Application of random walk algorithm into finite element numerical groundwater model for capture zone depiction

Abstract

Determination of wells’ capture zones is one of the most remarkable issues that should be carried out in each aquifer. Methods used for depicting this area has been divided into two simple and complex method. Through the simple one several mathematical equations are used and in the complex approaches, numerical models are applied. In this study, the capture zone of extraction wells in a confined aquifer is determined using random walk algorithm and finite element numerical model. The studied aquifer consists of three extraction wells and one injection well in which the extraction and injection operation are performed for 10,000 days. After the simulation procedure, the groundwater head is obtained. Simulation results show high accuracy which its root mean square error is 0.141 m while this value for finite difference solution is 0.249 m. then the capture zone for each well was depicted individually in two periods of 50 and 180 days. Results showed that the extension of the capture zone for all three wells is toward the part of the aquifer, which has a higher groundwater level than other areas. Also, the results revealed that, in areas of the aquifer that have a higher transmissivity coefficient, the zone is more extended and for the areas with lower transmissivity coefficient, its width decreased and became narrower. In the second well, the width of capture zone in zone 2 and 3 were 302.86 m and 267.46 m, respectively.

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Sustainable Water Resources Management (2022) 8:40
https://doi.org/10.1007/s40899-022-00618-z
ORIGINAL ARTICLE
Application ofrandom walk algorithm intofinite element numerical
groundwater model forcapture zone depiction
NahidMajidiKhalilabad1· AliMohtashami2· AbolfazlAkbarpour3
Received: 9 January 2021 / Accepted: 4 January 2022 / Published online: 7 February 2022
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022
Abstract
Determination of wells’ capture zones is one of the most remarkable issues that should be carried out in each aquifer. Methods
used for depicting this area has been divided into two simple and complex method. Through the simple one several math-
ematical equations are used and in the complex approaches, numerical models are applied. In this study, the capture zone
of extraction wells in a confined aquifer is determined using random walk algorithm and finite element numerical model.
The studied aquifer consists of three extraction wells and one injection well in which the extraction and injection operation
are performed for 10,000days. After the simulation procedure, the groundwater head is obtained. Simulation results show
high accuracy which its root mean square error is 0.141m while this value for finite difference solution is 0.249m. then the
capture zone for each well was depicted individually in two periods of 50 and 180days. Results showed that the extension of
the capture zone for all three wells is toward the part of the aquifer, which has a higher groundwater level than other areas.
Also, the results revealed that, in areas of the aquifer that have a higher transmissivity coefficient, the zone is more extended
and for the areas with lower transmissivity coefficient, its width decreased and became narrower. In the second well, the
width of capture zone in zone 2 and 3 were 302.86m and 267.46m, respectively.
Keywords Confined aquifer· Depiction of the capture zone· Finite element numerical model· Random walk algorithm
Introduction
In the areas with limited surface water resources, ground-
water resources are used as the only available source and
supply the human needs (Goodarzi and Eslamian 2019).
To attain these resources, well drilling operation is done in
aquifers. The main point in drilling new wells is to ensure
that they do not exceed the capture zones of previous wells.
This issue indicates the importance of the wells capture zone
determination.
Delineation of the exact capture zone of wells is a remark-
able concern. Because computing this area as a small region
and considering it for management scenarios increases
the risk of well management. In another hand, computing
it wider than the real amount, has some disadvantages as
well (Ferreiraet al. 2004; Sabetraftar 2013) Therefore, it is
required to determine the optimal area of it.
Several methods have been proposed and used for the
computation of capture zones, which comprises simple and
complex methods (Goodarzi and Eslamian 2019). Simple
methods include some mathematical equations to derive the
considered zone. Furthermore, complex methods refer to the
utilized numerical methods in the field.
Nowadays, researchers have used numerical models to
delineate capture zone of wells. These models apply the gov-
erning equation of groundwater flow to nodes or elements
scattered in the aquifer. With ensembling the equations of
each node or element in three matrices, a set of linear equa-
tions is generated. With using matrix solver methods, the
unknown matrix, the groundwater level, is computed. After-
ward, using other methods and algorithms, the capture zone
of wells is determined.
Puchalski (2009) has shown that the capture zones deter-
mined by numerical models are well-adapted to the real
ones. Therefore, depicting the capture zone using these
* Nahid Majidi Khalilabad
mohtashamiali@yahoo.com
1 East Water andEnvironment Research Institute (EWERI),
Mashhad, Iran
2 Civil Engineering Department, University ofSistan
andBaluchestan, Zahedan, Iran
3 Department ofCivil Engineering, Faculty ofEngineering,
University ofBirjand, Birjand, Iran
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