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.     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

A Leaky Aquifer below Champlain Sea Clay: Closed‐Form Solutions for Natural Seepage

Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.     

Hydraulic parameters of a multilayered aquifer system in Kuwait City

The Kuwait Group consists mainly of clastic sediments overlying unconformably the Dammam Formation of Tertiary age. The Kuwait Group is generally divided into three main hydrostratigraphic units: the upper and lower aquifers separated by an aquitard. The upper aquifer is further divided into the water table aquifer, an aquitard and a semiconfined aquifer. This semiconfined unit was pumped and the drawdowns were observed in piezometers screened in various subunits of the Kuwait Group. Some pumping tests of short duration were carried out in the top water table aquifer as well. These tests showed that the subunits of the Kuwait Group are hydraulically interconnected to a varying degree.

The pumping test data were analysed using conventional analytical solutions. The semiconfined pumping test was also simulated by a quasi-three-dimensional model using a leaky multiaquifer modelling technique. The initial hydraulic parameters were improved manually in the model till best fit drawdowns were obtained.

The final parameters obtained by simulation of the pumping tests were used in designing a pilot drainage system for the control of a rising groundwater table in parts of Kuwait City.     

Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers

Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head–constant head wedge, constant head–barrier wedge and barrier–barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.     

Radial groundwater flow to a finite diameter well in a leaky confined aquifer with a finite‐thickness skin

A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.     

Non-Darcian flow to a well in an aquifer–aquitard system

In this study, we use a linearization procedure and a finite difference method to solve non-Darcian flow to a well in an aquifer–aquitard system. The leakage effect is considered. Flow in the aquifer is assumed to be non-Darcian and horizontal, whereas flow in the aquitard is assumed to be Darcian and vertical. The Izbash equation [Izbash SV. O filtracii V Kropnozernstom Materiale. USSR: Leningrad; 1931 [in Russian]] is employed to describe the non-Darcian flow. The wellbore storage is also considered in this study. An approximate semi-analytical solution has been obtained by the linearization procedure, and a numerical solution has been obtained by using a finite difference method. The previous solutions for Darcian flow case and non-Darcian flow case without leakage can be described as special cases of the new solutions. The error caused by the linearization procedure has also been analyzed. The relative error caused by the linearization procedure is nearly 100% at early times, and decreases to zero at late times. We have also compared the results in this study with Wen et al. [Wen Z, Huang G, Zhan H. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. J Hydrol, 2008d [in revision]] in which the leakage effect is not considered, and Hantush and Jacob [Hantush MS, Jacob CE. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union 1955;36(1):95–100] who investigated a similar problem in Darcian flow case. The comparison of this study and Wen et al. (2008d) indicates the dimensionless drawdown in the aquifer with leakage is less than that without leakage, and the leakage has little effect at early times. The comparison between the results of this study and that of Hantush and Jacob (1955) indicates that the dimensionless drawdown in the aquifer for non-Darcian flow is larger at early times and smaller at late times, than their counterparts for Darcian flow. A larger dimensionless non-Darcian conductivity k_D results in a smaller dimensionless drawdown in the aquifer at late times, and leads to a larger dimensionless drawdown in the aquifer at early times. A smaller dimensionless leakage parameter B_D results in a smaller drawdown at late times, and the leakage does not affect the early-time drawdown. The analysis of the dimensionless drawdown inside the well has also been included in this study when the wellbore storage is considered.     

Optimal design of pumping tests in leaky aquifers for stream depletion analysis

We analyze the optimal design of a pumping test for estimating hydrogeologic parameters that are subsequently used to predict stream depletion caused by groundwater pumping in a leaky aquifer. A global optimization method is used to identify the test’s optimal duration and the number and locations of observation wells. The objective is to minimize predictive uncertainty (variance) of the estimated stream depletion, which depends on the sensitivities of depletion and drawdown to relevant hydrogeologic parameters. The sensitivities are computed analytically from the solutions of Zlotnik and Tartakovsky [Zlotnik, V.A., Tartakovsky, D.M., 2008. Stream depletion by groundwater pumping in leaky aquifers. ASCE Journal of Hydrologic Engineering 13, 43–50] and the results are presented in a dimensionless form, facilitating their use for planning of pumping test at a variety of sites with similar hydrogeological settings. We show that stream depletion is generally very sensitive to aquitard’s leakage coefficient and stream-bed’s conductance. The optimal number of observation wells is two, their optimal locations are one close to the stream and the other close to the pumping well. We also provide guidelines on the test’s optimal duration and demonstrate that under certain conditions estimation of aquitard’s leakage coefficient and stream-bed’s conductance requires unrealistic test duration and/or signal-to-noise ratio.     

Groundwater response to tidal fluctuations in a leaky confined coastal aquifer with a finite length

The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.     

A new method for aquifer system identification and parameter estimation

The standard practice for assessing aquifer parameters is to match groundwater drawdown data obtained during pumping tests against theoretical well function curves specific to the aquifer system being tested. The shape of the curve derived from the logarithmic time derivative of the drawdown data is also very frequently used as a diagnostic tool to identify the aquifer system in which the pumping test is being conducted. The present study investigates the incremental area method (IAM) to serve as an alternative diagnostic tool for the aquifer system identification as well as a supplement to the aquifer parameter estimation procedure. The IAM based diagnostic curves for ideal confined, leaky, bounded and unconfined aquifers have been derived as part of this study, and individual features of the plots have been identified. These features were noted to be unique to each aquifer setting, which could be used for rapid evaluation of the aquifer system. The effectiveness of the IAM methodology was investigated by analyzing field data for various aquifer settings including leaky, unconfined, bounded and heterogeneous conditions. The results showed that the proposed approach is a viable method for use as a diagnostic tool to identify the aquifer system characteristics as well as to support the estimation of the hydraulic parameters obtained from standard curve matching procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

Rainfall infiltration‐derived submarine groundwater discharge from multi‐layered aquifer system terminating at the coastline

This article investigates the quantity of submarine groundwater discharge (SGD) from a coastal multi‐layered aquifer system in response to constant rainfall infiltration. The system comprises an unconfined aquifer, a leaky confined aquifer and an aquitard between them and terminates at the coastline. An approximate analytical solution is derived based on the following assumptions: (i) flow is horizontal in the aquifers and vertical in the aquitard, and (ii) flow in the unconfined aquifer is described by nonlinear Boussinesq equation. The analytical solution is compared with numerical solutions of the strictly two‐dimensional nonlinear model to validate the model assumptions used for the analytical solution. The SGD from the leaky confined aquifer increases with the inland rainfall infiltration recharge and the specific leakage of aquitard. The maximum SGD ranges from 1·87 to 10·37 m³ per day per meter of shoreline when rainfall infiltration ranges from 18·2 to 182 mm/year and the specific leakage of aquitard varies from 10^?9 to 10^?1 l/day. Copyright © 2011 John Wiley & Sons, Ltd.     

Maximizing Net Extraction Using an Injection‐Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection‐extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation‐point locations and recirculation ratio, assuming steady‐state, sharp‐interface conditions. The injection‐extraction well‐pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m²/d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well‐pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.     

A Method to Determine the Formation Constants of Leaky Aquifers, and Its Application to Pumping Test Data

Abstract. A method to calculate aquifer transmissivity, storage coefficient, and the leakage coefficient from pumping test data for a leaky aquifer is presented. The method is carried out by a computer program and is based on a minimization of the sum of squares of differences between drawdown in the observation well and the theoretical values from the Hantush and Jacob formula. No user defined starting points are necessary. Random error estimates for the parameters are given. Applications of the method are illustrated using data from pumping tests performed in leaky aquifers at the Cauca River Valley, Colombia.     

稳定井流抽水含水层参数计算及富水性评价

针对目前单孔稳定流求参存在的问题,本文在分析新生界松散含水层条件及三次降深抽水过程基础上,利用其抽水试验恢复阶段的数据,分别求得各含水层多个参数,其值真实反映了含水层的实际情况。利用多元回归方法,求得降深与流量关系,通过其系数值大小分析,间接得出各含水层的富水性程度,为地下水的勘探与评价提供一定借鉴。     

The Effect of Modeled Recharge Distribution on Simulated Groundwater Availability and Capture

Simulating groundwater flow in basin‐fill aquifers of the semiarid southwestern United States commonly requires decisions about how to distribute aquifer recharge. Precipitation can recharge basin‐fill aquifers by direct infiltration and transport through faults and fractures in the high‐elevation areas, by flowing overland through high‐elevation areas to infiltrate at basin‐fill margins along mountain fronts, by flowing overland to infiltrate along ephemeral channels that often traverse basins in the area, or by some combination of these processes. The importance of accurately simulating recharge distributions is a current topic of discussion among hydrologists and water managers in the region, but no comparative study has been performed to analyze the effects of different recharge distributions on groundwater simulations. This study investigates the importance of the distribution of aquifer recharge in simulating regional groundwater flow in basin‐fill aquifers by calibrating a groundwater‐flow model to four different recharge distributions, all with the same total amount of recharge. Similarities are seen in results from steady‐state models for optimized hydraulic conductivity values, fit of simulated to observed hydraulic heads, and composite scaled sensitivities of conductivity parameter zones. Transient simulations with hypothetical storage properties and pumping rates produce similar capture rates and storage change results, but differences are noted in the rate of drawdown at some well locations owing to the differences in optimized hydraulic conductivity. Depending on whether the purpose of the groundwater model is to simulate changes in groundwater levels or changes in storage and capture, the distribution of aquifer recharge may or may not be of primary importance.     

An analytical solution for the head distribution in a tidal leaky confined aquifer extending an infinite distance under the sea

A mathematical model is developed to investigate the effects of tidal fluctuations and leakage on the groundwater head of leaky confined aquifer extending an infinite distance under the sea. The leakages of the offshore and inland aquitards are two dominant factors controlling the groundwater fluctuation. The tidal influence distance from the coast decreases significantly with the dimensionless leakage of the inland aquitard (u_i). The fluctuation of groundwater level in the inland part of the leaky confined aquifer increases significantly with the dimensionless leakage of the offshore aquitard (u_o). The influence of the tidal propagation parameter of an unconfined aquifer on the head fluctuation of the leaky confined aquifer is comparatively conspicuous when u_i is large and u_o is small. In other words, ignoring water table fluctuation of the unconfined aquifer will give large errors in predicting the fluctuation, time lag, and tidal influence distance of the leaky confined aquifer for large u_i and small u_o. On the contrary, the influence of the tidal propagation parameter of a leaky confined aquifer on the head fluctuation of the leaky confined aquifer is large for large u_o and small u_i.     

Flow to a well in a five-layer system with application to the Oxnard Basin

Nearly 40 years ago, Neuman (1968) developed an analytical solution for drawdown in a system of three aquifers separated by two aquitards when one of the aquifers is pumped at a constant rate. Whereas the simpler case of two aquifers separated by one aquitard has been presented by Neuman and Witherspoon (1969a), the full five-layer solution has not been previously evaluated. We do so here using numerical inversion of its Laplace-transformed version and present selected results graphically in dimensionless form. The solution demonstrates that the effect of pumping propagates across all five layers, adding emphasis to a question previously raised by Neuman and Witherspoon about the validity of leaky aquifer theories that disregard drawdowns in unpumped aquifers. A large-scale, long-term pumping test spanning three aquifers separated by two aquitards near Oxnard, California, has been conducted and analyzed by Neuman and Witherspoon (1972). They evaluated the vertical hydraulic diffusivities of the aquitards using the Neuman-Witherspoon ratio method and their specific storage values on the basis of laboratory consolidation tests. We reinterpret the Oxnard pumping test by coupling the five-layer analytical solution of Neuman (1968) with the parameter estimation code PEST (Doherty 2002) and validate our results against drawdowns from a subsequent pumping test at the site. Our parameter estimates compare favorably with those of Neuman and Witherspoon (1972).     

Groundwater Deterioration of Shallow Groundwater Aquifers Due to Overexploitation in Northeast Jordan

Groundwater is the major water resource in Jordan and most of the groundwater basins are already exploited beyond their estimated safe yield. Azraq basin is one of the most important groundwater basins in Jordan, which supplies Amman with drinking water. However, due to overpumping from the shallow groundwater aquifers, the water level dropped dramatically and signs of salinization and depletion are starting to occur. The severe drawdown in the Azraq well‐field caused a reverse in the hydraulic gradient and consequently, the saltwater in the center of the basin (Qa‐Azraq) started to move in the direction of the well‐field. The salinization in the shallow aquifer (basalt/B5/B4) is believed to result from one of the following scenarios: (i) a reverse flow from Sabkha to the AWSA well field, (ii) an upward leakage from the middle aquifer system (B2/A7) and the combined B3 Aquitard‐B2/A7 aquifer, (iii) a dissolution process between the water and rock matrix due to lowering of the dynamic water levels during pumping which reached the mineralized formations underlying the Basalt. The salinization trend of some AWSA wells represented by the gradual increase of major ions is associated with rather constant stable isotopic contents. This indicates that these constituents originate from the main minerals existing in the matrix of the aquifers and thus this scenario is the most likely to occur.     

Steady flow to a partially penetrating blind‐wall well in a confined aquifer

Wells in aquifers of loose collapsible sediment are cased so that they have a blind wall and gain water only from the bottom. The hydraulic gradient established at the bottom of these wells during pumping brings the aquifer materials in a quicksand state, which may cause abrasion of pipes and pumps and even the destruction of well structure. To examine the quicksand occurrence, an analytical solution for the steady flow to a partially penetrating blind‐wall well in a confined aquifer is developed. The validity of the proposed solution is evaluated numerically. The sensitivity of maximum vertical gradient along the well bottom in response to aquifer and well parameters is examined. The solution is presented in the form of dimensionless‐type curves and equations that can be easily used to design the safe pumping rate and optimum well geometry to protect the well against sand production. The solution incorporates the anisotropy of aquifer materials and can also be used to determine the hydraulic conductivity of the aquifer. Copyright © 2012 John Wiley & Sons, Ltd.