Flow In Unconfined Aquifer Research Articles

Double parametric based solution of fuzzy unconfined aquifer problem using Laplace transforms method

The Boussinesq equation describes the model for horizontal water flow in unconfined aquifers without precipitation, a topic that has been extensively studied in the literature. However, the parameters, as well as the initial and boundary conditions, are often assumed to be exact. In reality, these conditions may be incomplete or uncertain due to limited knowledge, insufficient information, or errors introduced by humans or machines. The fuzzy set theory has recently been successfully employed to model such uncertainties. This article investigates the analytical solution of the one-dimensional Boussinesq equation in a fuzzy environment. The objective of this research is to investigate the recharge and discharge of a semi-infinite unconfined aquifer adjacent to a lake. For the present investigation, uncertainties in terms of fuzzy are considered only for the involved initial and boundary conditions of the problem, whereas other parameters are considered as crisp or exact. The analysis employed the double parametric form of a fuzzy number alongside Laplace transform techniques. The obtained solutions were then compared with existing results in specific cases to validate their accuracy.

Fuzzy Finite Elements Solution Describing Recession Flow in Unconfined Aquifers

In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while the introduced hydraulic parameters (Conductivity K and Porosity S) present significant uncertainties for various reasons (e.g., spatial distribution, human errors, etc.). Considering the general lack of in situ measurements for these parameters as well as the certain spatial variability that they present in field scales, a fuzzy approach was adopted to include the problem uncertainties and cover the disadvantage of ground truth missing data. The overall problem is encountered with a new approximate fuzzy FEM numerical solution, leading to a system of crisp boundary value problems. To prove the validity and efficiency of the new fuzzy FEM, a comparative analysis between the proposed approach and other well-known and tested approximations was carried out. According to the results, the proposed FEM numerical solution agrees with Karadinumerical method for the crisp case and is in close agreement with the original analytical solution proposed by Boussinesq in 1904 with the absolute reduced error to be 4.6‰. Additionally, the possibility theory is applied, enabling the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decisions for rational and productive engineering studies.

Design of open drains by solving Richards equation and artificial neural networks

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.

A coupled flow and transport model for simulation of multi-species reactive transport in unconfined aquifer using meshless local Petrov Galerkin (MLPG) method.

An understanding of natural degradation of multiple reactive contaminants in the aquifers is essential before designing the monitoring or remediation programs for polluted aquifers. Since such reactive contaminants are ubiquitous, a number of research works has been performed in the past three decades for the modelling of multi-species reactive transport (MSRT) phenomenon. The widely used finite difference method (FDM) and finite element method (FEM)-based models suffer a drawback of relying on a grid/mesh, which makes the solution unstable. Addressing such difficulties, the latest research on the MSRT models is directed towards the meshless methods. In this study, the meshless local Petrov Galerkin (MLPG) method-based multi-species reactive transport model (MLPG-MSRT) is presented, with an objective to create a robust simulation tool for the prediction of fate of multiple contaminants of the first-order reaction network. The developed model is validated for reversible as well as irreversible reaction networks with the available analytical solutions. Also, the MLPG model for unconfined aquifer flow (UF) is developed, validated, and coupled with the MLPG-MSRT model. The MLPG-UF-MSRT model results are further compared with the established FDM-based MODFLOW-RT3D model solutions for a rectangular and a real field type study. The results showed that the proposed model can simulate MSRT as accurately as the FDM-based models with an additional advantage of simplicity and stability, and thus, is more efficient for complex field problems.

Investigating steady unconfined groundwater flow using Physics Informed Neural Networks

A deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of partial differential equations (PDEs) alongside data obtained from physical observations. In this work, we consider the Dupuit–Boussinesq equation, which is based on the Dupuit–Forchheimer approximation, as well as a recent, more complete model derived by Di Nucci (2018) as underlying models. We then train PINNs on data obtained from steady-state analytical solutions and laboratory based experiments.Using PINNs, we predict phreatic surface profiles given different input flow conditions and recover estimates for the hydraulic conductivity from the experimental observations. We show that PINNs can eliminate the inherent inability of the Dupuit–Boussinesq equation to predict flows with seepage faces. Moreover, the inclusion of physics information from the Di Nucci and Dupuit–Boussinesq models constrains the solution space and produces better predictions than training on data alone. PINNs based predictions are robust and show a little effect from added noise in the training data. Furthermore, we compare the PINNs solutions obtained via the Di Nucci and Dupuit–Boussinesq flow models to examine the effects of higher order flow terms that are included in the Di Nucci formulation but are neglected by the Dupuit–Boussinesq approximation. Lastly, we discuss the effectiveness of using PINNs for examining groundwater flow.

An efficient method to solve the fuzzy Crank–Nicolson scheme with application to the groundwater flow problem

Abstract In this paper, we propose a comprehensive methodological framework for solving the fuzzy groundwater flow problem in a simpler and faster way based on numerical analysis. In particular, a novel simplified matrix explicit inverse formula is proposed as an efficient method to solve the fuzzy Finite Difference numerical scheme, called Crank–Nicolson implicit scheme. The main advantage of the proposed method is that it offers an efficient and simpler solution to the algebraic tridiagonal system of equations that appeared in the fuzzy Crank–Nicolson scheme, without affecting the accuracy of the results. Without doubt, the simulation of an unconfined aquifer flow, using the Finite Difference Method, is often time-consuming due to the costly calculations required to solve the implicit Finite Difference schemes. This process becomes even more difficult when the physical problem is solved in its fuzzy form where the calculations become more complex and greatly increase. However, problem uncertainties are not considered negligible and must be included in the final calculations for a more rational management of the water body. This creates the need to find a new and faster way to solve the fuzzy implicit schemes, as proposed in this work. The simplified matrix explicit inverse formula was applied to the fuzzy Crank–Nicolson scheme to solve the fuzzy partial differential equation of Boussinesq and, hence, the simulation of the physical problem. Its results were compared with the corresponding results of the Thomas algorithm, which until today, is the most common method of solving the tridiagonal system of equations. The case under consideration refers to a sudden rise in the lake's water level, thus resulting in the aquifer recharging from the lake. The performance of the proposed method was more than satisfactory in terms of calculation accuracy and reliability where the numerical results are matched with the differences appearing from the 12 decimal point onward between the two examined methods. The proposed method tested also considered the running times, achieving much better times compared with the Thomas algorithm, where the differences ranged from a few seconds to several hours depending on the examined time and space steps.

Simulation of Unconfined Aquifer Flow Based on Parallel Adaptive Mesh Refinement

AbstractThe density of a numerical mesh is a key component for the quality of the numerical solution. Common methods in groundwater simulations rely on meshes generated prior to simulation, which lead to unnecessary or insufficient degrees of freedom (dofs). In this study we use Adaptive Mesh Refinement (AMR) to substitute the subjective mesh generation process with a more rigorous approach where new dofs are iteratively added to the solution of an initial coarse mesh based on a solution error estimation. The simulation is solved on a succession of meshes through which the mesh density is increased in areas of steep gradients in the solution variable. Here, we apply the approach to unconfined aquifer flow which is a non‐linear problem commonly encountered in groundwater modeling. By taking advantage of the iterative nature of AMR we arrive at an efficient solver approach. We treat the position of the unconfined boundary as an additional unknown which is estimated iteratively. The first iterations are executed rapidly as the mesh is rather coarse, while the free boundary adapts to the computed water table position as close as the mesh density allows. In this study we demonstrate the viability of the proposed unconfined aquifer simulation method to a series of 2D hypothetical examples under several conditions and stresses as well as a 3D test case. In all cases the AMR was able to automatically resolve the solution in areas with steep hydraulic head gradient, using appropriately higher density to achieve high localized refinement and accuracy.

Modeling variable-density flow in saturated-unsaturated porous media: An advanced numerical model

Modeling variable-density flow in unconfined aquifers is a challenging task because of the nonlinear coupling between variably saturated flow and contaminant transport. This results in a highly nonlinear system since the strongly nonlinear Richards flow equation is, in addition, coupled to the advection-dispersion transport equation by viscosity and density variation. The solution of such a nonlinear system is often subject to convergence issues and can be very expansive in terms of computational time, especially for large-scale problems. Conventional numerical algorithms based on the sequential approach and the classical finite difference or finite element methods with the first-order backward Euler time integration scheme are generally inefficient and/or do not provide satisfactory results. In this work, we develop a new efficient and accurate 2D numerical model for the transport of dense contaminants in unsaturated porous media that allows for the simulation of large-scale problems. This research describes a new model that combines advanced spatial discretization methods (mixed hybrid finite element method, discontinuous Galerkin finite element method, and multipoint flux approximation method) with higher-order time integration techniques via the method of lines (MOL). The latter allows one to adapt the time step's size and the order of the time integration to improve the computational efficiency while maintaining accuracy. The robustness and accuracy of the new model are shown by comparison against a widely used commercial code based on the standard finite element method. The applicability of the developed model to a large-scale problem is then investigated by simulating saltwater intrusion under a climate change projection and long-term pumping regimes for the Akkar coastal aquifer in Lebanon using a simplified 2D conceptual model.

Modelling of Irrigation Return Flow in Unconfined Aquifer of Dharoi Command in Mehsana District of Gujarat, India

Surface water flow and subsurface flow have traditionally been investigated separately and simulators have been developed over the years, to model each of these systems. Growing interest in conjunctive water management, and need for simulations of surface/subsurface flow and their interactions has lead to the linking of models of the respective domains. This study from Dharoi command area, using MODFLOW, showed pertaining to the second layer of the calibrated model. The first layer is a thin soil cover layer of about 3 m uniform thickness. Top layer is kept under unconfined water table condition, where as the next layer is given the scope of transforming between water table to confined state and vice versa depending upon the fluctuation of the computed water level with respect to the bottom boundary of the top layer. No recharge and discharge options other than a single boundary condition of average May water level in the extreme north-east grid has been allowed. This calibration is based upon matching the observed and computed average gradient of the water table (hydraulic gradient) and nothing to do with matching the point to point values of the observation wells as that could lead to misappropriation in respect of hydrologic condition. Over all gradient of the water table in the area of interest is computed as 0.23 m per km in comparison to an observed hydraulic gradient of 0.3 m per km. The rivers such as Sabarmati downstream of Dharoi dam and up to Bijapur, Rupen and Pushpawati are activated in the transient run. Conductance value is considered as 0.0001 m/sec for all the rivers. proximity of the second layer under unconfined state. Comparisons of water levels in selected locations. Overall match between the trends and the point values indicate that the calibrated model transient run can be considered as base case and various options can be studied with this model. Visual MODFLOW is very effective to know the present scenario of ground water flow, water level of aquifer, wells, also point values indicate that the calibrated model transient run can be considered as base case and various options can be studied with this model. Visual MODFLOW is very effective to know the present scenario of ground water flow, water level of aquifer, wells, also distribution of spatial recharge, specific yield distribution. It gives very close result to the observed value.

The solution of unconfined groundwater flow with an innovative lattice Boltzmann method

Lattice Boltzmann method (LBM) has emerged as a fast, precise, and efficient numerical solution to solve differential equations. There seems to be a dearth of research regarding the solution for groundwater flow in unconfined aquifer using LBM. Accordingly, in this study, an innovative numerical solution based on LBM was introduced to solve groundwater flow in unconfined aquifers, taking into account D2Q9 scheme. The solutions obtained from the proposed LBM were compared to results stemmed from three different unconfined groundwater problems with known solutions. Both steady and transient conditions for groundwater flow were considered in simulations. It was deduced that the proposed LBM could simulate the unconfined groundwater flow satisfactorily.

Experimental evaluation of self-remediation mechanism by groundwater flow in unconfined aquifers.

The main goal of this study is to investigate the effect of soil properties such as permeability on the dispersion and movement of a water dissolved contaminant in three types of soil in saturated and 2D conditions. The experimental modeling was conducted using a constructed sand box. In order to evaluate the effect of soils particle size on the distribution and self-remediation of the contaminant, three types of soil, as coarse, medium, and fine-grained sand were used. Results of experiments showed that, at the first 25% of the test time, the contaminated area reduction rate in all three specimens varies significantly, so that for the medium and coarse sand, it is 2.2 and 3 times that of fine sand, respectively. The contaminant width reduction at the first 25% of the test time was 5%, 6%, and 35% for the fine, medium, and coarse sand, respectively, while the contaminant length reduction was 13%, 18%, and 37% for the fine, medium, and coarse sand, respectively. In addition, by comparing the contaminant movement in the saturated and semi-saturated areas, it was observed that the longitudinal and transverse movement of the contaminant under the water level are almost 2.5 times of the semi-saturated area. PRACTITIONER POINTS: Reduction rate of solution area in fine, medium and coarse-grained sample are nearly convex, linear and concave-shaped, respectively. The remediation process in saturated zones is implemented in both directions with higher intensity in a shorter time than unsaturated zones. In the strip formed plumes, the volume of the self-remediation is proportional to the time intervals during the test. In the elliptic masses the self-purification amount is lower at the beginning, due to the small cross-section ending of the contamination mass.

A Steady-State Model to Simulate Groundwater Flow in Unconfined Aquifer

The hydraulic and hydrogeological features of the Caposele aquifer have been investigated by using a numerical groundwater flow model. In particular, groundwater flow simulations were performed for a multilayered, unconfined aquifer in steady-state conditions for different thicknesses of the aquifer’s saturated zone. The Caposele groundwater model was carried out starting from a generic model drained by a unique spring outlet in accordance with the geo-hydrological features of the study area. The conceptual model was built considering hydrogeological features of spring catchment, and was then implemented with the MODFLOW numerical code. A combined 2D-3D approach was adopted, and the model was calibrated on borehole data available for the time period 2012–2019. Different thicknesses of the aquifer were set, and a reliable relationship was found between the hydraulic head, saturated zone and hydraulic conductivity of the aquifer. Using the MODPATH package, the mean travel time (Darcian) of groundwater was computed for five different scenarios, corresponding to the model’s depths; the analysis that was performed shows that the travel time is higher for a greater and lower for a smaller thickness of the aquifer’s saturated zone, respectively. The Caposele aquifer model was zoned in different sectors, named flow pipe areas, that play different roles in groundwater recharge-discharge processes. A vector analysis was also carried out in order to highlight the ascendant flow near the spring zone.

Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

Abstract. In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.

New analytical solution for stream\u2013aquifer interaction under constant replenishment

In the present paper, approximate analytical solutions for flow in unconfined aquifers with streams are obtained assuming one-dimensional horizontal groundwater flow in homogeneous and isotropic aquifer with recharge effect using variational homotopy perturbation method which is a combination of variational iteration method and homotopy perturbation method. The governing nonlinear Boussinesq equation is obtained by using a basic principle of conservation of mass followed by Dupuit’s assumptions. Sensitivity of the parameters has been analyzed. The obtained approximate analytical solutions are numerically validated. The present analytical method is reliable and can be equally well applied to other nonlinear equations arising in the stream–aquifer interaction problems.

Enhanced removal of PhACs in RBF supplemented with biofilm coated adsorbent barrier: Experimental and model studies

The present study focussed on potential application of river bank filtration (RBF) for the effective removal of pharmaceutically active compounds (PhACs), namely, atenolol, ciprofloxacin and gemfibrozil. Experiments on RBF were performed in a pilot scale reactor (3.0 m × 1.0 m × 0.5 m) in which two dimensional unconfined aquifer flow conditions were induced by pumping to depict realistic field conditions. Initially, experiments were carried out in a reactor filled with natural river bed material. The natural attenuation efficiencies were found to be 21, 35 and 8% for atenolol, ciprofloxacin and gemfibrozil, respectively. Pumping experiments conducted through clean sand in RBF indicated that PhACs were highly mobile with minimal degradation. In order to improve the treatment efficiency of RBF, biofilm coated clay composite adsorbent was synthesized and used in a reactive barrier. The reactive barrier could significantly eliminate PhACs up to 80, 90, 75% for atenolol, ciprofloxacin and gemfibrozil, respectively, at the extracting well (located at 125 cm from the inlet) even after 150 h. Pumping experiments showed that 20 cm thick barrier was able to contain the movement of contaminant plume up to 4 h when water was pumped at a rate of 0.0075 L/s and up to 3.2 h when the pumping rate was 0.01 L/s. Further, a 2D reactive transport model was developed and validated based on the experimental data. The transport model would be useful for developing a management model for the optimal design of reactive barrier for enhancing the performance of RBF.

A GPGPU-accelerated implementation of groundwater flow model in unconfined aquifers for heterogeneous and anisotropic media

The application of computer simulation models plays a significant role in the understanding of water dynamics in basins. The recent and explosive growth of the processing capabilities of General-Purpose Graphics Processing Units (GPGPUs) has resulted in widespread interest in parallel computing from the modelling community. In this paper, we present a GPGPU implementation of finite-differences solution of the equations of the 2D groundwater flow in unconfined aquifers for heterogeneous and anisotropic media. We show that the GPGPU-accelerated solution implemented using CUDA1 C/C++ largely outperforms the corresponding serial solution in C/C++. The results show that the GPGPU-accelerated implementation is capable of providing up to a 56-fold speedup in the solution using an ordinary office computer equipped with an inexpensive GPU2 card. The code developed for this research is available for download and use at http://modelagemambientaluffs.blogspot.com.br/.

Boundary Integral Equation Method for Unsteady Two Dimensional Flow in Unconfined Aquifer

In this paper, we employed the use of Boundary Integral Equation Method to obtain numerical solutions of specific unconfined aquifer flow problems. Of the two formulations presented in this paper, that in which the piezometric head and its normal derivative are assumed to vary linearly with time over each time step has proved more accurate than that in which both piezometric head and its normal derivative remain constant at each node throughout each time step. Comparisons between Method 2 of section-3 and the analytical solutions have demonstrated the superior accuracy of the integral equation formulation.

Effects of Water Seepage on the Stability of Soil-slopes

Landslide is a kind of severe natural disaster and societal hazard throughout the world.Among various effecting factors, water is commonly known as one of the major triggers for landslide failures. In this paper, a coupling model of water-seepage and stability analysis has been developed for analyzing the effect of water on the stability of slopes. A combination of spline curves and genetic algorithm is used to locate the critical slip surface for slope stability calculations. A new analytical solution of the linearized Boussinesq equation was developed for one-dimensional groundwater flow in unconfined aquifer. An actual landslidelocated in the Three Gorges Reservoir was analyzed by simulating the changes of the seepage field caused by rainfall and water level fluctuation. The influences of water seepage on the stability of landslide were discussed with emphasis.The results show that rainfall infiltration and the variation of water level can tremendously influence the stability of slopes.

Ground Behaviors due to Seepage Force of Groundwater

Well pumping leads to both horizontal and vertical displacement, and fluctuation of groundwater level can cause serious damage to structures in a lagre affected area. Ground behaviors due to seepage force in traditional methods were rarely considered. This paper presents a numerical solution of ground displacement behaviors due to unsteady groundwater flow in unconfined aquifer by considering the effect of capillary zone based on the saturated-unsaturated seepage theory, and the numerical simulation code implemented by FORTRAN is applied to predict the flow velocity distribution and the results of ground displacement. The model uses the finite element method and finite difference method to study the problem. The analysis shows that the seepage force and the effect of capillary zone play a very important role in both seepage flow and displacement field.

Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method

For appropriate management of available groundwater, the flow behavior in the porous media has to be analyzed. The complex problem of groundwater flow can be studied by solving the governing equations analytically or by using numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used for field problems. Meshfree (MFree) method is an alternative numerical approach to solve complex groundwater problems in simple manner. MFree method eliminates the drawback of meshing and remeshing as in FDM and FEM which can translate to substantial cost and time savings in modeling. In this paper, a model using MFree point collocation method (PCM) with multi-quadric radial basis function (MQ-RBF) is proposed for 2D groundwater flow simulation. The accuracy of the developed model is verified with available analytical solution in literature. The developed model is applied initially for a hypothetical problem and further for a field problem to compute head distribution. The PCM model results for the hypothetical problem are compared with FEM simulations while that of field problem are compared with boundary element based model results. The PCM model results are found to be satisfactory showing the applicability of the present approach.