Research article
6 June 2022

Simulating the effect of injection well on groundwater table in unconfined aquifer using numerical model of isogeometric analysis and optimization of injection rate with PSO algorithm

Publication: Quarterly Journal of Engineering Geology and Hydrogeology
Volume 55


Currently, one of the solutions to improve the decline in the water table of aquifers owing to their uncontrolled extraction is artificial recharge schemes, especially in arid and semi-arid regions. The present study applies a nonuniform rational B-spline functions (NURBS) based isogeometric method to investigate the effects of an injection well on the rise of water table, unconfined aquifer hydrodynamic parameters and injection rate. Also, the best injection rate was determined by linking the isogeometric analysis (IGA) simulation model to the particle swarm optimization (PSO) model. Initially, the IGA method was implemented to simulate a water table over an unconfined aquifer with two extraction wells with discharges of 1142.85 and 1428.57 m3 day−1 for 210 days and was compared with the Modflow model. The model was tuned and run by constructing an injection well with 8214.28 m3 day−1 injection rate for 1500 days. The IGA simulation results with ME = −0.0096, MAE = 0.0111 and RMSE = 0.0146 indicated the accuracy of the model in water table simulation compared with the Modflow model with ME = −0.0188, MAE = 0.023 and RMSE = 0.0284. The findings revealed that the use of an injection well has a positive impact on raising the water table, with a rise of 1.24 m in the observation well. Investigating the effect of the parameters on the water table changes indicated that the injection rate directly affects changes in the water table. The water table rises by more than 43% with a 50% increase in the injection rate. Also, compared with the effect of the injection rate on the water table, the transmissivity and specific yield effects were not substantial. The results of IGA–PSO showed that the best value of injection rate is 2000 m3 day−1, whereby the aquifer water table rises by an average of 37.12 cm.

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Author contributions

FP: formal analysis (lead), investigation (lead), methodology (lead), validation (lead), writing – review & editing (lead); AA: resources (lead), validation (supporting), writing – review & editing (supporting); SRH: conceptualization (lead), resources (lead)


This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Data availability

All data generated or analysed during this study are included in this published article (and its supplementary information files).
Scientific editing by Jonathan Smith

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Published In

cover image Quarterly Journal of Engineering Geology and Hydrogeology
Quarterly Journal of Engineering Geology and Hydrogeology
Volume 55Number 47 November 2022


Received: 25 August 2021
Revision received: 4 February 2022
Accepted: 8 April 2022
Published online: 6 June 2022
Published in print: 7 November 2022



F. Poursalehi
Department of Water Resources Engineering, University of Birjand, Birjand, Iran
Author Contributions: [Formal analysis (Lead)], [Investigation (Lead)], [Methodology (Lead)], [Validation (Lead)], and [Writing – review & editing (Lead)].
Department of Civil Engineering, University of Birjand, Birjand, Iran
Author Contributions: [Resources (Lead)], [Validation (Supporting)], and [Writing – review & editing (Supporting)].
S. R. Hashemi
Department of Water Engineering, University of Birjand, Birjand, Iran
Author Contributions: [Conceptualization (Lead)] and [Resources (Lead)].


Correspondence: [email protected]

Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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