Analytic elements method and particle swarm optimization based simulation–optimization model for groundwater management

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 design of an in-situ bioremediation system using support vector machine and particle swarm optimization

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location and well control optimization problems separately. Rather, they should be considered simultaneously as a joint problem. In this work, we present noninvasive, derivative-free, easily parallelizable procedures to solve this joint optimization problem. Specifically, we consider Particle Swarm Optimization (PSO), a global stochastic search algorithm; Mesh Adaptive Direct Search (MADS), a local search procedure; and a hybrid PSO–MADS technique that combines the advantages of both methods. Nonlinear constraints are handled through use of filter-based treatments that seek to minimize both the objective function and constraint violation. We also introduce a formulation to determine the optimal number of wells, in addition to their locations and controls, by associating a binary variable (drill/do not drill) with each well. Example cases of varying complexity, which include bound constraints, nonlinear constraints, and the determination of the number of wells, are presented. The PSO–MADS hybrid procedure is shown to consistently outperform both stand-alone PSO and MADS when solving the joint problem. The joint approach is also observed to provide superior performance relative to a sequential procedure.

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

The productivity evaluation of gas reservoirs is used to determine the optimal number of well pattern, which is an important part of the preparation of gas reservoir development plan. Using integral transformation and asymptotic analyses to solve the pseudo steady-state flow model in closed rectangular gas reservoir of constant thickness, analytic solution of pressure distribution of eccentric well can be obtained. This paper presents mathematical model of multiple wells producing from a closed gas reservoir by applying the principle of pressure superposition. The pseudo steady-state dimensionless production index is introduced to solve the multiple well mathematical models under the constant pressure, and the number of production wells and cumulative production in different production interval are obtained. The results of the calculation shows that the curve of the cumulative production and economic benefits have a maximum value when the producing time, gas price, and drilling costs are given, so it can determine the optimal number of wells and provide the basis for making gas reservoir development plan.

Application of DOE and metaheuristic bat algorithm for well placement and individual well controls optimization

Optimisation of the wells placement in gas reservoirs using SIMPLEX method

A whirlpool foundation pit is a small-diameter, deep circular pit. Because of its depth and small diameter, a large drawdown is required, and a limited number of wells can be installed inside the pit. During excavation, partially penetrating wells inside and outside the foundation pit have to be installed to lower the water level when the aquifer is too thick. However, partially penetrating wells near partially penetrating curtains cannot be treated by analytical methods. Therefore, it is necessary to use numerical methods to predict dewatering during excavation. Field experiments were performed on whirlpool foundation pit 1880 of Baosteel Group, Shanghai, China, to obtain pumping rates and drawdown, pumping with a single well and two wells in the confined aquifer. The results indicate that the drawdown inside the pit induced by pumping wells outside the foundation pit was small, whereas it was large for pumping wells inside the pit. The pumping wells inside and outside the pit had to be combined to lower the water level. A three-dimensional numerical model was developed to simulate the dewatering process. The hydraulic conductivities of the confined aquifers were inversed by using the pumping tests. Operation schedules were simulated with the corrected model for different combinations of wells inside and outside the pit. The results suggest that different schedules and operation conditions affect drawdown. The monitored results during dewatering indicate that the simulation and field measurements were in agreement. The results can be applied to similar situations.

The simulation-optimization approach is often used to solve water resource management problem although repeated use of the simulation model enhances the computational load. In this study, Artificial Neural Network (ANN) and Bagged Decision Trees (BDT) models were developed as an approximator for Analytic Element Method (AEM) based groundwater flow model. Developed ANN and BDT models were coupled with Particle Swarm Optimization (PSO) model to solve the well-field management problem. The groundwater flow model was developed for the study area and used to generate the dataset for the training and testing of the ANN & BDT models. These coupled ANN-PSO & BDT-PSO models were employed to find the optimal design and cost of the new well-field system by optimizing discharge & co-ordinate of wells along with the cost effective layout of piping network. The Minimum Spanning Tree (MST) based model was used to find out the optimal piping network layout and checking the hydraulic constraints in the piping network. The results show that the ANN & BDT models are good approximators of AEM model and they can reduce the computational burden significantly although ANN model performs better than BDT model. The results show that the coupling of piping network model with simulation-optimization model is very significant for finding the cost effective and realistic design of the new well-field system.

When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.

Arnold Verruijt (1940‐2022)

This research aims at optimizing the monitoring network used to consistently identify pollution’s origin in the pollution source identification problem in groundwater hydraulics under real-time/operational applications. For this task, Machine Learning (ML) and Deep Learning (DL) methods are introduced, which can outperform metaheuristics, such as Genetic Algorithms (GAs), in terms of total computational load. To test the approach, a theoretical aquifer with two pumping wells is studied, where one of six possible pollution sources may spread a conservative pollutant. An existing own software simulates a 2D surrogate steady state flow field, using particle tracking to simulate advective mass transport only. A large number of combinations of possible source locations (4 different layout scenarios), hydraulic gradients and pumping wells’ flow-rates is used to calculate various features (such as pollutant arrival times, hydraulic drawdowns) in a 29 × 29 grid. Three ML/DL methods (Random Forests, Multi-Layer Perceptron, Convolutional Neural Networks) are tested for prediction accuracy, while Correlation based Feature Selection (CFS), and targeted tests are used to select subsets/sampling frequencies that can provide similar accuracy with the full datasets. This evaluation process bears promising results and paves the way for monitoring network optimization.KeywordsMachine LearningSource IdentificationMonitoring network

Each university has different regulations in making lecture schedule according to the conditions of respective institution. In this study, regulation on lecture scheduling used the maximum limit of credits of lecturer in a day, in which if exceeds the maximum limit, then the schedule of course will be moved on another day. This study attempts to optimize the schedule preparation in each semester by considering the maximum limit of credits of a lecturer in a day. Lecture scheduling is a combination of space, time, and resources. It is categorized into combinatorial optimization group. There are two methods for solving the combinatorial optimization problems, i.e. exact and approximation method. The approximation method consists of two types, heuristics and metaheuristics. The algorithm metaheuristics categories include genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), bee colony optimization (BCO), simulated annealing, and so on. This paper employed metaheuristics approach. Research on the preparation of lecture scheduling using ACO algorithm has been conducted and proven to be able to prepare the lecture scheduling. The ACO algorithm has numbers of parameters that in solving issues, one must manually set a number of parameters by using the Design of Experiments (DoE) tool, which takes time to solve the optimization problem. Hence, to solve the issue, an automated parameter optimization is required. PSO algorithm has fewer parameters compared to the ACO. Therefore, the purpose of this paper is a hybrid between PSO and ACO in preparing lecture scheduling.

Solving complex problems with higher dimensions involving many constraints is often a very challenging task. While solving multidimensional problems with particle swarm optimization involving several constraint factors, the penalty function approach is widely used. This paper provides a comprehensive survey of some of the frequently used constraint handling techniques currently used with particle swarm optimization. In this paper some of the penalty functional approaches for solving evolutionary algorithms are discussed and a comparative study is being performed with respect to various benchmark problems to assess their performance.

Freshwater demand will increase in the coming years due to climate change and socio-economic developments. One approach to help combat this is through aquifer storage and recovery (ASR), whereby excess fresh water is stored in the subsurface and recovered later as required. Furthermore, brackish groundwater extraction (BWE) can also be used to combat salinization and produce fresh groundwater. COASTAR is a Dutch research consortium that focuses on the use of ASR and BWE to secure sustainable access to freshwater in coastal areas. Previous research within this program produced geohydrological suitability maps at a national level through the assessment of several geohydrological factors using existing data. In this study, we test previous results using numerical validation by ‘blindly’ placing ASR and BWE well systems into the centre of 10 x 10km sub models, using 3D variable-density groundwater flow and coupled salt transport modelling. In total, 12 scenarios were simulated for approximately 170 locations in Dutch coastal areas, resulting in over 2000 model simulations. The scenarios were implemented in two different aquifers (shallow or deep) with extraction rates of 1200, 6.000, and 12.000m3/d. The resulting suitability of BWE and ASR systems at a given location was decided by how the system performs and affects the surrounding environment. A sensitivity analysis provided insights into the main geohydrological parameters and threshold values ​​applicable to ASR and BWE. Overall, results were like the pre-existing geohydrological suitability maps but offered further quantitative insights. On an international level, this knowledge can help to better understand suitability in other areas with similar subsurface characteristics. Additionally, a quick-scan analysis was performed to quantify the total potential extractable volumes for ASR and BWE. The results of this are based on maximum possible extraction/infiltration rates for each model area, by estimating the summed environmental effects of multiple wells. The method used an extrapolation approach based on the numerical model results. For this approach two factors were considered: 1) the effect of multiple extractions on the environment (changes in phreatic groundwater head), and 2) the optimal number of wells given the width of the freshwater ‘bubble’ for ASR scenarios. The quick-scan analysis showed that ASR and BWE systems have the potential to fulfill the increase in freshwater demand in the Netherlands in 2050.