Series solutions for saturated–unsaturated flow in multi-layer unconfined aquifers

A semi-analytical mesh-free series solution method is presented for modeling regional steady-state subsurface saturated–unsaturated flow in 2-D geometrically complex homogenous and stratified hill-slope cross sections. Continuous solutions for pressure in the saturated and unsaturated zone are determined iteratively, as is the location of the water table surface. Mass balance is satisfied exactly over the entire domain except along boundaries and interfaces between layers, where errors are in an acceptable range. The solutions are derived and demonstrated on multiple test cases. The errors for specific cases are assessed and discussed.     

Regression method for estimating rainfall recharge at unconfined sandy aquifers with an equatorial climate

A reliable estimate of rainfall recharge is essential for groundwater system managements. This study develops a method based on regression equations for estimating rainfall recharge at unconfined sandy aquifers with an equatorial climate. The developed method (GR-I method) is generally efficient for estimating long-term regional recharge, as the computational procedures could be formulated and executed easily using Microsoft's Excel spreadsheet. More importantly, its application could be extended to sand textures different from the sand texture used in developing the regression equations. To evaluate its reliability, the method was applied to estimate monthly gross recharge percentages at the Changi reclaimed land. When ignoring the effect of rainfall clusters, the GR-I method was found to underestimate the monthly gross recharge percentages for those months with high monthly rainfall depths. By integrating the effect of rainfall clusters, the GR-I method yields reliable estimates of monthly gross recharge percentages. By including daily potential evaporation as an additional input variable, the Extended GR-I method was found to be not superior to the GR-I method, implying that soil moisture availability is the major governing factor for actual soil evaporation in the highly porous sand medium, instead of atmospheric demand represented by the potential evaporation rate. Using the GR-I method, the mean annual net recharge percentage of the study site was found to fall between 56·9 and 69·9%, which corresponds to a net recharge depth of 1073·8–1745·8 mm. Although the developed method provides a good alternative to other widely used methods, its recharge estimates still needs to be collaborated with estimates from other methods, as multiple techniques are highly recommended in any groundwater recharge estimations. Copyright © 2007 John Wiley & Sons, Ltd.     

A grid generating algorithm for simulating a fluctuating water table boundary in heterogeneous unconfined aquifers

An algorithm is presented for generating finite element grids that can be used to calculate the position of a fluctuating water table and the formation of seepage faces within a heterogeneous unconfined aquifer. Our approach overcomes limitations with existing techniques by allowing the water table to rise or decline through hydrostratigraphic boundaries yet maintains numerical and conceptual accuracy with respect to hydrostratigraphic geometry. The algorithm involves (1) limited stretching or shrinking of elements along the water table if the change in the position of the water table is small with respect to the vertical grid spacing, and (2) the addition or removal of nodes and elements in the finite element mesh along the water table as the change becomes large with respect to the vertical grid spacing. This technique is applicable to any 2-D or 3-D finite element code that contains an automatic finite-element grid generator.     

Air and water flows induced by pumping tests in unconfined aquifers with low‐permeability zones

Air flows from the atmosphere into an unconfined aquifer when the water table falls during pumping tests. Pumping test results in unconfined aquifers may be significantly affected by low‐permeability zones (LPZs) near the initial water table position, because they restrict the downward movement of air. A transient, three‐dimensional air–water two‐phase flow model is employed to investigate numerically the effects of local heterogeneity on pumping test results in unconfined aquifers. Two cases of local heterogeneities are considered herein: a LPZ around the pumping well and on one side of the pumping well. Results show that the drawdown with the LPZ is significantly greater than that of the homogeneous aquifer. The differences in drawdown are the most significant at intermediate times and gradually diminish at later times. The LPZ significantly reduces air flow from the atmosphere to the aquifer. The pore air velocity in the LPZ is very low. The air pressure at the observation point under the LPZ when air begins to enter is significantly lower than the air pressure of the homogeneous aquifer at the same point. After that, the air pressure increases quickly and then increases slowly. The time for the air pressure to reach the atmospheric pressure is significantly longer. Copyright © 2013 John Wiley & Sons, Ltd.     

Describing near surface, transient flow processes in unconfined aquifers below irrigated lands: A deforming finite element model for heterogeneous aquifers

Hydrologic models of irrigated lands generally adopt either a basin-scale or a root-zone perspective. While basin-wide macro-scale models rely on the aggregation of important spatial and temporal data across large areas, micro-scale root-zone models depend on the definition of rigid boundaries around the zone of plant–soil–water interaction. In reality, irrigation management decisions are made on a field by field basis and can interact across field boundaries. This paper first describes a shallow water table model, based on deforming finite element (DFE) framework, to characterize the near-surface field-to-field hydrologic response to various irrigation and drainage management regimes along a gently sloping alluvial fan. The model is then enhanced through changing geometry of a fluctuating water table below a series of irrigated fields. Such an enhancement also offers computational flexibility relative to the saturated–unsaturated models commonly used in micro-scale studies. The model is designed with the alluvial fan aquifers of California’s western San Joaquin Valley as reference systems.     

Effects of meteorological and hydrogeological factors on gross recharge percentage at unconfined sandy aquifers with an equatorial climate

A thorough understanding of rainfall recharge processes and their controlling factors is essential for management of groundwater systems. This study investigates the effects of various meteorological and hydrogeological factors on the gross recharge percentages, the rainfall–recharge relationships and the recharge threshold values for unconfined sandy aquifers under an equatorial climate. Among the meteorological factors investigated, rainfall intensity was found to have the most significant impact on the gross recharge rate. The effects of potential evaporation rate, relative humidity and air temperature on the gross recharge percentage were significant when the vadose zone thickness is larger than 2·5 m. The recharge threshold values were found to depend strongly on the vadose zone thickness. The rainfall–recharge relationships could generally be well defined by a normal–log relationship. The rainfall–recharge relationships derived here are applicable to yield estimates of gross recharge percentages for unconfined sandy aquifers under an equatorial climate, using rainfall intensity and vadose zone thickness as input variables. In this study, a theory was developed and validated to provide physical explanations for the observations, based on the residence time of the percolated rainwater within the vadose zone. Among the soil hydraulic parameters tested, porosity and saturated hydraulic conductivity were found to have the most pronounced effects on the gross recharge percentage. Utilizing the sensitivity results and the theory derived, an approach was developed for extending the application of the derived rainfall–recharge relationships to other sand textures. The approach was found to be capable of producing rough and fast estimations of gross recharge percentage for other sand textures. Copyright © 2007 John Wiley & Sons, Ltd.     

Tidal effects on groundwater dynamics in unconfined aquifers

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi‐steady‐state rise in the mean water‐table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed and this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water‐table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright © 2001 John Wiley & Sons, Ltd.     

An analytical solution for ground water transit time through unconfined aquifers

An exact, closed-form analytical solution is developed for calculating ground water transit times within Dupuit-type flow systems. The solution applies to steady-state, saturated flow through an unconfined, horizontal aquifer recharged by surface infiltration and discharging to a downgradient fixed-head boundary. The upgradient boundary can represent, using the same equation, a no-flow boundary or a fixed head. The approach is unique for calculating travel times because it makes no a priori assumptions regarding the limit of the water table rise with respect to the minimum saturated aquifer thickness. The computed travel times are verified against a numerical model, and examples are provided, which show that the predicted travel times can be on the order of nine times longer relative to existing analytical solutions.     

Scaling snowdrift development rate

For successful snowdrift modelling, measured drift shapes should be geometrically similar to full-scale shapes and develop at rates that scale in a known manner. Consensus exists on most modelling methods and the similitude requirements needed to meet these objectives. A notable exception is the manner to scale drift development rates. A rationale is presented for rate scaling based on an independent model and prototype mass transport measurements. This approach is validated by comparing the rate of drift development for a model Wyoming snow fence with corresponding field data. This method yields excellent agreement, whereas the alternatives differ substantially.     

Approximate solutions for radial travel time and capture zone in unconfined aquifers

Radial time-of-travel (TOT) capture zones have been evaluated for unconfined aquifers with and without recharge. The solutions of travel time for unconfined aquifers are rather complex and have been replaced with much simpler approximate solutions without significant loss of accuracy in most practical cases. The current "volumetric method" for calculating the radius of a TOT capture zone assumes no recharge and a constant aquifer thickness. It was found that for unconfined aquifers without recharge, the volumetric method leads to a smaller and less protective wellhead protection zone when ignoring drawdowns. However, if the saturated thickness near the well is used in the volumetric method a larger more protective TOT capture zone is obtained. The same is true when the volumetric method is used in the presence of recharge. However, for that case it leads to unreasonableness over the prediction of a TOT capture zone of 5 years or more.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

Random domain decomposition for flow in heterogeneous stratified aquifers

We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which employs random domain decomposition in the context of groundwater flow moment equations to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. Flow parallel and perpendicular to the layering in a two-material composite layered medium is considered. The hydraulic conductivity of each material is log-normally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is random and normally distributed with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyze the impact of unknown geometry of materials on statistical moments of head and flux. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudo-homogeneous random fields. This work was performed under the auspices of the US Department of Energy (DOE): DOE/BES (Bureau of Energy Sciences) Program in the Applied Mathematical Sciences contract KC-07–01–01 and Los Alamos National Laboratory under LDRD 98604. This work made use of STC shared experimental facilities supported by the National Science Foundation under Agreement No. EAR-9876800. This work was supported in part by the European Commission under Contract No. EVK1-CT-1999–00041 (W-SAHaRA).     

Spatial moments for colloid-enhanced radionuclide transport in heterogeneous aquifers

We consider colloid facilitated radionuclide transport by steady groundwater flow in a heterogeneous porous formation. Radionuclide binding on colloids and soil-matrix is assumed to be kinetically/equilibrium controlled. All reactive parameters are regarded as uniform, whereas the hydraulic log-conductivity is modelled as a stationary random space function (RSF). Colloid-enhanced radionuclide transport is studied by means of spatial moments pertaining to both the dissolved and colloid-bounded concentration. The general expressions of spatial moments for a colloid-bounded plume are presented for the first time, and are discussed in order to show the combined impact of sorption processes as well as aquifer heterogeneity upon the plume migration. For the general case, spatial moments are defined by the aid of two characteristic reaction functions which cannot be expressed analytically. By adopting the approximation for the longitudinal fluid trajectory covariance valid for a flow parallel to the formation bedding suggested by Dagan and Cvetkovic [Dagan G, Cvetkovic V. Spatial Moments of Kinetically Sorbing Plume in a Heterogeneous Aquifers. Water Resour Res 1993;29:4053], we obtain closed form solutions.     

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.     

Estimation of the effective precipitation recharge coefficient in an unconfined aquifer using stochastic analysis

Effectively managing groundwater relies heavily on estimating the amount of precipitation that may infiltrate the subsurface and supply groundwater. In this study, we present a novel estimation method based on a stochastic approach to evaluate the quantity of precipitation that may recharge groundwater. The precipitation recharge coefficient is also investigated based on an unconfined aquifer with an unbound, infinitely extended boundary condition. Moreover, a spectrum's relationship to the precipitation and groundwater level variation is also derived. The precipitation recharge coefficient can be obtained from the solution of the spectrum equation. Furthermore, sensitivity analysis is performed in order to determine the key variable on the precipitation recharge coefficient. Analysis results indicate that the location of an observation well affects the estimated precipitation recharge coefficient. If the precipitation recharge area is large enough, the precipitation recharge coefficient becomes insensitive to the location of the observation well. The spectrum's relationship between the precipitation recharge and groundwater level variation is also applied when estimating the precipitation recharge coefficient upstream of the Cho‐Shui River alluvial fan. According to those results, the precipitation recharge coefficient is 0·03 and the amount of groundwater recharge from precipitation is 35 million tons of water annually upstream of the Cho‐Shui River alluvial fan. Copyright © 2000 John Wiley & Sons, Ltd.     

Uncertainty in applying the linear poroelasticity model to field situations as a result of periodic loading in heterogeneous aquifers

The solid Earth's surface frequently experience changes in total stresses as a result of periodic loading. When the fluid‐saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (lnK). It is important for the rational management of groundwater resources. A closed‐form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of lnK process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright © 2014 John Wiley & Sons, Ltd.     

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.     

Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions

An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum K_max/K_min tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.