Estimation of the Well’s Dynamic Water Level Using Empirical Formulas, Dimensional Analysis, and Energy Conservation Law (Case Study: Alborz Province)
Subject Areas : Aquifer Management and Artificial RechargeSara Fakouri 1 , Mohammad Bijankhan 2
1 - Msc student Water Sciences and Engineering Department, Imam Khomeini International University, Qazvin, Iran.
2 - Assistant Prof. Water Sciences and Engineering Department Imam Khomeini International University, Qazvin, Iran.
Keywords: Videometry, Well loss, Aquifer loss, Dynamic water level,
Abstract :
Background and Aim: Over-groundwater exploitation leads to severe water table decline and critical consequences in Iran’s fields. Water level at wells (dynamic water level) has reduced due to groundwater table decrease. It may reach the pump level and would result in air entrance into the suction pipe. Such two-phase flow would damage the electromotor finally. On the other hand, field measurement of the dynamic water level is always very difficult. Hence, it is aimed at this study to present a model to estimate the dynamic water level indirectly. Method: Water well Videometry is a useful tool to read the dynamic water level. It is however costly and not always possible. Therefore, a method to find the dynamic water level is of great practical importance. In this regard, energy balance equation is applied to a well pumping system to formulate the dynamic water level. Also, the empirical Jacob’s (1947) and Rorabaugh’s (1953) equations describing the well and aquifer losses are employed to develop a mathematical model of the dynamic water level. Finally, Buckingham analysis was employed to present a dimensionless model of the dynamic water level. Dimensional analyses could be applied using the information on the well discharge, well depth, and pump performance curve to estimate the well loss. The models were calibrated using the observed data of 17 water wells in Karaj, Kamalshahr, and Garmdareh of Alborz province. Results: The results indicated that the performance of Jacob’s (1947) and Rorabaugh’s (1953) methods are similar with the associated mean relative error of 5.1% compared to the measured dynamic water well values. Also, employing the dimensional analysis and energy balance methods the dynamic water level could be estimated with the mean absolute relative errors of 4 and 12.39% respectively. The results indicated that the three first models were much better than the energy balance model to predict the dynamic water level. Well performance is directly connected to the position of the dynamic water level, hence, the proposed methods could be used effectively to evaluate the well efficiency. Conclusion: To evaluate the relative error of estimating the dynamic water level RMSE values of different methods were calculated for the areas under study. The results indicated the proposed methods could be used more accurately for Kamalshahr area. The associated RMSE values of 6.58, 6.5, and 16.87 m was found for Jacob (1947) and Rorabaugh (1953), dimensional analysis, and energy balance models respectively. The method proposed based on the energy balance could not predict the observed dynamic water levels correctly. The reason might be attributed to the fact that there was no information about the pressure values at the outlet pipe. Also, there was no significant difference between the performances of Jacob (1947), Rorabaugh (1953) models. Among all, with the advantage of having dimensionless parameters, the model proposed based on the dimensional analysis was the best with the least mean absolute relative error.
Akbari, M. (2021). Monitoring land subsidence due to geological and water resources factors using Differential Radar Interferometry method (Case Study: Arak city). Journal of Water and Soil Resources Conservation, 10(3), 115-132. [in Persian]
Babaei, S., Hamdami, G., and Ghasemieh, H. (2017). “Identify the Effective Wells in Determination of Groundwater Depth in Urmia Plain Using Principle Component Analysis .” Journal of Water and Soil, 31(1), 40–50.[in Persian]
Faraji, Z., Kaviani, A., and Ashrafzadeh, A., (2016). “Assessment of GRACE satellite data for estimating the groundwater level changes in Qazvin province. ”Journal of Ecohydrology, 4(2), 463-476. doi: 10.22059/ije.2017.61482. [in Persian]
Gonga, Y., Zhanga, J., Zhoua, J., Wangb, G., Wangb, H., and He, X. (2021). “10.1016_j.egyr.2021.10.012_2hok.pdf.” Energy Reports, Hangzhou, China, 505–511.
Houben, G. J. 2015. “Review: Hydraulics of water wells—head losses of individual components.” Hydrogeol. J., 23 (8): 1659–1675. https://doi.org/10.1007/s10040-015-1313-7.
Jacob, C. E. (1947). “Drawdown test to determine effective radius of artesian well.” Trans, ASCE, 112((paper 2321)), 1047–1070.
Jamdar, M., Sarai Tabrizi, M., & Saremi, A. (2019). Management and optimization for conjunctive operation of water resources in order to reduce Hashtgerd aquifer decline. Journal of Water and Soil Resources Conservation, 8(3), 85-102. [in Persian]
Kurtulus, B., Yaylim, T. N., Avşar, O., Kulac, H. F., and Razack, M. (2019). “The well efficiency criteria revisited-development of a generalwell efficiency criteria (GWEC) based on rorabaugh’s model.” Water (Switzerland).
Mawlood, D. K., and Mustafa, J. S. (2016). “Analyze the Well Losses and Aquifer Losses on the Pumping Test Results.” The official scientific journal of Salahaddin University-Erbil, 28(S6), 61–67.
Möller, G., Detert, M. & Boes, R.M., 2015. Vortex-induced air entrainment rates at intakes. Journal of Hydraulic Engineering, pp.1–8.
Polak, K., Górecki, K., and Kaznowska-Opala, K. (2019). “The dynamics of water wells efficiency reduction and ageing process compensation.” Water (Switzerland).
Rorabaugh, M. J. (1953). “Graphical and theoretical analysis of step-drawdown test of artesian well.” Proc Amer Soc Civil Engrs, 79(362), 23.
Saraskanroud, A. S., Safari, S., and Elham, M. (2021). “Estimation of the levels of Groundwater Aquifers under the Influence of Land-Use Changes by Using GRACE Satellite Data.” Journal of Geography and Environmental Planning, 32(4), 1–26.
_||_