Abstract
Adequate groundwater management requires models capable of representing the heterogeneous nature of aquifers. A key point is the theoretical knowledge of flow behaviour in various heterogeneous archetypal conditions, using analytically or numerically based models. This study numerically investigates transient pressure transfers between linearly contiguous homogeneous domains with non-equal hydraulic properties, optionally separated by a conductive fault. Responses to pumping are analysed in terms of time-variant flow dimension, n. Two radial stages are predicted (n: 2 – 2) with a positive or negative vertical offset depending of the transmissivity ratio between domains. A transitional n = 4 segment occurs when the non-pumped domain is more transmissive (n: 2 – 4 – 2), and a fractional flow segment occurs when the interface is a fault (n: 2 – 4 – 1.5 – 2). The hydrodynamics are generally governed by the transmissivity ratio; the storativity ratio impact is limited. The drawdown log-derivative late stabilization, recorded at any well, does not tend to reflect the local transmissivity but rather the higher transmissivity region, possibly distant and blind, as it predominantly supplies groundwater to the well. This study provides insights on the behaviour of non-uniform aquifers and on theoretical responses that can aid practitioners to detect such conditions in nature.
Résumé
Une gestion adéquate des eaux souterraines requiert des modèles capables de représenter la nature hétérogène des aquifères. Un point clef est la connaissance théorique du comportement de l’écoulement dans des conditions variées d’hétérogénéité, en utilisant des modèles analytiques ou numériques. Cette étude explore du point de vue numérique les transferts de pression entre des domaines hétérogènes linéairement contigus avec des propriétés hydrauliques non-égales, séparées de manière optionnelle par une faille conductrice. Les réponses au pompage sont analysées en termes de dimension d’écoulement, n, variant dans le temps. Deux stades de rayon sont prédits (n: 2 – 2) avec un décalage vertical positif ou négatif en fonction du rapport de transmissivité entre les domaines. Un segment transitoire correspondant à n = 4 se produit lorsque le domaine non pompé est plus transmissif (n: 2 – 4 – 2), et qu’un segment d’écoulement fractionnel prend place lorsque l’interface est une faille (n: 2 – 4 – 1.5 – 2). L’hydrodynamique est généralement gouvernée par le rapport de transmissivité ; l’impact du rapport du coefficient d’emmagasinement est limité. La stabilisation tardive de la dérivée logarithmique du rabattement du niveau piézométrique, enregistrée dans n’importe quel puits, n’a pas tendance à refléter la transmissivité locale mais plutôt la région de transmissivité supérieure, éventuellement éloignée et aveugle, car elle fournit de manière prédominante l’eau souterraine au puits. Cette étude fournit des informations sur le comportement des aquifères non uniformes et sur les réponses théoriques qui peuvent aider les professionnels à détecter de telles conditions dans la nature.
Resumen
Una gestión adecuada del agua subterránea requiere modelos capaces de representar la naturaleza heterogénea de los acuíferos. Un punto clave es el conocimiento teórico del comportamiento del flujo en diversas condiciones arquetípicas heterogéneas, utilizando modelos analíticos o numéricos. Este estudio investiga numéricamente las transferencias de presión transitoria entre dominios homogéneos linealmente contiguos con propiedades hidráulicas no iguales, opcionalmente separadas por una falla conductora. Las respuestas al bombeo se analizan en términos de la dimensión del flujo variante en el tiempo, n. Se predicen dos etapas radiales (n: 2 – 2) con un desplazamiento vertical positivo o negativo dependiendo de la relación de la transmisividad entre dominios. Un segmento de transición n = 4 se produce cuando el dominio no bombeado es más transmisivo (n: 2 – 4 – 2), y un segmento de flujo fraccional ocurre cuando la interfaz es una falla (n: 2 – 4 – 1.5 – 2). La hidrodinámica está generalmente gobernada por la relación de transmisividad; el impacto de la relación de almacenamiento es limitado. La estabilización tardía de la derivación logarítmica registrada en cualquier pozo no tiende a reflejar la transmisividad local, sino más bien la transmisividad más alta de la región, posiblemente distante y ciega, ya que suministra predominantemente agua subterránea al pozo. Este estudio proporciona información sobre el comportamiento de los acuíferos no uniformes y sobre las respuestas teóricas que pueden ayudar a los profesionales a detectar tales condiciones en la naturaleza.
摘要
适当的地下水管理需要能够展示含水层异质特性的模型。关键要点就是利用基于解析和数值的模型掌握各种异质原型条件下水流习性的理论知识。本研究从数值上调查了由传导断层随意分开的、具有非均等水力特性的线性连续均质域之间的瞬时压力转移。根据时间变量水流维n分析了对抽水的响应。用一个正的或者负的垂直补偿预测了两个径向阶段(n: 2 – 2),用正的或者负的垂直补偿取决于域之间的导水系数比值。当非抽水域透水性更强时(n: 2 – 4 – 2),就会出现过渡的n = 4段,当界面是断层时(n: 2 – 4 – 1.5 – 2),就会出现分数流段。水动力特性通常受导水系数比值控制;释水系数比值有限。任何井记录的水位下降录井--派生的后期稳定性并不反映局部导水系数,而是反映具有较高导水系数的区域,可能是更遥远的区域及导水系数不明的区域,因为这些区域向井供水。本研究提供了非均一含水层习性及理论上响应方面的认识,这些认识可以帮助研究人员从本质上发现这样的状况。
Resumo
Um gerenciamento adequado das águas subterrâneas requer modelos capazes de representar a natureza heterogênea dos aquíferos. O ponto chave é o conhecimento teórico do comportamento do fluxo em várias condições arquetípicas heterogêneas, usando modelos analíticos ou numéricos. Este estudo investiga numericamente a transferência de pressão transitória entre domínios homogêneos linearmente contínuos com propriedades hidráulicas variadas, opcionalmente separado por uma falha condutora. Respostas do bombeamento são analisadas em termos da dimensão de variação temporal do fluxo, n. São previstos dois estágios radiais (n: 2 – 2) com uma compensação positiva ou negativa dependendo da proporção da transmissividade entre os domínios. Um segmento transicional n = 4 ocorre quando o domínio não bombeado é mais transmissivo (n: 2 – 4 – 2), e um segmento de fluxo fracionado ocorre quando a interface é uma falha (n: 2 – 4 – 1.5 – 2). As hidrodinâmicas geralmente são governadas pela proporção da transmissividade; o impacto da capacidade de armazenamento é limitado. A estabilização tardia do rebaixamento derivado logarítmico, registrada em qualquer poço, não tende a refletir a transmissividade local, mas preferivelmente a região de maior transmissividade, possivelmente distante e imperceptível, uma vez que fornece predominantemente água subterrânea ao poço. Este estudo proporciona conhecimento sobre o comportamento de aquíferos heterogêneos e respostas teóricas que podem auxiliar profissionais a detectar tais condições na natureza.
Similar content being viewed by others
References
Abbaszadeh M, Cinco-Ley H (1995) Pressure-transient behavior in a reservoir with a finite-conductivity fault. SPE Form Eval 10:26–32. doi:10.2118/24704-PA
Avci CB, Şahin AU, Çiftçi E (2013) A new method for aquifer system identification and parameter estimation. Hydrol Process 27:2485–2497. doi:10.1002/hyp.9352
Ambastha AK (1989) Pressure transient analysis for composite systems. DOE/BC/14126-11, SUPRI TR 68, US Department of Energy, Washington, DC, 178 pp
Ambastha AK, McLeroy PG, Sageev A (1989) Effects of a partially communicating fault in a composite reservoir on transient pressure testing. SPE Form Eval 4(2):210–218
Batu V (1998) Aquifer hydraulics: a comprehensive guide to hydrogeologic data analysis. Wiley, New York, 727 pp
Banton O, Bangoy L (1999) Hydrogeologie: multiscience environnementale des eaux souterraines [Hydrogeology: environmental multidisciplinary study of groundwater]. Presse de l’Université du Québec, AUPELF-UREF, Sainte-Foy, QB
Barker J (1988) A generalized radial flow model for hydraulic tests in fractured rock. Water Resour Res 24:1796–1804. doi:10.1029/WR024i010p01796
Barker JA, Herbert R (1982) Pumping tests in patchy aquifers. Groundwater 12(2):150–155
Beauheim RL, Roberts RM, Avis JD (2004) Well testing in fractured media: flow dimensions and diagnostic plots. J Hydraul Res 42:69–76. doi:10.1080/00221680409500049
Boulton NS, Streltsova TD (1977) Unsteady flow to a pumped well in a two-layered water-bearing formation. J Hydrol 35(3–4):245–256
Bourdet D (2002) Well test analysis: the use of advanced interpretation models, In: Handbook of petroleum exploration and production, Elsevier, Amsterdam, 439 pp
Bourdet D, Ayoub JA, Pirard YM (1989) Use of pressure derivative in well test interpretation. SPE Form Eval 4:293–302. doi:10.2118/12777-PA
Bourdet D, Whittle T, Douglas A, Picard Y (1983) A new set of types curves simplifies well test analysis. World Oil 196:95–106
Brunner P, Simmons CT (2012) HydroGeoSphere: a fully integrated, physically based hydrological model. Groundwater 50(2):170–176
Butler JJ Jr (1988) Pumping tests in nonuniform aquifers: the radially symmetric case. J Hydrol 101:15–30
Butler JJ, Liu WZ (1991) Pumping tests in non-uniform aquifers: the linear strip case. J Hydrol 128:69–99
Cello PA, Walker DD, Valocchi AJ, Loftis B (2009) Flow dimension and anomalous diffusion of aquifer tests in fracture Networks. Vadose Zone J 8(1):258–268. doi:10.2136/vzj2008.0040
Chesnaux R, Rafini S, Elliott AP (2012) A numerical investigation to illustrate the consequences of hydraulic connections between granular and fractured-rock aquifers. Hydrogeol J 20:1669–1680. doi:10.1007/s10040-012-0912-9
Cooper HH Jr, Jacob CE (1946) A generalized graphical method for evaluating formation constants and summarizing well-field history. Trans Am Geophys Union 27:526–534. doi:10.1029/TR027i004p00526
Cinco-Ley H, Samaniego F (1981) Transient pressure analysis for fractured wells. J Petrol Techn 33:1749–1766
Dewandel B, Lachassagne P, Zaidi FK, Chandra S (2011) A conceptual hydrodynamic model of a geological discontinuity in hard rock aquifers: example of a quartz reef in granitic terrain in South India. J Hydrol 405:474–487. doi:10.1016/j.jhydrol.2011.05.050
Dewandel B, Aunay B, Maréchal JC, Roques C, Bour O, Mougin B (2014) Aquilina C (2014) Analytical solutions for analysing pumping tests in a sub-vertical and anisotropic fault zone draining shallow aquifers. J Hydrol 509:115–131
Fenske PR (1984) Unsteady drawdown in the presence of a linear discontinuity. In: Rosenshein JS, Bennett GD (eds) Water Resources Monograph. American Geophysical Union, Washington, DC, pp 125–145
Ferris J (1949) Ground water. In: Hydrology. Wiley, New York, pp 198–272
Gringarten AC, Henry J, Ramey HJ, Raghavan R (1974) Unsteady state pressure distributions created by a well in a well with single infinite conductivity vertical fracture. SPE J 14:347–360
Guo JJ, Zhang LH, Wang HT, Qi-Guo L (2012) Well responses in three-zone linear composite dual-porosity reservoirs, In: Zheng J-H (ed) Hydrodynamics: theory and model. InTech, Rijeka, Croatia
Hammond PA, Field MS (2014) A reinterpretation of historic aquifer tests of two hydraulically fractured wells by application of inverse analysis, derivative analysis, and diagnostic plots. J Water Resour Prot 06:481–506. doi:10.4236/jwarp.2014.65048
Hantush MS (1960) Modification of the theory of leaky aquifers. J Geophys Res 65:3713–3725. doi:10.1029/JZ065i011p03713
Issaka MB, Ambastha AK (1999) A generalized pressure derivative analysis for composite reservoirs. J Can Pet Technol 38(16):96–115
Jordan CL, Mattar L (2000) Comparison of pressure transient behaviour of composite and multi-layer reservoirs. Paper 2000-45, Canadian International Petroleum Conference, Calgary, AB, 4–8 June 2000
Levitan MM, Crawford GF (1995) General heterogeneous radial and linear models for well test analysis. SPE paper 30554, 70th Annual Fall Meeting, Dallas, TX, Oct 1995
Meier PM, Carrera J, Sanchez-Vila X (1998) An evaluation of Jacob’s method for the interpretation of pumping tests in heterogeneous formations. Water Resour Res 34(5):1011–1025
Moench AF (1997) Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer. Water Resour Res 33:1397–1407. doi:10.1029/97WR00651
Moench AF (1984) Double-porosity models for a fissured groundwater reservoir with fracture skin. Water Resour Res 20:831–846. doi:10.1029/WR020i007p00831
Oliver DS (1990) The averaging process in permeability estimation from well-test data. SPE paper 19845. SPE Form Eval 5(3):319–324
Oliver DS (1993) The influence of nonuniform transmissivity and storativity on drawdown. Water Resour Res 29(1):169–178
Pechstein A, Attinger S, Krieg R, Copty NK (2016) Estimating transmissivity from single-well pumping tests in heterogeneous aquifers. Water Resour Res 52:495–510. doi:10.1002/2015WR017845
Rafini S (2008) Comportement hydraulique des milieux faillés [The hydraulic behaviour of faulted media]. PhD Thesis, Université du Québec à Montréal, Canada
Rafini S, Larocque M (2009) Insights from numerical modeling on the hydrodynamics of non-radial flow in faulted media. Adv Water Resour 32:1170–1179. doi:10.1016/j.advwatres.2009.03.009
Rafini S, Larocque M (2012) Numerical modeling of the hydraulic signatures of horizontal and inclined faults. Hydrogeol J 20:337–350. doi:10.1007/s10040-011-0812-4
Renard P (2005) The future of hydraulic tests. Hydrogeol J 13:259–262. doi:10.1007/s10040-004-0406-5
Renard P, Glenz D, Mejias M (2008) Understanding diagnostic plots for well-test interpretation. Hydrogeol J 17:589–600. doi:10.1007/s10040-008-0392-0
Roberts RM, Ruskauff GJ, Avis JD (1996) A generalized method for analyzing well tests in complex flow systems. SPE-36023, Petroleum Computer Conference, Dallas, TX, 2–5 June 1996
Rushton KR (2003) Groundwater hydrology: conceptual and computational models. Wiley, Chichester, UK, 433 pp
Samani N, Pasandi M, Barry D (2006) Characterizing a heterogeneous aquifer by derivative analysis of pumping and recovery test data. J Geol Soc Iran 1:29–41
Spane FA (1993) Selected hydraulic test analysis techniques for constant-rate discharge tests. PNL-8539, Pacific Northwest Laboratory, Richland, WA
Spane FA, Wurstner SK (1993) DERIV: a computer program for calculating pressure derivatives for use in hydraulic test analysis. Ground Water 31:814–822. doi:10.1111/j.1745-6584.1993.tb00855.x
Sun X, Xu Y, Lin L (2015) The diagnostic plot analysis of artesian aquifers with case studies in Table Mountain Group of South Africa. Hydrogeol J 23:567–579. doi:10.1007/s10040-014-1203-4
Theis CV (1935) The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage. Trans Am Geophys Union 16:519–524. doi:10.1029/TR016i002p00519
Tiab D, Kumar A (1980) Application of the p’D function to interference analysis. J Pet Technol 32:1465–1470. doi:10.2118/6053-PA
Verweij JM (1995) Analysis of pumping test data from hard rock aquifers. Report GG R-95-39(A), TNO Institute of Applied Geoscience, Delft, The Netherlands, 62 pp
Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. Soc Pet Eng J 3:245–255. doi:10.2118/426-PA
Xiao L, Xu Y (2014) Diagnostic analysis of pumping tests using derivative of dlgs/dlgt with case study. Groundwater. doi:10.1111/gwat.12175
Acknowledgements
The authors would like to thank the National Sciences and Engineering Research Council of Canada (NSERC - individual discovery grants program) and the Fonds de recherche du Québec - Nature et technologies (FRQNT- new university researchers start-up program) grant programs held by Prof. Romain Chesnaux for their financial contribution in supporting this study. The manuscript benefited from fruitful review by R. Beauheim and an anonymous associate editor. The manuscript was kindly checked by Josée Kaufmann.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rafini, S., Chesnaux, R. & Ferroud, A. A numerical investigation of pumping-test responses from contiguous aquifers. Hydrogeol J 25, 877–894 (2017). https://doi.org/10.1007/s10040-017-1560-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10040-017-1560-x