Optimal pumping locations of skimming wells

Abstract

A real-life problem involving pumping of groundwater from a series of existing wells along a river flood plain underlain with geologically saline water is examined within a conceptual framework. Unplanned pumping results in upconing of saline water. Therefore, it is necessary to determine optimal locations of fixed capacity pumping wells in space and time from a set of pre-selected candidate wells that minimize total salinity concentration in space and time. The nonlinear, non-convex, combinatorial problem involving zero—one decision variables is solved in a simulation—optimization (S/O) framework. Optimization is accomplished by using simulated annealing (SA)—a search algorithm. The computational burden is primarily managed by replacing the numerical model with a surrogate simulator—artificial neural network (ANN). The computational burden is further reduced through intuitive algorithmic guidance. The model results suggest that the skimming wells must be operated from optimal locations such that they are staggered in space and time to obtain least saline water.     

Using a hybrid genetic algorithm–simulated annealing algorithm for fuzzy programming of reservoir operation

We present a novel approach for optimizing reservoir operation through fuzzy programming and a hybrid evolution algorithm, i.e. genetic algorithm (GA) with simulated annealing (SA). In the analysis, objectives and constraints of reservoir operation are transformed by fuzzy programming for searching the optimal degree of satisfaction. In the hybrid search procedure, the GA provides a global search and the SA algorithm provides local search. This approach was investigated to search the optimizing operation scheme of Shihmen Reservoir in Taiwan. Monthly inflow data for three years reflecting different hydrological conditions and a consecutive 10‐year period were used. Comparisons were made with the existing M‐5 reservoir operation rules. The results demonstrate that: (1) fuzzy programming could effectively formulate the reservoir operation scheme into degree of satisfaction α among the users and constraints; (2) the hybrid GA‐SA performed much better than the current M‐5 operating rules. Analysis also found the hybrid GA‐SA conducts parallel analyses that increase the probability of finding an optimal solution while reducing computation time for reservoir operation. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi-Objective Optimization of Managed Aquifer Recharge

This study demonstrates the utilization of a multi-objective hybrid global/local optimization algorithm for solving managed aquifer recharge (MAR) design problems, in which the decision variables included spatial arrangement of water injection and abstraction wells and time-variant rates of pumping and injection. The objective of the optimization was to maximize the efficiency of the MAR scheme, which includes both quantitative and qualitative aspects. The case study used to demonstrate the capabilities of the proposed approach is based on a published report on designing a real MAR site with defined aquifer properties, chemical groundwater characteristics as well as quality and volumes of injected water. The demonstration problems include steady state and transient scenarios. The steady state scenario demonstrates optimization of spatial arrangement of multiple injection and recovery wells, whereas the transient scenario was developed with the purpose of finding optimal regimes of water injection and recovery at a single location. Both problems were defined as multi-objective problems. The scenarios were simulated by applying coupled numerical groundwater flow and solute transport models: MODFLOW-2005 and MT3D-USGS. The applied optimization method was a combination of global (the non-dominated sorting genetic algorithm [NSGA-2]) and local (the Nelder-Mead downhill simplex search algorithms). The analysis of the resulting Pareto optimal solutions led to the discovery of valuable patterns and dependencies between the decision variables, model properties, and problem objectives. Additionally, the performance of the traditional global and the hybrid optimization schemes were compared.     

Identification of Pumping Influences in Long‐Term Water Level Fluctuations

Identification of the pumping influences at monitoring wells caused by spatially and temporally variable water supply pumping can be a challenging, yet an important hydrogeological task. The information that can be obtained can be critical for conceptualization of the hydrogeological conditions and indications of the zone of influence of the individual pumping wells. However, the pumping influences are often intermittent and small in magnitude with variable production rates from multiple pumping wells. While these difficulties may support an inclination to abandon the existing dataset and conduct a dedicated cross‐hole pumping test, that option can be challenging and expensive to coordinate and execute. This paper presents a method that utilizes a simple analytical modeling approach for analysis of a long‐term water level record utilizing an inverse modeling approach. The methodology allows the identification of pumping wells influencing the water level fluctuations. Thus, the analysis provides an efficient and cost‐effective alternative to designed and coordinated cross‐hole pumping tests. We apply this method on a dataset from the Los Alamos National Laboratory site. Our analysis also provides (1) an evaluation of the information content of the transient water level data; (2) indications of potential structures of the aquifer heterogeneity inhibiting or promoting pressure propagation; and (3) guidance for the development of more complicated models requiring detailed specification of the aquifer heterogeneity.     

Information effect on remediation design of contaminated aquifers using the pump and treat method

We examine the effect of uncertainty due to limited information on the remediation design of a contaminated aquifer using the pump and treat method. The hydraulic conductivity and contaminant concentration distributions for a fictitious contaminated aquifer are generated assuming a limited number of sampling locations. Stochastic optimization with multiple realizations is used to account for aquifer uncertainty. The optimization process involves a genetic algorithm (GA). As the number of realizations increases, a greater extraction rate and more wells are needed. There was a total cost increase, but the optimal remediation designs became more reliable. Stochastic optimization analysis also determines the locations for extraction wells, the variation in extraction rates as a function of the change of well locations, and the reliability of the optimal designs. The number of realizations (stack number) that caused the design factors to converge could be determined. Effective stochastic optimization may be achieved by reducing computational resources. An increase in the variability of the conductivity distribution requires more extraction wells. Information about potential extraction wells can be used to prevent failure of the remediation task.     

Fuzzy ruling between core porosity and petrophysical logs: Subtractive clustering vs. genetic algorithm–pattern search

Porosity, the void portion of reservoir rocks, determines the volume of hydrocarbon accumulation and has a great control on assessment and development of hydrocarbon reservoirs. Accurate determination of porosity from core analysis is highly cost, time, and labor intensive. Therefore, the mission of finding an accurate, fast and cheap way of determining porosity is unavoidable. On the other hand, conventional well log data, available in almost all wells contain invaluable implicit information about the porosity. Therefore, an intelligent system can explicate this information. Fuzzy logic is a powerful tool for handling geosciences problem which is associated with uncertainty. However, determination of the best fuzzy formulation is still an issue. This study purposes an improved strategy, called hybrid genetic algorithm–pattern search (GA–PS) technique, against the widely held subtractive clustering (SC) method for setting up fuzzy rules between core porosity and petrophysical logs. Hybrid GA–PS technique is capable of extracting optimal parameters for fuzzy clusters (membership functions) which consequently results in the best fuzzy formulation. Results indicate that GA–PS technique manipulates both mean and variance of Gaussian membership functions contrary to SC that only has a control on mean of Gaussian membership functions. A comparison between hybrid GA–PS technique and SC method confirmed the superiority of GA–PS technique in setting up fuzzy rules. The proposed strategy was successfully applied to one of the Iranian carbonate reservoir rocks.     

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.     

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.     

Optimizing remediation of an unconfined aquifer using a hybrid algorithm

We present a novel hybrid algorithm, integrating a genetic algorithm (GA) and constrained differential dynamic programming (CDDP), to achieve remediation planning for an unconfined aquifer. The objective function includes both fixed and dynamic operation costs. GA determines the primary structure of the proposed algorithm, and a chromosome therein implemented by a series of binary digits represents a potential network design. The time-varying optimal operation cost associated with the network design is computed by the CDDP, in which is embedded a numerical transport model. Several computational approaches, including a chromosome bookkeeping procedure, are implemented to alleviate computational loading. Additionally, case studies that involve fixed and time-varying operating costs for confined and unconfined aquifers, respectively, are discussed to elucidate the effectiveness of the proposed algorithm. Simulation results indicate that the fixed costs markedly affect the optimal design, including the number and locations of the wells. Furthermore, the solution obtained using the confined approximation for an unconfined aquifer may be infeasible, as determined by an unconfined simulation.     

Advantages of the analytic element method for the solution of groundwater management problems

In the simulation‐optimization approach, a coupled optimization and groundwater flow/transport model is used to solve groundwater management problems. The efficiency of the numerical method, which is used to simulate the groundwater flow, is one the major reason to obtain the best solution for a management problem. This study was carried out to examine the advantages of the analytic element method (AEM) in the simulation‐optimization approach, for the solution of groundwater management problems. For this study, the AEM and finite difference method (FDM) based flow models were developed and coupled with the particle swarm optimization (PSO)‐based optimization model. Furthermore, the AEM‐PSO and FDM‐PSO models developed were applied in hypothetical as well as real field conditions to address groundwater management problems and the results were compared. For the real field situation, the models developed were applied to the Dore River basin in France to minimize the installation and operational cost of new pumping wells taking the location and discharge of the pumping wells as decision variables. The constraints of the problem were identified with the help of stakeholders and water authority officials. The AEM flow model was developed to facilitate the management model particularly when at each iteration, the optimization model calls for a simulation model to calculate the values of groundwater heads. The results show that, at some points, the AEM‐PSO model is efficient in identifying the optimal location of wells and consequently results in optimal costs, sometimes difficult when using the FDM. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Fecal Indicator Bacteria Variability in Samples Pumped from Monitoring Wells

The detection of microbiological contamination in drinking water from groundwater wells is often made with a limited number of samples that are collected using traditional geochemical sampling protocols. The objective of this study is to examine the variability of fecal indicator bacteria, as observed using discrete samples, due to pumping. Two wells were instrumented as multilevel piezometers in a bedrock aquifer, and bacterial enumeration was conducted on a total of 166 samples (for total coliform, fecal coliform, Escherichia coli, and fecal streptococci) using standard membrane filtration methods. Five tests were conducted using pumping rates ranging from 0.3 to 17 L/min in a variety of purging scenarios, which included constant and variable (incremental increase and decrease) flow. The results clearly show a rapid and reproducible, 1 to 2 log‐unit decrease in fecal indicator bacteria at the onset of pumping to stabilized, low‐level concentrations prior to the removal of three to five well volumes. The pumping rate was not found to be correlated with the magnitude of observed bacterial counts. Based on the results, we suggest sampling protocols for fecal indicator bacteria that include multiple collections during the course of pumping, including early‐time samples, and consider other techniques such as microscopic enumeration when assessing the source of bacteria from the well‐aquifer system.     

A combined simulation–genetic algorithm optimization model for optimal rule curves of a reservoir: a case study of the Nam Oon Irrigation Project,Thailand

A combined simulation–genetic algorithm (GA) optimization model is developed to determine optimal reservoir operational rule curves of the Nam Oon Reservoir and Irrigation Project in Thailand. The GA and simulation models operate in parallel over time with interactions through their solution procedure. A GA is selected as an optimization model, instead of traditional techniques, owing to its powerful and robust performance and simplicity in combining with a simulation technique. A GA is different from conventional optimization techniques in the way that it uses objective function information and does not require its derivatives, whereas in real‐world optimization problems the search space may include discontinuities and may often include a number of sub‐optimum peaks. This may cause difficulties for calculus‐based and enumerative schemes, but not in a GA. The simulation model is run to determine the net system benefit associated with state and control variables. The combined simulation–GA model is applied to determine the optimal upper and lower rule curves on a monthly basis for the Nam Oon Reservoir, Thailand. The objective function is maximum net system benefit subject to given constraints for three scenarios of cultivated areas. The monthly release is calculated by the simulation model in accordance with the given release policy, which depends on water demand. The optimal upper and lower rule curves are compared with the results of the HEC‐3 model (Reservoir System Analysis for Conservation model) calculated by the Royal Irrigation Department, Thailand, and those obtained using the standard operating policy. It was found that the optimal rule curves yield the maximum benefit and minimum damages caused by floods and water shortages. The combined simulation–GA model shows an excellent performance in terms of its optimization results and efficient computation. Copyright © 2007 John Wiley & Sons, Ltd.     

Capture Versus Capture Zones: Clarifying Terminology Related to Sources of Water to Wells

The term capture, related to the source of water derived from wells, has been used in two distinct yet related contexts by the hydrologic community. The first is a water‐budget context, in which capture refers to decreases in the rates of groundwater outflow and (or) increases in the rates of recharge along head‐dependent boundaries of an aquifer in response to pumping. The second is a transport context, in which capture zone refers to the specific flowpaths that define the three‐dimensional, volumetric portion of a groundwater flow field that discharges to a well. A closely related issue that has become associated with the source of water to wells is streamflow depletion, which refers to the reduction in streamflow caused by pumping, and is a type of capture. Rates of capture and streamflow depletion are calculated by use of water‐budget analyses, most often with groundwater‐flow models. Transport models, particularly particle‐tracking methods, are used to determine capture zones to wells. In general, however, transport methods are not useful for quantifying actual or potential streamflow depletion or other types of capture along aquifer boundaries. To clarify the sometimes subtle differences among these terms, we describe the processes and relations among capture, capture zones, and streamflow depletion, and provide proposed terminology to distinguish among them.     

Identifying groundwater pumping source information using simulated annealing

This study develops an approach referred to as SA‐MF using simulated annealing (SA) and a three‐dimensional groundwater flow model (MODFLOW‐2000) to determine the pumping source information, namely the pumping source location, the pumping rate and the pumping period. Eight scenarios, each with various cases for aquifers with homogeneous or heterogeneous conductivities, are used to test the applicability and accuracy of SA‐MF in determining the pumping source information. The results show that at least five measured heads should be used to analyse the pumping source identification problem and at least three observation wells are required to effectively determine the pumping source information. The SA‐MF gives good estimated results in both synthetic and real problems even if the measured heads contain measurement errors. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Field Test of a Hybrid Finite‐Difference and Analytic Element Regional Model

Regional finite‐difference models often have cell sizes that are too large to sufficiently model well‐stream interactions. Here, a steady‐state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell‐by‐cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real‐world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined “benchmark” MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost‐effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite‐difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady‐state conditions.     

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.     

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.     

Application of an integrated surface water‐groundwater model to multi‐aquifers modeling in Choushui River alluvial fan,Taiwan

This research proposes a combination of SWAT and MODFLOW, MD‐SWAT‐MODFLOW, to address the multi‐aquifers condition in Choushui River alluvial fan, Taiwan. The natural recharge and unidentified pumping/recharge are separately estimated. The model identifies the monthly pumping/recharge rates in multi‐aquifers so that the daily streamflow can be simulated correctly. A multi‐aquifers condition means a subsurface formation composed of at least the unconfined aquifer, the confined aquifer, and an in‐between aquitard. In such a case, the variation of groundwater level is related to pumping/recharge activities in vertically adjacent aquifer and the river‐aquifer interaction. Both factors in turn affect the streamflow performance. Results show that MD‐SWAT‐MODFLOW performs better than SWAT alone in terms of simulated streamflow, especially during low flow period, when pumping/recharge rates are properly estimated. A sensitivity analysis of individual parameter suggests that the vertical leakance may be the most sensitive among all investigated MODFLOW parameters in terms of the estimated pumping/recharge among aquifers, and the Latin‐Hypercube‐One‐factor‐At‐a‐Time sensitivity analysis indicates that the hydraulic conductivity of channel is the most sensitive to the model performance. It also points out the necessity to simultaneously estimate pumping/recharge rates in multi‐aquifers. The estimated net pumping rate can be treated as a lower bound of the actual local pumping rate. As a whole, the model provides the spatio‐temporal groundwater use, which gives the authorities insights to manage groundwater resources. Copyright © 2012 John Wiley & Sons, Ltd.