Groundwater Flow In Unconfined Aquifer Research Articles

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.

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.

Analytic Solution of Time Fractional Boussinesq Equation for Groundwater Flow in Unconfined Aquifer

An approximate analytical solution to the nonlinear time fractional Boussinesq equation is presented here. Derivative with respect to time variable is replaced with Caputo fractional derivative. The Natural transform method and Adomian decomposition method are employed to obtain the solution. Some test problems are solved to show the accuracy of the proposed method. Behavior of water table head is depicted graphically for various time values.

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/.

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.

A semi-analytical time integration for numerical solution of Boussinesq equation

A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method.

Two-dimensional DNAPL migration affected by groundwater flow in unconfined aquifer

The dense non-aqueous phase liquid (DNAPL) migration process was experimentally investigated in a laboratory-scale tank (150 cm width, 82.5 cm height, and 15 cm depth) to assess a site characterization on DNAPL contamination below a groundwater table. The heterogeneous ground of the tank model consisted of Toyoura sand (hydraulic conductivity, k=1.5×10 −2 cm/s for void ratio, e=0.62) and silica #7 sand ( k=2.3×10 −3 cm/s for e=0.72). A series of experiments was carried out with or without lateral groundwater flow. Hydrofluoroether was used as a representative DNAPL. The main results obtained in this study are as follows: (1) the DNAPL plume does not invade into the less permeable soil layer with higher displacement pressure head; (2) the DNAPL plume migrates faster with lateral groundwater flow than without it; (3) lateral groundwater flow does not affect lateral DNAPL migration; rather, it promotes downward migration; and (4) pore DNAPL pressure without groundwater flow is higher than that with it. The above experimental results were compared with numerical analysis. The fundamental behaviors of DNAPL source migration observed experimentally are expected to be useful for assessing the characteristics of two-dimensional DNAPL migration in an aquifer.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated–unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face.

Numerical solution of 3-D groundwater flow involving free boundaries by a fixed finite element method

Groundwater flow in unconfined aquifers involves the determination of the free surface. Additionally, difficulties arise when dealing with seawater intrusion into unconfined aquifers, because this requires the location of both the phreatic surface and the interface separating freshwater from salt-water. A numerical procedure is developed for solving these problems in steady state with the finite element technique, assuming that groundwater flow is considered to occur only in the freshwater region of the saturated zone. The problem is solved with a fixed finite element mesh by iteratively adjusting the moving boundaries. This is achieved without explicitly changing the coefficient matrix of the finite element equations, which makes the method computationally fast. For the free surface problem, test examples demonstrate that the technique is accurate when compared to Polubarinova Kochina's analytical solution and laboratory measurements, and efficient when compared to the moving finite element mesh technique. For the saltwater intrusion interface, test problems, including saltwater intrusion into confined and unconfined aquifers, demonstrate that the technique is also accurate when compared to analytical solutions and laboratory measurements.

Computation of the unsteady two-dimensional free surface of groundwater by the finite-element method

A numerical solution of unsteady two-dimensional groundwater flow in unconfined aquifers with pumping and/or artificial recharge is presented. Problems of nonhomogeneous and anisotropic aquifers with pumping wells and/or artificial recharge and of various type of boundary conditions are considered. A governing equation is formulated in terms of the finite-element process using the Galerkin approach and triangular elements in the x-y-plane. The continuous time Galerkin approximation is used for the time dimension. The obtained nonlinear system of algebraic equations is solved by a predictor-corrector approximation. The results of the numerical solutions are presented in diagrams from which useful observations, comparisons and conclusions can be drawn.

Factors affecting the flow of aflaj in Oman: A modelling study

Shallow sloping drainage tunnels dug into the hillsides to intercept water tables are an important source of water supply in many semi-arid countries. This paper deals with the modelling of such drainage tunnels, with particular reference to the aflaj (singular falaj) of Oman; factors affecting their flow, their response to recharge and their imposition on the surrounding aquifer are investigated. The equations governing groundwater flow in unconfined aquifers are modified to realistically reproduce the observed flow response. In this way the effect of falaj flow can be incorporated into the strategy for the management of scarce water resources. The modelling results show that the falaj flow follows an exponential recession and its rate is related to aquifer geometry and parameters. The results have been used to estimate the contributing length of aflaj under various hydrological conditions and to indicate the most likely recharge mechanism for a falaj situated in wadi gravels. Furthermore, the close resemblance between the predicted falaj flow and field flow measurements, from Oman, is a measure of the model's applicability.