Hydrogeology Journal

, Volume 18, Issue 6, pp 1357–1373 | Cite as

Upscaling facies models to preserve connectivity of designated facies

  • Erick R. Burns
  • Larry R. Bentley
  • Rene Therrien
  • Clayton V. Deutsch
Paper

Abstract

An upscaling algorithm has been developed that generates an irregular coarse grid that preserves flow connectivity by applying a rule-based upscaling algorithm to a fine-scale facies distribution. The algorithm is demonstrated using stochastically generated paleo-fluvial facies distributions. First, an irregular grid honoring the channel facies is created, followed by computation of effective anisotropic parameters for all coarse-grid cells. For the apparent layer-cake geometry of overbank deposits seen in outcrop, two local upscaling methods are compared: (1) the layered system approximation and (2) the mode. To assess upscaling performance, flow simulations for the original and upscaled grids are compared. The horizontal layered approximation (arithmetic mean) performs poorly, over-predicting lateral connectivity where even infrequent disconnection becomes important. Performance of the mode as an upscaling algorithm depends on the probability that a coarse-grid cell will be dominated by a single facies, and it performs surprisingly well because the upscaled grid-generation algorithm honors the channels, informing the upscaling process. Lastly, the irregular coarse grid was compared to a uniform coarse grid, showing superior performance with the irregular grid. The reduction in grid size achieved by irregular-grid generation will be a function of the geometrical complexity of the geologic objects to be honored.

Keywords

Geostatistics Numerical modeling Scale effects Groundwater flow 

Interpolation de modèles de faciès avec conservation du flux interstitiel

Résumé

On a développé un algorithme d’interpolation générant une grille irrégulière grossière conservant le flux interstitiel et appliqué cet algorithme à une distribution de faciès à granulométrie fine. L’algorithme est structuré en simulant des distributions aléatoires de faciès paléo-fluviaux. D’abord, une grille simulant le faciès irrégulier du chenal est créée, puis les paramètres d’anisotropie effective de toutes les cellules à grille grossière sont calculés. Pour les dépôts sur berge affleurant présentant une texture en mille-feuille, deux méthodes d’interpolation adaptées au cas local sont comparées : (1) l’approximation par système stratifié et (2) le mode. Pour évaluer l’effet de l’interpolation, on compare les flux simulés à travers les grilles originales et les grilles traitées. L’assimilation à des couches horizontales (moyenne arithmétique) fonctionne mal, surestimant le flux interstitiel latéral, y compris lorsqu’une rare discontinuité devient importante. La performance du mode en tant qu’algorithme d’interpolation dépend de la probabilité qu’un faciès unique prédomine dans une cellule à grille grossière. C’est une surprise, le mode fonctionne bien car l’algorithme traite les chenaux, orientant le processus d’interpolation. Enfin, par comparaison, la performance de la grille grossière irrégulière est supérieure à celle d’une grille grossière uniforme. La réduction de la dimension de la grille réalisée par génération de grille irrégulière sera une fonction de la complexité géométrique des objets géologiques à traiter.

Reescalamiento de modelos de facies para preservar la conectividad de las facies designadas

Resumen

Se desarrolló un algoritmo de reescalamiento para generar una grilla gruesa irregular que preserve la conectividad de flujo aplicando un algoritmo reescalante basados en reglas de distribución de facies a escala fina. Se demuestra el algoritmo usando distribuciones de facies paleofluviales estocásticamente generadas. Primero, se crea una grilla irregular respetando la facies de canales, seguida por el cálculo de los parámetros anisotrópicos efectivos para todas las celdas de la grilla gruesa. Para una geometría similar de torta de capas de los depósitos de banco visto en afloramientos, se compararon dos métodos de reescalamiento: (1) la aproximación del sistema de capas y (2) el modo. Para evaluar el rendimiento del reescalamiento se comparan las simulaciones de flujo para las grillas original y reescalada. La aproximación de capas horizontales (promedio aritmético) se desempeñó pobremente, sobreprediciendo la conectividad lateral, aún incluso donde la desconexión infrecuente resulta importante. El rendimiento del modo como un algoritmo de reescalamiento depende de la probabilidad que una celda de grilla gruesa esté dominada por facies simples, y se desempeña sorprendentemente bien porque el algoritmo reescalado de generación de grilla respeta los canales, informando el proceso de reescalamiento. Finalmente, la grilla gruesa irregular fue comparada a la grilla gruesa uniforme, lo que demostró un rendimiento superior a la grilla irregular. La reducción en el tamaño de la grilla lograda por la generación de grilla irregular es función de la complejidad geométrica de los objetos geológicos a ser respetados.

一个不破坏相之间水流连通性的升尺度相模型

摘要

通过将基于规则的算法应用于小尺度相分布, 开发了一个可生成保留水流连通性的不规则粗网格的升尺度算法。该算法由随机生成的古冲积相分布进行了示范。首先, 生成一个概化河道相的不规则网格, 然后计算所有粗网格单元的有效各向异性参数。对于露头处所见的层状蛋糕状漫滩沉积, 比较了两个局部升尺度方法 : 1) 分层系统近似 ; 2) 模式。为评估升尺度性能, 比较了初始与升尺度的网格水流模拟。水平层状近似 (算数平均) 表现很差, 高估了侧向连通, 即使在不常见的间断变得重要时也是如此。模式作为升尺度算法的性能决定于粗网格单元被单相占据的概率, 其表现非常好, 因为升尺度网格生成算法适于河道, 提供了升尺度过程。最后, 将不规则粗网格与均一粗网格比较。由不规则网格生成使网格尺寸变小, 将是要概化的地质目标几何形态复杂性的参数.

Incremento de escala em modelos de fácies preservando a conectividade entre determinadas fácies

Resumo

Desenvolveu-se um algoritmo de incremento de escala (upscaling) que gera uma malha grosseira irregular, a qual preserva a conectividade do escoamento por aplicação de um algoritmo baseado numa regra de incremento de escala aplicada a uma distribuição de fácies de pequena escala. O algoritmo é demonstrado usando distribuições de fácies paleo-fluviais geradas por processos estocásticos. Primeiro, é criada uma malha irregular que respeita a fácies de canal, seguida do cálculo de parâmetros anisotrópicos efectivos para todas as células da malha grosseira. Para a geometria aparente de camadas sucessivas dos depósitos de transbordo de margem (overbank deposits) observáveis em afloramento são comparados dois métodos de incremento de escala local: (1) o sistema de aproximação em camadas e (2) a moda. Para avaliar o desempenho do incremento de escala, são comparadas simulações de escoamento para o modelo original e para as malhas incrementadas. A aproximação em camadas horizontais (média aritmética) tem fraco desempenho, prevendo de forma excessiva a conectividade lateral, onde mesmo as raras desconexões se tornam importantes. O desempenho do método da moda como um algoritmo de incremento de escala depende da probabilidade de uma célula de malha grosseira ser dominada por uma única fácies e tem um desempenho surpreendentemente bom em resultado do algoritmo de geração da malha de escala incrementada respeitar os canais, transferindo a informação para o processo de incremento de escala. Por fim, a malha grosseira irregular foi comparada com uma malha grosseira uniforme, mostrando melhor desempenho a malha irregular. A redução na dimensão da malha conseguida por uma geração de malha irregular será função da complexidade dos objectos geológicos que devem ser respeitados.

Notes

Acknowledgements

Funding for this project was received from the Alberta Ingenuity Fund post doctoral fellowship program and the Alberta Ingenuity Centre for Water Research. Thanks also to the Hydrogeology Journal editors, Professor Maria-Theresia Schafmeister and Sue Duncan, and two anonymous reviewers for their thoughtful and helpful comments.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Erick R. Burns
    • 1
  • Larry R. Bentley
    • 1
  • Rene Therrien
    • 2
  • Clayton V. Deutsch
    • 3
  1. 1.Department of GeoscienceUniversity of CalgaryCalgaryCanada
  2. 2.Département de géologie et de génie géologiqueUniversity of Laval, Faculté des sciences et de génieQuébecCanada
  3. 3.School of Mining and Petroleum EngineeringUniversity of AlbertaEdmontonCanada

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