Estimating confined aquifer parameters using a simple derivative-based method

Abstract

The confined aquifer parameters, transmissivity and storage coefficient, are commonly determined using the pumping tests. Several methods have been developed to estimate confined aquifer parameters using pumping tests, but different methods suffer from different drawbacks. Those methods that use the truncated Theis well functionwtrue(utrue), apply just early or late drawdowns, depending on the case, to estimate the aquifer parameters. Those methods, such as Theis (1935), that use non-truncated well functionwtrue(utrue), can apply all drawdown data for aquifer parameter estimation but may still suffer from subjectivities such as personsal judgment in curve matching, time-consuming procedure and requiring values for Theis well function, wtrue(utrue), and its argument utrue(u=r2S4Tttrue). The aim of this study is to present a new method to overcome the aforementioned drawbacks and subjectivities involved in available published methods. In this paper, a simple derivative-based method is presented to estimate confined aquifer parameters applicable for entire drawdowns during the pumping period. The time derivative of drawdowns relate non-linearly with pumping timet, and therefore, aquifer parameters are estimated using developed equations based on the least squares optimization approach. The method is applied to three sets of synthetic, published and field data and results show that the estimation accuracy is acceptable. The drawdown time interval measurement has a marginal effect on parameters estimation due to the analytical basis of derivative calculations. The method does not require construction of graphs, and numerical calculations may be performed on a calculator to determine the aquifer parameters on site. It does not require curve matching, initial guess of the parameters and values of wtrue(utrue) and u.

Hydraulic characteristics of a fractured crystalline basement aquifer in Nzhelele area, Limpopo Province, South Africa

“…MAE and RMSE values were mostly comparable with those of Alzraiee et al (2014) with exception of those of borehole H27-0165 and H27-0290 which were higher. The RMSE values computed from measured and drawdowns estimated from simple derivative-based and curve type methods for a confined aquifer located in Fars province, southern Iran ranged from 0.091 to 0.82 m in a study conducted by Naderi (2019). The RMSE values for four boreholes (H27-0002, H27-0052, H27-0136 and H27-0138) were within the range of values obtained by Naderi (2019).…”

“…The RMSE values computed from measured and drawdowns estimated from simple derivative-based and curve type methods for a confined aquifer located in Fars province, southern Iran ranged from 0.091 to 0.82 m in a study conducted by Naderi (2019). The RMSE values for four boreholes (H27-0002, H27-0052, H27-0136 and H27-0138) were within the range of values obtained by Naderi (2019). Fan et al (2020) obtained RMSE values ranging from 0.124 to 5.197, 0.039 to 0.24, 0.094 to 2.627 when estimating aquifer parameters based on neural network (ANN), random forest (RF), and support vector machine (SVR) methods, respectively.…”

PyTheis—A Python Tool for Analyzing Pump Test Data

“…To further test the performance of the PyTheis code under different types of flow conditions, we solved the following eight different problems reported in the literature: Walton [31], Fetter and Rayne [32], Driscol [33], McWhorter and Sunda [34], Viessman and Lewis [35], Todd and Mays [36], and two sets of data from Naderi [23]. Our results indicated that the PyTheis code, with the default initial values and parameter bounds, was able to solve all eight problems.…”

“…Most automatic curve fitting tools employ a nonlinear fitting algorithm to minimize the sum of squared error between observations and model predictions [7,8,10,[21][22][23] In a recent study, Bateni et al [24] compared the performance of various nonlinear programming methods including the genetic algorithms (GA) and ant colony (AC) methods to estimate aquifer parameters using five different time-drawdown datasets. The authors concluded that both GA and AC are reliable methods for evaluating aquifer parameters, and they performed better than the graphical methods.…”

On the Reliability of Variable‐Rate Pumping Test Results: Sensitivity to Information Content of the Recorded Data

“…Further, this study has investigated the sensitivity of the parameter estimates to different types of information loss in homogenous aquifers and has not considered spatial dependency of the aquifer parameters. In reality, of course, aquifers are typically heterogeneous and any estimated values for the aquifer parameters are representative of the average characteristics of the cone of depression at a given time during the pumping test (Naderi, 2019; Wen et al, 2010; Wu et al, 2005). Above we saw that different values for the aquifer parameters (e.g., different value of T and S in a confined aquifer), resulted in different amounts of sensitivity under the same type of information loss.…”