A “fractal” modification of Torricelli’s formula

A modification is proposed of Torricelli’s (1608–1647) formula for the velocity of water discharging from a small hole at the bottom of a large tank filled with fractal solid material. The new formula takes proper account of the mechanical energy losses due to flow in the solid matrix, thus expanding the area of validity of the classical Torricelli’s formula. Moreover, it offers a convenient alternative to Darcy’s law for estimating the discharge rate from an aquifer. The new formula was derived from laboratory experiments, with a low-Reynolds number discharge flow (Darcian flow). It was tested in a natural karst aquifer where the flow is non-Darcian, at Almiros spring on the island of Crete (Greece). In both cases, the predictive capability of the modified formula is established.     

Analysis of karst spring recession curves,west of Iran

The recession hydrographs of karst springs provide important information about aquifer characteristics such as storage properties and drainage potential, karstification degree, and other hydrological features. The Faresban, Famaasb, Gonbad-e-Kabood, and Gian springs are the important karst springs which drain main karst aquifers in west of Iran. In this study, we evaluate hydrological characteristics of these four karst springs using different analytic equations. Almost, all the recession curves were well fitted by a function that consists of three main exponential terms. The initial portion of the recession curve represents the fast drainage of large fractures and conduits, ending with the slowly decreasing curve, where the drainage of rock matrix and small fissures or baseflow is dominant. The Gian spring has the largest storage volume but the lowest drained water (7%). Using Mangin’s equation, it is apparent that the baseflow supplies over 85% of the total drained water to the Gian spring, while a small quantity of total outflow is made up of quickflow periods. Of the water available to the Famaasb, Faresban, and Gonbad-e-Kabood springs, 85, 80, and 70% are drained during period of baseflow, respectively, whereas the quickflow periods have minor importance in some springs. Based on the Coutagne’s equation results, it can be concluded that the catchment of the Famaasb and Gonbad-e-Kabood springs have a karstified saturation zone with drainage channels that provide a rapid discharge with little storage capacity. At Gian catchment area, the initial discharge is not as rapid as karstification but is fairly homogeneous throughout the aquifer.     

Development of a Darcy-Brinkman model to simulate water flow and tracer transport in a heterogeneous karstic aquifer (Val d’Orléans, France)

Darcy’s law is the equation of reference widely used to model aquifer flows. However, its use to model karstic aquifers functioning with large pores is problematic. The physics occurring within the karstic conduits requires the use of a more representative macroscopic equation. A hydrodynamic model is presented which is adapted to the karstic aquifer of the Val d’Orléans (France) using two flow equations: (1) Darcy’s law, used to describe water flow within the massive limestone, and (2) the Brinkman equation, used to model water flow within the conduits. The flow equations coupled with the transport equation allow the prediction of the karst transfer properties. The model was tested by using six dye tracer tests and compared to a model that uses Darcy’s law to describe the flow in karstic conduits. The simulations show that the conduit permeability ranges from 5?×?10^?6 to 5.5?×?10^?5?m² and the limestone permeability ranges from 8?×?10^?11 to 6?×?10^?10?m². The dispersivity coefficient ranges from 23 to 53 m in the conduits and from 1 to 5 m in the limestone. The results of the simulations carried out using Darcy’s law in the conduits show that the dispersion towards the fractures is underestimated.     

Development of a simple method for determining the influence radius of a pumping well in steady-state condition

Influence radius of a pumping well is a crucial parameter for hydrogeologists and engineers. Knowing the radius of influence for a designed drawdown enables one to calculate the pumping rate required to layout a project foundation that may need lowering of groundwater level to a certain depth due to dewatering operation. In addition, this is important for hydrogeologists to determine ground water contamination flow paths and contributing recharge area for domestic water supply and aquifer management purposes. Empirical formulas that usually neglect vital parameters to determine the influence radius accurately have been traditionally utilized due to lack of adequate methods. In this study, a physically based method, which incorporates aquifer hydraulic gradient for determining the influence radius of a pumping well in steady-state flow condition, was developed. It utilizes Darcy and Dupuit laws to calculate the influence radius, where Darcy's law and Dupuit equation, in steady-state condition, represent the inflow and the outflow of the pumping well, respectively. In an untraditional manner, this method can be also used to determine aquifer hydraulic conductivity as an alternative to other pumping test methods with high degree of accuracy. The developed method is easy to use; where a simple mathematical calculator may be used to calculate the influence radius and the pumping rate or hydraulic conductivity. By comparing the results from this method with the MODFLOW numerical model outputs with different simulated scenarios, it is realized that this method is much superior and more advantageous than other commonly used empirical methods.     

Interactions between the surface water and groundwater in the western shoreline of Lake Nasser, Upper Egypt

The present study indicates that the factors controlling the hydraulic relation between surface water and groundwater at the western lake shoreline change from one locality to another. This depends upon the lithological characteristics and the major structures. In the southern sectors, sedimentation at the bottom and sides of the lake prevents the water movement to the Nubian sandstone aquifer. The potentiometric map reveals that the water level altitudes range between 170 m in the vicinity of the lakeshore line and 110 m west of the lake. The groundwater flow lines show that the main recharge to the aquifer comes from the southwest direction, as well as from the lake inland to variable distances (about 30 Km). During the present study, Darcy’s law was applied to calculate the recharge from the western shoreline of Lake Nasser to the adjacent Nubian aquifer. The maximum value of seepage was at Garf Hussein (27.71?×?10⁶ m³/year), which may be related to high permeability and hydraulic gradient. Also, it may be related to the N–S strike faults that cut the area on both sides of the Lake, and the groundwater is expected to have free circulation through the faults of this trend. The minimum value was recorded in Adindan section (0.61?×?10⁶ m³/year). This may be related to the limited recharge from the lake to the aquifer, due to the sedimentation that dislocates this recharge.     

河南省新安县郁山铝土矿床水文地质特征

[摘 要] 基于区域水文地质条件研究,结合新安县郁山铝土矿床的地质结构特征,详细论述了郁 山铝土矿床的水文地质特征。矿区内主要含水层为碳酸盐岩类裂隙岩溶水含水层和碎屑岩类裂隙水含 水层,中等-弱富水性;主要隔水层为石炭系本溪组顶部泥岩、石炭-二叠系太原组泥岩隔水层( 顶板隔 水层)和石炭系本溪组中、下部泥岩隔水层( 底板隔水层)。大气降水和地下径流是矿区地下水的主要 补给来源,人工开采和泉是矿区地下水的主要排泄方式。断裂带具储水与导水性质,通常构成联通各含 水层的垂向通道。地下水是矿床充水的主要水源,地表水及大气降水为矿床充水的影响因素。充水通 道以渗入性通道为主,局部可以形成溃入性充水通道。所以,新安县郁山铝土矿为顶、底板直接充水的 水文地质条件中等复杂的以溶蚀裂隙为主的岩溶充水矿床。     

Using radon-222 to study coastal groundwater/surface-water interaction in the Crau coastal aquifer (southeastern France)

Radon has been used to determine groundwater velocity and groundwater discharge into wetlands at the southern downstream boundary of the Crau aquifer, southeastern France. This aquifer constitutes an important high-quality freshwater resource exploited for agriculture, industry and human consumption. An increase in salinity occurs close to the sea, highlighting the need to investigate the water balance and groundwater behavior. Darcy velocity was estimated using radon activities in well waters according to the Hamada “single-well method” (involving comparison with radon in groundwater in the aquifer itself). Measurements done at three depths (7, 15 and 21 m) provided velocity ranging from a few mm/day to more than 20 cm/day, with highest velocities observed at the 15-m depth. Resulting hydraulic conductivities agree with the known geology. Waters showing high radon activity and high salinity were found near the presumed shoreline at 3,000 years BP, highlighting the presence of ancient saltwater. Radon activity has also been measured in canals, rivers and ponds, to trace groundwater discharges and evaluate water balance. A model of the radon spatial evolution explains the observed radon activities. Groundwater discharge to surface water is low in pond waters (4 % of total inputs) but significant in canals (55 l/m²/day).     

Simulating flow in karst aquifers at laboratory and sub-regional scales using MODFLOW-CFP

Groundwater flow in a well-developed karst aquifer dominantly occurs through bedding planes, fractures, conduits, and caves created by and/or enlarged by dissolution. Conventional groundwater modeling methods assume that groundwater flow is described by Darcian principles where primary porosity (i.e. matrix porosity) and laminar flow are dominant. However, in well-developed karst aquifers, the assumption of Darcian flow can be questionable. While Darcian flow generally occurs in the matrix portion of the karst aquifer, flow through conduits can be non-laminar where the relation between specific discharge and hydraulic gradient is non-linear. MODFLOW-CFP is a relatively new modeling program that accounts for non-laminar and laminar flow in pipes, like karst caves, within an aquifer. In this study, results from MODFLOW-CFP are compared to those from MODFLOW-2000/2005, a numerical code based on Darcy’s law, to evaluate the accuracy that CFP can achieve when modeling flows in karst aquifers at laboratory and sub-regional (Woodville Karst Plain, Florida, USA) scales. In comparison with laboratory experiments, simulation results by MODFLOW-CFP are more accurate than MODFLOW 2005. At the sub-regional scale, MODFLOW-CFP was more accurate than MODFLOW-2000 for simulating field measurements of peak flow at one spring and total discharges at two springs for an observed storm event.     

Analytical descriptions of subaqueous groundwater seepage

Direct measurements of groundwater seepage show the importance of subaqueous discharges as sources of fresh water and of dissolved chemicals to lakes and the coastal ocean. The rate of seepage decreases rapidly offshore; an analytical solution was developed that describes the discharge as Ki(In(coth πxk/4l))/k where i is the hydraulic gradient, K is the vertical hydraulic conductivity,l is the aquifer thickness, x is the distance from the shoreline, and k² is K divided by the horizontal hydraulic conductivity. In addition to variations due to the inhomogeneities in the aquifer, seepage into the coastal ocean involves some recirculation of the salt water. In Great South Bay, New York measured fluxes were as great as 150 I m^?2 d^?1. The discharge near the shore was typically 50 I m^?2 d^?1, decreasing to 30 1 m^?2 d^?1 at a distance of 100 m offshore. Secondary convection due to an unstable density structure at the sediment-water interface may also be superimposed on the seepage distribution. Fingers of salt should be capable of carrying marine water many decimenters downward against the fresh groundwater advection. As a result, care must be exercised in interpreting direct measures of seepage flux to recognize the contribution of recirculated seawater.     

Quantitative analysis of springs

Growing demand for groundwater resources and stringent environmental concerns has led to large groundwater investigations, including characterization of aquifer systems that are hydraulically connected to springs. A pumping test is one of the most reliable means of quantifying hydraulic characteristics and the response of natural springs to pumping because it yields results that, in general, are representative of a larger area than are results from a single point observation. Recharge to the aquifer sustaining discharge from springs must be evaluated prior to the utilization of springs. The spring hydrograph is analyzed, as the shape of a hydrograph is a reflection of the response of the aquifer to recharge. The form and rate of recession provide significant information on the storage, lithological composition, and structural characteristics of the aquifer system sustaining the spring. Water tracing techniques have been developed and used over a period of centuries to delineate catchment boundaries, estimate groundwater flow velocities, determine areas of recharge, and identify sources of pollution of spring water.     

Modelling hydrostratigraphy and groundwater flow of a fractured and karst aquifer in a Mediterranean basin (Salento peninsula, southeastern Italy)

The control exerted by the hydrostratigraphic structure on aquifer recharge, groundwater flow and discharge along the coastal areas of a Mediterranean basin (Salento peninsula, about 5,000?km² wide, southern Italy) is assessed through the development and application of a groundwater flow model based on the reconstruction of the hydrostratigraphic architecture at the regional scale. The hydrostratigraphic model, obtained by processing surface and subsurface data, is applied to map the top of the main aquifer, which is hosted in the deep hydrostratigraphic unit corresponding to Cretaceous and Oligocene limestones with complex geometrical relationships with the sea. It is also used to estimate the aquifer recharge, which occurs by percolation through overlying younger sediments with low permeability. These data are completed with information about the soil use to estimate water abstraction for irrigation and with literature data to estimate the water abstraction for drinking and industrial purposes. The above-sketched conceptual model is the basis for a finite difference groundwater 2D pseudo-stationary flow model, which assumes the following fundamental approximations: the fractured and karst limestone hydrostratigraphic unit can be approximated, at the model scale, as a continuous medium for which the discrete Darcy??s law is valid; the transition zone between salt and fresh water is so small with respect to the grid spacing that the Ghyben?CHerzberg??s approximation for a sharp interface can be applied. Along the coastline different boundary conditions are assigned if the top of the limestone hydrostratigraphic unit lies either above the sea level (the aquifer has a free surface and fresh water is drained), or below the sea level (the aquifer is under pressure and the contact with sea occurs off-shore). The groundwater flow model correctly predicts the areas where the aquifer is fully saturated with salt water.     

Comparison of pumping at constant head and at a constant rate for determining the sustainable yield of a well

Determining the yield of a production well remains one of the main problems in hydrogeological studies. Starting from the results of a 3-year-long monitoring of a continuously exploited well functioning at constant head (i.e., at a variable discharge rate), a new pumping style has been examined using numerical models. The objective is to control the impact of pumping on the aquifer in accordance with the principle of sustainability. Different models were developed in a transient state and were calibrated using discharge data of the well during the recession periods. Successively, the trends of the residual outflow from the aquifer system with the well operating at variable discharge and at constant discharge were simulated. The results indicate that the ratio of the volume of water pumped from the well to the volume of residual outflow is a significant indicator of the sustainability of groundwater withdrawals. Modeling confirms that a constant discharge rate can be derived from the information gained through a preliminary production phase of a well at constant head. This approach appears to be particularly useful when the problem is determining the sustainable yield of a single well from aquifers with low hydraulic diffusivity.     

Vulnerability assessment of coastal aquifer system for irrigation suitability — A classical approach from southern India

The vulnerability of the shallow aquifer system for saline water intrusion has been evaluated using the classical tools at a coastal area, southern India. Groundwater samples (N=144) from Quaternary aquifer system within 25 km² area in pre- and post-monsoon seasons were analyzed for major ion chemistry including Electrical Conductivity (EC). The hydrochemical parameters are examined applying classical irrigation suitability tools. Based on their weight percentages (ratios in meq/l) the dominance of cations and anions was established as Na-Cl and Ca-SO₄ type. Results show that high hydraulic conductivity (10_?2 to 1 cm/s) of the sandy aquifer enhanced the vertical recharge leading to major spatial distribution suitable for irrigation use in post-monsoon. The overexploitation of groundwater resources has generated reversal of hydraulic gradient enhancing salinity intrusion from marine sources in pre-monsoon. Further, the Differential Global Positioning System (DGPS) survey and water level measurements are assessed to demarcate the study area into zones of water table ‘above mean sea level (amsl)’ and ‘below mean sea level (bmsl)’. It was deduced that, the industrial effluent and seawater were the prime sources of groundwater salinity of water table ‘amsl’ and ‘bmsl’ zones, respectively. The area up to 600 m from marine source is found vulnerable which is falling under ‘Unsuitable’ category of irrigation classifications. The remedial measures are also framed to protect further extension of aquifer vulnerability for sustainable agriculture.     

Hydrogeology,water quality,and microbial assessment of a coastal alluvial aquifer in western Saudi Arabia: potential use of coastal wadi aquifers for desalination water supplies

Wadi alluvial aquifers located along coastal areas of the Middle East have been assumed to be suitable sources of feed water for seawater reverse osmosis facilities based on high productivity, connectedness to the sea for recharge, and the occurrence of seawater with chemistry similar to that in the adjacent Red Sea. An investigation of the intersection of Wadi Wasimi with the Red Sea in western Saudi Arabia has revealed that the associated predominantly unconfined alluvial aquifer divides into two sand-and-gravel aquifers at the coast, each with high productivity (transmissivity?=?42,000 m²/day). This aquifer system becomes confined near the coast and contains hypersaline water. The hydrogeology of Wadi Wasimi shows that two of the assumptions are incorrect in that the aquifer is not well connected to the sea because of confinement by very low hydraulic conductivity terrigenous and marine muds and the aquifer contains hypersaline water as a result of a hydraulic connection to a coastal sabkha. A supplemental study shows that the aquifer system contains a diverse microbial community composed of predominantly of Proteobacteria with accompanying high percentages of Gammaproteobacteria, Alphaproteobacteria and Deltaproteobacteria.     

鄂尔多斯盆地北部深埋煤层工作面涌水量预测方法

鄂尔多斯盆地北部侏罗纪深埋区中生代地层以河流相沉积为主,呈分阶段的多旋回演化特点,导致煤层顶板含隔水层交替分布;由于地表大部分为毛乌素沙漠,降水入渗补给系数大,第四系松散层储水能力强,充足的补给水源造成煤层顶板直接充水含水层富水性较强,其中最主要的充水含水层为七里镇砂岩,以七里镇砂岩为关键层,将煤层至七里镇砂岩概化为一...     

Re-evaluating the US Geological Survey’s pumping tests (1967) in the Punjab region of Pakistan for use in groundwater studies

In 1967, the US Geological Survey (USGS) published the results of 141 pumping tests carried out throughout the Pakistani Punjab to establish representative hydraulic parameters of its large aquifer. Many authors have since concluded that the USGS had over-estimated the horizontal hydraulic conductivity (k _r) by 25–100 %, leaving vertical anisotropy and aquifer depth unresolved. No test wells have ever been drilled below 450 m to reach the base of the aquifer, although petroleum explorations mention depths between 1,500 and 4,500 m. After comparison and re-evaluation of all related papers, this study concludes that the USGS interpretation was correct, that its hydraulic values still stand without change, and that the USGS’s applied distance drawdown interpretation is valid to prevent influence of partial penetration on the results. This study also uniquely resolved vertical anisotropy and aquifer thickness by using early- and late-time drawdowns separately and proper scaling of the coordinates, which has often been omitted. With appropriate scaling, all interpretations match the data. The representative hydraulic aquifer values are: k _r?=?65 m/d, vertical anisotropy k _r/k _z?=?25 and aquifer depth 500–1,500 m. The conclusion is that these values can be used, at least as first estimates, for groundwater studies in the Pakistani Punjab.     

朝阳露天采区水文地质特征与矿坑充水因素分析

通过对朝阳勘查区露天采区的三个含水层和三个隔水层特征、地下水的补给、径流和排泄条件及含水层之间的水力联系等因素分析，认为三个含水层对矿坑均有充水影响，并预计了各含水层对矿坑的充水水量，为今后矿坑疏干排水提供了依据。     

Identification and regional quantification of hydrochemical processes at the contact zone between anoxic groundwater and surface water in poldered floodplains (Oderbruch polder,Germany)

The hydrochemistry in the largest polder of the Oder River, named Oderbruch, is affected by long-term infiltration of water from the Oder into the aquifer below an alluvial loamy top layer of the polder. These exceptional hydraulic conditions are a result of dyke constructions which were built more than 250 a ago. The objective of this investigation is a better understanding and a characterisation of the contact zone between the anaerobic groundwater and the surface water of a vast drainage system. Induced by changing water levels, different hydraulic conditions occur, which strongly influence the hydrochemistry of the shallow aquifer and therefore the natural sink function of the polder area.Field investigations with a hydrochemical and hydraulic characterisation of selected drainage ditch locations show considerable chemical interactions between groundwater and surface water. Depending on the drainage ditch type, which is defined by the hydraulic situation, the redox processes create a chemical gradient combined with a distinct enrichment of Fe and Mn. The source of the high amounts of Fe and Mn in the groundwater are reduced Fe- and Mn-hydroxides from the aquifer sediments.Under exfiltrating conditions interrupted by dry phases, more than 50 g kg⁻¹ Fe and 0.25 g kg⁻¹ Mn have accumulated in the drainage ditch floor sediments since the construction of the drainage ditches 35 a ago. The results show a very effective fixation of trace metals in the drainage ditch sediments under these conditions. Under permanent exfiltration conditions, the enrichment of Fe and Mn is relatively low. The maximum Fe content was 4 g kg⁻¹ sediment and the Mn content reached only 0.4 g kg⁻¹. This is less than 10% of the mobile Fe²⁺ and less than 1% of the Mn²⁺ which migrates from the aquifer into the surface water.     

软土地层浅埋圆形隧道非达西渗流场解析研究

软土在低水力坡降下的渗流会偏离达西定律,即为非达西渗流模式。假设孔隙水渗透服从指数渗流模式,采用镜像法原理推导了浅埋单孔和双孔圆形隧道非达西渗流场的解析解。结合算例,对浅埋圆形隧道非达西渗流解析解与达西渗流解析解进行了对比分析与验证,并对非达西渗流指数、隧道周围土体与衬砌渗流系数比值对隧道渗流场的影响进行了讨论。结果表明：非达西渗流指数、渗流系数比值对隧道渗流量和周围土体孔压均有较大的影响;随着渗流指数逐渐增大,土体内水头损失加快,隧道周围土体孔压及渗流量逐渐减小;随着土体与衬砌渗流系数比值逐渐增大,衬砌排水能力增强,隧道渗流量逐渐增大,隧道周围土体孔压减小更大。     

Application of genetic algorithm technique to inverse modeling of tide–aquifer interaction

Modeling of tide–aquifer interaction plays a vital role in the management of coastal aquifer systems. A novel and robust methodology is presented in this paper for estimating aquifer parameters of coastal aquifers from tide–aquifer interaction data using tide–aquifer interaction model and genetic algorithm (GA). Two stand-alone computer programs were developed to optimize hydraulic diffusivities of unconfined and confined coastal aquifers at multiple sites using GA technique and tide–aquifer interaction model and considering two approaches (‘lumped tidal component approach’ and ‘multi-tidal component approach’). Five sets of real-world tide–aquifer interaction data at two sites of an unconfined aquifer and one set of tide–aquifer interaction data at three sites of a confined aquifer were used to demonstrate the efficacy of the methodology. The analysis of the GA-based inverse modeling results indicated that the ‘multi-tidal component approach’ yields more accurate and reliable hydraulic diffusivities for the unconfined aquifer (RMSE = 0.0129–0.0521 m, NSE = 0.70–0.97, and d1 = 0.91–0.99) as well as for the confined aquifer (RMSE = 0.0204–0.0545 m, NSE = 0.95–0.97, and d1 = 0.99) compared with the ‘lumped tidal component approach’. A comparative evaluation of data-size revealed that the short-duration datasets of the unconfined aquifer provide more reliable estimate of hydraulic diffusivity than the long-duration datasets. Further, it was found that the spring and neap tidal data yield unreasonable values of hydraulic diffusivity with considerably high values of RMSE and very low values of r ², NSE, and d1, thereby suggesting that spring and neap tidal data are not suitable for aquifer parameter estimation. Overall, it is concluded that the GA-based tide–aquifer interaction model following ‘multi-tidal component approach’ is the most efficient tool for estimating aquifer parameters of unconfined and confined aquifers from tide–aquifer interaction data. The developed methodology is also applicable to other coastal basins of the world irrespective of hydrogeological settings.