Isotropic Aquifer Research Articles

RBFsim – A tool for early planning stage of riverbank filtration systems

Riverbank filtration (RBF) is increasingly being considered an effective method to support the management of water supply and the management of groundwater-river water exchange. Literature, however, provides very limited methods for the initial evaluation of the RBF system. Specifically, initial evaluations need to rely on limited data, be cost-effective, and provide sufficient useful output. The paper provides the development of a tool called RBFsim, designed for the early assessment of flow hydraulics in a riverbank filtration (RBF) scheme during site selection and optimization of well operation. The developed tool allows simplified computation (based on the Analytical Element Method or AEM) of the flow field for single and multiple wells in a 2D homogeneous and isotropic aquifer with uniform flow. The tool superimposes analytical solutions for key RBF quantities such as residence time (the time required for river water to reach the well) and the proportions of water (contributed by the river and groundwater) in the well discharge. These solutions are superimposed on the developed flow field. Additionally, the tool can be used to evaluate the impact of riverbed clogging on the operation of the RBF system. The simplified computation due to AEM and limited data requirements allows the tool to be used in handheld (smartphones) or desktop devices with or without internet connection. RBFsim results are verified by comparing them with results from MODFLOW and MODPATH simulations, which are based on entirely different (finite difference) computational schemes. The obtained results from both these models match within the error margin of less than 5%. Further, the practicality and applicability of RBFsim are illustrated using synthetic and field data. While the tool provides a matching river water contribution ratio with field data, it demonstrates the best-fit residence times primarily for higher well discharge rates. These limitations are attributed to complexities observed in the field, such as a heterogeneous aquifer and nonuniform flow. Overall, the developed tool simplifies the complex computations required, particularly for assessing the feasibility and risk of RBF schemes. The developed tool’s methods and code are open-sourced (licensed under CC-BY 4.0), which promotes personalized modifications and extensions.

Physics-Informed Neural Networks for solving transient unconfined groundwater flow

Neural networks excel in various machine learning applications; however, they lack the physical interpretability and constraints crucial for numerous scientific and engineering problems. This limitation hinders their ability to accurately capture and predict complex physical systems’ behavior, potentially yielding inaccurate or unreliable results. Physics-Informed Neural Networks (PINNs) are a class of machine learning models that integrate the power of neural networks with the physical laws governing natural phenomena. PINNs provide an effective tool for solving intricate physical problems, ranging from fluid dynamics to materials science, by incorporating physical constraints into the neural network architecture. PINNs can substantially enhance the accuracy and efficiency of model predictions, even in data-limited situations. This work offers insight into recent developments in the PINN field, including their mathematical formulation and training algorithms, and emphasizes their application in solving transient unconfined groundwater flow. In this context, the phreatic surface acts as a spatiotemporally varying boundary condition, and properly accounting for its position is vital for precise predictions of unconfined groundwater flow and related environmental and engineering applications. The study’s objective is to develop a reliable model for estimating the phreatic surface and the spatiotemporal distribution of piezometric heads in a vertical cross-section of an unconfined aquifer. Two cases are examined: the first involves a homogeneous and isotropic aquifer, while the second comprises a mildly heterogeneous and anisotropic one. The challenges and opportunities arising from this emerging research area are also explored, and essential directions for future research are underscored.

Large-scale arsenic mobilization from legacy sources in anoxic aquifers: Multiple methods and multi-decadal perspectives

While geogenic arsenic (As) contamination of aquifers have been intensively investigated across the world, the mobilization and transport of As from anthropogenic sources have received less scientific attention, despite emerging evidence of poor performance of widely used risk assessment models. In this study we hypothesize that such poor model performance is largely due to insufficient attention to heterogeneous subsurface properties, including the hydraulic conductivity K and the solid-liquid partition (Kd), as well as neglect of laboratory-to-field scaling effects. Our multi-method investigation includes i) inverse transport modelling, ii) in-situ measurements of As concentrations in paired samples of soil and groundwater, and iii) batch equilibrium experiments combined with (iv) geochemical modelling. As case study we use a unique 20-year series of spatially distributed monitoring data, capturing an expanding As plume in a Chromated Copper Arsenate (CCA)-contaminated anoxic aquifer in southern Sweden. The in-situ results showed a high variability in local Kd values of As (1 to 107 L kg−1), implying that over-reliance of data from only one or few locations can lead to interpretations that are inconsistent with field-scale As transport. However, the geometric mean of the local Kd values (14.4 L kg−1) showed high consistency with the independently estimated field-scale “effective Kd” derived from inverse transport modelling (13.6 L kg−1). This provides empirical evidence for the relevance of using geometric averaging when estimating large-scale “effective Kd” values from local measurements within highly heterogenous, isotropic aquifers. Overall, the considered As plume is prolonged by about 0.7 m year−1, now starting to extend beyond the borders of the industrial source area, a problem likely shared with many of the world's As-polluted sites. In this context, geochemical modelling assessments, as presented here, provided a unique understanding of the processes governing As retention, including local variability in, e.g., Fe/Al-(hydr)oxides contents, redox potential and pH.

Exact simulation of the groundwater flow in anisotropic confined aquifer near time-varying streams by comprehensive new analytical solutions

This paper presents some new analytical solutions to an accurate prediction of the behavior of the groundwater flow in aquifers in response to changes in surface water. The new analytical solutions are obtained using integral transforms. An anisotropic rectangular confined aquifer bounded with four time-varying streams is undertaken. The effects of anisotropy on groundwater head and flow rate near time-varying streams are investigated. Depending on the change rates of the streams level, an anisotropic aquifer may render either lower or higher hydraulic head than an isotropic aquifer. In addition, an anisotropic aquifer has provided less water exchange at the interfaces than an isotropic one. The sensitivity of the hydraulic head to change rate of the streams level in both isotropic and anisotropic aquifers is evaluated. It is shown that the aquifer response is more sensitive to change rate of the streams parallel to y-direction and less sensitive to change rate of the streams parallel to x-direction in an anisotropic aquifer and vice versa in an isotropic aquifer. The results of the present new analytical solutions are compared with numerical model of MODFLOW. The results obtained from the presented solutions showed good agreement with the results of MODFLOW. The results show that the presented new analytical solutions are accurate, robust and efficient. Therefore, the results indicate that the presented new analytical solutions are very effective in the simulation of the groundwater flow in river–aquifer systems. Furthermore, one of the advantages of the new analytical solutions is to investigate the sensitivity analysis of aquifer parameters, which has been carried out in this paper. Also, some other new analytical solutions for steady-state conditions and sudden fall in streams level are provided as well. Feasibility of the proposed new analytical solutions is presented via calculating and simulating the hydraulics of groundwater flow in river–aquifer systems by means of integral transforms.

Analytical solutions for steady-state, axisymmetric seepage to toroidal and disk-shaped drainages and tunnels: the Gauss and Weber legacy revisited

Axisymmetric, steady-state, Darcian flows in homogeneous and isotropic aquifers towards a toroid or disk intake are analytically studied. Both unbounded (infinite) and bounded (by a an equipotential soil surface or by an impermeable horizontal caprock-bedrock) aquifers are considered. The Gauss closed-form solution from astronomy for a gravitating circle having a uniform mass distribution and the Weber solution from electrostatics for an equipotential disk are utilized. The scalar/vector fields of piezometric head (potential)/specific discharge allow for reconstruction of stream lines, isobars, isochrones, and isotachs. An air-filled toroid drains much more water than equipotential, or – inversely - at a given flow rate, the size of an empty toroid is much smaller than that of a water-filled one. The hydraulic gradients in the vicinity of modeled wells/tunnels are very high, triggering colmation and suffusion. The functionals of dissipation and drawdown over a specified zone in the far field are evaluated.

Sigma mapping for drainage problems with a time-dependent water table

Regional groundwater flow forecasting is frequently accomplished using model equations based on Darcy's law, the continuity equation, and kinematic and dynamic boundary conditions for a time-dependent water table, to predict hydraulic heads and fluxes. For homogeneous and isotropic aquifers, the model reduces to Laplace's equation for the hydraulic head and a transient non-linear free surface boundary condition. These equations are solved in the literature and in computer packages by a variety of numerical methods, including finite difference, finite element, and boundary element methods. The solution of this model is not simple and subject to instability problems. Computations in a vertical plane using finite-difference methods are not easy due to the irregular mesh needed near a highly curved water table, frequently involving smoothing of the numerical results to ensure stability. A technique to avoid the complications related to mesh generation near a curved boundary and its tracking entails using mappings to produce transformed domains. However, this is not so frequent to compute unsteady seepages. In particular, the so-called sigma mapping is widely used to model irrotational water waves; it applies to any flow involving a time-dependent free surface boundary. This mapping transforms the domain into a rectangle, so that the free surface becomes static in the transformed plane. There is close similarity between the mathematical model describing irrotational water waves and that of unsteady seepage flow, e.g., both are governed by Laplace's equation involving relevant boundary conditions at the moving boundary. Both moving free surfaces are different in character, e.g., the seepage is dissipative whereas the water wave is dispersive. However, it is possible to transfer mathematical approximations between both fields of research. This transfer is exploited in this work and the sigma mapping is newly and successfully applied to seepage flows involving both a steady and unsteady water table either receiving, or not, a recharge from rainfall or an artificial source.

Analytical solutions of contaminant transport in homogeneous and isotropic aquifer in three-dimensional groundwater flow.

Modeling three-dimensional contaminant transport released from arbitrary shape source geometries is useful in hydrological and environmental sciences. This article produces several analytical solutions for three-dimensional contaminant transport in a homogeneous and isotropic aquifer by using Green's function with the groundwater flow which is assumed to be in three directions. The solutions are obtained for both finite depth aquifer and semi-infinite depth aquifer. Various types of sources are discussed: point, line, plane, or cuboid sources. The continuous and instantaneous sources are also investigated. A MATLAB coding is developed to calculate the numerical integrals which occur at the solutions. Some solutions are verified with the solutions obtained in the literature. This study confirms the effect of groundwater velocities in all directions on the degree and the directions of contaminant spreading. Additionally, the results highlight the significant effect of the geometrical shape of the contaminant sources on contaminant concentrations for instantaneous and continuous sources. In particular, the cuboid source and the horizontal rectangular source provide the highest concentrations. The analytical solutions developed in this article can be applied for a wide range of contaminant transport.

Complex wave propagation from open water bodies into aquifers: A fast analytical approach

Aquifers are of particular interest in the vicinity of rivers, lakes and coastal areas due to their extensive usage. Hydraulic properties such as transmissivity and storativity can be deduced from periodical water level fluctuations in both open water bodies and groundwater. Here, we model the effect of complex wave propagation into adjacent isotropic and homogeneous aquifers. Besides confined aquifers, we also study wave propagation in leaky aquifers and situations with flow barriers near open water bodies as encountered in harbours where sheet piling are in place. We present a fast analytical solution for the hydraulic head distribution which allows for determining the hydraulic diffusivity (Ss/K) of the aquifer, with low investigational efforts. We make use of the Fast Fourier Transform to decompose complex wave boundary conditions and derive solutions through superposition. Analytical solutions are verified by comparing to numerical MODFLOW models for three application examples: a tidal wave measured in the harbour of Rotterdam, a synthetic square wave and river fluctuations in the river Rhine near Lobith. We setup a parameter estimation routine to identify hydraulic diffusivity, which can be easily adapted to real observation data from piezometers. Inverse estimates show relative differences of less than 2% to numerical input data. A sensitivity study further shows how to achieve reliable estimates depending on the piezometer location or other influencing factors such as resistance values of the confining layer (for leaky aquifers) and flow barriers.

Seawater Intrusion in Extremely Heterogeneous Laboratory-Scale Aquifer: Steady-State Results

This work used experimental and numerical methods to investigate seawater intrusion (SWI) in a complex heterogeneous laboratory-scale aquifer. We started the analysis with a homogeneous isotropic aquifer as a reference case, then moved to heterogeneous layered aquifers. The study also investigated block-wise synthetic aquifers with different configurations. The seawater wedge toe length generally decreased under heterogeneous conditions, while the freshwater–saltwater dispersion/mixing zone generally increased when compared to the homogenous case. The saltwater–freshwater interface shows a distinct gradient change across boundaries at differing hydraulic conductivities. This was attributed to streamline refraction, which caused a reduction to the angle of intrusion when transitioning from high to low permeability zones and vice versa. The refraction also affected the mixing zone, where additional spreading was also observed when transitioning from high to low permeability zones and vice versa. When low permeability zones predominated the shoreline at the saline water boundary, this produced a shorter saline wedge in the horizontal direction, but it was more expanded vertically. This study provides insight into the general processes of SWI in heterogeneous aquifers and could be used as a basis for defining conceptual models of real-world systems. It highlights the capabilities of the image analysis to capture small perturbations.

An analytical solution for groundwater flow incorporating the effect of water bodies with sloping surfaces

Determination of hyporheic flow between surface water and groundwater is crucial to clarify the coupled water systems’ hydrological and ecological behaviour. Therefore, this study focuses on groundwater systems interacting with water bodies with sloping surfaces. A sloping stream is defined as an aquifer’s boundary condition. A recharge/discharge term is incorporated into the groundwater flow equation to represent the flux between groundwater and a water body with a sloping surface. An analytical solution of the groundwater flow equation is derived for a homogeneous and isotropic aquifer of a steady-state case. Additionally, a numerical algorithm is written for comparison purposes. The effect of water surface slope on the groundwater head distribution in horizontal plane and the flux between surface water and groundwater is investigated. The results show that the analytical solution represents the hydrodynamics of the stream-water body-aquifer system well, and the water surface slope is dominant on surface water-groundwater interactions.

Porosity change in heterogeneous and isotropic limestone coastal aquifer during mixing of seawater and freshwater

Calcite dissolution, porosity development are strongly influenced by mixing phenomenon, fluid density and heterogeneity (variability of the hydraulic proprieties). This study presents an approach for calculating porosity change in a heterogeneous porous media during mixing of seawater and freshwater. The proposed approach is based on the Phillip’s analytical solution and is determined by five main steps: (1) Generate a random K-field, (2) Calculate the flow and transport of the heterogeneous porous media, (3) Evaluate the dispersivity coefficient results of the heterogeneity aspect, (4) Evaluate the dissolution capacity of calcite during mixing of two solutions and (5) calculate the porosity change. This approach takes into account the effect of the aquifer heterogeneity on the dispersivity and is applied to simulate the effect of calcite dissolution on the porosity development in a heterogeneous idealized aquifer during seawater intrusion. Results presented in this work are preliminary to assess the effect of heterogeneity on the geochemical reaction during mixing.

Actual and Predictive Transport Modeling of Fluoride Contamination of the Sfax-Agareb Coastal Aquifer in the Mediterranean Basin

The Tunisian coast is suffering from several active or abandoned polluted sites, suspected to have released high concentrations of various contaminants infiltrating the environment and probably causing groundwater degradation. Within this scope, this study comes to assess and model the Sfax-Agareb aquifer contamination by fluoride released through phosphogypsum leachate percolation. For that, a spatial-temporal monitoring of fluoride contents was achieved for the period between October 2013 and October 2014. Observed data show that hazardous water contamination is occurring especially close to the phosphogypsum leachate collection basins. At this level, groundwater fluoride concentrations may reach up to 29 mg/L. Flow and transport modeling to evaluate fluoride contamination plume expansion in 2030 was achieved using MODFLOW and MT3DMS software packages based on a homogeneous and isotropic aquifer conceptual model. Flow and transport model calibrations were assessed by varying hydraulic conductivity, effective porosity, and dispersivity and then validated through observed data for two reference dates (October 2013 and October 2014). Based on the Tunisian NT 106-002 liquid discharge norms, fluoride contamination front was set at 3 mg/L. Numerical simulation shows that, in 2014, plume contamination by fluoride in the saturated zone extended over 250 m from the contamination source. In 2030, the spatial extent of this contamination will extend over a distance of 900 m towards the sea, following the aquifer flow direction. At the control piezometer, fluoride concentrations will increase from 29 mg/L in 2014 to 86 mg/L in 2030. This study, using numerical modeling, gives new insights for short- and medium-term prediction of eventual fluoride concentrations in the saturated zone of the Sfax-Agareb aquifer.

Analytical solution for groundwater recharge on a hill

We present an exact solution to the problem of two-dimensional flow with a free surface from a recharge area on a hill with vertical faces to valleys on either side of the hill. The valleys are at different elevations, and the question we address is to what extent the difference in elevation of the valleys affects the amount each valley receives from the recharge. We find that the difference in elevation has a major effect, a result that may be of interest in farming, where similar conditions exist.We solve the problem by means of the hodograph method and conformal mapping. The domain in the hodograph plane is constructed according to the boundary conditions, which leads to a domain bounded by a combination of straight lines and a circular arc. The domain in the hodograph plane is transformed into a domain bounded by straight lines, which makes conformal mapping of the reference upper half plane onto this domain possible, by means of the Schwarz–Christoffel transformation. The solution is obtained by the use of a second function, the Zhukovski function, which is mapped onto the same reference plane.The results are presented in terms of graphs of discharges into the valleys for both isotropic and anisotropic aquifers; flow nets are presented as well.

Positive L 1 ‐filter design for continuous‐time positive Markov jump linear systems: full‐order and reduced‐order

This study addresses the positive filter design problem for continuous-time positive Markov jump linear systems (PMJLSs). Based on the necessary and sufficient condition for L 1 -gain performance, two sufficient conditions to design positive full-order and reduced-order L 1 -filters for PMJLSs are provided in terms of linear programming, respectively. A practical numerical example of an isotropic, homogeneous and unidimensional aquifer is presented at last to show the effectiveness of the proposed schemes.

Analysis of Transient Flow to an Extended Fully Penetrating Well at Constant-Head Pumping.

Vertical wells with radial extension at the well bottom can improve the rate of water production. No study has yet investigated the effects of the transient state and anisotropy in directional hydraulic conductivities on the wellbore flux rate for this type of well. This study derives a semianalytical transient drawdown solution for constant-head pumping at a fully penetrating well radially extended at the bottom of a confined, anisotropic aquifer by applying Laplace transform and separation of variables as well as conducting a Fourier analysis. The results of this new solution indicate that transient and steady-state wellbore flux rates can be increased by a factor of two for greater radial extension of the well. Compared with an isotropic aquifer (a ratio of vertical and horizontal hydraulic conductivities equal to one), an anisotropic aquifer with the ratio less than one may produce a higher transient wellbore flux rate and lower steady-state wellbore flux rate. Moreover, the time required to achieve the steady-state wellbore flux rate can be substantially affected by anisotropy of the aquifer.

Analytic solutions for fresh groundwater lenses floating on saline water under desert dunes: The Kunin-Van Der Veer legacy revisited

A fully-saturated lens of steady fresh groundwater floating in a homogeneous and isotropic desert sandy aquifer is analytically studied based on a hydrological model by Kunin and interface solution by Van Der Veer. A static saline groundwater is beneath the lens. A phreatic surface of moving fresh water inside the lens is partially recharged (either naturally or by managed aquifer recharge) from the vadose zone and partially exfiltrates to it. A spatially focused recharge and intensive evapotranspiration preserve a steady downward-upward topology of fresh water motion. In terms of the 1-D Dupuit-Forchheimer approximation in a horizontal in-lens saturated flow a boundary value problem (BVP) for an ODE for the Strack potential is solved. The shape of the water table and, based on the Ghijben-Herzberg assumption, the interface are found. The total volume of the positive-pore pressure water flowing within the lens is evaluated. Constant infiltration and evaporation rates as well as evaporation linearly decreasing with depth of the water table (counted from the ground surface) are considered. The case of 2-D flow is tackled by the Toth model. A triangular analytic element approximates a half of the flow domain and consists of an isobaric side and two no-flow sides. Conformal mapping of this triangle onto a reference plane and solution of the Dirichlet BVP in a half-plane deliver the distribution of infiltration-exfiltration intensity along the water table, total flow rate and locus of the hinge point. A mathematically more cumbersome approximation of the flow domain assumes the water table to be a tilted straight line but the interface to be found as a free boundary. Solution of the corresponding BVP uses a curvilinear triangle in the hodograph plane.

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.

Saltwater Intrusion and Recirculation of Seawater in Isotropic and Anisotropic Coastal Aquifers

AbstractSaltwater intrusion and the recirculation of seawater that occur at the seacoast in coastal aquifers are investigated for vertically isotropic and anisotropic aquifers as dependent function...

On the interpretation of multi-well aquifer-pumping tests in confined porous aquifers using the Cooper and Jacob (1946) method

The Cooper and Jacob (Trans Am Geophys Union 27:526–534. https://doi.org/10.1029/TR027i004p00526 ; Cooper, Jacob, Trans Am Geophys Union 27:526534, 1946) method is widely used to interpret data from both single- and multi-well aquifer-pumping tests in a porous homogenous and isotropic confined aquifer system. The method can be used to interpret both pumping and observation well drawdown. For observation wells (piezometers), the method said to be valid when u < 0.01 when drawdown observations are made in the near vicinity of the pumping well after a sufficiently long time of pumping. Despite the wide use of the method, the effects of using the Cooper and Jacob method to interpret multi-well aquifer-pumping test data are hardly discussed. The study illustrates and discusses the effect of using the Cooper and Jacob method to interpret multi-well aquifer-pumping tests. This is achieved with the help of simulations in 3 homogeneous one-layered confined and isotropic aquifer models using MODFLOW. Simulated drawdown is interpreted using the Cooper–Jacob method. The study shows that the transmissivity estimated from observation well data exponentially increases with the observation distance irrespective of the value of u. Only interpretation of pumping-well data with the Cooper and Jacob method correctly estimated the prescribed model transmissivity. Storativity estimates from observation data appears to decrease with increase in the observation distance as controlled by the Copper and Jacob equation but remained in the same order of magnitude as the prescribed model storativity. The study contributes towards a better practical understanding of the effects of using of using the Cooper and Jacob method to interpret multi-well aquifer-pumping test data for groundwater practitioners.

Impact of model complexity and multi-scale data integration on the estimation of hydrogeological parameters in a dual-porosity aquifer

This study investigates the impact of model complexity and multi-scale prior hydrogeological data on the interpretation of pumping test data in a dual-porosity aquifer (the Chalk aquifer in England, UK). In order to characterize the hydrogeological properties, different approaches ranging from a traditional analytical solution (Theis approach) to more sophisticated numerical models with automatically calibrated input parameters are applied. Comparisons of results from the different approaches show that neither traditional analytical solutions nor a numerical model assuming a homogenous and isotropic aquifer can adequately explain the observed drawdowns. A better reproduction of the observed drawdowns in all seven monitoring locations is instead achieved when medium and local-scale prior information about the vertical hydraulic conductivity (K) distribution is used to constrain the model calibration process. In particular, the integration of medium-scale vertical K variations based on flowmeter measurements lead to an improvement in the goodness-of-fit of the simulated drawdowns of about 30%. Further improvements (up to 70%) were observed when a simple upscaling approach was used to integrate small-scale K data to constrain the automatic calibration process of the numerical model. Although the analysis focuses on a specific case study, these results provide insights about the representativeness of the estimates of hydrogeological properties based on different interpretations of pumping test data, and promote the integration of multi-scale data for the characterization of heterogeneous aquifers in complex hydrogeological settings.