Model-aided design and optimization of artificial recharge-pumping systems

Abstract

This paper presents a methodology for the design and optimization of artificial recharge-pumping systems (ARPS). The objective of ARPS is to provide a maximum abstraction rate through artificial recharge, while meeting two operational constraints: (a) the influences of the system operation on groundwater levels should be no more than 25 mm in the vicinity of the system; and (b) the travel time of the infiltrated water from the recharge pond to the pumping wells should be more than 60 days. The combined use of a 3-dimensional generic groundwater simulation model with particle tracking analyses has identified the two best ARPS systems: the circular pond system and the island system. By coupling the simulation model with linear and mixed integer programming optimization, the optimal pumping scheme (number, locations and rates of the pumping wells) has been determined. An unsteady state model has been used to simulate the response of the operation of the two systems under natural seasonal variations. The implementation aspects of the two systems are compared.     

Artificial neural networks as an alternative approach to groundwater numerical modelling and environmental design

Classical optimization methodologies based on mathematical theories have been developed for the solution of various constrained environmental design problems. Numerical models have been widely used to represent an environmental system accurately. The use of methodologies such as artificial neural networks (ANNs), which approximate the complicated behaviour and response of physical systems, allows the optimization of a large number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical model would be prohibitive. In this paper, a combination of an ANN with a differential evolution algorithm is proposed to replace the classical finite‐element numerical model in water resources management problems. The objective of the optimization problem is to determine the optimal operational strategy for the productive pumping wells located in the northern part of Rhodes Island in Greece, to cover the water demand and maintain the water table at certain levels. The conclusions of this study show that the use of ANN as an approximation model could (a) significantly reduce the computational burden associated with the accurate simulation of complex physical systems and (b) provide solutions very close to the optimal ones for various constrained environmental design problems. Copyright © 2008 John Wiley & Sons, Ltd.     

A Hybridized GA with LP‐LP Model for the Management of Confined Groundwater

A novel hybrid methodology is introduced in this paper for the optimal solution of the groundwater management problem. The problem to be addressed is the optimal determination and operation of a predefined number of wells out of a priori known set of potential wells with fixed locations to minimize the pumping cost of utilizing a two‐dimensional (2D) confined aquifer under steady‐state flow condition. The solution to this problem should satisfy a downstream demand, a lower/upper bound on the pumping rates, and a lower/upper bound on the water level drawdown in the wells. The problem is solved by hybridizing a genetic algorithm (GA) which suggests the candidate configurations for the operational wells and a hybrid linear programming (LP‐LP) approach with the duty of finding the optimal operation policy of the candidate wells defined by their pumping rates. Two different codings, namely binary and integer codings, are used for the GA and their performances are compared. The ability of the proposed hybrid method is tested against two benchmark problems: (1) finding the optimal configuration and pumping rates of a predefined number of wells out of potential wells and (2) finding the optimal number, configuration and pumping rates of the operating wells out of potential wells and the results are presented and compared with the available ones showing superior efficiency and effectiveness of the proposed method.     

Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models

Pumping optimization of coastal aquifers involves complex numerical models. In problems with many decision variables, the computational burden for reaching the optimal solution can be excessive. Artificial Neural Networks (ANN) are flexible function approximators and have been used as surrogate models of complex numerical models in groundwater optimization. However, this approach is not practical in cases where the number of decision variables is large, because the required neural network structure can be very complex and difficult to train. The present study develops an optimization method based on modular neural networks, in which several small subnetwork modules, trained using a fast adaptive procedure, cooperate to solve a complex pumping optimization problem with many decision variables. The method utilizes the fact that salinity distribution in the aquifer, depends more on pumping from nearby wells rather than from distant ones. Each subnetwork predicts salinity in only one monitoring well, and is controlled by relatively few pumping wells falling within certain control distance from the monitoring well. While the initial control area is radial, its shape is adaptively improved using a Hermite interpolation procedure. The modular neural subnetworks are trained adaptively during optimization, and it is possible to retrain only the ones not performing well. As optimization progresses, the subnetworks are adapted to maximize performance near the current search space of the optimization algorithm. The modular neural subnetwork models are combined with an efficient optimization algorithm and are applied to a real coastal aquifer in the Greek island of Santorini. The numerical code SEAWAT was selected for solving the partial differential equations of flow and density dependent transport. The decision variables correspond to pumping rates from 34 wells. The modular subnetwork implementation resulted in significant reduction in CPU time and identified an even better solution than the original numerical model.     

Geometry and dynamics of the freshwater—seawater interface in a coastal aquifer in southeastern Spain

Abstract

The contact between freshwater and seawater in coastal aquifers is studied using a relatively simple model for homogeneous aquifers. However, for real aquifers it is not so simple. The desalination plant built to supply water to the city of Almería is situated over the aquifer in the southern part of the River Andarax Delta. Its design capacity is 1100 L s^?1, and it is supplied from boreholes pumping water from beneath the freshwater—seawater contact in this aquifer. Well logs kept over a period of two years have allowed us to accurately define the interface geometry of the freshwater—seawater contact. Lithological data collected from 31 boreholes have also indicated the existence of strata with low hydraulic conductivity, within others of high conductivity. During a simultaneous pumping test of six wells with 690 L s^?1 total discharge, electrical conductivity measurements showed the influx of seawater 6–10 m below sea level and a drawdown of the interface in the piezometers closest to the pumping wells.     

Analytical Modeling of Well Design in Riverbank Filtration Systems

Analytical studies for well design adjacent to river banks are the most significant practical task in cases involving the efficiency of riverbank filtration systems. In times when high pollution of river water is joined with increasing water demand, it is necessary to design pumping wells near the river that provide acceptable amounts of river water with minimum contaminant concentrations. This will guarantee the quality and safety of drinking water supplies. This article develops an analytical solution based on the Green's function approach to solve an inverse problem: based on the required level of contaminant concentration and planned pumping time period, the shortest distance to the riverbank that has the maximum percentage of river water is determined. This model is developed in a confined and homogenous aquifer that is partially penetrated by the stream due to the existence of clogging layers. Initially, the analytical results obtained at different pumping times, rates and with different values of initial concentration are checked numerically using the MODFLOW software. Generally, the distance results obtained from the proposed model are acceptable. Then, the model is validated by data related to two pumping wells located at the first riverbank filtration pilot project conducted in Malaysia.     

Optimal control algorithm and neural network for dynamic groundwater management

Researchers have found that obtaining optimal solutions for groundwater resource‐planning problems, while simultaneously considering time‐varying pumping rates, is a challenging task. This study integrates an artificial neural network (ANN) and constrained differential dynamic programming (CDDP) as simulation‐optimization model, called ANN‐CDDP. Optimal solutions for a groundwater resource‐planning problem are determined while simultaneously considering time‐varying pumping rates. A trained ANN is used as the transition function to predict ground water table under variable pumping conditions. The results show that the ANN‐CDDP reduces computational time by as much as 94·5% when compared to the time required by the conventional model. The proposed optimization model saves a considerable amount of computational time for solving large‐scale problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Intelligent Space Tube Optimization for speeding ground water remedial design

An innovative Intelligent Space Tube Optimization (ISTO) two-stage approach facilitates solving complex nonlinear flow and contaminant transport management problems. It reduces computational effort of designing optimal ground water remediation systems and strategies for an assumed set of wells. ISTO's stage 1 defines an adaptive mobile space tube that lengthens toward the optimal solution. The space tube has overlapping multidimensional subspaces. Stage 1 generates several strategies within the space tube, trains neural surrogate simulators (NSS) using the limited space tube data, and optimizes using an advanced genetic algorithm (AGA) with NSS. Stage 1 speeds evaluating assumed well locations and combinations. For a large complex plume of solvents and explosives, ISTO stage 1 reaches within 10% of the optimal solution 25% faster than an efficient AGA coupled with comprehensive tabu search (AGCT) does by itself. ISTO input parameters include space tube radius and number of strategies used to train NSS per cycle. Larger radii can speed convergence to optimality for optimizations that achieve it but might increase the number of optimizations reaching it. ISTO stage 2 automatically refines the NSS-AGA stage 1 optimal strategy using heuristic optimization (we used AGCT), without using NSS surrogates. Stage 2 explores the entire solution space. ISTO is applicable for many heuristic optimization settings in which the numerical simulator is computationally intensive, and one would like to reduce that burden.     

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.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Data-Worth Assessment for a Three-Dimensional Optimal Design in Nonlinear Groundwater Systems

Groundwater model predictions are often uncertain due to inherent uncertainties in model input data. Monitored field data are commonly used to assess the performance of a model and reduce its prediction uncertainty. Given the high cost of data collection, it is imperative to identify the minimum number of required observation wells and to define the optimal locations of sampling points in space and depth. This study proposes a design methodology to optimize the number and location of additional observation wells that will effectively measure multiple hydrogeological parameters at different depths. For this purpose, we incorporated Bayesian model averaging and genetic algorithms into a linear data-worth analysis in order to conduct a three-dimensional location search for new sampling locations. We evaluated the methodology by applying it along a heterogeneous coastal aquifer with limited hydrogeological data that is experiencing salt water intrusion (SWI). The aim of the model was to identify the best locations for sampling head and salinity data, while reducing uncertainty when predicting multiple variables of SWI. The resulting optimal locations for new observation wells varied with the defined design constraints. The optimal design (OD) depended on the ratio of the start-up cost of the monitoring program and the installation cost of the first observation well. The proposed methodology can contribute toward reducing the uncertainties associated with predicting multiple variables in a groundwater system.     

Dynamic optimal ground water remediation including fixed and operation costs

In time-varying ground water remediation, the lack of an optimal control algorithm to simultaneously consider fixed costs and time-varying operating costs makes it nearly impossible to obtain an optimal solution. This study presents a novel algorithm that integrates a genetic algorithm (GA) and constrained differential dynamic programming (CDDP) to solve this time-varying ground water remediation problem. A GA can easily incorporate the fixed costs associated with the installation of wells. However, using a GA to solve for time-varying policies would dramatically increase the computational resources required. Therefore, the CDDP is used to handle the subproblems associated with time-varying operating costs. A hypothetical case study that incorporates fixed and time-varying operating costs is presented to demonstrate the effectiveness of the proposed algorithm. Simulation results indicate that the fixed costs can significantly influence the number and locations of wells, and a notable total cost savings can be realized by applying the novel algorithm herein.     

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.     

Monitoring strategies at phreatic wellfields: a 3D travel time approach

Ground water quality networks for monitoring phreatic drinking water wellfields are generally established for two main purposes: (1) the short-term safeguarding of public water supply and (2) signaling and predicting future quality changes in the extracted ground water. Six monitoring configurations with different well locations and different screen depths and lengths were evaluated using a numerical model of the 3D ground water flow toward a partially penetrating pumping well in a phreatic aquifer. Travel times and breakthrough curves for observation and pumping wells were used to judge the effectiveness of different design configurations for three monitoring objectives: (1) early warning; (2) prediction of future quality changes; and (3) evaluation of protection measures inside a protection zone. Effectiveness was tested for scenarios with advective transport, first-order degradation, and linear sorption. It is shown that the location and especially the depth of the observation wells should be carefully chosen, taking into account the residence time from the surface to the observation well, the residual transit times to the extraction well, and the transformation and retardation rates. Shallow monitoring was most functional for a variety of objectives and conditions. The larger the degradation rates or retardation, the shallower should the monitoring be for effective early warning and prediction of future ground water quality. The general approach followed in the current study is applicable for many geohydrological situations, tuning specific monitoring objectives with residence times and residual transit times obtained from a site-specific ground water flow model.     

Optimizing Wellfield Operation in a Variable Power Price Regime

Wellfield management is a multiobjective optimization problem. One important objective has been energy efficiency in terms of minimizing the energy footprint (EFP) of delivered water (MWh/m³). However, power systems in most countries are moving in the direction of deregulated markets and price variability is increasing in many markets because of increased penetration of intermittent renewable power sources. In this context the relevant management objective becomes minimizing the cost of electric energy used for pumping and distribution of groundwater from wells rather than minimizing energy use itself. We estimated EFP of pumped water as a function of wellfield pumping rate (EFP‐Q relationship) for a wellfield in Denmark using a coupled well and pipe network model. This EFP‐Q relationship was subsequently used in a Stochastic Dynamic Programming (SDP) framework to minimize total cost of operating the combined wellfield‐storage‐demand system over the course of a 2‐year planning period based on a time series of observed price on the Danish power market and a deterministic, time‐varying hourly water demand. In the SDP setup, hourly pumping rates are the decision variables. Constraints include storage capacity and hourly water demand fulfilment. The SDP was solved for a baseline situation and for five scenario runs representing different EFP‐Q relationships and different maximum wellfield pumping rates. Savings were quantified as differences in total cost between the scenario and a constant‐rate pumping benchmark. Minor savings up to 10% were found in the baseline scenario, while the scenario with constant EFP and unlimited pumping rate resulted in savings up to 40%. Key factors determining potential cost savings obtained by flexible wellfield operation under a variable power price regime are the shape of the EFP‐Q relationship, the maximum feasible pumping rate and the capacity of available storage facilities.     

Strategies for offsetting seasonal impacts of pumping on a nearby stream

Ground water pumping from aquifer systems that are hydraulically connected to streams depletes streamflow. The amplitude and timing of stream depletion depend on the stream depletion factor (SDF(i)) of the pumping wells, which is a function of aquifer hydraulic characteristics and the distance from the wells to the stream. Wells located at different locations, but having the same SDF and the same rate and schedule of pumping, will deplete streamflow equally. Wells with small SDF(i) deplete streamflow approximately synchronously with pumping. Wells with large SDF(i) deplete streamflow at approximately a constant rate throughout the year, regardless of the pumping schedule. For large values of SDF(i), artificial recharge that occurs on a different schedule from pumping can offset streamflow depletion effectively. The requirements are (1) that the pumping and recharge wells both have the same SDF(i) and (2) that the annual total quantities of recharge and pumping be equal. At larger SDF(i) values, it takes longer for pumping to impact streamflow in a wide aquifer than it does in a narrow aquifer. In basins that are closed to further withdrawals because streamflow is fully allocated, water-use changes replace new allocations as the source of water for new developments. Ground water recharge can be managed to offset the impacts of new ground water developments, allowing for changes in the timing and source of withdrawals from a basin without injuring existing users or instream flows.     

Management of the Wellfield Contaminated by Dense Chlorinated Hydrocarbons in Vilnius,Lithuania

Drinking water supply in Lithuania is entirely based on groundwater. Wellfields of Vilnius develop intermorainic ca. 50 m deep (in average) aquifer which is locally contaminated by chlorinated hydrocarbons— volatile organic compounds (VOCs). Groundwater abstraction activates VOCs migration from an abandoned factory into the pumping wells of one wellfield named “Vingis.” However monitoring data testify that only traces of VOCs were detected on the territory of this factory. Subsequent studies revealed the “secret”: dense VOCs have migrated from the territory of the polluter and have accumulated in lowermost places of pumped aquifer inside the wellfield. An attempt to ensure low concentration of VOCs in pumped water manipulating by pumping rates of more or less contaminated abstraction wells was not effective. Finally, an acceptable concentration of VOCs in supplied drinking water was ensured by permanent pumping out of the most polluted groundwater from some abstraction wells of the wellfield and diverting this water to the Neris River.     

Stochastic control of a micro-dam irrigation scheme for dry season farming

Micro-dams are expected to be feasible options for water resources development in semi-arid regions such as the Guinea savanna agro-ecological zone of West Africa. An optimal water management strategy in a micro-dam irrigation scheme supplying water from an existing reservoir to a potential command area is discussed in this paper based on the framework of stochastic control. Water intake facilities are assumed to consist of photovoltaic pumping system units and hoses. The knowledge of current states of the storage volume of the reservoir and the soil moisture in the command area is fed-back to the intake flow rate. A system of two stochastic differential equations is proposed as a model for the dynamics of the micro-dam irrigation scheme, so that temporally backward solution of the Hamilton–Jacobi–Bellman equation determines an optimal control, which represents the optimal water management strategy. A computational procedure using the finite element method is successfully implemented to provide comprehensive information on the optimal control. The results indicate that the water initially stored in the reservoir can support full irrigation for about 80 days under the optimal water management strategy, which is predominantly based on the demand-side principle. However, the volatility of the soil moisture in the command area must be reasonably small.     

Monitoring of drawdown pattern during pumping in an unconfined physical aquifer model

In this study, we attempted to analyse a drawdown pattern around a pumping well in an unconfined sandy gravelly aquifer constructed in a laboratory tank by means of both experimental and numerical modelling of groundwater flow. The physical model consisted of recharge, aquifer and discharge zones. Permeability and specific yield of the aquifer material were determined by Dupuit approximation under steady‐state flow and stepwise gravitational drainage of groundwater, respectively. The drawdown of water table in pumping and neighbouring observation wells was monitored to investigate the effect of no‐flow boundary on the drawdown pattern during pumping for three different boundary conditions: (i) no recharge and no discharge with four no‐flow boundaries (Case 1); (ii) no recharge and reservoir with three no‐flow boundaries (Case 2); (iii) recharge and discharge with two no‐flow boundaries (Case 3). Based on the aquifer parameters, numerical modelling was also performed to compare the simulated drawdown with that observed. Results showed that a large difference existed between the simulated drawdown and that observed in wells for all cases. The reason for the difference could be explained by the formation of a curvilinear type water table between wells rather than a linear one due to a delayed response of water table in the capillary fringe. This phenomenon was also investigated from a mass balance study on the pumping volume. The curvilinear type of water table was further evidenced by measurement of water contents at several positions in the aquifer between wells using time domain reflectometry (TDR). This indicates that the existing groundwater flow model applicable to an unconfined aquifer lacks the capacity to describe a slow response of water table in the aquifer and care should be taken in the interpretation of water table formation in the aquifer during pumping. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing the restoration time of surface water and groundwater systems under groundwater pumping

Since surface water and groundwater systems are fully coupled and integrated, increased groundwater withdrawal during drought may reduce groundwater discharges into the stream, thereby prolonging both systems’ recovery from drought. To analyze watershed response to basin-level groundwater pumping, we propose a modelling framework to understand the resiliency of surface water and groundwater systems using an integrated hydrologic model under transient pumping. The proposed framework incorporates uncertainties in initial conditions to develop robust estimates of restoration times of both surface water and groundwater and quantifies how pumping impacts state variables such as soil moisture. Groundwater pumping impacts over a watershed were also analyzed under different pumping volumes and different potential climate scenarios. Our analyses show that groundwater restoration time is more sensitive to variability in climate forcings as opposed to changes in pumping volumes. After the cessation of pumping, streamflow recovers quickly in comparison to groundwater, which has higher persistence. Pumping impacts on various hydrologic variables were also discussed. Potential for developing optimal conjunctive management plans using seasonal-to-interannual climate forecasts is also discussed.