Parameter identification for leaky aquifers using global optimization methods

In the past, graphical or computer methods were usually employed to determine the aquifer parameters of the observed data obtained from field pumping tests. Since we employed the computer methods to determine the aquifer parameters, an analytical aquifer model was required to estimate the predicted drawdown. Following this, the gradient‐type approach was used to solve the nonlinear least‐squares equations to obtain the aquifer parameters. This paper proposes a novel approach based on a drawdown model and a global optimization method of simulated annealing (SA) or a genetic algorithm (GA) to determine the best‐fit aquifer parameters for leaky aquifer systems. The aquifer parameters obtained from SA and the GA almost agree with those obtained from the extended Kalman filter and gradient‐type method. Moreover, all results indicate that the SA and GA are robust and yield consistent results when dealing with the parameter identification problems. Copyright © 2006 John Wiley & Sons, Ltd.     

Aquifer parameter estimation using an incremental area method

Theoretical well functions have been derived over the years to predict ground water level behaviour in aquifer systems under stress owing to groundwater extraction. The drawdown data collected during pump tests are typically analysed using graphical curve‐matching procedures to estimate aquifer parameters based on these well functions. Difficulty in aquifer characteristic identification and parameter estimation may arise when the field data do not perfectly match the drawdown curves obtained from the well functions. The present study provides a new method for the interpretation of aquifer pump tests which supplements the existing curve‐matching procedures in case ideal conditions do not exist; the proposed method provides a greater degree of flexibility in the data analysis for diagnostic tool purposes. The method, referred to as the Incremental Area Method (IAM) is based on integrating the logarithmic‐based drawdown curves within a discrete time and matching the results with a corresponding time integral of the Theis ( 1935 ) Well Function which governs ideal confined aquifers. The application of the proposed method to synthetically generated data and field data showed that IAM represents a viable method which yields information on potential non‐idealness of the aquifer and provides aquifer parameter estimates thus potentially overcoming drawdown data curve‐matching difficulties. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Multivariate approaches optimize locations of groundwater pumping facilities for different hydrogeological scales

A number of optimization approaches regarding the design location of groundwater pumping facilities in heterogeneous porous media have elicited little discussion. However, the location of groundwater pumping facilities is an important factor because it affects water resource usage. This study applies two optimization approaches to estimate the best recharge zone and suitable locations of the pumping facilities in southwestern Taiwan for different hydrogeological scales. First, for the regional scale, this study employs numerical modelling, MODFLOW‐96, to simulate groundwater direction and the optimal recharge zone in the study area. Based on the model's calibration and verification results, this study preliminarily utilizes the simulated spatial direction of groundwater and compares the safe yield for each well group in order to determine the best recharge zone. Additionally, for the local scale, the micro‐hydrogeological characteristics are considered before determining the design locations of the pumping facilities. According to drawdown record data from six observation wells derived from pumping tests at the best recharge area, this study further utilizes the modified artificial neural network approach to improve the accuracy of the estimation parameters as well as to analyse the direction and anisotropy of the hydraulic conductivities of an equivalent homogeneous aquifer. The results suggested that the best locations for the pumping facilities are along the more permeable major direction. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

Identification of illegal groundwater pumping in semi-confined aquifers

Abstract

Illegal pumping from underground reservoirs is approached as an inverse problem. The procedure seeks among a set of suspected potential areas the ones from which water is effectively pumped out (or in) and at what rate does this take place? Influence coefficient and finite element are combined in order to simulate the aquifer response to hypothetical pumping scenarios. Then the optimal scenario which makes of simulated head distribution the best fit to the observed headset is retained as solution to the foregoing question. This optimal scenario is derived by minimizing the classical least squares error using the Levenberg-Marquardt Algorithm (LMA). Under the conditions of the treated aquifer example it is observed that LMA is non-convergent unless a regularizing measure is taken during the calculation of the correction applied to the parameter-vector between two successive iterations. The procedure is tested with uniform and non-uniform pumping. In both cases, it yields good identified pumping rates within the observation period, but its performance deteriorates markedly for the rates corresponding to the days when no monitoring well is yet active.

Citation Saffi, M. & Cheddadi, A. (2010 Saffi, M. 2008. Contribution of Influence Coefficients in Solving Groundwater Problems, Rabat, Morocco: Mémoire d'Habilitation Universitaire, Ecole Mohammadia d'Ingénieurs.  [Google Scholar]) Identification of illegal groundwater pumping in semi-confined aquifers. Hydrol. Sci. J. 55(8), 1348–1356.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

Assessment of hydrogeological conditions in basement aquifers of the Precambrian Oban massif, southeastern Nigeria

A combined analysis of lineament length density from radar imagery and surface resistivity data is used to assess the hydrogeological conditions in the Oban massif, Nigeria. The results show that the data guided the qualitative and quantitative estimation of some aquifer parameters. These include resistivity of the water bearing formations (280–740 ω m), thickness (5–140 m), limited hydraulic conductivity (8.53-13.18 m/day) and transmissivity (410.65–725.88 m²/day) data. In addition, the lineament length density for the area ranged between less than 0.2 to slightly more than 0.4. Site evaluation for the location of productive boreholes/wells using a groundwater potential index (GWPI) indicates that areas with a GWPI of greater than 35 are consistent with relatively high yield.     

Performance of the steady-state dipole flow test in layered aquifers

Steady-state numerical simulations of the dipole flow test in layered aquifers demonstrate that the test produces a good estimate of the equivalent hydraulic conductivity anisotropy ratio for the part of the aquifer spanned by the well chambers. The effects of chamber size, different conductivity of layers and layer location on the estimated anisotropy ratios are presented. The steady-state dipole flow test, when performed at different levels in the well, can yield estimates of the down-hole anisotropy ratio distribution. Numerical simulations also illustrate that the skin effect can significantly distort the anisotropy estimates produced by the dipole flow test. © 1997 John Wiley & Sons, Ltd.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

The role of hydrogeological setting in two Canadian peatlands investigated through 2D steady-state groundwater flow modelling

This study investigated how hydrogeological setting influences aquifer–peatland connections in slope and basin peatlands. Steady-state groundwater flow was simulated using Modflow on 2D transects for an esker slope peatland and for a basin peatland in southern Quebec (Canada). Simulations investigated how hydraulic heads and groundwater flow exported toward runoff from the peatland can be influenced by recharge, hydraulic properties, and heterogeneity. The slope peatland model was strongly dominated by horizontal flow from the esker. This suggests that slope peatlands are dependent on the hydrogeological conditions of the adjacent aquifer reservoir, but are resilient to hydrological changes. The basin peatland produced groundwater outflow to the surface aquifer. Lateral and vertical peat heterogeneity due to peat decomposition or compaction were identified as having a significant influence on fluxes. These results suggest that basin peatlands are more dependent on recharge conditions, and could be more susceptible to land use and climate changes.     

Identification of aquifer parameters from residual drawdowns: an optimization approach

Abstract

An optimization method based on nonlinear least squares is proposed for the identification of aquifer transmissivity and two storage coefficients, one for the pumping phase and the other for the recovery phase, using only residual drawdowns at an observation well. The method is applicable irrespective of whether pumping and recovery storage coefficients are the same or are different and the argument of well function during recovery is less than or greater than 0.01. The method can check for the changed value of storage coefficient during the recovery phase and can quantify this change. Use of the method is illustrated through examples, which show that the parameters are estimated reliably.     

Inversion of interference hydraulic pumping tests in both homogeneous and fractal dual media

This work proposes a complete method for automatic inversion of data from hydraulic interference pumping tests based on both homogeneous and fractal dual-medium approaches. The aim is to seek a new alternative concept able to interpret field data, identify macroscopic hydraulic parameters and therefore enhance the understanding of flow in porous fractured reservoirs. Because of its much contrasted sensitivities to parameters, the dual-medium approach yields an ill-posed inverse problem that requires a specific optimization procedure including the calculation of analytical sensitivities and their possible re-scaling. Once these constraints are fulfilled, the inversion proves accurate, provides unambiguous and reliable results. In the fractal context inverting several drawdown curves from different locations at the same time reveals more accurate. Finally, hydraulic parameters drawn from inversion should be taken into account to improve in various situations the conditioning of up-scaled flow in fractured rocks.     

Integration of aquifer geology,groundwater flow and arsenic distribution in deltaic aquifers – A unifying concept

Groundwater arsenic (As) presents a public health risk of great magnitude in densely populated Asian delta regions, most acutely in the Bengal Basin (West Bengal, India and Bangladesh). Research has focused on the sources, mobilisation, and heterogeneity of groundwater As, but a consistent explanation of As distribution from local to basin scale remains elusive. We show for the Bengal Aquifer System that the numerous, discontinuous silt‐clay layers together with surface topography impose a hierarchical pattern of groundwater flow, which constrains As penetration into the aquifer and controls its redistribution towards discharge zones, where it is re‐sequestered to solid phases. This is particularly so for the discrete periods of As release to groundwater in the shallow subsurface associated with sea level high‐stand conditions of Quaternary inter‐glacial periods. We propose a hypothesis concerning groundwater flow ( S ilt‐clay layers I mpose H ierarchical groundwater flow patterns constraining A rsenic progression [SIHA]), which links consensus views on the As source and history of sedimentation in the basin to the variety of spatial and depth distributions of groundwater As reported in the literature. SIHA reconciles apparent inconsistencies between independent, in some cases contrasting, field observations. We infer that lithological and topographic controls on groundwater flow, inherent to SIHA, apply more generally to deltaic aquifers elsewhere. The analysis suggests that groundwater As may persist in the aquifers of Asian deltas over thousands of years, but in certain regions, particularly at deeper levels, As will not exceed low background concentrations unless groundwater flow systems are short‐circuited by excessive pumping.     

Simulation of the spatio‐temporal extent of groundwater flooding using statistical methods of hydrograph classification and lumped parameter models

This article presents the development of a relatively low cost and rapidly applicable methodology to simulate the spatio‐temporal occurrence of groundwater flooding in chalk catchments. In winter 2000/2001 extreme rainfall resulted in anomalously high groundwater levels and groundwater flooding in many chalk catchments of northern Europe and the southern United Kingdom. Groundwater flooding was extensive and prolonged, occurring in areas where it had not been recently observed and, in places, lasting for 6 months. In many of these catchments, the prediction of groundwater flooding is hindered by the lack of an appropriate tool, such as a distributed groundwater model, or the inability of models to simulate extremes adequately. A set of groundwater hydrographs is simulated using a simple lumped parameter groundwater model. The number of models required is minimized through the classification and grouping of groundwater level time‐series using principal component analysis and cluster analysis. One representative hydrograph is modelled then transposed to other observed hydrographs in the same group by the process of quantile mapping. Time‐variant groundwater level surfaces, generated using the discrete set of modelled hydrographs and river elevation data, are overlain on a digital terrain model to predict the spatial extent of groundwater flooding. The methodology is applied to the Pang and Lambourn catchments in southern England for which monthly groundwater level time‐series exist for 52 observation boreholes covering the period 1975–2004. The results are validated against observed groundwater flood extent data obtained from aerial surveys and field mapping. The method is shown to simulate the spatial and temporal occurrence of flooding during the 2000/2001 flood event accurately. British Geological Survey © NERC 2011. Hydrological Processes © 2011 John Wiley & Sons, Ltd.     

ARX结构模态参数识别方法对比(I)——基于理论地震反应时程的对比

结构参数识别是结构抗震安全性能鉴定和健康诊断的基础。利用地震观测记录来识别结构模态参数,是地震工程领域备受关注的研究课题之一。本文利用三层平面框架结构的理论地震反应时程,对一维、多维和整体ARX模型三种模态参数识别方法进行了对比分析。结果表明：整体ARX模型的识别结果较为稳定且精度较高,更适合于进行多自由度结构参数识别。     

Simulation of groundwater flow in a crystalline rock aquifer system in Southern Ghana – An evaluation of the effects of increased groundwater abstraction on the aquifers using a transient groundwater flow model

Monitored groundwater level data, well logs, and aquifer data as well as the relevant surface hydrological data were used to conceptualise the hydrogeological system of the Densu Basin in Southern Ghana. The objective was to numerically derive the hydraulic conductivity field for better characterization of the aquifer system and for simulating the effects of increasing groundwater abstraction on the aquifer system in the basin. The hydraulic conductivity field has been generated in this study through model calibration. This study finds that hydraulic conductivity ranges between a low of 2 m/d in the middle sections of the basin and about 40 m/d in the south. Clear differences in the underlying geology have been indicated in the distribution of aquifer hydraulic conductivities. This is in consonance with the general assertion that the hydrogeological properties of the aquifers in the crystalline basement terrains are controlled by the degree of fracturing and/or weathering of the country rock. The transient model suggest aquifer specific storage values to range between 6.0 × 10^?5 m^?1 and 2.1 × 10^?4 m^?1 which are within acceptable range of values normally quoted for similar lithologies in the literature. There is an apparent subtle decrease in groundwater recharge from about 13% of the annual precipitation in 2005 to about 10.3% of the precipitation in 2008. The transient model was used to simulate responses of the system to annual increment of groundwater abstraction by 20% at the 2008 recharge rates for the period 2009 – 2024. The results suggest that the system will not be able to sustain this level of abstraction as it would lead to a basin wide drawdown in the hydraulic head by 4 m by the end of the prediction period. It further suggests a safe annual increment in groundwater abstraction by 5% under business as usual recharge conditions. Identification and protection of groundwater recharge areas in the basin are recommended in order to safeguard the integrity of the resource under the scenario of increased abstraction for commercial activities in the basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Deciphering groundwater flow between the Complex Terminal and Plio-Quaternary aquifers in Chott Gharsa plain (southwestern Tunisia) using isotopic and chemical tools

Abstract

The Complex Terminal (CT) and Plio-Quaternary (P-Q) aquifers in the Chott Gharsa plain in southwestern Tunisia have been investigated with the aid of chemical and isotopic tools. It has been demonstrated that groundwater from the CT is mainly of palaeo-origin, especially in the western and central parts of the plain where the most negative values of δ¹⁸O and δ²H were observed (between??8.1 and??7.6‰ for δ¹⁸O, and??60 to??57‰ for δ²H), combined with low concentrations of radiocarbon (6.8–7.5 pmc) and absence of tritium. Modern recharge of the aquifer occurs only in the eastern part of the system where younger waters were observed, as indicated by their stable isotope composition, relatively high radiocarbon content and presence of tritium. Groundwater from the P-Q multi-layer aquifer represents mixtures of ascending deep CT waters and modern water recharging the P-Q aquifer system. Isotope mass balance was used to quantify mixing proportions. The calculations showed that the contribution of deep CT groundwater to the P-Q aquifer system reaches about 75% in the western and central parts of the plain where the CT aquifer remains strongly artesian. This contribution decreases to about 15% towards the eastern part of the plain, as a consequence of significant reduction of artesian pressure in this area of the CT aquifer. Chemical data suggest that mineralization of the studied groundwater systems is controlled mainly by dissolution of evaporative minerals (halite, anhydrite and gypsum) and cation exchange reactions with the matrix, possibly enhanced by recent anthropogenic disturbance of the system caused by lowering of the water table due to heavy exploitation and return flow of saline irrigation water into the P-Q aquifer.

Editor D. Koutsoyiannis; Associate editor E. Custodio

Citation Yangui, H., Abidi, I., Zouari, K., and Rozanski, K., 2012. Deciphering groundwater flow between the Complex Terminal and Plio-Quaternary aquifers in Chott Gharsa plain (southwestern Tunisia) using isotopic and chemical tools. Hydrological Sciences Journal, 57 (5), 967–984.