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A Robin type boundary condition (BC), commonly adopted at stream-aquifer interface, excludes a term associated with streambed accounting for the effects of streambed storage and width. This study presents two new analytical models for describing confined flow induced by pumping in a stream-aquifer system. One model considers a single-zone aquifer and treats the streambed as a lagging Robin BC with a time lag parameter related to the effects. The other considers a two-zone aquifer consisting of aquifer and streambed zones. A Dirichlet BC for stream water level is specified at the edge of the streambed. The time-domain solutions of both models are developed to describe spatiotemporal drawdown and temporal stream filtration/depletion rate (SDR). The finite element solutions (FESs) of both models are also built. Results suggest the lag time equals the half of the squared streambed width divided by the streambed hydraulic diffusivity. The effects of streambed width and storage on SDR should be considered when their lumped parameter exceeds 0.1. Neglecting their effects causes 25% difference in SDR when the lumped parameter equals 10. Based on the FESs, the use of the lagging Robin BC takes nearly a tenth of computing time of obtaining accurate steady-state SDR for the simulation of the two-zone aquifer. In addition, the present solutions agree to a field SDR experiment conducted by Hunt et al. (2001Hunt et al. ( , https://doi.org/10.1111Hunt et al. ( /j.1745Hunt et al. ( -6584.2001. To conclude, this study presents two new models for describing groundwater flow in a stream-aquifer system and explores the joint effect of streambed width and storage on SDR.

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This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant‐rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual‐porosity model. The Laplace‐domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time‐domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.

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In the past, the analytical model developed for a radially divergent heat flow in an aquifer thermal energy storage (ATES) system considers only the process of either thermal conduction or thermal dispersion. In addition, the existing models commonly regarded the inner boundary at the injection well as the constant‐temperature condition, which does not meet the continuity condition of heat flux at the wellbore. We herein propose an analytical model for a realistic representation of heat flow in an ATES system by considering the effects of both thermal conduction and thermal dispersion in the heat transfer equation and a Robin‐type boundary condition at the injection well. The model consists of three heat flow equations depicting the temperature distributions in the confined aquifer and its underlying and overlying rocks. The Laplace transform method is applied to solve the proposed model. The solutions for the cases of dispersion‐ and conduction‐dominant flow fields are also developed and discussed. Comparisons between the present solutions with five existing solutions developed for similar heated water injection problems are made. A global sensitivity method is also performed to analyze the thermal response to the change in each of the aquifer parameters. Finally, our solution is validated through the comparison with the finite difference solution and observed data from an ATES experiment site in Mobile, Alabama.

In the past, many mathematical models based on the dual‐porosity (DP) concept were developed to describe the groundwater flow in fractured aquifer systems. Most of them seemingly have problems in predicting accurate drawdown at the early and/or intermediate times as compared with field measured data. Thus, this study proposes a new analytical model with a generalized transfer term (GTT) to describe the flow induced by pumping in such systems. The new model is nonlinear because the GTT representing the matrix‐to‐fracture flux gives different weights to the fracture and matrix drawdowns. The GTT reduces to the existing first‐order transfer term if the weight equals zero and second‐order term if the weight is one. The present model also includes a leakage term accounting for flow from the overlain or underlain aquitard. The drawdown solution of the model is developed based on the Laplace transform method and integration by parts formula and then verified through the comparison with the finite‐element solution. The effect of different weight values in the GTT on the DP flow is investigated. Additionally, the sensitivity analysis is performed to assess the impact of the change in each of the aquifer parameters on the flow. Furthermore, the present solution is used to analyze two sets of pumping drawdown data from test sites in Canada and India. We found that the drawdown predictions from the present solution fit field measured data very well, suggesting that the present model can adequately describe the real‐world DP flow system.