Average Permeabilities of Heterogeneous Oil Sands

Cardwell, William; Parsons, Robert L.

doi:10.2118/945034-g

Cited by 141 publications

(109 citation statements)

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“…Moreover, even if the nature of these variations were known, the difficulties of exact analytical treatment would still force the use of averaging procedure and reduction to an equivalent permeability system." He then goes on to mention the Cardwell and Parsons (1945) bounds for averaging, and treats some special cases where simple geometric trends in permeability are known.…”

Section: The Early Approachmentioning

confidence: 99%

Dealing with spatial heterogeneity

et al. 2005

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Heterogeneity can be dealt with by defining homogeneous equivalent properties, known as averaging, or by trying to describe the spatial variability of the rock properties from geologic observations and local measurements. The techniques available for these descriptions are mostly continuous Geostatistical models, or discontinuous facies models such as the Boolean, Indicator or Gaussian-Threshold models and the Markov chain model. These facies models are better suited to treating issues of rock strata connectivity, e.g. buried high permeability channels or low permeability barriers, which greatly affect flow and, above all, transport in aquifers. Genetic models provide new ways to incorporate more geology into the facies description, an approach that has been well developed in the oil industry, but not enough in hydrogeology. The conclusion is that future work should be focused on improving the facies models, comparing them, and designing new in situ testing procedures (including geophysics) that would help identify the facies geometry and properties. A world-wide catalog of aquifer facies geometry and properties, which could combine site genesis and description with methods used to assess the system, would be of great value for practical applications.RØsumØ On peut aborder le problme de l'hØtØrogØnØitØ en s'efforçant de dØfinir une permØabilitØ Øquivalente homogne, par prise de moyenne, ou au contraire en dØ-crivant la variation dans l'espace des propriØtØs des roches à partir des observations gØologiques et des mesures locales. Les techniques disponibles pour une telle description sont soit continues, comme l'approche GØosta-tistique, soit discontinues, comme les modles de facis, BoolØens, ou bien par Indicatrices ou Gaussiennes SeuillØes, ou enfin Markoviens. Ces modles de facis sont mieux capables de prendre en compte la connectivitØ des strates gØologiques, telles que les chenaux enfouis à forte permØabilitØ, ou au contraire les facis fins de barrires de permØabilitØ, qui ont une influence importante sur les Øcoulement, et, plus encore, sur le transport. Les modles gØnØtiques rØcemment apparus ont la capacitØ de mieux incorporer dans les modles de facis les observations gØologiques, chose courante dans l'industrie pØ-trolire, mais insuffisamment dØveloppØe en hydrogØo-logie. On conclut que les travaux de recherche ultØrieurs devraient s'attacher à dØvelopper les modles de facis, à les comparer entre eux, et à mettre au point de nouvelles mØthodes d'essais in situ, comprenant les mØthodes gØo-physiques, capables de reconnaître la gØomØtrie et les propriØtØs des facis. La constitution d'un catalogue mondial de la gØomØtrie et des propriØtØs des facis aquifres, ainsi que des mØthodes de reconnaissance utilisØes pour arriver à la dØtermination de ces systmes, serait d'une grande importance pratique pour les applications.Resumen La heterogeneidad se puede manejar por medio de la definición de características homogØneas equivalentes, conocidas como promediar o tratando de describir la variabilidad espacia...

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Section: The Early Approachmentioning

confidence: 99%

Dealing with spatial heterogeneity

et al. 2005

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“…Field dykes were observed to be relatively homogeneous due to an equal fracture density in its parallel and perpendicular directions, suggesting a K of 5 × 10 −9 m s −1 , while the sandstone value from the literature is well established at 1.2 × 10 −5 m s −1 . Those permeability values were upscaled to a regional scale using the model defined for banded structures by Cardwell and Parsons (1945). This model suggests that equivalent K for groundwater flow parallel and perpendicular to the banded heterogeneity trend is defined as the arithmetic (μ a ) and harmonic (μ h ) mean of individual units of K, respectively.…”

Section: Previous Hydrogeological Model Of the Lagan Valley Aquifermentioning

confidence: 99%

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

et al. 2015

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The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively 'noisy' magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

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“…Simple averaging techniques are local methods and assume that KV depends only on the Kf values within the block (Cardwell & Parsons, 1945;Matheron, 1967). For a perfectly layered soil, it can be shown that KV is equal to the harmonic mean (Kh) of the cell conductivities inside the block when the flow is perpendicular to the layers, and to the arithmetic mean (Ka) when the flow is parallel to the them .…”

Section: Hydraulic Conductivity Upscaling Methodsmentioning

confidence: 99%

“…It is well established that KV must be between the arithmetic mean and the harmonic mean (Cardwell & Parsons, 1945). The p-norm average was proposed as a flexible easy-to-compute alternative since it can provide a value for KV between those two limits as a function of the exponent p (A. :…”

Section: Hydraulic Conductivity Upscaling Methodsmentioning

confidence: 99%

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Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

Godoy¹

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Numerical models are becoming fundamental tools to predict a range of complex problems faced by geotechnical and geo-environmental engineers. However, to render the model reliable for future predictions, the model input parameters must be determined with consideration of the scale effects. If there is a difference of scales between the observation and the model scales there are two possible ways to consider it: or models are constructed with elements of a size similar to that at which the data were measured, or some upscaling rules must be defined. In this context, this thesis focuses on upscaling of water flow and mass transport in a tropical soil by means of numerical, laboratory and field studies. This thesis is organized in four parts.First, the heterogeneity, correlation and cross-correlation between solute transport parameters (dispersivity, α, and partition coefficient, Kd) and soil properties are studied in detail. In this part, it is verified that the hydraulic conductivity (K) and solute transport parameters are highly heterogeneous, while soil properties are not. Spatial correlation of α, K, and statistically significant variables are studied, and it would probably improve the estimation only in a small-scale study, since the spatial correlation are only observed up to 2.5 m. This study is a first attempt to evaluate the spatial variation in the correlation coefficient of transport parameters of a reactive and a nonreactive solute, indicating the more relevant variables and the one that should be included in future studies.In the second part, scale effect on K, dispersivity and partition coefficient of potassium and chloride are studied experimentally by means of laboratory and field experiments. The purpose is to contribute to the discussion about scale effects on K, α and Kd and understanding how these parameters behave with the change in the scale of measurement. Results show that K values increases with scale, regardless of the method of measurement, except for the results obtained from double-ring infiltrometer tests. Dispersivity trends to increase exponentially with the sample height.Partition coefficient tends to increase with sample length, diameter and volume. These differences in the parameters according to the scale of measurement must be considered when these observations are later used as input to numerical models, otherwise the responses can be misrepresented.x Third, stochastic analysis of three-dimensional hydraulic conductivity upscaling is performed using a simple average and the Laplacian-with-skin methods for a variety of block sizes based on real K measurements. In this part it is demonstrated the errors that can be introduced by using a deterministic upscaling using simple averages of the measured K without accounting for the spatial correlation. Results show that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler.The aspects to consider when performing the upscaling are also discussed. Finally, the dependence of the exponent of the p-n...

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Average Permeabilities of Heterogeneous Oil Sands

Cited by 141 publications

References 0 publications

Dealing with spatial heterogeneity

Dealing with spatial heterogeneity

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

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