Finite Aquifer Research Articles

A Nonlinear Recession Model for Horizontal Aquifers

AbstractRecession analysis is a powerful tool for determining the hydraulic characteristics of a riparian aquifer. The basis of the method relies on two analytical solutions of the nonlinear Boussinesq equation: one applies to a uniform water table profile in a semi‐infinite aquifer while the other pertains to a hypothetical initial profile in a finite aquifer. Both solutions assume that the water depth in the adjoining stream is negligible. In the present work, a nonlinear solution of the one‐dimensional Boussinesq equation is derived using the traveling wave approximation. The solution better represents the field conditions as it pertains to a uniform water table profile in a finite aquifer that is adjoining a stream with a non‐zero water level. It allows the derivation of simple algebraic expressions for the recession of the water table, the flow rate, and the associated drainage volume. Approximations relating the discharge rate to the outflow volume were also obtained for practical implementation in the estimation of the hydraulic parameters of the aquifer. A comparison of the proposed methodology of parameter estimation with the standard method of recession analysis showed that the present approach is superior as it avoids the pitfalls associated with the classical method, especially when daily discharge values with inherent observational errors are used. Application of the recession model to real‐world cases demonstrates its effectiveness in the estimation of the catchment‐scale hydraulic conductivity and drainable porosity.

Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model

AbstractThis study develops a novel, two‐dimensional analytical model to study capillary effects on Earth tidal responses of groundwater in unconfined aquifers. It differs from the previous model by accounting for effects of finite aquifer thickness, anisotropy and wellbore storage. We test the present model against the previous model and numerical simulations and apply it to the field data. Several significant results are obtained: (a) At high conductivity ( m/s), the effect of capillary zones dominates tidal responses of groundwater and causes higher amplitude ratio and smaller phase shift compared with that predicted by the unconfined aquifer model without a capillary zone. At low conductivity ( m/s), the effect of capillary zones on the tidal responses diminishes. (b) The impact of the finite thickness on the tidal response is regulated by the anisotropy. If the anisotropic ratio is small (), the impact of thickness may be negligible; at high anisotropic ratio (), however, the amplitude ratio decreases and the phase shift increases, and the response differs substantially from that of the previous model, which is caused by a change in the flow pattern. (c) Wellbore storage have significant impacts on the tidal response at low conductivity ( 10−5 m/s) but negligible impact at higher conductivity. (d) The present model marginally improved the fit by the half‐space model to the field data from a well in SW China, showing that the remaining misfit to the field data by models with capillarity cannot be due to finite aquifer thickness, anisotropy, or wellbore storage.

Perturbation solutions of the Boussinesq equation for horizontal flow in finite and semi-infinite aquifers

Groundwater flow in an unconfined aquifer can be described by the Boussinesq equation. The Boussinesq equation is nonlinear and approximate solutions exist only for specific flow conditions. In the present work, the nonlinear equation is tackled analytically via a refinement of its linearized solution in a perturbation series framework. The perturbation series solution applies for any time-dependent variation of the stream level, and they are evaluated for various flow recharge and drainage conditions. Particular results for a sudden change and a piecewise linear variation are presented for both finite and semi-infinite aquifers. The approximate solutions can simulate the original nonlinear behavior with high accuracy due to the introduction of the representative depth parameter α that is evaluated in an optimal fashion for any given flow condition. The derivation of the optimal α parameter has also allowed the generalization and improvement of the classical series results pertaining to the abrupt rise or drop of the stream level in a semi-infinite aquifer. In the case of a gradual variation of the stream level in a finite aquifer domain, the linear solution with a time-varying estimate of α is of sufficient accuracy for practical purposes. Explicit algebraic expressions are presented for the exchange flow rates and the associated flow volumes that are of prime interest in stream-aquifer interaction studies.

Artificial neural network models for reservoir-aquifer dimensionless variables: influx and pressure prediction for water influx calculation

Calculation of water influx into petroleum reservoir is a tedious evaluation with significant reservoir engineering applications. The classical approach developed by van Everdingen–Hurst (vEH) based on diffusivity equation solution had been the fulcrum for water influx calculation in both finite and infinite-acting aquifers. The vEH model for edge-water drive reservoirs was modified by Allard and Chen for bottom-water drive reservoirs. Regrettably, these models solution variables: dimensionless influx (WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{{{\ ext{eD}}}}$$\\end{document}) and dimensionless pressure (PD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{D}$$\\end{document}) were presented in tabular form. In most cases, table look-up and interpolation between time entries are necessary to determine these variables, which makes the vEH approach tedious for water influx estimation. In this study, artificial neural network (ANN) models to predict the reservoir-aquifer variables WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{{{\ ext{eD}}}}$$\\end{document} and PD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{D}$$\\end{document} was developed based on the vEH datasets for the edge- and bottom-water finite and infinite-acting aquifers. The overall performance of the developed ANN models correlation coefficients (R) was 0.99983 and 0.99978 for the edge- and bottom-water finite aquifer, while edge- and bottom-water infinite-acting aquifer was 0.99992 and 0.99997, respectively. With new datasets, the generalization capacities of the developed models were evaluated using statistical tools: coefficient of determination (R2), R, mean square error (MSE), root-mean-square error (RMSE) and absolute average relative error (AARE). Comparing the developed finite aquifer models predicted WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{{{\ ext{eD}}}}$$\\end{document} with Lagrangian interpolation approach resulted in R2, R, MSE, RMSE and AARE of 0.9984, 0.9992, 0.3496, 0.5913 and 0.2414 for edge-water drive and 0.9993, 0.9996, 0.1863, 0.4316 and 0.2215 for bottom-water drive. Also, infinite-acting aquifer models (Model-1) resulted in R2, R, MSE, RMSE and AARE of 0.9999, 0.9999, 0.5447, 0.7380 and 0.2329 for edge-water drive, while bottom-water drive had 0.9999, 0.9999, 0.2299, 0.4795 and 0.1282. Again, the edge-water infinite-acting model predicted WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{{{\ ext{eD}}}}$$\\end{document} and Edwardson et al. polynomial estimated WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{eD}$$\\end{document} resulted in the R2 value of 0.9996, R of 0.9998, MSE of 4.740 × 10–4, RMSE of 0.0218 and AARE of 0.0147. Furthermore, the developed ANN models generalization performance was compared with some models for estimating PD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{D}$$\\end{document}. The results obtained for finite aquifer model showed the statistical measures: R2, R, MSE, RMSE and AARE of 0.9985, 0.9993, 0.0125, 0.1117 and 0.0678 with Chatas model and 0.9863, 0.9931, 0.1411, 0.3756 and 0.2310 with Fanchi equation. The infinite-acting aquifer model had 0.9999, 0.9999, 0.1750, 0.0133 and 7.333 × 10–3 with Edwardson et al. polynomial, then 0.9865, 09,933, 0.0143, 0.1194 and 0.0831 with Lee model and 0.9991, 0.9996, 1.079 × 10–3, 0.0328 and 0.0282 with Fanchi model. Therefore, the developed ANN models can predict WeD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{{{\ ext{eD}}}}$$\\end{document} and PD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{D}$$\\end{document} for the various aquifer sizes provided by vEH datasets for water influx calculation.

Fractional flow equation in fractured aquifer using dual permeability model with non-singular kernel

In this paper, a finite fractured aquifer, bounded by a stream and impervious layers on the other sides, has been considered. Variation in the level of groundwater is analyzed in confined aquifer for the unsteady flow. The governing differential equation for piezometric head involves the Caputo–Fabrizio fractional derivative operator with respect to time and is based on dual-porosity model with the assumption that the flow from fracture to block is in pseudo steady state. The obtained solutions can be used to anticipate the fluctuations in the waterlevels of the confined aquifer and for the numerical validation of a model in an aquifer.

Tide‐induced head fluctuations in coastal aquifers of variable thickness

AbstractIn this work, a new analytical solution to describe tide‐induced head fluctuations in aquifers of variable thickness is presented. The proposed model assumes a finite and confined aquifer with a thickness that increases or decreases quadratically with the distance to the coast. A closed‐form analytical solution is obtained by solving a boundary‐value problem with both a separation of variables method and a change of variables method. This solution is a generalization of the solution obtained by Cuello et al., Hydrogeological Journal, 2017, 25, 1509–1515. The analytical solution is expressed in terms of the wedging parameter, a parameter that depends on the length and thicknesses at the coast and at the inland edge of the aquifer. Positive values of the wedging parameter describe aquifers with increasing thickness towards land and negative values describe aquifers with a decreasing thickness in the inland direction. The comparison of the new solution and the solution for a finite aquifer with constant thickness indicates that the sign of the wedging parameter enhances or decreases the amplitude of the tide‐induced signal. However, the differences in time‐lag between both solutions are negligible near the coast. The slope factor, which quantifies the inconsistencies between aquifer diffusivities estimated from attenuation and time‐lag data, is computed and analysed. Near the coast, slope factor values greater than one are obtained for negative wedging parameters while slope factor values less than one are obtained for positive wedging parameters. The analysis of the new solution also indicates that more reliable estimates of the hydraulic diffusivity can be obtained from time‐lag data.

Reactive transport with wellbore storages in a single-well push–pull test

Abstract. Using the single-well push–pull (SWPP) test to determine the in situ biogeochemical reaction kinetics, a chase phase and a rest phase were recommended to increase the duration of reaction, besides the injection and extraction phases. In this study, we presented multi-species reactive models of the four-phase SWPP test considering the wellbore storages for both groundwater flow and solute transport and a finite aquifer hydraulic diffusivity, which were ignored in previous studies. The models of the wellbore storage for solute transport were proposed based on the mass balance, and the sensitivity analysis and uniqueness analysis were employed to investigate the assumptions used in previous studies on the parameter estimation. The results showed that ignoring it might produce great errors in the SWPP test. In the injection and chase phases, the influence of the wellbore storage increased with the decreasing aquifer hydraulic diffusivity. The peak values of the breakthrough curves (BTCs) increased with the increasing aquifer hydraulic diffusivity in the extraction phase, and the arrival time of the peak value became shorter with a greater aquifer hydraulic diffusivity. Meanwhile, the Robin condition performed well at the rest phase only when the chase concentration was zero and the solute in the injection phase was completely flushed out of the borehole into the aquifer. The Danckwerts condition was better than the Robin condition even when the chase concentration was not zero. The reaction parameters could be determined by directly best fitting the observed data when the nonlinear reactions were described by piece-wise linear functions, while such an approach might not work if one attempted to use nonlinear functions to describe such nonlinear reactions. The field application demonstrated that the new model of this study performed well in interpreting BTCs of a SWPP test.

Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM.

This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation.

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

AbstractThis study presents a Laplace‐transform‐based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin‐type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi‐analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two‐zone and three‐zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two‐zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two‐zone aquifers is investigated. Finally the drawdown distribution in three‐zone aquifers with arbitrarily shaped boundary for constant‐rate tests (CRT) and flow rate distribution for constant‐head tests (CHT) are analyzed.

The history of hydrocarbon exploration and development in North Yorkshire

Abstract Hydrocarbon exploration in North Yorkshire began in 1937, targeting Triassic and Permian reservoirs below the surface expression of the Cleveland Anticline. D’Arcy drilled the successful well Eskdale-2, marking the first gas discovery in the Zechstein carbonates in the UK. Since then approximately 100 wells have been drilled in the basin with exploration success relatively high. Out of the 25 pure exploration wells in the region, 13 have found hydrocarbon accumulations (flowed gas) and eight of the discoveries have been developed to date. The primary reservoir is the Permian-aged Zechstein carbonate sequence and, more specifically, the Z2, Kirkham Abbey Formation (KAF), which is a tight carbonate reservoir overprinted by a high permeability fracture system. Despite considerable investment and effort over the years, the historical development story of these fields has been very much one of repeated technical and investment failure, with approximately 39 Bcf (billion cubic feet) of the mapped gas initial in-place (GIIP) of c . 326 Bcf produced to date, an estimated recovery factor of 12%. Historical production data show that all the Zechstein reservoirs have experienced early water breakthrough, leading to impaired gas rates and low recoveries. The water influx is due to a highly mobile, but finite aquifer, which under field production conditions preferentially flows through the high permeability fracture system, bypassing the gas stored in the tighter matrix. Third Energy is aiming to resolve the issue of water influx by using artificial lift to encourage the gas to flow. A trial is currently being undertaken at the Pickering gas field and, if this programme is successful, this will provide sufficient confidence for a phased redevelopment programme of surrounding fields. Whilst North Yorkshire has experienced only limited exploration and production (E&P) activity in the last decade, solving the issue of premature water influx in the KAF fields, combined with the search for unconventional resources in the Bowland section of the Mid and Lower Carboniferous strata will herald a new and exciting phase of E&P activities for this province.

Analytical Solutions to Coupled HM Problems to Highlight the Nonlocal Nature of Aquifer Storage

AbstractSpecific storage reflects the volumetric deformation capacity of permeable media. Classical groundwater hydrology equates elastic storage to medium compressibility (plus fluid compressibility times porosity). However, it is unclear if storage behavior can be represented by a single parameter. Hydraulic gradients act as body forces that push the medium in the direction of flow causing it to deform instantaneously everywhere, i.e., even in regions where pressure would not have changed according to conventional fluid flow. Therefore, actual deformation depends not only on the mechanical properties of the medium but also on aquifer geometry and on surrounding strata, which act like constraints to displacements. Here we discuss the question and highlight the nonlocal nature of storage (i.e., the volume of water released at a point depends on the poroelastic response over the whole aquifer). Proper evaluation of transient pressure and water release from storage requires acknowledging the hydromechanical coupling, which generally involves the use of numerical methods. We propose analytical solutions to the HM problem of fluid injection (extraction) into finite aquifers with one‐dimensional or cylindrical geometries. We find that pressure response is much faster (virtually instantaneous) and larger than expected from traditional purely hydraulic solutions when aquifer deformation is restrained, whereas the pressure response is reversed (i.e., pressure drop in response to injection) when the permeable medium is free to deform. These findings suggest that accounting for hydromechanical coupling may be required when hydraulic testing is performed in low permeability media, which is becoming increasingly demanded for energy‐related applications.

Flow Characteristics of Steam and Gas Push in the Presence of Heat Thief Zones Overlying Oil Sands Deposits

This paper presents the effects of the top water-bearing zone on the performance of the steam and gas push, i.e., nitrogen as a non-condensable gas injected with steam into an oil sands deposit. The flow characteristics of fluid mixtures are examined in the presence of different-sized water-bearing formations overlying oil sands deposits, i.e., a finite aquifer with no-flow boundaries and an infinite aquifer with continuous mass flux. The performance efficiency is investigated by respectively implementing the cumulative steam to oil ratio, a simple thermal efficiency parameter, and the oil production on the surface. The top water-bearing area serves as a heat thief zone and negatively impacts bitumen recovery; furthermore, it increases the cumulative steam to oil ratio while decreasing the simple thermal efficiency parameter, as well as the oil production rate. When the steam chamber encounters the top aquifer, a severe heat loss occurs. As increasing mol % of nitrogen, the producing time with energy efficiency increases but the chamber growth is limited. The specific operational conditions would be possible for the finite-sized aquifer, while the continuous water influx and the significant heat loss obstructs the thermal processes for the infinite aquifer.

Solutions for groundwater flow with sloping stream boundary: analytical, numerical and experimental models

AbstractProtecting groundwater resources plays an important role in watershed management. For this purpose, studies on groundwater flow dynamics incorporating surface water–groundwater interactions have been conducted including analytical, numerical, and experimental models. In this research, a stream–aquifer system was considered to understand the physical behavior of surface water–groundwater interactions. Interactions in a stream–aquifer system were incorporated into the mathematical modeling by defining the stream head as a boundary condition for the groundwater flow equation. This boundary was chosen as a sloping stream boundary, which is an approach in representing the natural conditions of the stream and may be used to define continuous interactions between stream and aquifer. A semi-analytical solution for transient 2D groundwater flow was developed for the considered problem. Isotropic, homogeneous, and finite aquifer assumptions were made in order to define the aquifer characteristics. Then, a series of laboratory experiments was conducted to simulate this stream–aquifer system. Finally, a numerical model was developed by using Visual MODFLOW to verify analytical and experimental results. Numerical results matched with both analytical solutions and the experimental observations.

A general analytical model for pumping tests in radial finite two-zone confined aquifers with Robin-type outer boundary

This study develops a general analytical model for describing transient drawdown distribution induced by pumping at a finite-radius well in a radial two-zone confined aquifer of finite areal extent with Robin-type condition at both inner and outer boundaries. This model is also applicable to heat conduction problems for a composite hollow cylinder on the basis of the analogy between heat flow and groundwater flow. The time-domain solution of the model is derived by the methods of Laplace transform, Bromwich integral, and residue theorem. This new solution can reduce to the solution for constant-head test (CHT) or constant-rate test (CRT) problem by specifying appropriate coefficients at the Robin inner boundary condition. The solution describing the flow rate across the wellbore due to CHT is further developed by applying Darcy’s law to the new solution. In addition, steady-state solutions for both CHT and CRT are also developed based on the approximation for Bessel functions with very small argument values. Many existing solutions for transient flow in homogeneous or two-zone finite aquifers with Dirichlet or no-flow condition at the outer boundary are shown to be special cases of the present solution. Furthermore, the sensitivity analysis is also performed to investigate the behaviors of the wellbore flow due to CHT and the aquifer drawdown induced by CRT in response to the change in each of aquifer parameters.

Mathematical modeling for solute transport in aquifer

Groundwater pollution may occur due to human activities, industrial effluents, cemeteries, mine spoils, etc. This paper deals with one-dimensional mathematical modeling of solute transport in finite aquifers. The governing equation for solute transport by unsteady groundwater flow is solved analytically by the Laplace transform technique. Initially, the aquifer is subjected to the spatially dependent source concentration with zero-order production. One end of the aquifer receives the source concentration and is represented by a mixed-type boundary condition in the splitting time domain. The concentration gradient at the other end of the porous media is assumed to be zero. The temporally dependent velocity and the dispersion coefficients are considered. A numerical solution is obtained by using an explicit finite difference scheme and compared with the analytical result. Accuracy of the solution is discussed by using the root mean square error method. Truncation error is also explored for the parameters like numerical dispersion and velocity terms. The impact of Peclet number is examined. For graphical interpretation, unsteady velocity expressions (i.e., such as exponential, sinusoidal, asymptotic, and algebraic sigmoid) are considered. The work may be used as a preliminary predictive tool for groundwater resource and management.

Modeling of a Groundwater Mound in a Two-Dimensional Heterogeneous Unconfined Aquifer in Response to Precipitation Recharge

AbstractThe paper deals with the transient semi-analytical solution of linearized Boussinesq equations characterizing the development of groundwater mound in an unconfined two-dimensional heterogeneous aquifer under vertical recharge conditions. The finite aquifer consists of two rectangular basins surrounded by open water bodies and shares a common impermeable or permeable boundary at the mid plane. The governing equations are solved by applying the Laplace transform and finite Fourier sine transform techniques. Accordingly, analytical expressions for water heads for two rectangular basins are obtained for various scenarios. The applicability of the solutions has been illustrated with the help of a case study and numerical examples, considering various cases. The region wise development of the groundwater mound indicates that the effect of heterogeneity becomes significant for small time duration whereas for long time it becomes insignificant. This result can have application in land reclamation problems...

A Mathematical Study of Contaminant Transport with First-order Decay and Time-dependent Source Concentration in an Aquifer

A mathematical model describing the transport of a conservative contaminant through a homogeneous finite aquifer under transient flow is presented. We assume the aquifer is subjected to contamination due to the time-dependent source concentration. Both the sinusoidally varying and exponentially decreasing forms of seepage velocity are considered for the purposes of studying seasonal variation problems. We use the parameter-expanding method and seek direct eigenfunctions expansion technique to obtain analytical solution of the model. The results are presented graphically and discussed. It is discovered that the contaminant concentration decreases along temporal and spatial directions as initial dispersion coefficient increases and initial groundwater velocity decreases. This concentration decreases as time increases and differs at each point in the domain.

Transient Solutions to Groundwater Mounding in Bounded and Unbounded Aquifers

In this study, the well-known Hantush solution procedure for groundwater mounding under infinitely long infiltration strips is extended to finite and semi-infinite aquifer cases. Initially, the solution for infinite aquifers is presented and compared to those available in literature and to the numerical results of MODFLOW. For the finite aquifer case, the method of images, which is commonly used in well hydraulics, is used to be able to represent the constant-head boundaries at both sides. It is shown that a finite number of images is enough to obtain the results and sustain the steady state. The effect of parameters on the growth of the mound and on the time required to reach the steady state is investigated. The semi-infinite aquifer case is emphasized because the growth of the mound is not symmetric. As the constant-head boundary limits the growth, the unbounded side grows continuously. For this reason, the groundwater divide shifts toward the unbounded side. An iterative solution procedure is proposed. To perform the necessary computations a code was written in Visual Basic of which the algorithm is presented. The proposed methodology has a wide range of applicability and this is demonstrated using two practical examples. The first one is mounding under a stormwater dispersion trench in an infinite aquifer and the other is infiltration from a flood control channel into a semi-infinite aquifer. Results fit very well with those of MODFLOW.

Modeling Steady Sea Water Intrusion with Single‐Density Groundwater Codes

Steady interface flow in heterogeneous aquifer systems is simulated with single-density groundwater codes by using transformed values for the hydraulic conductivity and thickness of the aquifers and aquitards. For example, unconfined interface flow may be simulated with a transformed model by setting the base of the aquifer to sea level and by multiplying the hydraulic conductivity with 41 (for sea water density of 1025 kg/m(3)). Similar transformations are derived for unconfined interface flow with a finite aquifer base and for confined multi-aquifer interface flow. The head and flow distribution are identical in the transformed and original model domains. The location of the interface is obtained through application of the Ghyben-Herzberg formula. The transformed problem may be solved with a single-density code that is able to simulate unconfined flow where the saturated thickness is a linear function of the head and, depending on the boundary conditions, the code needs to be able to simulate dry cells where the saturated thickness is zero. For multi-aquifer interface flow, an additional requirement is that the code must be able to handle vertical leakage in situations where flow in an aquifer is unconfined while there is also flow in the aquifer directly above it. Specific examples and limitations are discussed for the application of the approach with MODFLOW. Comparisons between exact interface flow solutions and MODFLOW solutions of the transformed model domain show good agreement. The presented approach is an efficient alternative to running transient sea water intrusion models until steady state is reached.

Longitudinal dispersion with constant source concentration along unsteady groundwater flow in finite aquifer: analytical solution with pulse type boundary condition

Analytical solution is obtained to predict the contaminant concentration with presence and absence of pollution source in finite aquifer subject to constant point source concentration. A longitudinal dispersion along unsteady groundwater flow in homogeneous and finite aquifer is considered which is initially solute free that is, aquifer is supposed to be clean. The constant source concentration in intermediate portion of the aquifer system is considered with pulse type boundary condition and at the other end of the aquifer, concentration gradient is supposed to be zero. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution of the formulated solute transport model with suitable initial and boundary conditions. The time varying velocities are considered. Analytical solutions are perhaps most useful for benchmarking the numerical codes and models. It may be used as the preliminary predictive tools for groundwater management.