Effective Properties for Flow Calculations

King, Micháel J.; King, Peter R.; McGill, C. A.; Williams, John K.

doi:10.1007/978-94-017-2372-5_7

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…From Figure 1, it can be seen that the standard upscaling methods based on local ow solutions or assumptions produce the better approximations to the stationary value, and that the tight bounds obtained with the upscaled permeability ÿelds illustrate the advantage in having similarly resolved numerical discretizations and permeability ÿelds. The comparison method employed in the consistent upscaling method illuminates the nonlinear nature of upscaling in which p is an arithmetic mean weighted by the solution (∇p) 2 and q is as a harmonic mean weighted byq 2 . As a consequence of constructing upscaling methods that are independent of the solutionsp andq, in general, an error will always be generated by the second term in (28) and the corresponding q principle (42).…”

Section: Discussion Of Consistent Methodsmentioning

confidence: 99%

“…The ÿrst category consists of explicit averaging methods including arithmetic, geometric and harmonic means, applied directly to regions of the original permeability ÿeld [1]. The second category consists of methods involving local ow simulations from which an e ective coarse permeability is attributed to the region [2]. The upscaling methods in this category attempt to model the response of a ow over the original permeability data but require assumptions to be made regarding the boundary conditions for the local ow simulations.…”

Section: Introductionmentioning

confidence: 99%

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A variational approach to consistent single‐phase upscaling

Wakefield

2002

Numerical Methods in Fluids

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SUMMARYA consistent upscaling methodology is outlined, which bounds the stationary value of the original governing functional and highlights the source of errors that arise when an upscaled permeability ÿeld is substituted. The stationary value is identiÿed as an important physical measure and the existence of bounds on this quantity enables conÿdence to be placed in upscaled predictions, including well productions, as opposed to empirical error estimates associated with conventional upscaling methods.

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Section: Discussion Of Consistent Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A variational approach to consistent single‐phase upscaling

Wakefield

2002

Numerical Methods in Fluids

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“…In general, the different methods used in upscaling parameters like absolute permeability or transmissibility and relative permeability can be classified based on what is being upscaled and the technique used (see reviews by Smith, 1991;Desbarats, 1992;King et al 1995;Christie, 1996;Renard and Marsily, 1997;Chiles and Delfiner, 1999). In single-phase upscaling, the absolute permeability or transmissibility of the geologic model is upscaled, while in multi-phase in addition upscaling the absolute permeability or transmissibility, the relative permeabilities and capillary pressure are upscaled.…”

Section: General Upscaling Methodsmentioning

confidence: 99%

Upscaling for Thermal Recovery

Abubakar¹,

Muggeridge²,

King³

2014

SPE International Heavy Oil Conference and Exhibition

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Thermal recovery is one of the most widely applied EOR methods worldwide. It is used mainly to improve the recovery of more viscous oils. Heat is used primarily to reduce the viscosity of oil but may also improve recovery by other mechanisms such as oil expansion, steam distillation and reduction in capillary forces. As a result, the prediction of thermal recovery performance requires more complex and computationally demanding numerical simulations than is the case when evaluating a waterflood. The simulator has to evaluate the impact of both heat transfer and compositional behaviour on the fluid flows.In most cases the engineer will have to use coarser grids in the simulation models than would be needed for a waterflood in order to keep simulation times within acceptable limits. However, it has been shown in the modelling of other EOR processes that in fact much finer grids may be needed to capture the frontal dynamics of the displacement than would be the case in waterflooding. As a result, the simulation of steamflooding on the field scale is unlikely to capture the impact of small scale heterogeneity on flow, as well as being severely affected by numerical dispersion. The ideal solution is to use homogenization to capture the effects of sub-grid-block heterogeneity combined with advanced numerical techniques such as dynamic/adaptive gridding or higher order schemes to reduce the impact of numerical diffusion and dispersion. However, such methods are not currently available in the commercial simulators available to most engineers.The alternative is to use upscaling, but as yet there are no upscaling methodologies suitable for thermal oil recovery methods. Upscaling is a way of altering the inputs to numerical flow models so that simulations run on a coarse grid. These will a) predict the impacts on flow of sub-grid heterogeneity (homogenization) and b) will be less affected by numerical dispersion. For waterflooding this is typically achieved by calculating the effective absolute permeability for each coarse grid cell. In many cases, it is also necessary to upscale the well index and the transmissibilities of the well blocks. Upscaling the absolute permeability, the well index and the well block transmissibilities, ensures that the overall pressure drop for single phase flow between wells is correctly predicted in the coarse grid, whilst upscaling the relative permeabilities ensures that the two-phase flow effects (pressure drop, breakthrough time and water cut development) are correctly modelled. Although there is a significant literature on single-phase upscaling and the development of pseudo relative permeabilities for waterflooding applications, these methods do not capture the heat transport or the impact of temperature on the oil mobility. ivIn this research, a combination of pseudoisation procedures (by making reasonable assumptions) with the Buckley-Leverett solution approximated for thermal EOR processes is used to derive analytical pseudo-relative permeabilities for both hot water and steam ...

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“…Knowledge of flow in micrometre pore scale is required to understand macroscopic characteristics of flow in porous media; thus, prior to performing upscaling exercises of petrophysical properties [24][25][26][27], the accurate characterisation of the porous media at pore scale is crucial for quantifying the heterogeneity of a large system. The pore-scale properties can then be upscaled to core scale or even larger scales.…”

Section: Introductionmentioning

confidence: 99%

Representative Elementary Volume of Rock Using X-Ray Microcomputed Tomography: A New Statistical Approach

et al. 2020

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Rock heterogeneity is a key parameter influencing a range of rock properties such as fluid flow and geomechanical characteristics. The previously proposed statistical techniques were able to rank heterogeneity on a qualitative level to different extents; however, they need to select a threshold value for determination of representative elementary volumes (REV), which in turn makes the obtained REV subjective. In this study, an X-ray microcomputed tomography (μCT) technique was used to obtain images from different porous media. A new statistical technique was then used to compute REV, as a measure of heterogeneity, without the necessity of defining a threshold. The performance of the method was compared with other methods. It was shown that the calculated sum of the relative errors of the proposed method was lowest compared to the other statistical techniques for all tested porous media. The proposed method can be applied to different types of rocks for more accurate estimation of a REV.

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Effective Properties for Flow Calculations

Cited by 9 publications

References 9 publications

A variational approach to consistent single‐phase upscaling

A variational approach to consistent single‐phase upscaling

Upscaling for Thermal Recovery

Representative Elementary Volume of Rock Using X-Ray Microcomputed Tomography: A New Statistical Approach

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