DYNAMIC RESPONSE OF AQUIFER SYSTEMS TO LOCALIZED RECHARGE1

ABSTRACT. The response of stream-unconfined aquifer systems to localized recharge is investigated by means of a two-dimensional finite element model. A variational approach is used in conjunction with the finite element method to solve the ground water flow equation. Linear approximated triangular elements are used to calculate the hydraulic head distribution in the flow region. The Crank-Nicholson centered scheme of numerical integration is employed to approximate the time derivative in the flow equation. A computer program is developed to calculate the hydraulic head distribution in the flow region. Solutions provided by the finite element model should prove useful in the evaluation of quantitative and qualitative changes in aquifer systems due to natural or artificial recharge. In addition, they should prove useful in the study of irrigation and drainage problems.     

OPTIMAL ESTIMATION OF CONTAMINANT TRANSPORT IN GROUND WATER1

ABSTRACT: Finite element and finite difference representations of the convective-dispersive equation have been widely used in determining contaminant transport in ground water. Due to inherent uncertainties of the transport process, those representations are inexact and contain errors. Errors in field measurements are unavoidable. By combining a numerical model, a measurement equation, and the Kalman filter, optimal estimates of the state variable (contaminant concentration) can be obtained. This paper describes the algorithm and gives a numerical example of contaminant transport in a two-dimensional ground water flow. The results show significant improvement in the estimated concentration distribution by using the filtering technique.     

Development and Integration of a Groundwater Simulation Model to an Open Geographic Information System

This study presents the implementation of a spatial decision support system (SDSS) named ARENA. The program has been developed based on object‐oriented concepts using the Java programming language. The SDSS is made up of a groundwater simulation tool coupled to an open geographic information system (open GIS). Both the open GIS and groundwater simulation package share common spatial and nonspatial entities during the modeling process. A dedicated interface provides direct access to the GIS data without the need of external files. The finite element method is used to solve the partial differential equation that governs groundwater flow. The system implementation is presented by depicting the main classes and coupling procedures. A study case demonstrates the applicability of the simulation tool.     

IDENTIFICATION OF AQUIFER DISPERSIVITIES: METHODS OF ANALYSIS AND PARAMETER UNCERTAINTY1

ABSTRACT: This paper presents a method for estimating aquifer dispersivities in solute transport models. Sensitivity equations are derived for the calculation of sensitivity coefficients. A modified Gauss-Newton algorithm is used to perform the least-squares minimization. A statistical procedure is outlined to assess reliability of the estimated parameters. The solute transport model is solved by the upstream weighted, multiple cell balance method which combines the concepts of local mass balance and finite element approximations. A one-dimensional solute transport problem in a vertical column system is first used to illustrate the inverse technique. A second example considers the parameter identification problem for three-dimensional solute transport with a unidirectional steady and uniform flow field. The third example solves the parameter identification problem in a three-dimensional, stream-aquifer, solute transport system with steady state flow. Numerical experiments are conducted to study data requirements for parameter identification.     

ANALYSIS OF ROCK STRESS AROUND A LIQUID WASTE INJECTION SYSTEM IN ILLINOIS1

: The danger to the environment associated with the injection of liquid industrial wastes into a deep, confined, subsurface rock formation may arise from the transport of the waste laterally or vertically in the formation. The pattern of lateral transport, which can take place as a result of convection as well as dispersion and diffusion, can be determined by an approximate analytical solution to the mass transport equation. Vertical transport may take place through both natural fractures and fractures created by hydrostatic stresses generated around the well during injection. To determine the stresses, we used the finite element method to get a numerical solution of the flow equation. We applied a solution of the flow equation to calculate the stress buildup and decay for the Jones & Laughlin Steel Corporation's injection well near Hennepin in Putnam County, Illinois. According to our computations, the stress buildup due to injection is about 0.16 pounds per square inch per foot - psi - (0.362 Newton per square centimeter per meter), which, added to normal pressure, makes an estimated total stress of 0.60 psi/ft (1.36 Newton/cm²/m). That pressure is insufficient to cause fracturing of the Cambrian Eau Claire aquitard, the confining bed for the disposal zone.     

Prediction of groundwater contamination with multivariate regression and probabilistic capture zones

Probabilistic capture zones are combined with a regression model and used as buffer zones around wells for Tobit regression analysis to predict contaminant concentration of groundwater in an agricultural region. A backward transport equation, which is a mathematical model based on the physical processes of solute transport, is used to delineate probabilistic capture zones. The probabilistic capture zone defines the area where contaminant discharge can have a direct influence, with pertinent probability, on the quality of groundwater pumped from a well. Tobit regression analysis is used to find the relationship between independent regression variables and a dependent variable, which is contaminant concentration in this study. The capture zone and the regression are combined into a model, and its applicability for prediction of nitrate concentration is tested in a small agricultural basin in Chuncheon, Korea, which is occupied mainly by vegetation fields, orchards, and small barns. Three cases of Model 1, Model 2, and Model 3 are compared in which buffer zones are circles, capture zones with probability over 0.1, and capture zones divided into sections with different probabilities, respectively. The resulting regression model describes nitrate concentration in terms of selected independent variables. When the concentrations are calculated with the model, the best fit with the observed concentrations was in Model 3. This result supports the applicability of the method proposed in this study to prediction of contaminant concentration of groundwater.     

COMPARATIVE STUDY OF FRESH-SALT WATER INTERFACES USING FINITE ELEMENT AND SIMPLE APPROACHES

ABSTRACT: The fresh-salt water interface in artesian aquifers has been investigated by various techniques on the basis of its analogy to the free surface in earth dams or cores of dams. Although various approximations are used, some more or less exact solutions exist. One of the simple methods, that would appeal to practical workers, was developed by the analysis of hydraulic forces. However, this method has not been checked thoroughly due to the lack of wide ranges of coverage by the more or less exact solutions. In this paper a suggested finite element method is used for the purpose of comparing with the method of hydraulic forces. The presented procedure eliminates some of the difficulties and uncertainties in current finite element procedures. Both methods proved to be in close agreement. Moreover, the hydraulic heads along the upper boundary of the artesian aquifer were found to be in close agreement with Dupuit's equation. The results of this investigation would greatly simplify the more complex management problems when the effects of discharge and/or recharge wells are added to the natural flow effects.     

NONLINEAR DUPUIT EQUATIONS FOR THE PHREATIC SURFACE OF A SEMI-INFINITE AQUIFER1

ABSTRACT. We present a new approach to the nonlinear equations for the phreatic surface of groundwater flow from or into a reservoir. The differential equation is converted into an equivalent integral equation, which is then solved by a method of iteration. We obtain exact results for both drawdown and infiltration, including the special case of groundwater penetration into dry soil.     

沈阳市某装备制造产业园地下水污染物运移模拟研究

为摸清沈阳市某装备制造产业园地下水污染运移规律,科学指导当地生态环境管理部门开展工作,以该园区为研究对象,采用有限差分法,建立了该区域地下水水流数值模型,并利用地下水数值模拟软件(GMS软件)模拟预测了连续源强和瞬态源强污染物泄漏情景下1年、5年、10年及20年后污染物在地下水中的运移情况.经计算得到结论如下:①连续源...     

NUMERICAL AND ANALYTICAL SOLUTIONS OF DISPERSION IN A FINITE,ADSORBING POROUS MEDIUM1

ABSTRACT Numerical and analytical solutions are developed for the distribution of a contaminant within an adsorbing porous medium in a unidirectional flow field subject to a step function for input concentration. The medium is considered to be homogeneous, isotropic, and areally finite. As a by-product, solutions are also obtained for the case of a non-absorbing porous medium. An example that demonstrates the applicability of the solutions is presented.     

Modelling hydroenvironmental and health risk assessment parameters along the South Wales Coast

This paper highlights the increasing concerns relating to hydroenvironmetal issues and cites recent examples of the challenges now being regularly faced by hydroenvironmetal scientists and engineers. The limitations and restrictions of both physical (or laboratory) and numerical (or computer based) hydraulic models used in the planning and management of aquatic basins are discussed. General details are given of numerical models used for flow and water quality concentration predictions in estuarine waters, with particular application to the challenges occurring along the South Wales coast. A highly accurate and non-diffusive finite difference scheme that solves the transport equation for predicting water quality indicators and suspended sediment concentration distributions is also discussed. In particular, details are outlined of the extension of the water quality indicators of faecal coliforms, as required to comply with the EU Bathing Water Directive, to predict health risk assessment, in the form of predicting the risk of gastroenteritis. Three example research projects along the South Wales coast are described; the projects involve the application of two-dimensional and three-dimensional hydroenvironmetal models to predict flow patterns and water quality indicator organism distributions in the coastal receiving waters. These studies include: (i) a curvilinear finite difference approach to modelling flows in the Bristol Channel, (ii) coastal health risk predictions in Swansea Bay using combined water quality and epidemiological models, and (iii) combined sewer overflow discharges into Cardiff Bay.     

Solute movement through an allophanic soil

Allophanic soils are widespread around the world, but little research has been done on their transport properties. This study reveals the effect of two soil water potential heads and two water-flow regimes of continuous and intermittent flow on solute transport through undisturbed soil columns of Horotiu silt loam (Typic Hapludand), an allophanic soil. Two different methods--breakthrough curves (BTCs) and time domain reflectometry (TDR)--were employed to determine the extent of preferential solute transport in the topsoil. The TDR data were also used to look at the depth dependence of the transport properties. The convection-dispersion equation (CDE) with the appropriate boundary conditions adequately described the movement of both Br and Cl under the various flow conditions. Although no preferential flow was found under the imposed unsaturated flow conditions, the flow of water and transport of solute became more uniform with depth. The results show that both Br and Cl are retarded in this allophanic soil. Retardation values range from 1.5 to 1.9, and, as the TDR data showed, increase from the depth of 5.0 to 10.0 cm. Intermittent leaching results showed that there was no effect on solute concentrations in the leachate following no-flow periods. This suggests that water and solute transport in this soil were either relatively uniform or that transverse mixing during flow was already fast enough to eliminate concentration gradients between regions of different "mobility."     

A DISTRIBUTED DYNAMIC WATERSHED MODEL1

ABSTRACT: A distributed watershed model was developed to mathematically simulate overland and channel flow for a single-event storm. The modeled watersheds in the study were subdivided into rectangular grid elements. All hydrologically significant parameters, such as land slope, rainfall and precipitation excess, were assumed to be uniform within each element. The Green-Ampt method was adopted to generate precipitation excess for each element during the simulation period. A two-dimensional diffusion wave model was used for overland flow routing and an iterative Alternative Direction Implicit scheme was used to solve the simultaneous overland flow equations. Once the overland flow became inflow to the channel, a one-dimensional dynamic wave flood routing technique, based on a four-point, implicit, non-linear finite difference solution of the St. Venant equation of unsteady flow, was applied. A limited number of comparisons were made between simulated and observed hydrographs for areas of about one square mile. Given the appropriate parameters, the model was able to accurately simulate runoff for single-event storms. This paper describes a distributed watershed model developed to simulate overland and channel flow. Comparisons were made between simulated and observed hydrographs for three watersheds. The model was able to accurately simulate the runoff for single-event storms using 61-m by 61-m (200 ft by 200 ft) watershed grid elements.     

Transport of particulate matter fractions in urban source area pavement surface runoff

This study used manual full cross-sectional flow discrete sampling and suspended sediment concentration (SSC) methods to gravimetrically characterize noncolloidal hetero-disperse particulate matter (PM). This PM was examined as suspended, settleable, and sediment fractions to assess the distinct transport behavior of each PM fraction throughout each runoff event. Eight runoff events loading an urban paved source area watershed were examined to characterize transport of PM (as SSC) and fractions thereof. An event-based PM mass balance demonstrated recoveries exceeding 90%. With respect to PM transport, two phases were differentiated using a first flush index (m = DeltaM/DeltaV) developed in this study. The m >/= 1 and m < 1 transport phases of the coarser settleable/sediment PM accounted for a higher mass fraction of PM transported during higher flow rates, whereas delivery of the finer suspended fraction became more significant at lower flows. A positive relationship between PM concentration and particle size distribution was found for all events. Event mean concentrations (EMCs) of PM (as SSC) were compared with literature EMCs, sampling methods, and PM analysis method (as total suspended solids [TSS]). Particulate matter study results (as SSC) were higher than many published EMCs (as TSS) (p < 0.05). Differences are attributed to full cross-sectional flow sampling and the use of the the SSC method in contrast to automated sampling combined with TSS methods. Representative characterization of hetero-disperse source area PM is important for water chemistry monitoring, regulatory decisions, best management practice performance and maintenance, and PM inventories in urban systems.     

CRITICAL EVALUATION OF CERTAIN METHODS OF UNSTEADY GROUNDWATER HYDRAULICS1

The basic theories and fundamental assumptions usually employed in the solution of unsteady groundwater flow problems are reviewed critically. The best known method of analysis for such problems is based on the Dupuit-Forchheimer approximation and leads to a nonlinear parabolic differential equation which is generally solved by linearization or numerical methods. The accuracy of the solution to this equation can be improved by use of a different approach which does not employ the Dupuit Forchheimer assumption, but rather is based on a semi-numerical solution of the Laplace equation for quasi-steady conditions. The actual unsteady process is replaced by a sequence of steady-state conditions, and it is assumed that the actual unsteady flow characteristics during a short time interval can be approximated by those associated with “average” steady state flow. The Laplace equation is solved by a semi-discretization method according to which the horizontal coordinate is divided into subintervals, while the vertical coordinate is maintained continuous. The proposed method is applied to a typical tile drainage problem, and, based on a comparison of calculated results with experimental data, the method is evaluated and practical conclusions regarding its applicability are advanced.     

ADVANCES IN THE BOUNDARY INTEGRAL EQUATION METHOD IN SUBSURFACE FLOW1

ABSTRACT: This paper explores some of the advances of the boundary element method, as applied to ground-water problems, during the last five years. Although the method is still somewhat limited compared to solution by finite elements, the range of solutions has increased considerably. Diffusion and advection-diffusion solutions are done efficiently. These include the incorporation of inhomogeneity, anisotropy, and nonlinear diffusion. The difficult problem of stream-aquifer interaction is an important application as it is much easier to follow a free surface with its multiple configurations. The application must be able to cycle between ground-water connection and disconnection with the stream and include seepage surfaces. Flow in fractured media is a natural application where the flow in fractures can usually be treated without a computational exception in spite of extremely high aspect ratios. The case of seawater intrusion forms a type of free surface problem and thus is a case for which the method has special advantages. For these and other applications the boundary element method provides an inexpensive technique for calculation where the data preparation and setup time is minimal. In most of these cases, programs can and have been written on microcomputers.     

VELOCITY AND CONCENTRATION DISTRIBUTIONS OF SEDIMENT‐LADEN OPEN CHANNEL FLOW1

ABSTRACT: A mathematical model to predict both velocity and concentration distributions for sediment‐laden open channel flow is developed. Velocity profiles are derived by theoretical analysis and numerical method. Logarithmic law and semi‐empirical wake function concept are not adopted. An empirical equation for the ratio of sediment exchange and fluid diffusion coefficients is considered to solve the diffusion equation for suspended‐sediment concentration profiles. Four sets of experimental data from previous researchers are compared to numerical calculation. In the engineering applications, velocity and concentration profiles of sediment‐laden flow can be predicted simultaneously by the present model with the measured velocity and sediment‐concentration at reference level.     

NONSTEADY FLOW TO A WELL WITH TIME DEPENDENT DRAWDOWN1

Confined flow toward a single well of finite radius in an extensive aquifer of uniform transmissibility is studied under the assumption of time-dependent drawdown. Three particular cases are considered: (a) linear drawdown (including constant drawdown); (b) exponential drawdown; (c) periodic (sinusoidal) drawdown. The differential equation governing unsteady axial symmetric flow toward a single well in a confined aquifer is solved for the three different situations by the use of the Laplace transform method. The resulting expressions are integrated by adapting a modified Gemant scheme. General computer programs have been developed and operated for several combinations of characteristics. The results are plotted to show the effect of time dependent drawdown on the variation of the well discharge and the piezometric head distribution.