Non-Darcian flow toward a larger-diameter partially penetrating well in a confined aquifer

In this study, non-Darcian flow to a larger-diameter partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian and described by the Izbash equation, and the flow in the vertical direction was assumed to be Darcian. A linearization procedure was used to approximate the nonlinear governing equation. The Laplace transform associated with the finite cosine Fourier transform was used to solve such non-Darcian flow model. Both the drawdowns inside the well and in the aquifer were analyzed under different conditions. The results indicated that the drawdowns inside the well were generally the same at early times under different conditions, and the features of the drawdowns inside the well at late times were similar to those of the drawdowns in the aquifer. The drawdown in the aquifer for the non-Darcian flow case was larger at early times and smaller at late times than their counterparts of Darcian flow case. The drawdowns for a partially penetrating well were the same as those of a fully penetrating well at early times, and were larger than those for a fully penetrating well at late times. A longer well screen resulted in a smaller drawdown in the aquifer at late times. A larger power index n in the Izbash equation resulted in a larger drawdown in the aquifer at early times and led to a smaller drawdown in the aquifer at late times. A larger well radius led to a smaller drawdown at early times, but it had little impact on the drawdown at late times. The wellbore storage effect disappears earlier when n is larger.     

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash’s equation. The solutions are derived by Boltzmann and dimensionless transformations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.     

Calculation of groundwater head distribution with a close barrier during excavation dewatering in confined aquifer

When pumping is conducted in confined aquifer inside excavation pit(waterproof curtain),the direction of the groundwater seepage outside the excavation changes from horizontal to vertical owing to the existence of the curtain barrier.There is no analytical calculation method for the groundwater head distribution induced by dewatering inside excavation.This paper first analyses the mechanism of the blocking effects from a close barrier in confined aquifer.Then,a simple equation based on analytical solution is proposed to calculate groundwater heads inside and outside of the excavation pit with waterproof curtain(hereafter refer to close barrier)in a confined aquifer.The distribution of groundwater head is derived according to two conditions:(i)pumping with a constant water head,and(ii)pumping with a constant flow rate.The proposed calculation equation is verified by both numerical simulation and experimental results.The comparisons demonstrate that the proposed model can be applied in engineering practice of excavation.     

Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation

Non-Darcian flow to a well in a leaky aquifer was investigated using a finite difference method. Flow in the leaky aquifer is assumed to be non-Darcian and horizontal, while flow in the aquitard is assumed to be Darcian and vertical. The Forchheimer equation was employed to describe the non-Darcian flow in the aquifer. The finite difference solution was compared with the solution of Birpinar and Sen (2004). The latter overestimates the drawdown at early times and underestimates the drawdown at late times; also, the impact of β _D on the drawdown depends on the value of B _D, where β _D is a dimensionless turbulent factor in the Forchheimer equation and B _D is the dimensionless leakage parameter. The impact of leakage on drawdown is similar to that of Darcian flow. A sensitivity analysis indicated that the drawdown is very sensitive to the change in the dimensionless well radius r _cD when B _D is relatively large, while it is sensitive to the change in B _D when B _D is relatively small. The numerical solution has been applied to analyze the pumping test data in Chaj-Doab area of Pakistan. Birpinar ME, Sen Z (2004) Forchheimer groundwater flow law type curves for leaky aquifers. J Hydrol Eng 9(1):51??9     

Analytical solutions for the capture zone of a pumping well near a stream

The capture zone for a fully penetrating well in an aquifer with regional flow to a stream boundary under steady-state conditions was delineated using complex algebra and image well theory. Regional flow in the aquifer was allowed to take different directions relative to the stream axis. Two critical pumping rates, Q _C1 and Q _C2, produce three capture-zone pattern scenarios: (1) at low pumping rates (Q?<?Q _C1) water is solely withdrawn from the aquifer and no water from the stream enters the aquifer, (2) at medium pumping rates (Q _C1?<?Q?<?Q _C2) a portion of stream water enters the aquifer but it is not captured by the well, and (3) at high pumping rates (Q?>?Q _C2) pumped water is supplied from both the aquifer and the stream with different proportions. For the second and third scenarios, the stream length interval through which stream water enters the aquifer was determined and found to be more sensitive to pumping rate as the regional flow direction approaches the stream axis. The portion of pumped water supplied by the stream was determined in the third scenario. Finally, the capture-zone asymmetry with respect to its axial line was delineated.     

Inverse modelling of aquifer parameters in basaltic rock with the help of pumping test method using MODFLOW software

The origin and movement of groundwater are the fundamental questions that address both the temporal and spatial aspects of ground water run and water supply related issues in hydrological systems. As groundwater flows through an aquifer, its composition and temperature may variation dependent on the aquifer condition through which it flows. Thus, hydrologic investigations can also provide useful information about the subsurface geology of a region. But because such studies investigate processes that follow under the Earth's shallow, obtaining the information necessary to answer these questions is not continuously easy. Springs, which discharge groundwater table directly, afford to study subsurface hydrogeological processes.The present study of estimation of aquifer factors such as transmissivity (T) and storativity (S) are vital for the evaluation of groundwater resources. There are several methods to estimate the accurate aquifer parameters (i.e. hydrograph analysis, pumping test, etc.). In initial days, these parameters are projected either by means of in-situ test or execution test on aquifer well samples carried in the laboratory. The simultaneous information on the hydraulic behavior of the well (borehole) that provides on this method, the reservoir and the reservoir boundaries, are important for efficient aquifer and well data management and analysis. The most common in-situ test is pumping test performed on wells, which involves the measurement of the fall and increase of groundwater level with respect to time. The alteration in groundwater level (drawdown/recovery) is caused due to pumping of water from the well. Theis (1935) was first to propose method to evaluate aquifer parameters from the pumping test on a bore well in a confined aquifer. It is essential to know the transmissivity (T = Kb, where b is the aquifer thickness; pumping flow rate, Q = TW (dh/dl) flow through an aquifer) and storativity (confined aquifer: S = bS_s, unconfined: S = S_y), for the characterization of the aquifer parameters in an unknown area so as to predict the rate of drawdown of the groundwater table/potentiometric surface throughout the pumping test of an aquifer. The determination of aquifer's parameters is an important basis for groundwater resources evaluation, numerical simulation, development and protection as well as scientific management. For determining aquifer's parameters, pumping test is a main method. A case study shows that these techniques have been fast speed and high correctness. The results of parameter's determination are optimized so that it has important applied value for scientific research and geology engineering preparation.     

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K _r2), and the specific storage of the formation zone (S _s2) at early times, and it is very sensitive to the parameters n, w and K _r2 at late times, especially to n, while it is not sensitive to the skin thickness (r _s).     

承压含水层中非完整井附近“非达西-达西”两区渗流模型近似解析解

抽水井附近由于流速过快往往发生非达西流,而远离抽水井随着流速下降又变为达西流.为了描述这些特征,建立了承压含水层中非完整井附近“非达西-达西”两区渗流模型,即距离抽水井较近的区域由于流速较快假设发生非达西渗流,并利用Izbash公式刻画,而距离抽水井较远由于流速较慢假设仍然满足达西定律,含水层中垂向流速较小也利用达西定律描述.通过线性化近似方法结合Laplace变换和有限Fourier余弦变换对模型进行了求解,分析探讨了该两区模型下水位降深曲线特征.结果表明:抽水初期,非达西渗流区域水位降深与全非达西渗流模型结果吻合,而抽水后期两区模型非达西渗流区域的水位降深与全达西模型水位降深基本一致,但大于全非达西渗流模型的水位降深;抽水初期,两区模型中达西渗流区域的水位降深比全达西渗流模型结果大,但比全非达西渗流模型结果小;对不同时间的水位降深随井距变化曲线分析发现非达西渗流区域水位降深随Izbash公式中的幂指数n增大而减小,而在达西渗流区域水位降深基本不受n值的影响.研究成果对非完整井抽水试验参数反演具有重要理论意义.      

Hydrogeologic and hydraulic characterization of aquifer and nonaquifer layers in a lateritic terrain (West Bengal,India)

The hydrogeologic and hydraulic characteristics of a lateritic terrain in West Bengal, India, were investigated. Test drilling was conducted at ten sites and grain-size distribution curves (GSDCs) were prepared for 275 geologic samples. Performance evaluation of eight grain-size-analysis (GSA) methods was carried out to estimate the hydraulic conductivity (K) of subsurface formations. Finally, the GSA results were validated against pumping-test data. The GSDCs indicated that shallow aquifer layers are coarser than the deeper aquifer layers (uniformity coefficient 0.19–11.4). Stratigraphy analysis revealed that both shallow and deep aquifers of varying thickness exist at depths 9–40 and 40–79 m, respectively. The mean K estimates by the GSA methods are 3.62–292.86 m/day for shallow aquifer layers and 0.97–209.93 m/day for the deeper aquifer layers, suggesting significant aquifer heterogeneity. Pumping-test data indicated that the deeper aquifers are leaky confined with transmissivity 122.69–693.79 m²/day, storage coefficient 1.01?×?10^?7–2.13?×?10^?4 and leakance 2.01?×?10^?7–34.56?×?10^?2 day^?1. Although the K values yielded by the GSA methods are generally larger than those obtained from the pumping tests, the Slichter, Harleman and US Bureau Reclamation (USBR) GSA methods yielded reasonable values at most of the sites (1–3 times higher than K estimates by the pumping-test method). In conclusion, more reliable aquifers exist at deeper depths that can be tapped for dependable water supply. GSA methods such as Slichter, Harleman and USBR can be used for the preliminary assessment of K in lateritic terrains in the absence of reliable field methods.     

基于解析法和数值法的非稳定流抽水试验参数反演

含水层的水文地质参数是进行地下水资源计算、地下水污染防控等所必需的基础数据,结合数值模拟技术进行含水层参数反演很有必要.按照1:5万水文地质调查规范在江汉平原仙桃市杨林尾镇复兴水厂不同含水层位开展抽水试验,包括深层含水层单孔抽水试验以及浅层含水层中群孔(2孔)抽水试验.对于单孔抽水试验,应用第1类越流系统井流理论进行参数反演;对于群孔抽水试验,推导了特定综合井函数,并利用特定标准曲线匹配法和直线图解法求解了含水层参数.随后利用FEFLOW软件建立了相应数值模型,拟合了含水层参数.结果表明:浅层含水层的渗透系数变化范围为21.66~54.00 m/d,贮水率变化范围为1.28×10-5~8.00×10-4 m-1;深层含水层渗透系数变化范围为1.27~7.00 m/d,贮水率变化范围为3.90×10-6~5.00×10-6 m-1.对于深层承压含水层而言,越流补给量较大.采用数值模拟方法结合抽水试验数据求参,综合考虑了含水层结构,拟合效果好,所得结果更加可靠.      

Hydrogeological studies on the Nubian sandstone aquifer in El-Bahariya Oasis, Western Desert, Egypt

The current study aimed to evaluate hydrogeologically the Nubian sandstone aquifer in El-Bahariya Oasis. It represents the main water-bearing horizon in the study area and consists of continental elastic sediments, mainly sandstone alternating with shale and clays. The general flow lines are directed from SW to NE direction, as detected from the constructed potentiometric head contour map. The piezometric surface reaches 149 m in El-Heiz area at the southern part, while it reaches 90 m at the northern, reflecting higher pressure head of the aquifer in the southern part. The map also illustrates that the southern part is considered as the most promising location for development. The structural elements play an important role in the deposition and distribution of the sedimentary succession of the Nubian sandstone sediments. Consequently, this sedimentary pattern affects the occurrences and movements of the groundwater within the aquifer system. Along the structurally high areas, in the study area, the piezometric head increases, while the reverse is recorded along the structurally low areas. The step-drawdown tests data were carried out by calculating the aquifer loss coefficient (B) and the well loss constant (C). The B values are smaller compared with C values, indicating that the aquifer under pressure has a behavior of leaky aquifer; therefore, it shows hydraulic connection with surrounding formation. The values of well efficiency range from 78.50% to 87.76%. Analysis of 12 pumping test data (constant discharge tests) was carried out in order to calculate the Nubian aquifer hydraulic parameters (transmissivity, hydraulic conductivity, and storage coefficient). The transmissivity values decrease from 3,045 m²/day in the southern part (El-Heiz area) to 236 m²/day in the northeastern part (El-Harra area). Accordingly, the aquifer classified as a high to moderate potentiality. Transmissivity contour map observes gradual increase of transmissivity values from the southern to northeastern direction. This may be due to the increase of shale or clay content in the concerned aquifer in that direction. The storage coefficient values range between 1.04 × 10^?4 and 5.22 × 10^?3, as obtained from the results of pumping test analysis, which ensure that the Nubian sandstone aquifer is classified as semi-confined to confined aquifer type. The S values show a decrease from southwest to northeast direction as detected from S-map. The hydraulic conductivity values vary from to 0.46 m/day in the northern part to 10.88 m/day in the southern part with an average of 5.67 m/day. According to the classification based on K values, the aquifer is mainly composed of coarse sand.     

Estimating hydraulic conductivity using grain-size analyses, aquifer tests, and numerical modeling in a riverside alluvial system in South Korea

Hydraulic conductivity (K) for an alluvial system in a riverbank filtration area in Changwon City, South Korea, has been studied using grain-size distribution, pumping and slug tests, and numerical modeling. The alluvial system is composed of layers: upper fine sand, medium sand, lower fine sand, and a highly conductive sand/gravel layer at the base. The geometric mean of K for the sand/gravel layer (9.89?×?10^?4 m s^?1), as determined by grain-size analyses, was 3.33 times greater than the geometric mean obtained from pumping tests (2.97?×?10^?4 m s^?1). The geometric mean of K estimates obtained from slug tests (3.08?×?10^?6 m s^?1) was one to two orders of magnitude lower than that from pumping tests and grain-size analyses. K estimates derived from a numerical model were compared to those derived from the grain-size methods, slug tests and pumping tests in order to determine the degree of deviation from the numerical model. It is considered that the K estimates determined by the slug tests resemble the uppermost part of the alluvial deposit, whereas the K estimates obtained by grain-size analyses and pumping tests are similar to those from the numerical model for the sand/gravel layer of the riverside alluvial system.     

Estimation of source parameters and attenuation using digital waveforms of Al-Ays 2009 earthquake,Saudi Arabia

On 19 May 2009, an earthquake sequence of M _w?=?4.8 occurred at 25.20°N 37.76°E about 60 km onshore of the Red Sea coastline, Saudi Arabia. In the present study, the digital waveform data from the largest four events were used to estimate the source parameters and attenuation characteristics along the source-to-station path in the Arabian Shield. A grid search technique, combined with an assumption of circular source model, was applied to find the best-fit spectral amplitude over the space parameters: long period spectral level (Ω ₀), corner frequency (f ₀) and asymptotic high-frequency fall-off (γ). Consequently, the spectral parameters were used to estimate source parameters: seismic moment, fault radius (assumed circular rupture model) and stress drop. Seismic moments are founded to be within the range of 2.34E+14 to 2.83E+16 Nm and their corresponding moment magnitudes range from 3.5 to 4.8; the fault radius ranges from 369 to 1,498 m, and stress drops are observed in the range of 8.7 to 32.0 b. The spectral slopes beyond the corner frequency displayed ω ^?2.4 to ω ^?2.6 behaviours in contrast with Brune's source model of ω ^?2. This finding requires more detailed investigations on large data sets to distinguish the behaviour mechanism of the spectral slopes at high frequencies. By taking the ratio between observed and calculated spectra, the attenuation curves for P and S waves were derived along the source-to-station paths. The preliminarily results exhibited high quality factors of Q _α?=?3,883 and Q _β?=?3,530 for P and S waves, respectively. To this end, the ratio Q _β/Q _α is founded to be slightly less than unity indicating that the body waves from source-to-station paths crossed a crustal volume that is partially saturated with fluids causing lower attenuation effect on P waves than on S waves in the Arabian Shield.     

Method to characterize aquitards above leaky aquifers with water supply wells

Leaky aquifers provide protected drinking water since the aquifer is overlain by an aquitard, and this study develops a method to estimate hydraulic properties of the latter deposit. Steady pumping, supply well shutdowns, and slug tests generate data in adjacent monitoring well clusters that characterize the aquitard. An existing steady model estimates a site-averaged value of the aquitard permeability k if its thickness is known, and this site-averaged estimate may be compared with local k estimates from conventional and extended slug tests. A shutdown attenuation model estimates a local value of the consolidation coefficient C _V, which combines with the local k value to specify the compressibility α of the aquitard. The method is illustrated for the Fowl Meadow Aquifer, a stratified drift deposit used as a drinking water supply in eastern Massachusetts (USA), with an overlying silt aquitard of 10 m thickness. Steady data and theory suggest a site-averaged k of 2.3?×?10^–17?m² for the aquitard, while the shutdown attenuation model generates local C _V values that vary from 10^–5 to 10^–3?m²/s. The slug tests yield a local k variation (10^–17–10^–13?m²) that brackets the site-averaged value, and an α range of 10^–9–10^–7?Pa^–1.     

Sources of groundwater pumpage in a layered aquifer system in the Upper Gulf Coastal Plain, USA

Understanding groundwater-pumpage sources is essential for assessing impacts on water resources and sustainability. The objective of this study was to quantify pumping impacts and sources in dipping, unconfined/confined aquifers in the Gulf Coast (USA) using the Texas Carrizo-Wilcox aquifer. Potentiometric-surface and streamflow data and groundwater modeling were used to evaluate sources and impacts of pumpage. Estimated groundwater storage is much greater in the confined aquifer (2,200?km³) than in the unconfined aquifer (170?km³); however, feasibility of abstraction depends on pumpage impacts on the flow system. Simulated pre-development recharge (0.96?km³/yr) discharged through evapotranspiration (ET, ～37%), baseflow to streams (～57%), and to the confined aquifer (～6%). Transient simulations (1980–1999) show that pumpage changed three out of ten streams from gaining to losing in the semiarid south and reversed regional vertical flow gradients in ～40% of the entire aquifer area. Simulations of predictive pumpage to 2050 indicate continued storage depletion (41% from storage, 32% from local discharge, and 25% from regional discharge capture). It takes ～100?yrs to recover 40% of storage after pumpage ceases in the south. This study underscores the importance of considering capture mechanism and long-term system response in developing water-management strategies.     

Fraction of young water as an indicator of aquifer vulnerability along two regional flow paths in the Mississippi embayment aquifer system,southeastern USA

Wells along two regional flow paths were sampled to characterize changes in water quality and the vulnerability to contamination of the Memphis aquifer across a range of hydrologic and land-use conditions in the southeastern United States. The flow paths begin in the aquifer outcrop area and end at public supply wells in the confined parts of the aquifer at Memphis, Tennessee. Age-date tracer (e.g. SF₆, ³H, ¹⁴C) data indicate that a component of young water is present in the aquifer at most locations along both flow paths, which is consistent with previous studies at Memphis that documented leakage of shallow water into the Memphis aquifer locally where the overlying confining unit is thin or absent. Mixtures of young and old water were most prevalent where long-term pumping for public supply has lowered groundwater levels and induced downward movement of young water. The occurrence of nitrate, chloride and synthetic organic compounds was correlated to the fraction of young water along the flow paths. Oxic conditions persisted for 10 km or more down dip of the confining unit, and the presence of young water in confined parts of the aquifer suggest that contaminants such as nitrate-N have the potential for transport. Long-term monitoring data for one of the flow-path wells screened in the confined part of the aquifer suggest that the vulnerability of the aquifer as indicated by the fraction of young water is increasing over time.     

Numerical modelling of the saline interface in coastal karstic aquifers within a conceptual model uncertainty framework

Numerical modelling is increasingly used as a tool for improving management strategies in aquifers and to support the design of comprehensive projects considering natural and anthropogenic processes. Overall, numerical simulation in karstic aquifers poses a major scientific challenge due to the non-Darcian groundwater flow dynamics. In specific cases, the equivalent porous medium approach has shown acceptable results, particularly in poorly karstified aquifers with regional/subregional scales such as this case. The Yucatan coastal karstic aquifer (Mexico) has been defined as a complex regional heterogeneous system, partially confined, thus allowing the discussion of multiple conceptual models. In this research, a two-dimensional numerical model of flow and transport was implemented using SEAWAT for the NW Yucatan aquifer. Four likely conceptual models were audited, calibrated and verified using hydrogeological field data, to select the best one, considering their fit and complexity. The numerical model accuracy was evaluated using the root-mean-square error, Nash Sutcliffe efficiency and the Pearson coefficient. The Akaike information criterion and Bayesian information criterion were included for evaluating the complexity of the numerical models. In addition, the signal of tide propagation into the aquifer was assessed as a proxy to improve the numerical calibration process. Results show that the most complex numerical model has a better calibration than the simpler models, but the model accuracy is worse when compared to less complex numerical models in the verification exercise. This research offers enhancement in the knowledge of numerical modelling in heterogeneous coastal aquifers within a conceptual-model uncertainty setting.

     

Complementary use of tracer and pumping tests to characterize a heterogeneous channelized aquifer system in New Zealand

The combined use of pumping and tracer test data enabled the derivation of equivalent average hydraulic conductivities (K_avg) for each test in a heterogeneous channelized alluvial aquifer, whereas K values of the preferential flow paths were two orders of magnitude higher. Greater and earlier drawdown was generally observed along preferential flow lines in a pumping test, within an array of 21 wells. The study aim was to characterize hydraulic properties of a channelized aquifer system in New Zealand by combining tracer and pumping test data. Estimates were able to be made of the percentage of highly permeable channels within the profile (～1.2%), effective porosity that reflected the maximum fraction of highly permeable channels within the aquifer (?_eff–pc ～0.0038), and flows through highly permeable channels (～98%) and the sandy gravel matrix material (～2%). Using ?_eff–pc, a tracer test K_avg value (～93 m/day) was estimated that was equivalent to pumping test values (～100 m/day), but two orders of magnitude smaller than K calculated solely from transport through permeable channels (K_pc ～8,400 m/day). Derived K values of permeable and matrix material were similar to values derived from grain size distribution using the Kozeny-Carman equation.     

Multi-aquifer pumping test to determine cutoff wall length for groundwater flow control during site excavation in Tokyo, Japan

Multi-aquifer pumping tests, using a multi-screen pumping well and multi-level piezometers, were carried out for groundwater flow control in a large-scale excavation site in Tokyo, Japan. The site was underlain by multi-layered confined aquifers. In the tests, pumping was carried out using a multi-aquifer pumping well in which a screen depth was chosen arbitrarily. Changes in groundwater pressure heads in each aquifer were measured at each screen position of the multi-aquifer pumping well. Hydraulic conductivity (K) and specific storage (S _s) of not only aquifers, but also for low permeability layers between the aquifers, were estimated using the Cooper-Jacob method, and calibrated by a finite element method (FEM) groundwater model. Four different cutoff wall lengths were assumed for final excavation depth, and correlations among wall length, pumping discharge and drawdown at the back of the cutoff wall were obtained from simulations using the K and S _s parameters in the FEM model. Then, the most suitable wall length was selected based on the simulated correlations considering environmental condition, construction period and cost of the cutoff wall.     

Time constant of hydraulic-head response in aquifers subjected to sudden recharge change: application to large basins

Analytical formulae are proposed to describe the first-order temporal evolution of the head in large groundwater systems (such as those found in North Africa or eastern Australia) that are subjected to drastic modifications of their recharge conditions (such as those in Pleistocene and Holocene times). The mathematical model is based on the hydrodynamics of a mixed-aquifer system composed of a confined aquifer connected to an unconfined one with a large storage capacity. The transient behaviour of the head following a sudden change of recharge conditions is computed with Laplace transforms for linear one-dimensional and cylindrical geometries. This transient evolution closely follows an exponential trend exp(?t/τ). The time constant τ is expressed analytically as a function of the various parameters characterizing the system. In many commonly occurring situations, τ depends on only four parameters: the width a _c of the main confined aquifer, its transmissivity T _c, the integrated storage situated upstream in the unconfined aquifer M?=?S _u a _u, and a curvature parameter accounting for convergence/divergence effects. This model is applied to the natural decay of large aquifer basins of the Sahara and Australia following the end of the mid-Holocene humid period. The observed persistence of the resource is discussed on the basis of the time constant estimated with the system parameters. This comparison confirms the role of the upstream water reserve, which is modelled as an unconfined aquifer, and highlights the significant increase of the time constant in case of converging flow.