Groundwater Flow Equation Research Articles

On the modified groundwater flow equation: analytical solution via iteration method

To take into account the variability of the medium through which the groundwater flow takes place, we presented the groundwater flow equation within a confined aquifer with prolate coordinates. The new equation is a perturbed singular equation. The perturbed parameters is introduced and can be used as accurately replicate the variability of the aquifer from one point to another. When the perturbed parameter tends to zero, we recover the Theis equation. We solved analytically and iteratively the new equation. We compared the obtained solution with experimental observed data together with existing solutions. The comparison shows that the modified equation predicts more accurately the physical problem than the existing model. Copyright © 2015 John Wiley & Sons, Ltd.

Resolution analysis of tomographic slug test head data: Two‐dimensional radial case

AbstractHydraulic tomography inverse problems, which are solved to estimate aquifer hydraulic properties between wells, are known to be ill‐conditioned and a priori information is often added to regularize numerical inversion of head data. Because both head data and a priori information have effects on the inversed solution, assessing the meaningful information contained in head data alone is required to ensure comprehensive interpretation of inverse solutions, whether they are regularized or not. This study thus aims to assess the amount of information contained in tomographic slug tests head data to resolve heterogeneity in Kh, Kv/Kh, and Ss. Therefore, a resolution analysis based on truncated singular value decomposition of the sensitivity matrix with a noise level representative of field measurements is applied using synthetic data reflecting a known littoral aquifer. As an approximation of the hydraulic behavior of a real aquifer system, synthetic tomographic experiments and associated sensitivity matrices are generated using a radial flow model accounting for wellbore storage to simulate slug tests in a plane encompassing a stressed well and an observation well. Although fine‐scale resolution of heterogeneities is limited by the diffusive nature of the groundwater flow equations, inversion of tomographic slug tests head data holds the potential to uniquely resolve coarse‐scale heterogeneity in Kh, Kv/Kh, and Ss, as inscribed in the resolution matrix. This implies that tomographic head data can provide key information on aquifer heterogeneity and anisotropy, but that fine‐scale information must be supplied by a priori information to obtain finer details.

Dual-Screened Vertical Circulation Wells for Groundwater Lowering in Unconfined Aquifers.

A new type of vertical circulation well (VCW) is used for groundwater dewatering at construction sites. This type of VCW consists of an abstraction screen in the upper part and an injection screen in the lower part of a borehole, whereby drawdown is achieved without net withdrawal of groundwater from the aquifer. The objective of this study is to evaluate the operation of such wells including the identification of relevant factors and parameters based on field data of a test site and comprehensive numerical simulations. The numerical model is able to delineate the drawdown of groundwater table, defined as free-surface, by coupling the arbitrary Lagrangian-Eulerian algorithm with the groundwater flow equation. Model validation is achieved by comparing the field observations with the model results. Eventually, the influences of selected well operation and aquifer parameters on drawdown and on the groundwater flow field are investigated by means of parameter sensitivity analysis. The results show that the drawdown is proportional to the flow rate, inversely proportional to the aquifer conductivity, and almost independent of the aquifer anisotropy in the direct vicinity of the well. The position of the abstraction screen has a stronger effect on drawdown than the position of the injection screen. The streamline pattern depends strongly on the separation length of the screens and on the aquifer anisotropy, but not on the flow rate and the horizontal hydraulic conductivity.

A control volume mixed finite element formulation for tetrahedral elements

SummaryThe control‐volume mixed finite element method is formulated for and applied to a computational domain consisting of a tetrahedral partitioning to solve the steady groundwater flow equations. Test functions consistent with piecewise constant and piecewise linear pressure distributions are used in the formulation. Comparisons are made with a standard mixed finite element formulation using lowest‐order Raviart Thomas basis functions. Results suggest that the control‐volume based formulation is a viable alternative to the standard formulation. Copyright © 2015 John Wiley & Sons, Ltd.

Vegetative Rhombic Pattern Formation Driven by Root Suction for an Interaction-Diffusion Plant-Ground Water Model System in an Arid Flat Environment

A rhombic planform nonlinear cross-diffusive instability analysis is applied to a particular interaction-diffusion plant-ground water model system in an arid flat environment. This model contains a plant root suction effect as a cross-diffusion term in the ground water equation. In addition a threshold-dependent paradigm that differs from the usually employed implicit zero-threshold methodology is introduced to interpret stable rhombic patterns. These patterns are driven by root suction since the plant equation does not yield the required positive feedback necessary for the generation of standard Turing-type self-diffusive instabilities. The results of that analysis can be represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. From those plots regions corresponding to bare ground and vegetative patterns consisting of isolated patches, rhombic arrays of pseudo spots or gaps separated by an intermediate rectangular state, and homogeneous distributions from low to high density may be identified in this parameter space. Then, a morphological sequence of stable vegetative states is produced upon traversing an experimentally-determined root suction characteristic curve as a function of rainfall through these regions. Finally, that predicted sequence along a rainfall gradient is compared with observational evidence relevant to the occurrence of leopard bush, pearled bush, or labyrinthine tiger bush vegetative patterns, used to motivate an aridity classification scheme, and placed in the context of some recent biological nonlinear pattern formation studies.

Simulation of Saltwater Intrusion in a Coastal Aquifer in Karnataka, India

A grid based variable density numerical model, SEAWAT-2000 is used to conceptually simulate groundwater flow and transport for a coastal stretch in Karnataka state, India. SEAWAT is a coupled version of MODFLOW and MT3DMS designed to simulate three-dimensional, variable density groundwater flow and multi-species transport. The variable density flow process uses the familiar and well established MODFLOW methodology to solve the variable density groundwater flow equation. The aquifer considered for the present study is bounded by Arabian sea on the west, the ridge line along the east andShambhaviand Pavanjerivers along the northern and southern sides respectively. The study has its focus on managing the available data in the most efficient manner to develop a reliable and sophisticated simulation model. The aquifer parameters are estimated by calibrating the model for two year period with daily time step. The aquifer can be categorized as unconfined having good groundwater potential with aquifer transmissivity and specific yield ranging from 10 to 810 m2/day and 0.0008 to 0.0122 respectively. The model evaluation in terms of the accuracy is carried out bycomparingwith the measured data on seasonal basis.From this, the model is found to be scientifically sound for further management applications. The model so developed can be applied in predicting the saltwater intrusion in coastal aquifers for various developmental and climate change scenarios like sea level rise.

A possible modification of groundwater flow equation using coordinate transformations

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

Modeling Water Table Fluctuations in Anisotropic Unconfined Aquifer Due to Time Varying Recharge from Multiple Heterogeneous Basins and Pumping from Multiple Wells

Prediction of water table fluctuations in response to proposed schemes of recharging and pumping is important to make judicious selection of an appropriate scheme out of many schemes to achieve the preset objective of sustainable management of groundwater resources without compromising the regional water balance. This is achieved by solving groundwater flow equation with suitable initial and boundary conditions, aquifer parameters, and recharge/pumping parameters. Earlier, analytical solutions were developed to predict water table fluctuations in aquifer due to time varying recharge rate from multiple basins considering spatially uniform recharge rate for the entire basin area. However, the recharge rate may vary spatially within a single basin due to many factors such as variation in the height of water column above the base of the basin, degree of siltation of the base of the basin etc. In the present work, we develop an analytical solution for modeling of water table fluctuations in an anisotropic aquifer due to intermittently applied spatio-temporally varying rate of recharge from multiple basins and pumping from multiple wells arbitrarily distributed within the model domain. In the present solution, wells are treated as point sources, which helps in reducing numerical artifacts. Some earlier obtained analytical solutions are the special cases of the present solution.

Complex groundwater flow systems as traveling agent models

Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective. Using a traveling agent model, we prove that this statistical behavior emerges when the medium is complex. Some heuristic reasoning is provided to justify both spatial and dynamic complexity, as the result of the superposition of an infinite number of stochastic processes. Even more, we show that this implies that non-Kolmogorovian probability is needed for its study, and provide a set of new partial differential equations for groundwater flow.

Using MODFLOW code to approach transient hydraulic head with a sharp‐interface solution

AbstractSaltwater intrusion problems have been usually tackled through analytical models because of its simplicity, easy implementation and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (ϕ). We propose to approach also the transient problem solving a single potential equation (using also the ϕ variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.

Reply to comment by Jeffrey Olsen et al. on “Traveling wave solution of the Boussinesq equation for groundwater flow in horizontal aquifers”

Olsen et al. [2014] are correct in pointing out the seemingly inconsistent assumption of a constant propagation speed ρ when the derived results show that ρ is in fact time-dependent. However, using a time-dependent ρ in the perturbation expansion does not alter the major results as Olsen et al. point out in the Comment. The reason is that ρ, or its new substitute , is just an intermediary variable that relates the flux rate with the head at the boundary. Therefore, the use of the more complicated definition of ρ is not warranted since it does not result in any improvement of the zero-order solution. On the other hand, a simplified definition of the traveling wave velocity ρ is intuitively more appealing and it leads to simple and elegant results. The fact that the first-order term is identically equal to zero is a consequence of the perturbation expansion used, as stated in sec. 3.3 in Basha [2013]. In any case, the zero-order solution provides a remarkably good approximation. The choice of would have improved the prediction slightly if a first-order correction were available. However, this is a particularly difficult task because the zero-order term is itself a nonlinear implicit solution that is not easily amenable to further manipulations. Instead, it is more worthwhile to consider tackling the Boussinesq equation via a refinement of its linearized solution in a perturbation series framework.

Comment on “Traveling wave solution of the Boussinesq equation for groundwater flow in horizontal aquifers” by H. A. Basha

Comment on “Traveling wave solution of the Boussinesq equation for groundwater flow in horizontal aquifers” by H. A. Basha

A coupled FE model for the joint resolution of the shallow water and the groundwater flow equations

Purpose – A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues. Design/methodology/approach – The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately. Findings – The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature. Originality/value – The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

Exact solution of the time-fractional groundwater flow equation within a leaky aquifer equation

The concern of this work was first to extend the model describing the groundwater flowing within a leaky aquifer to the scope of the fractional order derivative. We first derive the solution of the extended equation with an iteration method. We presented the stability of the method and also the uniqueness of the special solution. We further make use of the Laplace transform, the Boltzmann and the separation methods to derive the exact solution of the extended equation.

Parallel simulation of groundwater non-point source pollution using algebraic multigrid preconditioners

The simulation of non-point source pollution in agricultural basins is a computationally demanding process due to the large number of individual sources and potential pollution receptors (e.g., drinking water wells). In this study, we present an efficient computational framework for parallel simulation of diffuse pollution in such groundwater basins. To derive a highly detailed velocity field, we employed algebraic multigrid (AMG) preconditioners to solve the groundwater flow equation. We compare two variants of AMG implementations, the multilevel preconditioning provided by Trilinos and the BoomerAMG provided by HYPRE. We also perform a sensitivity analysis on the configuration of AMG methods to evaluate the application of these libraries to groundwater flow problems. For the transport simulation of diffuse contamination, we use the streamline approach, which decomposes the 3D transport problem into a large number of 1D problems that can be executed in parallel. The proposed framework is applied to a 2,600-km2 groundwater basin in California discretized into a grid with over 11 million degrees of freedom. Using a Monte Carlo approach with 200 nitrate loading realizations at the aquifer surface, we perform a stochastic analysis to quantify nitrate breakthrough prediction uncertainty at over 1,500 wells due to random, temporally distributed nitrate loading. The results show that there is a significant time lag between loading and aquifer response at production wells. Generally, typical production wells respond after 5–50 years depending on well depth and screen length, while the prediction uncertainty for nitrate in individual wells is very large—approximately twice the drinking water limit for nitrate.

Investigating the role of hydromechanical coupling on flow and transport in shallow fractured-rock aquifers

Fractured-rock aquifers display spatially and temporally variable hydraulic conductivity generally attributed to variable fracture intensity and connectivity. Empirical evidence suggests fracture aperture and hydraulic conductivity are sensitive to in situ stress. This study investigates the sensitivity of fractured-rock hydraulic conductivity, groundwater flow paths, and advection-dominated transport to variable shear and normal fracture stiffness magnitudes for a range of deviatoric stress states. Fracture aperture and hydraulic conductivity are solved for analytically using empirical hydromechanical coupling equations; groundwater flow paths and ages are then solved for numerically using groundwater flow and advection-dispersion equations in a traditional Toth basin. Results suggest hydraulic conductivity alteration is dominated by fracture normal closure, resulting in decreasing hydraulic conductivity and increasing groundwater age with depth, and decreased depth of long flow paths with decreasing normal stiffness. Shear dilation has minimal effect on hydraulic conductivity alteration for stress states investigated here. Results are interpreted to suggest that fracture normal stiffness influences hydraulic conductivity of hydraulically active fractures and, thus, affects flow and transport in shallow (<1 km) fractured-rock aquifers. It is suggested that observed depth-dependent hydraulic conductivity trends in fractured-rock aquifers throughout the world may be partly a manifestation of hydromechanical phenomena.

Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow

The Adomian decomposition method (ADM) is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be obtained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic Adomian decomposition method and use it to solve the nonlinear Boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic Adomian decomposition method.

3D hydro-mechanically coupled groundwater flow modelling of Pleistocene glaciation effects

Pleistocene glaciation led to temporal and spatial variations of sub-surface pore fluid pressure. In basins covered by ice sheets, fluid flow and recharge rates are strongly elevated during glaciations as compared to inter-glacial periods. Present-day hydrogeological conditions across formerly glaciated areas are likely to still reflect the impact of glaciations that ended locally more than 10 thousand years before present.3D hydro-mechanical coupled modelling of glaciation can help to improve the management of groundwater resources in formerly glaciated basins.An open source numerical code for solving linear elasticity, which is based on the finite element method (FEM) in 3D, has been developed. By coupling this code with existing 3D flow codes it is possible to enable hydro-mechanical coupled modelling.Results of two benchmark simulations are compared to existing analytical solutions to demonstrate the performance of the newly developed code. While the result for a fluid–structure coupled case is in reasonable agreement with the analytical model, the result for a classical structure–fluid coupled benchmark showed that the analytical solution only matches the numerical result when the relevant coupling parameter (loading efficiency) is known in advance. This indicates that the applicability of widely applied approaches using an extra term in the groundwater flow equation for vertical stress to simulate hydro-mechanical coupling might have to be re-evaluated.A case study with the commercial groundwater simulator FEFLOW demonstrates the newly developed solution.

A fully distributed spreadsheet modeling as a tool for analyzing groundwater level rise problem in Jeddah city

In this paper, a spreadsheet modeling is introduced as a tool for studying fully distributed real-world engineering problems. The merits of using the spreadsheet are the following: its simplicity, the spreadsheet is very well known to many researchers and engineers; it performs fast calculations; it has a user-friendly graphic interface; and it can also provide animated graphs. These merits provide engineers and scientists with a flexible tool to tackle environmental problems and quickly performing solution scenarios to their problems. A real-world case study has been presented to illustrate the application of such spreadsheet models. The groundwater level rise in Jeddah city is one of the problems that Jeddah city are facing. The reasons of groundwater level rise in Jeddah are the following: the leakage from septic tanks, leakage from freshwater pipe networks, landscape irrigation, annual rainfall, flash floods from eastern wadis, etc. These sources have been complied with a regional groundwater flow model (the general form of the partial differential equation for steady groundwater flow in a heterogeneous, unconfined aquifer with a fully distributed recharge, evaporation and pumping rates, and with a variable aquifer bottom elevation), discritized with a finite difference method, then formulated on a spreadsheet, and solved with the built-in macro-solver on the Excel software. The spreadsheet model has been tested and compared with analytical solution. The model has also been calibrated with observations, and the correlation coefficient was 0.96 for the hydraulic head data. The results have been displayed graphically in one, two, and three dimensions. Various scenarios have been investigated to show solutions of the problem. The results have shown that the spreadsheet modeling is a powerful, flexible, and a user-friendly tool in modeling fully distributed real-world engineering problems. Results can be transferred from spreadsheet to GIS software to present results over satellite images or base maps. Analysis of various solution scenarios can be done efficiently, and one can get quick answers to the decision makers at a preliminary stage of a project before going to a sophisticated modeling approach with specialized software.

Genetic Programming in Groundwater Modeling

AbstractDetermination of water-table elevation corresponding to aquifer recharge or discharge is an important issue in sustainable groundwater management. This approach necessitates the application of numerical simulation models that may require substantial amounts of input data related to aquifer parameters and specifications, even for modeling only part of the aquifer, which makes the calculations expensive. Moreover, comprehensive aquifer modeling is a time-consuming and computationally intensive process. Artificial intelligence tools can replace simulation models and decrease computational efforts by using input and output data sets without considering complex relations of the system to be modeled. This paper employs an adaptive neural fuzzy inference system (ANFIS) and genetic programming (GP) as artificial intelligence tools to extract governing groundwater flow equations in Ghaen and Karaj aquifers in Iran. For both aquifers, several input-output data sets, for both training and testing data sets, ...