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Objective The Dupuit model of well flow is a classical steady-state well flow model for a homogeneous unconfined aquifer in a round island. However, it does not consider the widely existing infiltration recharge from precipitation, and is also inapplicable for stratified heterogeneous aquifer systems. Therefore, it must be modified to address these issues. Methods On the basis of the revised Dupuit well flow model which incorporates infiltration recharge, this study further extended its application to a stratified heterogeneous unconfined aquifer. The Girinskii's potential function was used to construct the differential equations for the radial groundwater flow according to the water balance principle, and the analytical solutions satisfying the boundary conditions are then obtained as formulas of the flow rate, water table and groundwater divide. Taking the bilayer structure as an example, typical groundwater level curves with respect to 30 scenarios of different parameter values were investigated. A special phenomenon was found in which the curves of different hydraulic conductivities intersect at a single point, which could also be proven in theory. This analytical model still adopted the Dupuit assumption and did not consider the "hydraulic jump" phenomenon on the wall of the pumping well. To check the impact of these constraints on the applicability of the analytical formulas, a two-dimensional numerical model for axially symmetric seepage was built for comparison. Results As indicated by the results, the relative error of the groundwater level estimated from the analytical solution is generally less than 4%, except for the zone near the pumping well. On the groundwater divide, where the Dupuit assumption is mostly invalid, the relative errors of the analytical solution to both the distance and height of the divide are smaller than 0.1%. Conclusion The Dupuit assumption does not significantly influence applicability of the analytical model.

The perfect design of open drains requires understanding the effect of the different design parameters on groundwater table. The paper objective is to perform sensitivity analysis to show the effect of the drainage flow rate, the distance between the bed of the open drain and the bottom impervious layer, the drain bed width, the spacing between drains, and the soil type (design parameters) on the maximum height of groundwater table above the open drain bed. HYDRUS software, Dupuit equation, and artificial neural networks (ANNs) are used. Comparison is performed between HYDRUS and Dupuit equation for simulating water flow in unconfined aquifer between two water ways. The predicted groundwater table using HYDRUS is above the other one from Dupuit equation. ANNs were used to predict the maximum height of groundwater table from its design parameters. MATLAB code is written to simply use the previous ANNs to find the best drain design.

The perfect design of open drains requires understanding the effect of the different design parameters on groundwater table. The paper objective is to perform sensitivity analysis to show the effect of the drainage flow rate, the distance between the bed of the open drain and the bottom impervious layer, the drain bed width, the spacing between drains, and the soil type (design parameters) on the maximum height of groundwater table above the open drain bed. HYDRUS software, Dupuit equation, and artificial neural networks (ANNs) are used. Comparison is performed between HYDRUS and Dupuit equation for simulating water flow in unconfined aquifer between two water ways. The predicted groundwater table using HYDRUS is above the other one from Dupuit equation. ANNs were used to predict the maximum height of groundwater table from its design parameters. MATLAB code is written to simply use the previous ANNs to find the best drain design. [ABSTRACT FROM AUTHOR]

Prior works have discussed the appearance of a ceiling flux for the generalized Darcy model, but there has been no such discussion on the Forchheimer model. Moreover, the earlier results were obtained through numerical computations. Here we employ a semi-inverse solution to get analytical expressions for the solution and the volumetric flux, and we demonstrate, by direct comparison, that for the flux computation, the semi-inverse approximation is as accurate as a numerical solution to the problem. It is shown that neither model (Darcy or Forchheimer) has the desirable property of attaining a limiting flux for large driving pressures. However, when the pressure-dependence of viscosity is incorporated suitably to generalize the classical models, the generalized Darcy and Forchheimer models show the desirable behaviour of a ceiling flux for large pressures. Moreover, the volumetric flux obtained from the generalized models is always lesser than that obtained from the classical models. Such generalized models are most appropriate to model the flow in applications involving large pressure gradients, like enhanced oil recovery and carbon sequestration. [ABSTRACT FROM AUTHOR]

Pastures in beef cattle ranches are identified as one of the major land uses that contribute phosphorus (P) and nitrogen (N) loadings to Lake Okeechobee (LO), Florida. A study was conducted to quantify flow, P, and N contributions from groundwater to a 170 m ditch section within a beef cattle ranch located in the LO basin from June 2005 to May 2009. Groundwater depths and total N (TN) and total P (TP) concentrations measured in five wells, installed on each side (bank) of the ditch section, were combined with the ditch stage and N and P concentrations to quantify groundwater flow and nutrient loads. The Dupuit equation was used to estimate the groundwater flow to and from the ditch. The average net groundwater flow to the ditch section, estimated from a range (low and high) of saturated hydraulic conductivity (Ksat) values, ranged from 765 to 1,729 m³ per year. Annual groundwater flow contributions were positive (to the ditch) for all four years, while the groundwater nutrient contributions were positive for three years and negative (from the ditch) for one year (drought year). Average net annual TP loads to the ditch section ranged from 0.1 (low) to 0.2 (high) kg, while TN loads ranged from 2.1 (low) to 4.5 (high) kg. Extrapolating the results from this study to theLO basin indicated that groundwater was a major contributor ofTP loads to the lake. [ABSTRACT FROM AUTHOR]

Empirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term "radius of influence myth" is used by analogy with the water budget myth. Alternative formulations based on the well-known de Glee and Theis equations are presented, and the contested formula that estimates the radius of influence by balancing pumping and infiltration rate is derived from an asymptotic solution of an analytical model developed by Ernst in 1971. The transient state solution of this model is developed applying the Laplace transform, and it is verified against the finite-difference solution. Examining drawdown and total storage change reveals the relations between the presented one-dimensional radial flow solutions. The assumptions underlying these solutions are discussed in detail to show their limitations and to refute misunderstandings about their applicability. The discussed analytical models and the formulas derived from it to estimate the radius of influence cannot be regarded as substitutes for advanced modeling, although they offer valuable insights on relevant parameter combinations. [ABSTRACT FROM AUTHOR]