasonablebalance between its ability to provide an insight into the behavior of mass andheat flow and the computational efficiency. Comparisons with a commerciallyavailable simulator both validated the method and illustrated the cases inwhich this method is more useful to reservoir engineers. Introduction Higgins and Leighton1,2 and Higgins et al.3 inthe early 1960's are credited with being the first to apply the streamtubetechnique to model convective displacement in porous media and to set the stagefor a number of papers to follow by other authors. An important step forward inthe attempt to model real field problems is due to Doyle and Wurl4, Bommer and Schechter5, Lake et al.6, Emanuel etal.7, Pozucek and Ramirez8,9. In the 1990'sstreamtube methods continued to be explored. These efforts are described innumerous papers notably by Renard10, Thiele11, Thieleet al.12 and Baek and Hewett13. The application ofthe method for flood front management has been described by numerous otherauthors14–16. The reason behind using the approach has been that itallows a fast evaluation of reservoir performance, and that it has beenextended to accommodate realistic flow physics. These strong points have alsoled to a host of other applications, for example, multiphase upscaling throughthe use of pseudo relative permeability17 and flexible gridgeneration during reservoir simulation18. Previous streamtube methods so far focused on the isothermal flow. Limitedwork has been done to extend the application of streamtube/streamlinesimulation to thermal flood simulation. This is not surprising, as the couplingbetween mass and energy transport in thermal flood simulation adds considerablecomplexity. This then would be coupled with an appropriate thermodynamicformulation to account for condensation/vaporization and changes in propertieswith temperature and pressure. A paper written by Emanuel19 isrelated to the non-isothermal flow application. He developed a fixed streamtubemodel for estimating steam drive performance of single pattern and full fieldscale. Unfortunately this paper does not indicate how the mass and energyconservation is formulated and how to solve the coupled equations along thestreamtubes.

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Upscaling, Gridding, and Simulation Using Streamtubes

Cited by 5 publications

References 0 publications

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

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

Flexible Unstructured Gridding for 2D Reservoir Coarse Scale Modeling using Fine Scale Permeability Filtering

A Streamtube Approach for Modeling Mass and Heat Migration for Thermal Recovery Methods

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