Abstract
The question of how well the true underlying hydraulic conductivity statistics of heterogeneous media are captured by well tests is addressed. The hydraulic conductivity value and the corresponding support volume associated with a theoretical well are correlated, causing a bias in the statistics derived from well-test analyses. Statistics derived from numerically simulated well tests are compared with the known underlying conductivity statistics and the results indicate an under-prediction by simulations at higher hydraulic conductivities. The deviation starts at about mean conductivity and can be as large as an order of magnitude, with the conductivity in the vicinity of the well defining the upper boundary. In other words, the conductivity value interpreted from the well test cannot be larger than the value that the well test first encounters. Consequently, for data in this simulation exercise, the standard deviation, if only determined for the upper range of the conductivity values, would be underestimated by a factor of 1.6–2. While this specific range is likely to depend on the scale and degree of the underlying heterogeneity as well as the duration of the test, the results should be indicative of a more general behaviour and are likely to occur in other heterogeneous data as well.
Résumé
Nous posons ici la question de savoir dans quelle mesure les statistiques de la conductivité hydraulique des milieux hétérogènes pourrait être révélée par des essais de puits. La valeur de la conductivité hydraulique et le volume capté correspondant sont corrélés, créant un biais dans l’analyse des statistiques dérivées des essais de puits. Les statistiques en provenance de simulations numériques d’essais de puits sont comparées avec les statistiques de conductivités connues et les résultats indiquent une sous-évaluation par les simulations, pour les conductivités hydrauliques les plus élevées: la déviation commence à partir de la valeur moyenne de la conductivité et peut atteindre la magnitude d’un ordre de grandeur en considérant la conductivité mesurée au voisinage du puits. Autrement dit, la valeur de la conductivité interprétée via l’essais de pompage ne peut être plus importante que les premières valeurs rencontrées. Par conséquence, pour les données de cet exercice de simulation, la déviation standard sera sous-estimée d’un facteur compris entre 1.6–2 pour les valeurs les plus élevées. Tandis que l’échelle spécifique de valeurs est dépendante de l’échelle et du degré de l’hétérogénéité souterraine, de même que de la durée du test, les résultats pourraient être indicatifs d’un comportement plus général et seraient sans doute observables dans d’autres cas de données hétérogènes.
Resumen
Se plantea la pregunta de qué tan bien son representadas en las pruebas de pozo, las estadísticas reales de conductividad hidráulica subyacente de medios heterogéneos. Son correlacionados el valor de conductividad hidráulica y el volumen de apoyo correspondiente asociado con un pozo teórico, causando una distorsión en las estadísticas derivadas del análisis de la prueba de pozo. Las estadísticas derivadas de las pruebas de pozo simuladas numéricamente son comparadas con las estadísticas de conductividad subyacente conocidas, y los resultados indican una sub-predicción por las simulaciones hechas con conductividades hidráulicas más altas. La desviación empieza casi con la conductividad media y puede ser tan grande como un orden de magnitud, con la conductividad en la vecindad del pozo definiendo el límite superior. En otras palabras, el valor de conductividad interpretado a partir de la prueba del pozo no puede ser más grande que el valor que la prueba de pozo encuentre primero. Por consiguiente, para los datos en este ejercicio de simulación, la desviación estándar, si solamente fue determinada para el rango superior de los valores de conductividad, se subestimaría en un factor de 1.6–2. Mientras es probable que este rango específico dependa de la escala y del grado de la heterogeneidad subyacente, así como de la duración de la prueba, los resultados deben ser indicativos de un comportamiento más general y son probables también de ocurrir en otros datos heterogéneos.
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Acknowledgements
The authors wish to thank SKB (Swedish Nuclear Fuel and Waste Management Co.) for their financial support. The authors would also like to acknowledge the constructive comments by two anonymous reviewers for improving the paper.
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Odén, M., Niemi, A. From well-test data to input to stochastic continuum models: effect of the variable support scale of the hydraulic data. Hydrogeol J 14, 1409–1422 (2006). https://doi.org/10.1007/s10040-006-0063-y
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DOI: https://doi.org/10.1007/s10040-006-0063-y