Calculating the Effective Permeability Tensor of a Gridblock

Kasap, Ekrem; Lake, Larry W.

doi:10.2118/18434-pa

Cited by 54 publications

(16 citation statements)

References 14 publications

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“…Especially when upscaling channelized systems, as the upscaling volume increases, so the does the strength of the off diagonal terms in the effective permeability tensor [White and Horne 1987, Kasap 1990, Durlofsky 1991, Pickup et.al. 1994, King 1995.…”

Section: Permeability Upscalingmentioning

confidence: 99%

Improved Upscaling for Flow Simulation of Tight Gas Reservoir Models

Zhou

King

2011

SPE Annual Technical Conference and Exhibition

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Tight gas and shale gas reservoirs provide almost half of the current U.S. domestic gas production, with significant projected increases in the next several decades. These reservoirs constitute an important play type, with opportunities for improved reservoir management in the optimization of depleted volumes as functions of well spacing and fractured well design. Reservoir simulation, together with detailed 3D geologic models, may be used for improved management, but only if the flow simulation through these models can capture the essential heterogeneity and 3D continuity of these intermittently connected rock packages. The current work will examine tight gas reservoirs, but we recognize that similar issues will arise in source rock plays.The current approach has three key technical elements: (1) We explicitly preserve the local continuity of the reservoir sands in the geologic model through the design of the simulation grid. Each simulation cell is a 1x1xN amalgamation of the geologic scale corner point cells, where "N" will vary depending upon the local sand thickness.(2) We have developed a "Well Index" based upscaling, to determine the upscaled permeability and which preserves the local reservoir quality. It does not require knowledge of the well locations within the upscaled simulation model, but it will preserve the performance of these wells. (3) The heterogeneity within each sand is preserved through the use of transmissibility upscaling, which we show performs systematically better than the usual permeability upscaling. In combination, these three elements provide simulation results which are almost indistinguishable from the fine scale model. We also examine additional approximations in which we further coarsen the model areally, and reduce the simulation time further. We develop and demonstrate our calculations on a sector model taken from the center of a full field onshore U.S. tight gas reservoir. The results are then validated using the full field model. Our approach differs from earlier studies which have attempted to preserve the global heterogeneity of the reservoir models though layer-based statistical calculations. Although these statistical approaches are superior to uniformly coarsened models, they are not as robust or as accurate as the current work constrained by local continuity. Our approach also differs in the use of accurate property upscaling techniques that simultaneously preserve the internal contrast of permeability within each sand, and the performance of wells within the model.

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Section: Permeability Upscalingmentioning

confidence: 99%

Improved Upscaling for Flow Simulation of Tight Gas Reservoir Models

Zhou

King

2011

SPE Annual Technical Conference and Exhibition

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“…This preferred flow direction should be conserved when converting to a horizontal grid. This is actually an example of a case where the rescaled property is best described by full tensor permeabilities and multi-point flux approximation (MPFA): preserving the layer-aligned preferred flow direction from the geo-grid in a horizontal cells context can be achieved by including the non-diagonal permeability tensor terms, which contribute to noncell-aligned flow [1,3,8]. This approach was nevertheless rejected, mostly because full tensor permeabilities and MPFA are not available in most commercial simulators, but also because proper construction (averaging) of full tensors by rescaling from geo-cells to horizontal cells would require a significantly more elaborate procedure.…”

Section: Rescaling Of Permeabilitymentioning

confidence: 99%

Horizontal simulation grids as alternative to structure-based grids for thin oil-zone problems: a comparison study on a Troll segment

Pettersen¹

2011

Comput Geosci

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The layering in reservoir simulation grids is often based on the geology, e.g., structure tops. In this paper we investigate the alternative of using horizontal layers, where the link to the geology model is by the representation of the petrophysics alone. The obvious drawback is the failure to honor the structure in the grid geometry. On the other hand, a horizontal grid will honor the initial fluid contacts perfectly, and horizontal wells can also be accurately represented. Both these issues are vital in thin oil-zone problems, where horizontal grids may hence be a viable alternative. To investigate this question, a number of equivalent simulation models were built for a segment of the Troll Field, both geology-based and horizontal, and various combinations of these. In the paper, it is demonstrated that the horizontal grid was able to capture the essentials of fluid flow with the same degree of accuracy as the geology-based grid, and near-well flow was considerably more accurate. For grids of comparable resolution, more reliable results were obtained by a horizontal grid than a geo-grid. A geo-grid with local grid refinement and a horizontal grid produced almost identical results, but the ratio of computing times was almost 20 in favor of the horizontal grid. In the one-phase regions of the reservoir, relatively coarse cells can be used without significant loss of accuracy.

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“…Among the various upscaling methods used at present, two-phase dynamic methods ought to be more accurate than single-phase upscaling methods 18,19 , in that they are designed to take account of the effect of fine-scale heterogeneity and fluid forces.…”

Section: The Impracticality Of Dynamic Two-phase Upscalingmentioning

confidence: 99%

A New Method for Accurate and Practical Upscaling in Highly Heterogeneous Reservoir Models

Zhang¹,

Pickup²,

Christie³

2006

International Oil &Amp; Gas Conference and Exhibition in China

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractGeologists often generate highly heterogeneous descriptions of reservoirs, containing complex structures which are likely to give rise to very tortuous flow paths. However, these models contain too many grid cells for multiphase flow simulation and the number of cells must be reduced by upscaling for reservoir simulation. Conventional upscaling methods often have difficulty in the representation of tortuous flow paths, mainly due to the inappropriate assumptions concerning the boundary conditions. An accurate and practical upscaling method, which is able to preserve the flow behaviour caused by highly heterogeneous fine scale geological features, is therefore required.In this paper, the problems encountered in routinely used upscaling approaches are outlined, and a more accurate and practical way of performing upscaling is proposed. The new upscaling method, Well Drive Upscaling (WDU), employs the actual reservoir boundary conditions. The main advantage of this method is that the dominant flow paths can be preserved, and thus the geological knowledge can be assimilated appropriately. The new method has firstly been applied to a synthetic model with a tortuous channel, and is shown to have significant improvement over the traditional approach. The sensitivity study on the scale up factor using a bench mark model shows the advantage of the method with various scale up factors. The method was then applied to a model of a field in the central North Sea, which involves three phase flow. In the cases studied, the WDU method produced a comparable result to the dynamic Pore Volume Weighted approach which involves running the fine grid simulation and computing appropriate relative permeabilities and inter-block transmissibilities. The new method makes the upscaling process both practical and accurate and ensures that field predictions can be made more confidently with greater geological realism.

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Calculating the Effective Permeability Tensor of a Gridblock

Cited by 54 publications

References 14 publications

Improved Upscaling for Flow Simulation of Tight Gas Reservoir Models

Improved Upscaling for Flow Simulation of Tight Gas Reservoir Models

Horizontal simulation grids as alternative to structure-based grids for thin oil-zone problems: a comparison study on a Troll segment

A New Method for Accurate and Practical Upscaling in Highly Heterogeneous Reservoir Models

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