Spatial Connectivity: From Variograms to Multiple-Point Measures

Krishnan, Sunderrajan; Journel, André G.

doi:10.1023/b:matg.0000011585.73414.35

Cited by 81 publications

(26 citation statements)

References 5 publications

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“…To quantify the accuracy of the reconstructed systems, we compute a general connectivity function for both the TS and its reconstruction, which is the multiple-point connectivity (MPC) function that has been used [8,22] in reconstructing large-scale geological formations. The MPC is the probability p(r; s) of having a sequence of s points in a phase in a multiphase structure in a given direction r. If an indicator function I (i) (u) is defined by…”

Section: The Connectivity Functionmentioning

confidence: 99%

Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function

Tahmasebi

Sahimi

2015

Phys. Rev. E

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Nonstationary disordered materials and media -those for which the probability distribution function of any property varies spatially when shifted in space -are abundant and encountered in astrophysics, oceanography, air pollution patterns, large-scale porous media, biological tissues and organs, and composite materials. Their reconstruction and modeling is a notoriously difficult and largely unsolved problem. We propose a method for reconstructing a broad class

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Section: The Connectivity Functionmentioning

confidence: 99%

Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function

Tahmasebi

Sahimi

2015

Phys. Rev. E

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“…Various authors (e.g. Guardano & Srivastava 1993;Krishman & Journel 2003) have proposed that multipoint statistics could characterize the random function inherent in many geological bodies to a greater degree than conventional two-point statistics.…”

Section: Multipoint/multivariate Statisticsmentioning

confidence: 99%

Advances in carbonate exploration and reservoir analysis

Garland¹,

Neilson

Laubach

et al. 2012

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The development of innovative techniques and concepts, and the emergence of new plays in carbonate rocks are creating a resurgence of oil and gas discoveries worldwide. The maturity of a basin and the application of exploration concepts have a fundamental influence on exploration strategies. Exploration success often occurs in underexplored basins by applying existing established geological concepts. This approach is commonly undertaken when new basins 'open up' owing to previous political upheavals. The strategy of using new techniques in a proven mature area is particularly appropriate when dealing with unconventional resources (heavy oil, bitumen, stranded gas), while the application of new play concepts (such as lacustrine carbonates) to new areas (i.e. ultra-deep South Atlantic basins) epitomizes frontier exploration.Many low-matrix-porosity hydrocarbon reservoirs are productive because permeability is controlled by fractures and faults. Understanding basic fracture properties is critical in reducing geological risk and therefore reducing well costs and increasing well recovery. The advent of resource plays in carbonate rocks, and the long-standing recognition of naturally fractured carbonate reservoirs means that new fracture and fault analysis and prediction techniques and concepts are essential.A key area of progress has been integration of stratigraphic, structural, geomechanical and diagenetic analysis to populate reservoir models accurately. Dramatic increases in computing and digital imaging capabilities are being harnessed to improve spatial analysis and spatial statistics in reservoirs and ultimately improve 3D geocellular models.

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“…For instance, a meandering depositional environment would never be amenable to a simple bivariate Geostatistical approach, only multiple-point Geostatistics (still under development, see e.g. Strebelle 2002; Krishan and Journel 2003) could approach that, or bivariate Geostatistics where the correlation structure itself is a correlated random field function of the meander properties, see e.g. Carle et al (1998).…”

Section: Genetic/genesis Modelsmentioning

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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Spatial Connectivity: From Variograms to Multiple-Point Measures

Cited by 81 publications

References 5 publications

Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function

Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function

Advances in carbonate exploration and reservoir analysis

Dealing with spatial heterogeneity

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