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A simple model of leakage induced by deep pumping and its application to pollution beneath a city in Thailand

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Abstract

Many cities in developing countries are dependent upon groundwater for water supply. Frequently this groundwater is pumped from semi-confined aquifers in alluvial deposits. These deeper aquifers are often considered to be protected from polluted shallow water by intervening less-permeable layers. However, where groundwater is pumped from a semi-confined aquifer immediately beneath a city, significant induced leakage of contaminated shallow water can occur. This may lead to a serious deterioration of water quality in deeper aquifers in the longer-term. A simple model has been developed which provides insight into the hydraulic controls on water quality in such semi-confined aquifers. The model provides a tool for the initial assessment and prediction of the impact of urbanization on groundwater quality. Also, the model characterizes the key hydrogeological behaviour through a single parameter, here termed the ‘city leakage factor’, which can be used to assess the vulnerability to contamination by leakage. A case study of a city in Thailand illustrates the use of this model.

Résumé

Beaucoup de villes des pays en développement dépendent de l’eau souterraine pour leur alimentation en eau. Cette eau souterraine est souvent pompée dans des aquifères alluviaux semi-captifs. Ces aquifères plus profonds sont souvent considérés comme protégés des eaux peu profondes et polluées, grâce à des couches intercalaires moins perméables. Cependant, dans le cas où l’eau souterraine est pompée à partir d’un aquifère semi-captif situé directement sous une ville, une drainance importante des eaux peu profondes et polluées peut être induite. Ceci peut entraîner, à long terme, une détérioration significative de la qualité de l’eau dans les aquifères plus profonds. Un modèle simple a été construit fournissant un aperçu des contrôles hydrauliques agissant sur la qualité de l’eau dans des aquifères semi-captifs. Ce modèle est un outil permettant d’évaluer l’état initial et de prédire l’impact de l’urbanisation sur la qualité de l’eau souterraine. Le modèle caractérise également les comportements hydrogéologiques majeurs à travers un unique paramètre, nommé dans cette étude facteur de drainance de la ville“, et qui peut être utilisé pour évaluer la vulnérabilité de l’aquifère face à une contamination par drainance. L’étude de cas d’une ville en Thaïlande illustre l’utilisation de ce modèle.

Resumen

Muchas ciudades de paises en desarrollo dependen del agua subterránea para el abastecimiento de agua. Frecuentemente el agua subterránea se bombea de acuíferos semi-confinados en depósitos aluviales. Estos acuíferos más profundos se protegen frecuentemente de agua somera contaminada mediante la intervencción de capas menos permeables. Sin embargo, donde el agua subterránea se bombea de un acuífero semi-confinado inmediatamente debajo de una ciudad, pueden ocurrir fugas significativas inducidas de agua somera contaminada. Esto puede conducir a un serio deterioro de calidad de agua en acuíferos más profundos en el largo plazo. Se ha desarrollado un modelo simple el cual aporta idea acerca de los controles hidráulicos en la calidad del agua en tales acuíferos semi-confinados. El modelo aporta una herramienta para la evaluación inicial y predicción del impacto de urbanización en la calidad del agua subterránea. El modelo también caracteriza el comportamiento hidrogeológico clave a traves de un solo parámetro, que aquí se denomina ´factor de fuga de la ciudad´el cual puede usarse para evaluar la vulnerabilidad a la contaminación por fuga. El uso de este modelo se ilustra con un estudio de caso de una ciudad en Tailandia.

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Abbreviations

A:

Subscript denoting the aquifer

b :

Saturated thickness of the aquitard [L]

B:

Subscript denoting breakthrough of polluted water to the deep aquifer

c :

Concentration in (pumped) aquifer water [M L-3]

c B :

Background concentration (beyond city) [M L-3]

c L :

Concentration in water leaking from below the city [M L-3]

c rel :

Relative concentration in the water beneath the city, given by Eq.(18) [-]

h :

Head in the aquifer [L]

h 0 :

Head represented by the water table in the aquitard [L]

H :

Heaviside step function [-]

I n :

Modified Bessel function of the first kind of order n [-]

K v :

Vertical hydraulic conductivity of the aquitard [L T -1]

K n :

Modified Bessel function of the second kind of order n [-]

L :

\( = {\sqrt {{Tb} \mathord{\left/ {\vphantom {{Tb} K}} \right. \kern-\nulldelimiterspace} K} } \) Leakance of the aquitard / deep aquifer system [L]

n :

Kinematic porosity .[-]

P:

Subscript denoting pumping

q L :

Leakage flux [L T -1]

q P :

Pumped flux (total pumping divided by city area) [L T -1]

Q A :

Volumetric aquifer flow towards city centre as a function of radius [LT -1]

Q P :

Total abstraction rate from the aquifer [LT -1]

r :

Distance from city (pumping) centre [L]

r B :

Distance from city centre to which pollutant breakthrough has extended [L]

R :

Pumping radius of city [L]

t L :

Time of travel through the aquitard (function of distance from centre) [T]

T :

Transmissivity of the aquifer [LT -1]

α:

Parameter given by Eq. (20) [-]

β :

Constant in Eq. (19) [-]

λ :

‘City leakage factor’ = ratio of the pumping radius to the leakance: Eq. (10) [-]

ρ :

Radial distance from city centre relative to pumping radius, r/R [-]

ρ B :

= r B /R [-]

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Acknowledgements

The authors wish to thank the following people: V. Ramnarong, K. Anand and C. Samrit of the Department of Mineral Resources, Thailand; P. Kanatharana and W. Meesin of Prince Songkhla University; and D. Gooddy of BGS. The study was funded by the Overseas Development Administration (now Department for International Development) under project RS975. The paper is published with permission of the Director of the British Geological Survey, NERC.

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Barker, J.A., Lawrence, A.R. A simple model of leakage induced by deep pumping and its application to pollution beneath a city in Thailand. Hydrogeol J 16, 407–417 (2008). https://doi.org/10.1007/s10040-008-0277-2

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