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Drawdown log-derived analysis for interpreting constant-rate pumping tests in inclined substratum aquifers

Análisis de los registros de depresiones para interpretar los ensayos de bombeo a caudal constante en acuíferos de sustratos inclinados

Interprétation des essais de pompage à débit constant basée sur l’analyse de la dérivée logarithmique du rabattement dans des aquifères à substratum incliné

为解译倾斜下层含水层恒定流量抽水试验根据降深记录得出的分析

Análise do rebaixamento da derivada logarítmica para interpretação de teste de bombeamento de taxa constante em aquíferos de substrato inclinado

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Abstract

Constant-rate pumping tests (CRPT) performed in aquifers having an inclined substratum (IS) cannot be interpreted using Theis-like models, due to an increasing thickness that is beyond conventional hydraulic assumptions. Using an empirical process based on numerical modelling, this study submits original tools for the detection of IS aquifers and the interpretation of their hydrodynamic responses to CRPT, using derivative [ds/dlog(t)] and flow dimension (n) analyses. It is shown that IS aquifers produce a drawdown log-derivative signal composed of two radial regimes and one spherical flow regime (n-sequence = 2–2–3). Comprehensive sensitivity analyses make it possible to constrain relationships between, on one hand, characteristic derivative responses, and on the other hand, hydraulic conditions such as pumping rate, distance from the well to the corner, substratum inclination, and aquifer properties, including anisotropic hydraulic conductivity. This study contributes to widening the array of tools available for the interpretation of pumping tests, by implementing a novel conceptual model for a specific type of nonuniform aquifer that has remained unaddressed; further, it provides another interpretation of the spherical flow regime, which has been interpreted in the petroleum literature to reflect partially penetrating/completing wells. Finally, a field application of the submitted interpretative tools to a CRPT into an IS aquifer is presented.

Résumé

L’interprétation des essais de pompage à débit constant (EPDC) à partir de modèles theissiens s’avère impossible dans des aquifères à substratum incliné car l’augmentation d’épaisseur ne correspond pas aux hypothèses hydrauliques conventionnelles. À partir d’une approche empirique basée sur la modélisation numérique, cette étude propose des outils originaux basés sur l’analyse de la dérivée-log [ds/dlog(t)] et de la dimension d’écoulement (n) afin de détecter des aquifère à SI et d’interpréter leur réponse hydrodynamique. Il est montré que les aquifères à SI produisent un signal de la dérivée-log du rabattement composé de deux régimes d’écoulement radiaux et d’un régime d’écoulement sphérique (séquence de n = 2–2–3). Des analyses de sensibilité permettent d’établirdes relations entre, d’une part, le signal caractéristique de la dérivée-log du rabattement, et d’autre part, les conditions hydrauliques tels que le débit de pompage, la distance du puits à l’extrémité du coin, l’inclinaison du substratum et les propriétés de l’aquifère, y compris la conductivité hydraulique anisotrope. Cette étude contribue à élargir le catalogue d’outils disponibles pour l’interprétation des essais de pompage en proposant un nouveau modèle conceptuel pour un aquifère non-uniforme spécifique qui était encore non traité jusqu’à présent. De plus, cela fournit une nouvelle interprétation du régime d’écoulement sphérique qui a été, jusque-là interprétée dans la littérature pétrolière comme étant uniquement associée à des modèles d’aquifères partiellement captés. Enfin, les outils d’interprétation d’EPDC présentés dans l’article ont été appliqués à des données de terrain dans un contexte d’aquifère à SI.

Resumen

Los ensayos de bombeo a caudal constante (CRPT) realizados en acuíferos con sustrato inclinado (IS) no pueden ser interpretados utilizando modelos similares a los de Theis, debido a un espesor creciente que va más allá de los supuestos hidráulicos convencionales. Utilizando un proceso empírico basado en modelos numéricos, este estudio presenta herramientas originales para la detección de acuíferos IS y la interpretación de sus respuestas hidrodinámicas a los CRPT, utilizando análisis derivados [ds/dlog(t)] y de dimensión de flujo (n). Se muestra que los acuíferos IS producen una señal derivada de las depresiones de la extracción compuesta de dos regímenes radiales y un régimen de flujo esférico (n-sequence = 2–2–3). Los análisis exhaustivos de sensibilidad permiten limitar las relaciones entre, por un lado, las respuestas derivadas características y, por otro, las condiciones hidráulicas tales como: caudal de bombeo, distancia del pozo, inclinación del sustrato y propiedades del acuífero, incluida la anisotropía de la conductividad hidráulica. Este estudio contribuye a ampliar la gama de herramientas disponibles para la interpretación de los ensayos de bombeo, mediante la implementación de un modelo conceptual novedoso para un tipo específico de acuífero no uniforme lo cual ha permanecido sin abordarse; además, proporciona otra interpretación del régimen de flujo esférico, que ha sido interpretado en la literatura petrolera para reflejar pozos parcialmente penetrantes/completos. Finalmente, se presenta una aplicación práctica de las herramientas interpretativas presentadas a un CRPT en un acuífero de IS.

摘要

在具有倾斜下层的含水层中进行的恒定流量抽水试验不能够用类泰斯模型解译,这是因为厚度增加,超出了常规的水力假定。采用基于数值模拟的经验过程,本研究利用派生[ds/dlog(t)]和水流维数分析提供了探测倾斜下层含水层以及解译其对恒定流量抽水试验的水动力响应的独创性工具。结果显示,倾斜下层含水层产生了降深记录-派生信号,该信号包括两个放射状形态和一个球状形态(n-序列 = 2–2–3)。综合灵敏度分析有可能一方面约束特征派生响应之间的关系,另一方面也能约束水力条件诸如抽水量、井到偏远处的距离、下层倾角以及包括各向异性水力传导率等含水层特性之间的关系。对仍然处于未知的特殊类型的非均一含水层采用新的概念模型,本研究有助于拓宽现有的解译抽水试验的工具;而且,还提供了曾经在石油文献中解译过反映部分穿透/完成井的球形水流状态的另一种解译结果。最后,介绍了所提出的恒定流量抽水试验解译工具在倾斜下层含水层中的野外应用情况。

Resumo

Testes de bombeamento com vazão constante (TBVC) realizados em aquíferos com substrato inclinado (SI) não podem ser interpretados utilizando os modelos de Theis, devido a uma crescente espessura que está além das suposições da hidráulica convencional. Utilizando um processo empírico baseado em modelagem numérica, este estudo submete ferramentas originais para detecção de aquíferos de SI e a interpretação de suas respostas hidrodinâmicas aos TBVC, utilizando a análise da derivada [ds/dlog(t)] e dimensão do fluxo (n). É mostrado que aquíferos de SI produzem um rebaixamento baseado na derivada logarítmica composto de dois regimes radiais e um regime de fluxo esférico (sequência-n = 2–2–3). Análise abrangente de sensibilidade permite restringir relações entre, de um lado, respostas derivadas características, e de outro, condições hidráulicas como taxa de bombeamento, distância do poço até o canto, inclinação do substrato, e propriedades do aquífero, incluindo a condutividade hidráulica anisotrópica. Este estudo contribui para ampliar a matriz de ferramentas disponíveis para interpretação de testes de bombeamento, através da implementação de um novo modelo conceitual para um tipo de aquífero não uniforme que tem permanecido desconhecido; além disso, ele fornece outra interpretação do regime esférico de fluxo, que tem sido interpretado na literatura do petróleo para refletir poços parcialmente em perfuração/completos. Por fim, é apresentada uma aplicação de campo da ferramenta interpretativa para um TBVC em um aquífero de SI.

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Acknowledgements

We thank Dr. Therrien and Aquanty for providing the HGS code in the framework of collaborations between universities. Ms. Josée Kaufmann is thanked for editorial collaboration.

Funding

The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council (NSERC – federal funding) of Canada in the framework of the Individual Discovery Grant Program as well as the “Fonds de Recherche du Québec Nature et Technologies (FRQNT – provincial funding)” in the framework of the individual grant “Nouveaux-chercheurs” held by Prof. Romain Chesnaux.

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Authors and Affiliations

  1. Research Group R2Eau, Centre d’études sur les Ressources Minérales, Université du Québec à Chicoutimi, 555 boulevard de l’Université, Chicoutimi, Québec, G7H 2B1, Canada

    Anouck Ferroud, Romain Chesnaux & Silvain Rafini

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  1. Anouck Ferroud
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  2. Romain Chesnaux
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Correspondence to Anouck Ferroud.

Appendix: Nomenclature

Appendix: Nomenclature

α :

Angle of inclination of the substratum (radians)

d :

Distance from the well to the corner formed by the intersection of the inclined substratum and the top of the confined aquifer [L]

K :

Hydraulic conductivity of the confined aquifer [L T−1]

L w :

Length of the well intercepting the aquifer [L]

m 2-BC :

Y-intercept of the radial flow dimension (n = 2) before the pressure front pulse reaches the corner [L]

m 2-AC :

Y-intercept of the radial flow dimension (n = 2) after the pressure front pulse has reached the corner [L]

m 3 :

Value at log(t) = 0 of the tangent to the asymptotic curve of the spherical flow dimension (n = 3)

Q :

Pumping rate [L3 T−1]

s :

Drawdown [L]

S s :

Specific storage of the confined aquifer [L−1]

t :

Time of pumping [T]

t AC :

Time corresponding to the intersect between the predominant radial flow dimension (second plateau, n = 2) and the spherical flow dimension (n = 3) on a log-log plot of ds/dlog(t) versus t [T]

t C :

Time corresponding to the end of the compensated radial flow dimension (first plateau, n = 2) on a log-log plot of ds/dlog(t) versus t [T]

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Ferroud, A., Chesnaux, R. & Rafini, S. Drawdown log-derived analysis for interpreting constant-rate pumping tests in inclined substratum aquifers. Hydrogeol J 27, 2279–2297 (2019). https://doi.org/10.1007/s10040-019-01972-7

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