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Applications of Optimal Hydraulic Control to Ground-Water Systems
Abstract
Ground-water simulation models are increasingly used for the analysis, design, and management of water-resource problems including ground-water supply and remediation. The solution to these problems involves some degree of control of ground-water hydraulics. Combining simulation with linear optimization can provide a useful tool for problem solution. The optimal hydraulic-control problem for ground-water systems is defined in terms of controls on the ground-water system and typical design criteria. Commonly used linear formulations of the control problem are described in detail. Recent applications of the optimal hydraulic-control approach to field problems are reviewed. The deterministic hydraulic-control problem is contrasted with more sophisticated techniques which incorporate contaminant transport and uncertainty in aquifer parameters. Conclusions are drawn about the likely future applicability of this method for solving ground-water management problems.
... During the last few decades, a lot of works related to traditional optimization methods have been carried out to solve groundwater management problems. The LP technique has been used by , Ahlfeld and Heidari (1994), Deninger (1970), Hallaji and Yazicigil (1996), Mantoglou (2003), and Willis (1979). Mixed-integer programming (MIP) has been employed by Aguado and Remson (1980), Datta and Dhiman (1996), Loaiciga et al. (1992), Meyer and Brill (1988), Misirli and Yazicigil (1997), Ratzlaff et al. (1992), and Willis (1976), and NLP has been considered by Ahlfeld et al. (1988), Emch andYeh (1998), Finney et al. (1992), Gorelick et al. (1979Gorelick et al. ( , 1984, Mantoglou and Papantoniou (2008), Shamir et al. (1984), and Willis and Newman (1977). ...
... In order to meet the increasing needs for freshwater for growing population, it is important to develop appropriate management models for assessing the maximum feasible pumping rates in coastal aquifers which protects saltwater intrusion. The problem of pumping optimization using management models has been extensively studied in the past (Ahlfeld and Heidari, 1994;Bear et al., 1999;Cheng and Ouazar, 2004;Das and Datta, 1999a,b;Dhar and Datta, 2009a,b;Hallaji and Yazicigil, 1996;Katsifarakis and Petala, 2006;Maimone, 2002;Mantoglou and Papantoniou, 2008;Mantoglou et al., 2004;Mantoglou, 2003;Mayer et al., 2002;Shamir et al., 1984;Sreekanth and Datta, 2010;Willis and Finney, 1988). Different objective functions and sets of constraints have been used depending on the problem. ...
The optimal use of available resources is of paramount importance in the backdrop of the increasing food,
fiber, and other demands of the burgeoning global population and the shrinking resources. The optimal
use of these resources can be determined by employing an optimization technique. The comprehensive
reviews on the use of various programming techniques for the solution of different optimization problems
have been provided in this paper. The past reviews are grouped into nine sections based on the solutions
of the theme-based real world problems. The sections include: use of optimization modelling for
conjunctive use planning, groundwater management, seawater intrusion management, irrigation management,
achieving optimal cropping pattern, management of reservoir systems operation, management
of resources in arid and semi-arid regions, solid waste management, and miscellaneous uses which comprise,
managing problems of hydropower generation and sugar industry. Conclusions are drawn where
gaps exist and more research needs to be focused.
... Using this mechanism of phytoremediation, cleaning out metals such as Cd, Cr, Cu, Ni, Pb, and V and radionuclides (U, Cs, Sr) is possible (Jabeen et al., 2009;Singh and Santal, 2015). Longrooted trees can absorb a large quantity of water, which was employed as a primary component in this procedure (Ahlfeld and Heidari, 1994). Long-rooted trees operate as pumps, drawing vast amounts of water from the subsurface water table (Muthusaravanan et al., 2018). ...
The contamination of soils with heavy metals and its associated hazardous effects are a thrust area of today’s research. Rapid industrialization, emissions from automobiles, agricultural inputs, improper disposal of waste, etc., are the major causes of soil contamination with heavy metals. These contaminants not only contaminate soil but also groundwater, reducing agricultural land and hence food quality. These contaminants enter the food chain and have a severe effect on human health. It is important to remove these contaminants from the soil. Various economic and ecological strategies are required to restore the soils contaminated with heavy metals. Phytoremediation is an emerging technology that is non-invasive, cost-effective, and aesthetically pleasing. Many metal-binding proteins (MBPs) of the plants are significantly involved in the phytoremediation of heavy metals; the MBPs include metallothioneins; phytochelatins; metalloenzymes; metal-activated enzymes; and many metal storage proteins, carrier proteins, and channel proteins. Plants are genetically modified to enhance their phytoremediation capacity. In Arabidopsis, the expression of the mercuric ion-binding protein in Bacillus megaterium improves the metal accumulation capacity. The phytoremediation efficiency of plants is also enhanced when assisted with microorganisms, biochar, and/or chemicals. Removing heavy metals from agricultural land without challenging food security is almost impossible. As a result, crop selections with the ability to sequester heavy metals and provide food security are in high demand. This paper summarizes the role of plant proteins and plant–microbe interaction in remediating soils contaminated with heavy metals. Biotechnological approaches or genetic engineering can also be used to tackle the problem of heavy metal contamination.
... 24 Several simulation-based optimization approaches have been reported in the literature for several types of groundwater problems. 36,37 In the context of GCS management, Birkholzer et al. 12 applied a derivative-based method to find the optimum extraction scheme to control the reservoir pressure. Cihan et al., 19 argued that the irregularity of the objective function in the optimal well placement problems can lead to suboptimal solutions if derivative-based methods were employed. ...
Injecting CO2 into deep geologic formations for storage purposes induces large pressure build‐up that risks caprock integrity. Naturally occurring faults or pressure‐induced fractures in the caprock can act as conductive leakage pathways resulting in potential contamination of the overlying shallow aquifers. Previous studies explored using brine extraction to manage such elevated pressure in the storage formation. In this paper, we extended the use of this technique to control far‐field brine leakage. Extraction wells are placed in the storage zone to reduce the leakage flow through reversing the pressure‐gradient locally, while minimizing the brine concentrations in the escaped‐fraction by utilizing the dilution capacity of the overlying formations. The developed approach incorporated the Genetic Algorithm with transport model simulations to optimize well‐placements and extraction‐rates. An approximately 8m long intermediate‐scale tank designed to mimic brine leakage migration in the field was used to validate this approach as field data are not available. We further evaluated the approach numerically using a hypothetical leakage scenario at the Vedder storage formation in San‐Joaquin basin to assess its practicality for field implementation. The results showed that storage zone heterogeneity and fractures’ permeabilities can significantly affect the optimum locations and pumping rates of the extraction wells. Brine leakage can be controlled by extracting a native‐brine volume less than 50% of the injected CO2 volume. The target concentrations in the shallow aquifer determines the extraction rates required to control a leakage through a fracture or a buried thrust fault. The study is useful to develop remediation strategies for carbon storage operations. © 2022 Society of Chemical Industry and John Wiley & Sons, Ltd.
... In this study, considering the impact of climate change on seawater intrusion, the exploitation of the three well groups near the seawater-intrusion transition zone in the study area was taken as the decision variable, and the deep belief neural network substitution model was embedded into the optimization model as equality constraints using the simulation optimization method. Other constraints were considered by means of the linear programming optimization model (Ahlfeld and Heidari 1994). By optimizing the exploitation amount of these three well groups, the total production of these groups can reach the maximum under the constraint that the existing seawater invasion degree (taking the seawater invasion zone as an example) does not expand. ...
Seawater intrusion not only causes fresh water shortages in coastal areas, but also has a negative impact on regional economic and social development. Global climate change will affect precipitation, sea level, and many other factors, which will in turn affect the simulation and prediction results for seawater intrusion. By combining groundwater numerical simulation technology, an atmospheric circulation model, artificial intelligence methods, and simulation optimization methods, this study coupled a numerical simulation model of seawater intrusion with an optimization model to optimize the groundwater exploitation scheme in the study area under the condition of climate change. As a result, a groundwater exploitation scheme was obtained for a typical study area, which provided a scientific basis and a reference for the rational development of effective groundwater resource solutions. The results of this study can be described as follows. (1) By introducing the theory and method of deep learning from artificial intelligence, the problem of complex nonlinear mapping between the inputs and outputs of a three-dimensional variable-density seawater intrusion numerical simulation model under the condition of limited number of training samples is effectively solved, and the approximation accuracy of the surrogate model with respect to the simulation model is improved. (2) By solving the optimization model, a reasonable groundwater exploitation scheme was obtained, which provided a scientific basis for the rational development and efficient use of groundwater resources in the study area.
... It consists in a method by which plants act as natural pumps contributing to regulate groundwater's cycle/movement: roots take up water from groundwater, plants can use this or return it into the environment (through transpiration), and then this water can be condensed to return to the groundwater after raining. If, however, the groundwater contains pollutants, the hydraulic control can help to control, limit, and diminish migration or even clean up the area, removing contaminants among the water mass taken up and sometimes phytotransforming them (Ahlfeld and Heidari 1994;Muthusaravanan et al. 2018). The most interesting species to perform this kind of remediation are plants with large root mass and that can release a considerable part of the water taken up into the environment, in other words, species that can transpire large volumes of water, influencing the existing water balance. ...
Environmental pollution threatens life existence on Earth. It is necessary and urgent that human beings develop efficient and safe strategies to remediate the harmful impacts caused by anthropogenic action over ecosystems. The use of plants is an interesting tool to promote environs’ restoration through phytoremediation. This kind of remediation can be performed by different mechanisms depending on the type of pollutant to be remediated, if the target environment is aqueous or soil, and on the plant species chosen. This chapter will focus on phytoremediation mechanisms and their importance as a strategic method of dealing with the restoration of polluted environs: an essential step toward achieving sustained development respecting the environment and developing environmental awareness.
... However, these methods have been limited to small systems due to computational challenges involved in applying these techniques to groundwater problems with a large system of nonlinear equations [38]. For example, linear programming (LP) has been applied to such problems [4,6,104,209]. A major advantage of LP is that the computational cost for problems that change with time, like groundwater management problems, increases only linearly with the number of time steps, N , as opposed to nonlinear programming algorithms in which the computational cost scales with N α , where 2 < α < 3. ...
... However, these methods have been limited to small systems due to computational challenges involved in applying these techniques to groundwater problems with a large system of nonlinear equations (Dokou et al., 2016). For example, linear programming (LP) has been applied to such problems Ahlfeld and Heidari, 1994;Karterakis et al., 2007;Willis, 1979). A major advantage of LP is that the computational cost for problems that change with time, like groundwater management problems, increases only linearly with the number of time steps, N, as opposed to nonlinear programming algorithms in which the computational cost scales with N α , where 2 < α < 3. ...
Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of “noisy” observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.
... El primero usa el modelo de simulación de forma externa para obtener la respuesta de la carga hidráulica producto del bombeo y el segundo incorpora de forma explícita las ecuaciones del modelo de simulación dentro del modelo de optimización (Ayvaz, 2009;Cabrera, 2009). Ambos enfoques han sido utilizados en la solución de varios problemas de administración, entre los que se encuentran maximización del rendimiento de acuíferos, desarrollo de políticas para el uso conjunto de recursos de agua subterránea y agua superficial, protección de acuíferos costeros y minimización del costo de operación de un campo de pozos, entre otros (Gorelick, 1983;Ahlfeld & Heidari, 1994;Wagner, 1995;Singh, 2014;Gorelick & Zheng, 2015;Yeh, 2015). ...
Ramos-Arzola, L. C., Cabrera-Estupiñán, E., Molina-Pérez, D., Hernández-Valdés, A. O., & Marón-Domínguez, D. E. (mayo-junio, 2017). Modelo para la optimización del costo de operación de un campo de pozos en acuíferos. Tecnología y Ciencias del Agua, 8(3), 39-53.
El componente de mayor costo en la producción de agua subterránea en un sistema de suministro (una vez que los pozos están construidos) es el bombeo de agua desde los pozos. En la presente contribución se propone un nuevo módulo en MADA (modelo de administración de acuíferos), que se basa en la inclusión de un modelo de simulaciónoptimización para la minimización del costo de operación en acuíferos. La propuesta utiliza un modelo de simulación bidimensional del flujo del agua subterránea (AQÜIMPE) basado en el método de los elementos finitos. Se emplea el enfoque matriz respuesta para vincular AQÜIMPE con un problema de programación cuadrática, que se resuelve empleando la función quadprog del asistente matemático MATLAB. Se aplica el modelo en la administración de la explotación del acuífero Cuenca Sur y se obtiene una política de explotación que permite un 15% de ahorro del costo de bombeo en relación con el costo de la explotación real del año 2007. Además, el patrón de explotación obtenido satisface un conjunto de restricciones de demanda, de niveles en el acuífero y de capacidad instalada en cada pozo de explotación.
... Groundwater management studies also differ in terms of the optimization models used. Linear programming techniques were used extensively by researchers for groundwater management because of their simple formulation and application (Ahlfeld and Heidari, 1994;Hallaji and Yazicigil, 1996;Mantoglou, 2003), while some researchers used nonlinear programming algorithms (Gorelick et al., 1979(Gorelick et al., , 1984Shamir et al., 1984;Emch and Yeh, 1998;Mantoglou and Papantoniou, 2008) and dynamic programming techniques (Chang et al., 1992;Culver and Shoemaker, 1992). ...
The optimization of spatially complex groundwater management models over long time horizons requires the use of computationally efficient groundwater flow models. This paper presents a new stochastic multi-cell lumped-parameter aquifer model that explicitly considers uncertainty in groundwater recharge. To achieve this, the multi-cell model is combined with the constrained-state formulation method. In this method, the lower and upper bounds of groundwater heads are incorporated into the mass balance equation using indicator functions. This provides expressions for the means, variances and covariances of the groundwater heads, which can be included in the constraint set in an optimization model. This method was used to formulate two separate stochastic models: (i) groundwater flow in a two-cell aquifer model with normal and non-normal distributions of groundwater recharge; and (ii) groundwater management in a multiple cell aquifer in which the differences between groundwater abstractions and water demands are minimized. The comparison between the results obtained from the proposed modeling technique with those from Monte Carlo simulation demonstrates the capability of the proposed models to approximate the means, variances and covariances. Significantly, considering covariances between the heads of adjacent cells allows a more accurate estimate of the variances of the groundwater heads. Moreover, this modeling technique requires no discretization of state variables, thus offering an efficient alternative to computationally demanding methods.
... Simulation models provide solutions for governing equations and explain the state of resources. Optimization models provide the best strategy from a feasible set of strategies definable under the state of resources depicted by simulation models (Wagner and Gorelick 1989;Yeh 1992;Ahlfeld and Heidari 1994;Wagner 1995;Barlow et al. 1996;Wang and Zheng 1998;Cheng et al. 2000;Das and Datta 2001;Mantoglou et al. 2004;Katsifarakis and Petala 2006;Ayvaz and Karahan 2008;Gaur et al. 2011;Singh and Panda 2013). ...
A conjunctive-use model is developed for management of groundwater and surface water resources via mixed integer linear fractional programming (MILFP). The objective of the conjunctive-use model is to maximize the ratio of groundwater usage to surface water usage through a water supply network. A conditional head constraint is imposed to the conjunctive-use model to maintain aquifer sustainability. A transformation approach is introduced to transform the conditional head constraint into a set of mixed integer linear constraints in terms of groundwater head. Groundwater head is further linearized with respect to pumping rates that are decision variables. Eventually, the conjunctive-use model is to solve a successive MILFP problem by updating the response matrix in each iteration. To make an MILFP problem tractable, the study develops a transformation technique along with the Charnes–Cooper transformation approach to transform an MILFP problem into an equivalent problem of mixed integer linear programming (MILP) to be solved by CPLEX. The proposed conjunctive-use model is applied to northern Louisiana. A water supply network is proposed to utilize four existing reservoirs as alternative resources in order to raise groundwater level in the Sparta aquifer to acceptable target level in Ouachita, Lincoln, and Union Parishes while maximizing groundwater pumping. The results show that the conjunctive-use management framework increases groundwater levels by an average of 6.96 m (22.82 ft) from 2001 to 2010 by reducing total groundwater withdrawal 28.93%, which is counterbalanced by reservoir water.
... To avoid the vertical contamination of salinity in freshwater lens, the information about the aquifer geometry plays a key role in designing the water wells. The literature survey (Shamir et al. 1984;Ahlfeld and Heidari 1994;Cheng and Ouazar 2004;Dhar and Datta 2009;Kaleris and Ziogas 2013) of coastal belts around the world shows, majority of the water wells gets salinity intrusion due to the lack of precise mapping of the subsurface multi-layer aquifer systems, their disposition and saturated formation salinity. The coastal aquifers are fragile in nature and easily depleted due to overexploitation of groundwater resources in many parts of the world (Khair et al. 1994;Gossling 2001;Vengosh et al. 2005;Chidambaram et al. 2008). ...
Vertical disposition of the freshwater aquifer lens and their progressive change on lateral scale are relevant to understand the short circuiting of fresh and saline water at coastal areas. Since, half of the world population dwells within 50 km of coast line, the freshwater aquifers at coast are deteriorating at alarming rate. There are well-defined water well construction plans for coastal aquifer management, but mostly fails while execution due to lack of precise knowledge of subsurface lithological layer setup. In the present study, an attempt has been made to investigate such precise information about subsurface lithological layer setup to protect the freshwater resources at coastal area, applying noninvasive hydro-geophysical technique. Integrated electrical parameters, hydrochemistry, topography, and water table assessment have been applied to decipher the geometry of freshwater lens at Cuddalore coast, India. Results show in this study (1) the electrical resistivity (ρ) 1–10 Ω-m of subsurface formation, electrical conductivity (σ) 30,891 µS/cm of groundwater, and water table 1.55 m above mean sea level (MSL) confirms the zone of effluent contamination; (2) the zone showing ρ = 1–10 Ω-m, σ = 6172 µS/cm, water table 6.46 m below MSL is attributed to the saline water intrusion; (3) freshwater formations are identified in beach ridges underlain by clay layers with ρ = 30–60 Ω-m, σ = 453 µS/cm and water table above MSL; and (4) water well design is proposed to tap the freshwater aquifers avoiding vertical short circuiting of saline and freshwater.
... In order to focus on the impact of aquifer heterogeneity on total remediation costs for the pump-and-treat systems, we simplified the economical evaluation in assuming that pumping and on-site treatment are directly related to the pumping rate only (see Ahlfeld & Heidari, 1994). In fact, especially treatment costs depend on a number of parameters, e.g. ...
Addressing the need for cost-effective long-term groundwater remediation methods, pump-and-treat systems, supported by means of additional impermeable barriers, are proposed as a reasonable alternative to standard pump-and-treat systems. Compared to only pumping, the barriers yield a reduction of the pumping rate required to establish a certain capture zone. This paper presents the results of a comparative analysis of the hydraulic performance of both systems in heterogeneous aquifers and, based on that, an economic evaluation. Taking into account the fact that the description of heterogeneous aquifers is inevitably uncertain, the hydraulic analysis is based on Monte Carlo simulations which incorporate the reliability (probability of failure) of the specific pump-and-treat system. The reliability trade-offs obtained show that considerably less water has to be pumped (and treated) if an additional impermeable barrier is implemented. This joint economic evaluation reveals, however, that due to the additional costs for barrier installation, a barrier-supported pump-and-treat system is only advantageous if the unit costs for pumping and on-site treatment exceed a certain limit, which again depends on the degree of aquifer heterogeneity.
... In forming retention resources, it is very important to improve the methods of water regulation [19] and forecasting the effect of water systems on the water conditions of the agricultural and forest habitat. The mathematical modeling is helpful because of its effective means of solving the problems of optimal irrigation control [1,5,8,11,12,15,16]. ...
The results of the model tests referring to the water conditions on afforested (formerly arable) lands in Wrocław are presented in this paper. The studies showed that regulated runoff from 90 ha catchments kept groundwater table 50 cm then the non irrigated areas. It was also found that water resources stored in Spring were depleted by June. Its rebuilding in the second part of the vegetation period was possible only when precipitation exceeded the mean value.
... Many applications involving reservoir models with optimization algorithms, both derivative-based and global algorithms, exist in the literature for solving practical subsurface problems related to hydrocarbon production (e.g., Guyagular et al., 2000;Yeten et al., 2003;Sarma and Chen, 2008;Wang et al., 2012), or groundwater production and groundwater remediation (e.g., Gorelick, 1983;Ahlfeld and Heidari, 1994;Maskey et al., 2002;Montoglou et al., 2004). Specifically for optimal well placement problems, due to complex reservoir geometry and heterogeneity in reservoir rock properties, objective functions tend to be highly irregular with multiple local optima in the parameter space (Bayer and Finkel, 2004;Humphries et al., 2013). ...
Large-scale pressure increases resulting from carbon dioxide (CO2) injection in the subsurface can potentially impact caprock integrity, induce reactivation of critically stressed faults, and drive CO2 or brine through conductive features into shallow groundwater. Pressure management involving the extraction of native fluids from storage formations can be used to reduce such pressure increases. However, dealing with large volumes of extracted brine can be technically challenging and expensive. Selection of optimal well locations and pumping rates are critical for maximizing CO2 storage and minimizing brine extraction during geologic CO2 sequestration (GCS). Robust and efficient computerized algorithms combining reservoir models and optimization methods are needed to make proper decisions on well placement and pumping rates. This study presents a constrained differential evolution (CDE) algorithm for solving global optimization problems involving pressure management of GCS projects. Application of the CDE optimization methodology was demonstrated for a hypothetical CO2 storage scenario in a deep sandstone reservoir in the Southern San Joaquin Basin in California, USA. Industrial-scale storage of CO2 would generate significant pressure buildup in this formation, which in turn would raise concerns about induced seismicity due to presence of multiple faults surrounding the injection site. Through the CDE optimization algorithm coupled to a vertically-averaged reservoir simulator, we successfully estimated optimal solutions for brine extraction wells in the reservoir that would limit the local pressure along the faults to a prescribed threshold. Multiple realizations of the reservoir permeability field were created to understand the impact of reservoir heterogeneity on optimization results. Our results indicate that the reservoir slope and heterogeneity have significant impact on optimum extraction rates. Reservoir heterogeneity is also a significant factor for extraction well locations, suggesting that in practice decisions about extraction well placement through optimization should be made at later project stages when data from a few years of CO2 injection have allowed iterative updating and refining of the reservoir forward models. Although the study focused on optimization of brine extraction, the CDE optimization methodology presented in this paper has also potential to solve other complex optimization problems related to GCS, such as increasing storage efficiency by enhancing injectivity and capillary and dissolution trapping.
... Models that solve the governing groundwater flow or solute transport equations (simulation models) in conjunction with an optimization algorithm (optimization model) have been increasingly used as aquifer management tools and are known as S-O models. Models of this kind have been used for different groundwater management problems, such as aquifer remediation (Ahlfeld 1990;Ahlfeld and Heidari 1994;Kuo et al. 1992;Maskey et al. 2002), conjunctive use of surface and groundwater (Barlow et al. 2003;Belaineh et al. 1999;Nishikawa 1998;Peralta et al. 1995), controlling seawater intrusion (Abarca et al. 2006;Bray and Yeh 2008;Hallaji and Yazicigil 1996;Reichard and Johnson 2005;Willis and Finney 1988), and artificial groundwater recharge studies (Jonoski et al. 1997). The S-O approach is in fact quite general and can be applied to many other groundwater management problems. ...
This article presents a simulation-optimization approach for evaluating the feasibility of managed aquifer recharge (MAR) in the Samail Lower Catchment, Oman. The objective is to provide a maximum recharge and extraction rate through MAR in an annual cycle of two successive injection and recovery periods, while meeting operational and system constraints such as water level, gradient, and travel time. Three roundwater management problems were solved by coupling a simulation model with successive linear programming (SLP) and the nondominated sorting genetic algorithm (NSGA-II) multiobjective genetic algorithm. Sensitivity analysis was also completed to examine the overall response of the simulation-optimization results to changes in hydraulic conductivities and maximum injection rates. Results using the SLP algorithm showed that the total volume of injected water for 4 months of injection without recovery is as high as 8 × 106 m3, and the total recovered volume of water for 4 months injection and 8 months recovery is approximately 5.3 × 106 m3, giving a total recovery efficiency of approximately 66%. For the same setup the NSGA-II algorithm derived the entire nondominated front of solutions for two conflicting objectives: maximizing recovery rate and maximizing minimum groundwater head close to the sea (for preventing seawater intrusion). This algorithm includes travel time constraints directly in the optimization process. In conclusion, the proposed approach provides a cost-effective means to evaluate MAR in a coastal aquifer.
... Hsu and Yeh (1989) studied monitoring network design and several groundwater remediation design projects giving rise to combinatorial problems in which decision variables included location of wells and pumping rates. Ahlfeld and Heidari (1994) studied hydrogeological complex sites in which conditions were obscured an obvious intuitive design. Park and Aral (2003) presented a multi-objective optimization approach to determine pumping rates and well locations to prevent saltwater intrusion, while satisfying desired extraction rates in coastal aquifers. ...
Management of groundwater resources is very important for regions where freshwater supply is naturally limited. Long-term planning of groundwater usage requires method-based new decision support tools. These tools must be able to predict the change in the groundwater storage with sufficient accuracy, and must allow exploring management scenarios with respect to different criteria such as sustainability and cost. So, a multi-objective optimization algorithm is used for groundwater management problem. In this paper, a genetic algorithm with two additional techniques, Pareto optimality ranking and fitness sharing, is applied to simultaneously maximize the pumping rate and minimize pumping cost. The methodology proposed has more Pareto optimal solutions. However, it is desirable to get, and to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to help the decision maker. A groundwater resources management model in which performed through a combined simulation-optimization model is used. This multi-objective genetic algorithm (MOGA) of optimization combines the modular three-dimensional finite-difference (MODFLOW) and genetic algorithm (GA). MOGA model is applied in El-Farafra oasis, Egypt to develop the maximum pumping rate and minimum operation cost as well as the prediction of the future changes in both pumping rate and pumping operation cost. It also makes a feasible solution in groundwater management. Finally, a compromise solution is presented from a set of Pareto optimal solutions.
... When aquifers are an important source of water, representing groundwater is an essential part of water resource system management modeling. Groundwater management models and the use of systems analysis in groundwater engineering were reviewed by Gorelick (1983), Willis and Yeh (1987), Yeh (1992) and Ahlfeld and Heidari (1994). Integrating groundwater into systems models poses a challenge because groundwater flows and responses to stresses (e.g. ...
... The LP technique was extensively used for the management of seawater intrusion because of its easy formulation and application (Ahlfeld and Heidari, 1994), however this approach is limited to the problems where both, the objective function and constraints are linear. But the salt intrusion in coastal aquifers is a highly nonlinear process which requires an NLP approach for its appropriate solution (Gorelick et al., 1979;Casola et al., 1986). ...
... This report, however, is not a guide to the application of optimization modeling for aquifer management. For detailed guides to the application of management models, refer to textbooks by Willis and Yeh (1987), Gorelick and others (1993), and Ahlfeld and Mulligan (2000), and to literature reviews by Gorelick (1983), Yeh (1992), Ahlfeld and Heidari (1994), and Wagner (1995). ...
... [4] The three interrelated concerns above are addressed using an optimal design, data collection, and a Bayesian decision-making framework. Combined groundwater simulation and optimization is the tool used for optimal design (for reviews, see Gorelick [1983Gorelick [ , 1990, Yeh [1992], Ahlfeld and Heidari [1994], and Wagner [1995b]). Specifically, the design component employs stochastic simulation optimiza-tion to plan regionally distributed groundwater pumping while preserving the hydroecological balance in wetland areas. ...
... Large-scale constrained nonlinear optimization [Gill et al., 2002] is used to find optimal management strategies within the constraints of the physical and agricultural systems represented by the integrated simulation models. Simulation-optimization methods have been used extensively in groundwater management [e.g., Gorelick, 1983;Yeh, 1992;Ahlfeld and Heidari, 1994;Wagner, 1995;Bredehoeft et al., 1995;Freeze and Gorelick, 1999;Feyen and Gorelick, 2004] and in conjunctive use [e.g., Bredehoeft and Young, 1983;Matsukawa et al., 1992;Reichard, 1995;Rao et al., 2004;Vedula et al., 2005]. This paper builds on these previous simulation-optimization studies, and features three particular strengths: (1) A complex spatially distributed groundwater model is directly incorporated into the optimization procedure, (2) an efficient methodology is used for solving the resulting CPUintensive problem, i.e., using analytical Jacobians and a sequential solution procedure, and (3) the resulting integrated water management model is applied to a large-scale realworld problem in a developing country, generating insights that are also relevant to other irrigated systems. ...
... Hsu and Yeh (1989) studied the monitoring network design and several groundwater remediation design projects gave rise to combinatorial problems in which decision variables include location of wells and pumping rates. Ahlfeld and Heidari (1994) studied hydrogeological complex sites in which conditions obscure an obvious intuitive design; simulation-optimization techniques help decision makers in shedding light over alternate feasible options. Park and Aral (2003) presented a multi-objective optimization approach to determine pumping rates and well locations to prevent saltwater intrusion, while satisfying desired extraction rates in coastal aquifers. ...
Management of groundwater resources is very important for regions where freshwater supply is naturally limited. Long-term planning of groundwater usage requires method-based new decision support tools. These tools must be able to predict the change in the groundwater storage with sufficient accuracy and must allow exploring management scenarios with respect to different criteria such as sustainability and cost. So, a multi-objective optimization algorithm is used for groundwater management problem. In this paper, a genetic algorithm (GA) with two additional techniques, Pareto optimality ranking and fitness sharing, was applied to simultaneously maximize the pumping rate and minimize pumping cost. The methodology proposed herein has more Pareto optimal solutions, however, it is desirable to find the ones scattered uniformly over the Pareto frontier to provide a variety of compromise solutions to the decision maker. A groundwater resources management model is performed through a combined simulation–optimization model. This model is called the multi-objective genetic algorithm (MOGA) for optimization which combines the MODFLOW and GA. MOGA model applied in Wadi El-Farigh, Egypt, to develop the maximum pumping rate and minimum operation cost as well as to predict the future changes in both pumping rate and pumping operation cost. Model makes a feasible solution in groundwater management. Finally a compromise solution is presented from a set of Pareto optimal solutions to help the decision maker.
... [2] Coupled simulation-optimization models are increasingly used as decision models to find optimal solutions to groundwater management problems like optimal groundwater remediation design, optimal extraction of groundwater from coastal aquifers, and wetland management [Gorelick, 1983;Gorelick et al., 1984;Ahlfeld and Heidari, 1994;Hallaji and Yazicigil, 1996;Emch and Yeh, 1998;Wang and Zheng, 1998;Das and Datta, 1999a, 1999bCheng et al., 2000;Mantoglou, 2003;Mantoglou et al., 2004;Katsifarakis and Petala, 2006;Ayvaz and Karahan, 2008;Datta et al. 2009]. One of the major disadvantages of using the coupled simulation-optimization model is the huge computational burden involved due to multiple calls of the simulation model by the optimization algorithm. ...
Approximation surrogates are used to substitute the numerical simulation model within optimization algorithms in order to reduce the computational burden on the coupled simulation-optimization methodology. Practical utility of the surrogate-based simulation-optimization have been limited mainly due to the uncertainty in surrogate model simulations. We develop a surrogate-based coupled simulation-optimization methodology for deriving optimal extraction strategies for coastal aquifer management considering the predictive uncertainty of the surrogate model. Optimization models considering two conflicting objectives are solved using a multiobjective genetic algorithm. Objectives of maximizing the pumping from production wells and minimizing the barrier well pumping for hydraulic control of saltwater intrusion are considered. Density-dependent flow and transport simulation model FEMWATER is used to generate input-output patterns of groundwater extraction rates and resulting salinity levels. The nonparametric bootstrap method is used to generate different realizations of this data set. These realizations are used to train different surrogate models using genetic programming for predicting the salinity intrusion in coastal aquifers. The predictive uncertainty of these surrogate models is quantified and ensemble of surrogate models is used in the multiple-realization optimization model to derive the optimal extraction strategies. The multiple realizations refer to the salinity predictions using different surrogate models in the ensemble. Optimal solutions are obtained for different reliability levels of the surrogate models. The solutions are compared against the solutions obtained using a chance-constrained optimization formulation and single-surrogate-based model. The ensemble-based approach is found to provide reliable solutions for coastal aquifer management while retaining the advantage of surrogate models in reducing computational burden.
... For this particularly difficult kind of problem, discrete optimization algorithms, such as dynamic programming, branch and bound, local search, and evolutionary algorithms (e.g., genetic algorithms), have been applied successfully. For sites in which complex hydrogeological conditions obscure an obvious intuitive design, simulation-optimization techniques help decision makers in shedding light over alternate feasible options (Ahlfeld and Heidari 1994). ...
Increasing demands for water by competing users in semiarid regions pose new challenges for water resources managers. Decision makers must understand the interactions between surface water, groundwater, and the environmental system. Additionally, the decisions made with regard to water transfer and allocation must take into consideration the diverse objectives that include water supply, cost efficiency, and ecosystem protection. The work presented herein demonstrates the use of groundwater simulation and optimization to construct a decision support system (DSS) for solving a groundwater management problem associated with the Upper San Pedro River Basin, located in southeastern Arizona. The case is treated as a multiobjective optimization problem in which environmental objectives are explicitly considered by minimizing the magnitude and extent of drawdown within a prespecified region. The approach adopted uses the constraint method to derive the tradeoffs among three competing objectives. Once the proposed algorithm identifies a set of efficient solutions (alternatives), concepts borrowed from fuzzy set theory are applied to rank the alternatives and to assist decision makers in selecting a suitable policy among them, each of which is optimum with regard to its goal and the corresponding consequences.
... A considerable amount of work has been done to optimize the performance of various ground-water systems ranging from simple linear programming applications [e.g., Ahlfeld and Heidari (1994)] to complex nonlinear optimization techniques [e.g., Jones et al. (1987) and Ahlfeld and Hill (1996)]. In the current context, linear programming is clearly inappropriate for (9) since it is nonlinear. ...
Conventional landfill design attempts to control the downward seepage of leachate by using low permeability liners. The rate of leachate seepage into the underlying ground-water system can be controlled by decreasing the permeability of soil liners and/or by using synthetic membranes to form an additional barrier to leachate migration. However, loss of leachate from conventional landfills is likely to occur due to the inherent limitations of natural materials and the inevitable imperfections of installing synthetic liners. The artesian landfill liner system eliminates the downward seepage by reversing the direction of the hydraulic gradient so that seepage occurs into, and not out of, the landfill. A conceptual cost model incorporates the trade-offs between the capital cost of constructing robust liners and the operational costs of supplying recharge water and treating additional leachate produced by the artesian hydraulics. In addition, a two-dimensional, transient finite-element flow model demonstrates that the reverse hydraulic gradient limits the loss of leachate even if the integrity of the landfill liner is imperfect or deteriorates over time.
Environmental pollution is a global threat arising from growing human activities and release of unwanted particles and chemicals in the ecosystem. Since the industrial revolution, rapid industrialization and urbanization have led to uncontrolled release of waste in river streams and lakes. Large-scale and excessive use of fertilizers, pesticides in agricultural pastures, unsustainable manufacture, use and discard of plastic products together with industrial and chemical wastes such as heavy metals dumped into the environment cause many irreversible issues for human and plants. While a large number of research works are being carried out on the remediation of environmental pollution and policies such as the Sustainable Development Goal 12 seeking to “ensure sustainable consumption and production patterns,” plants have found their own way of living and surviving environmental pollution. This chapter discusses the approaches that plants have matured including antioxidant, photosynthesis, and growth characteristics in order to survive the challenging polluted soils they are growing in.
Heavy metals contamination in soil and water resources is a great threat to developing countries because of the lack of waste treatment facilities. A majority of wastewater treatment methods are known to be expensive and out of reach for municipalities and small pollution treatment enterprises. Phytotechnology is a promising, sustainable, environment-friendly, and cost-effective technique for domestic and industrial wastewater treatment in places where land is available. However, interest in conventional remediation methods and the lack of information on recent advances in a significant portion of the society in developing countries have restrained the applications of phytoremediation. This review discusses the concept of phytoremediation, mechanisms of heavy metals removal by the plants, and the potential application of enhanced phytoremediation technologies in developing countries like Nepal. The authors also review the commercially viable hyperaccumulator species with their native distribution, heavy metals intake capacity, and their availability in Nepal. Those native plants can be utilized locally or introduced strategically in other parts/countries as well. Thus, for a flora-rich country like Nepal, the study holds great potential and presents enhanced phytoremediation as an effective and sustainable strategy for the future.
The concerns of committed researchers and environmentalist for safety food production has pushed further to search for adequate information and experiment the use of plants (hyper-accumulators) for remediating polluted soils and water bodies. This review book has provided information on various conventional techniques and the shortcomings in their uses for remediation purposes. Out of all the techniques, bioremediation (phytoremediation/rhizofiltration) emerged a promising technique for removing pollutants from soil and water bodies. Different sources of pollution, associated contaminants, and their routes through which they cause pollution on soil and water bodies were reviewed. So also, notable plants for remediation purposes were mentioned and the particular heavy metals they mop up. The use of plants in combination with other techniques for instance; amendments with biochar before the use of hyperaccumulating plant, the use of mycorrhizal assisting and increasing the heavy metal absorption area, and introduction of microbes that consume some pollutants as food were discussed. The convincing results of many experimented research works concluded the ultimate application of this cost-effective, less laborious, and environmentally safe phytoremediation technique for safety food production.
Phytoremediation is a strategic, efficient, and eco-friendly tool to deal with environmental pollution, in order to attenuate the harmful impacts this contamination may cause to life on Earth, restoring polluted areas. Anthropic action without concern regarding sustainability can result in the accumulation of organic and inorganic substances on ecosystems, disrupting the balance previously existent, intoxicating living beings, and even causing their death. Different plant species can deal with environmental pollutants through mechanisms of phytoremediation that vary depending on the chemical nature of the contaminant to be remediated, contaminated environ, and plant species being used. This chapter will explore the main phytoremediation mechanisms by which plants can phytoremediate.
In contrast to management optimisation methods, which quantify decision variables to create plans, this study does not seek the “best” strategy. Instead, it simulates the sequential decision-making process implicit in environmental management, so that the effectiveness of management scenarios, when implemented as intended, can be evaluated. The purpose was to develop a methodology to quantitatively evaluate the effectiveness of groundwater management plans by simulating sequential management decisions that evolve based on aquifer/management feedback. A groundwater management scheme was structured as a system control loop to capture the aquifer/management feedback, and management decisions were based on realistically sparse observation times and locations. The method indicates how a plan may proceed in reality under alternate timings and frequencies of management decisions and in systems with differing response times. A synthetic example quantified the impact of a generic plan, specifying environmental objectives, extraction restrictions and entitlement limits (maximum volume/year that users are permitted), relative to no-management by combining a numerical model of “reality” with management rules under a stochastic climate. The management decision-making frequency varied from daily to decadal. Generally, effectiveness decreased as the interval between management interventions increased and intervals greater than annual showed minimal improvement compared to entitlement only. The timing of management decisions relative to the irrigation season also impacted plan effectiveness, and when decisions were made prior to the irrigation season, quarterly management was less effective than annual and biannual management. By testing the capacity of plans to achieve objectives, groundwater management can be systematically and objectively improved.
Polluted soil and water impact the quality of food and nutrients of human and animal biota. Soil and water are mainly polluted
by effluent discharges from industries, which are broadly classified into metallic and nonmetallic pollutant-bearing
effluents. In order to tackle this problem, a plant-based technology called phytoremediation is used to clean contaminated
lands. Phytoremediation is based upon several processes such as phytodegradation, phytovolatilization, phytoaccumulation
and phytoextraction. These methods are efficient, eco-friendly and economic. This paper reviews the methods and mechanisms
involved in phytoremediation of heavy metals, and enhancement processes.
Keywords Heavy metals · Phytoremediation · Eco-friendly · Mechanism · Enhancement
Water resources management is a challenging problem in Iran and in many other locations because of the unbalanced temporal and spatial distribution of available water and demands. Interbasin water transfer, in which water is transmitted from a basin with high water availability to a neighbor basin with high water use, has been proposed as a solution to water scarcity. Because of the various decision-making factors, studies of interbasin water transfer projects have been presented as complex and difficult in the literature. In this paper, an optimum design for the capacities of the Behesht-Abad interbasin water transfer system, from the upstream Karoun basin to the Gavkhooni basin in central Iran, has been studied using a simulation-optimization approach in which particle swarm optimization (PSO) is coupled with the river basin simulation model, to find the optimum values for decision variables. In another approach, by use of multicriteria decision making (MCDM) and quantifying selected criteria in the source and target basins, the most beneficial scenario for water transfer is selected by prioritizing six possible alternatives. Results obtained by both PSO-MODSIM and MCDM approaches are close to each other and show that under conditions consistent with recent drought years, the optimum capacity of the water transfer tunnel is obtained to be a maximum of 45% of the capacity under conditions consistent with long-term historical discharges of the rivers.
The implementation of environmental projects, which has been very successful when restoring degraded water
resources, is by itself not enough. The optimum combined operation of artificial water resources and natural systems, plays a crucial role in achieving sustainable management. This study presents a methodology for the simulation and optimization of Lake Karla watershed groundwater use for domestic water supply and irrigation, under two constraints of groundwater restoration. This is achieved by using a coupled modeling system of artificial and natural water resources simulation and a conjunctive groundwater optimization-simulation model. The groundwater flow model simulates the operation of the alluvial phreatic aquifer under different groundwater management scenarios. The management model GWM estimates the optimum pumping rates, the number and the locations of irrigation and domestic water supply wells. Optimal pumping rates were inserted into the groundwater flow model and the hydraulic head maps of the aquifer and the volumetric budget was estimated. Four alternative management scenarios for the location of 40 water supply wells for the city of Volos have been studied and optimized. These water supply wells are part of the Lake Karla restoration project and they will be located at the southern part of the aquifer, where the greatest drawdown of the water table has been observed. The management scenarios were evaluated regarding the two environmental constraints of groundwater rehabilitation and the optimal groundwater use.
An optimal pumping policy during groundwater extraction ensures the sustainability of groundwater resources. In this paper, a coupled finite element-particle swarm simulation–optimization model is implemented to assess the optimal pumping policy in a confined heterogeneous anisotropic synthetic aquifer. Pumping wells are set up in the aquifer to meet a specified water demand. The objective is to find the optimum number and pumping discharges of these wells such that their collective drawdown is minimized while meeting the demand at a reasonable cost. Constraints on the maximum allowable pumping discharge and the location of the wells are also imposed. After analysing the aquifer behaviour in the presence of 8, 9 and 10 pumping wells, the optimal number of wells is selected. The coupled FEM-PSO model also predicts the spatial distribution of the wells that incur the minimum cost for installation and pumping to a specified storage location. Adequate tuning of the PSO parameters involving population size, inertia weight, acceleration constants and number of iterations is performed to arrive at their optimal values.
Irrigation is essential for achieving food security to the burgeoning global population but unplanned and injudicious expansion of irrigated areas causes waterlogging and salinization problems. Under this backdrop, groundwater resources management is a critical issue for fulfilling the increasing water demand for agricultural, industrial, and domestic uses. Various simulation and optimization approaches were used to solve the groundwater management problems. This paper presents a review of the individual and combined applications of simulation and optimization modeling for the management of groundwater-resource problems associated with irrigated agriculture. The study revealed that the combined use of simulation-optimization modeling is very suitable for achieving an optimal solution for groundwater-resource problems, even with a large number of variables. Independent model tools were used to solve the problems of uncertainty analysis and parameter estimation in groundwater modelling studies. Artificial neural networks were used to minimize the problem of computational complexity. The incorporation of socioeconomic aspects into the groundwater management modeling would be an important development in future studies.
Protection, restoration and development of groundwater supplies and remediation of contaminated aquifers are the driving issues in groundwater resource management. These issues are further triggered on and driven by the population expansion and increasing demands. To transform the 'vicious circles' of groundwater availabilities into 'virtuous circles' of demands, understanding of the aquifer behavior in response to imposed stresses and/or strains is essentially required. If groundwater management strategies are directed towards balancing the exploitations in demand side with the fortune of supply side, the goals of groundwater management can be achieved when the tools used for solution of the management problems are derived considering mechanisms of supply-distribution-availability of the resource in the system. Groundwater modeling is one of the management tools being used in the hydro-geological sciences for the assessment of the resource potential and prediction of future impact under different stresses/constraints. Construction of a groundwater model follows a set of assumptions describing the system's composition, the transport processes that take place in it, the mechanisms that govern them, and the relevant medium properties. There are numerous computer codes of groundwater models available worldwide dealing variety of problems related to; flow and contaminants transport modeling, rates and location of pumping, artificial recharge, changes in water quality etc. Each model has its own merits and limitations and hence no model is unique to a given groundwater system. Management of a system means making decisions aiming at accomplishing the system's goal without violating specified technical and non-technical constrains imposed on it. A complete groundwater management model is the combination of groundwater simulation models and the optimization methods. A management approach has its own mathematical logic and constraints complemented by the simulation models. It is simulation models, which actually impart groundwater sciences to the management to evaluate potentiality and the fate of the resource for different options and constrained cases. Thus, to meet the increasing demands of water for variety of uses when the supply-side becomes a limiting case or being dragged by the pollution threats, the uses of groundwater models to the management problems are bound to increase and new modeling techniques with inclusion of more real world complexities with improved predictive capacity are bound to dominate the decision process.
Groundwater overpumping could cause serious land subsidence. Although groundwater management models have been widely applied to obtain optimal pumping strategies for land subsidence control, most of them have not explicitly incorporated the land subsidence into model’s constraints. This study presented a groundwater management model explicitly considering land subsidence. To quantify the relation between land subsidence and drawdown, the one-dimensional consolidation equation was adopted which simultaneously accounts for the elastic and inelastic compaction due to pumping. Based on the response matrix technique along with one-dimensional consolidation equation, a groundwater quantity management model was developed which enables the determination of maximum total pumpage subject that the land subsidence do not exceed the allowable value. The developed management model was non-smooth optimization problem. To improve the solution efficiency, the non-smooth optimization was transferred into mixed integer linear programming (MILP) by introducing the binary variables. A hypothetical example was utilized to demonstrate the applicability of developed model. The results indicated that the land subsidence should be explicitly incorporated into model’s constraints; otherwise the optimal total pumpage might be overestimated. Moreover, the simultaneous consideration of elastic and inelastic compaction in groundwater management was important, especially when the difference between initial head and preconsolidation head was significant.
The world population is increasing continuously and is expected to reach the 9.5billion mark in 2050 from the current 7.1billion. The importance of the groundwater resources is also increasing with the increase in population, because the quality and quantity of water resources are continuously declining because of urbanization, contamination, and climate change impact. Thus, under the current environment, the conservation and management of groundwater resources is a critical challenge for fulfilling the rising water demand for agricultural, industrial, and domestic uses. Various simulation and optimization approaches have been used to solve the groundwater management problems. Optimization methods have proved to be of great importance when used with simulation models, and the combined use of these two approaches gives the best results. The main objective of this review is to analyze combined uses of simulation and optimization modeling approaches and to provide an impression of their applications reported in literature. In addition to traditional optimization techniques, this paper highlights the application of computational intelligence techniques, such as artificial neural networks, response matrix approach, and multiobjective approach. Conclusions are drawn based on this review, which could be useful for system managers and planners for selecting the best suitable technique for their specific uses.
The management of groundwater resources is a critical issue against the backdrop of the increasing water demand for agricultural, industrial, and domestic uses and dwindling water resources. Various simulation and optimization approaches have been used to solve the groundwater management problems. This paper presents an overview of the simulation and optimization modeling approaches used in groundwater resources conservation and management. The main objective of this review is to analyze simulation and optimization modeling approaches and to provide an assessment of their applications reported in literature. Conclusions are provided based on this evaluation, which could be useful for system managers and planners for selecting the suitable modeling approach for their specific uses.
Good quality surface water and groundwater resources are limited furthermore they are shrinking because of the urbanization, contamination, and climate change impacts. In this backdrop, the proper allocation and management of these resources is a critical challenge for satisfying the rising water demands of agricultural sector. Because irrigated agriculture is the largest user of all the developed water resources and consumes over 70% of the abstracted freshwater globally. The computer-based models are useful tools for achieving the optimal allocation of limited water resources for the conjunctive use planning and management in irrigated agriculture. Various simulation and optimization modeling approaches have been used to solve the water allocation problems. Optimization models have been shown to be of great importance when used with simulation models and the combined use of these two approaches gives the best results. The reviews on the combined applications of simulation and optimization modeling for the conjunctive use planning and management of surface water and groundwater resources for sustainable irrigated agriculture are done and presented in this paper. Conclusions are provided based on this review which could be useful for all the stakeholders.
The coastal aquifers of the world are facing environmental problem of seawater intrusion. This problem is the results of indiscriminate and unplanned groundwater exploitation for fulfilling the growing need of freshwater for the burgeoning global population. There is a need to develop appropriate management models for assessing the maximum feasible pumping rates which protects seawater intrusion in coastal aquifers. The comprehensive reviews on the use of various programming techniques for the solution of seawater intrusion management problem of coastal aquifers have been provided in this paper. The literature review revealed that the management models used in the past mainly considered the objectives of maximization of pumping rate, minimization of drawdown, minimization of pumped water, minimization of seawater volume into the aquifer, and/or minimization of pumping cost. The past reviews are grouped into five sections based on the programming techniques adopted. The sections include: linear programming, nonlinear programming, genetic algorithms, artificial neural networks, and multiobjective optimization models. Conclusions are drawn where gaps exist and more research needs to be focused. This review provides the basis for the selection of appropriate methodology for the management of seawater intrusion problems of coastal aquifers.
Waterlogging and secondary salinization have become a serious problem in the canal irrigated areas of arid and semi–arid regions worldwide. In this study, a unique and simple technique was evolved in which a linear programming (LP) optimization model was first developed that allocates available land and water resources in order to maximize net annual returns by mitigating the waterlogging problems. A finite–difference two–dimensional simulation model was then used to evaluate the long–term impacts of various water management strategies on the groundwater table with the optimal land and water use parameters which were obtained through the optimization model. The model was used to combat the waterlogging and salinity problem of an area located in Haryana State of India. The calibration, validation, sensitivity analysis, and error analysis of the model was performed before it was used to study the impact of various water management scenarios on the long-term groundwater level. Based on the model results a change in cropping pattern with reduced rice area is suggested. Groundwater withdrawal should be increased by 1–7 % in the various nodes. It is concluded from the analysis of various scenarios that implementing multiple approaches simultaneously are more effective in controlling waterlogging problems as compared to individual interventions.
Typical groundwater remediation problems involve the design of the number, location and flow rate schedule of pumping and injection wells. Simulation models combined with optimization models are used to rank alternatives while considering management objectives, e.g. minimizing remediation cost and/or maximizing cleanup efficiency, and constraints, e.g. the maximum permissible concentrations at selected compliance sites. Mostly due to both high computational effort required and lack of data, the simulation models often are based on simplified 2D homogeneous hydrogeologic settings. The purpose of this work is to investigate how simplifying hypotheses may affect the final optimal remediation policy. In particular, the analysis addresses the case of a heterogeneous layered aquifer versus an homogeneous one with an equivalent (lumped) hydraulic conductivity. To simulate groundwater flow and contaminant transport, use is made of a fully 3D finite element unsaturated flow model along with a particle tracking transport code. The flow and transport code is then coupled to a genetic algorithm model to optimize the specified objective function. The problem considered is the remediation of a hypothetical aquifer-contaminant system using pump and treat. The objective is to minimize the cost of the remediation system. The cost function is a nonlinear function of decision variables (pumping rates) and state variables (hydraulic heads and contaminant concentrations). Constraints include limits on hydraulic head and the contaminant mass remaining in the aquifer at the end of the remediation. The results of homogeneous and heterogeneous simulations are compared in terms of cost and values of the decision variables.
A new optimization formulation for designing groundwater plume control systems is presented. The new formulation uses particle-tracking techniques in a two-step solution process. The two-step procedure is motivated by numerical and computational considerations; particle representation is defined to take advantage of specific properties and improve model convergence. The optimization formulation seeks the least cost control system that satisfies the two equivalent requirements that the contaminant plume be located within the capture zone (step 1) and that all particles representing contaminant solute travel to an extraction well (step 2). To date, optimization formulations for plume capture design have emphasized either hydraulic or concentration control; however, these formulations provide indirect representation of the plume control and containment problem. The model presented here explicitly represents the capture zone design problem using particle tracking and formalizes the design procedures used by many practitioners. Two example problems representing two- and three-dimensional flow systems are used to demonstrate the new advective control model. Hydraulic control formulations for the two problems are also developed, and designs are compared with those of the advective control model. Control systems resulting from the hydraulic control model are sensitive to constraint magnitude and location, highlighting the need for constraint calibration in order to best achieve design goals. Conversely, constraints in the new model directly represent the plume capture problem, and the model provides more efficient capture zone designs than the hydraulic control formulation.
Management models are developed and solved that are based on the advective-dispersive density-dependent miscible flow and transport processes in the aquifer. Various conflicting objectives of aquifer management are considered in this study. Two optimization models incorporating multiple objectives of coastal aquifer management are formulated. These models are solved for a hypothetical three-dimensional aquifer system for transient flow and transport conditions. The obtained solution results demonstrate potential feasibility of using the embedding technique for the development of multiple-objective coastal aquifer management models. In general, a planned, spatially and temporally, varying pumping strategy, obtained as solutions of an embedded optimization model, is shown to be a viable management method for beneficial exploitation and salinity control of a coastal aquifer. The potential feasibility of these management models for evolving a transient spatially dependent pumping strategy to facilitate beneficial exploitation of the aquifer and to control or remediate contamination due to seawater intrusion is also demonstrated.
A decision framework is presented for assessing the value of ground-water sampling within the context of ground-water management under uncertainty. The framework couples two optimization models-a chance-constrained ground-water management model and an integer-programing sampling network design model-to identify optimal pumping and sampling strategies. The methodology consists of four steps: (1) The optimal ground-water management strategy for the present level of model uncertainty is determined using the chance-constrained management model; (2) for a specified data collection budget, the monitoring network design model identifies, prior to data collection, the sampling strategy that will minimize model uncertainty; (3) the optimal ground-water management strategy is recalculated on the basis of the projected model uncertainty after sampling; and (4) the worth of the monitoring strategy is assessed by comparing the value of the sample information-i.e., the projected reduction in management costs-with the cost of data collection. Steps 2-4 are repeated for a series of data collection budgets, producing a suite of management/monitoring alternatives, from which the best alternative can be selected. A hypothetical example demonstrates the methodology's ability to identify the ground-water sampling strategy with greatest net economic benefit for ground-water management.
Models which solve the governing groundwater flow or solute transport
equations in conjunction with optimization techniques, such as linear
and quadratic programing, are powerful aquifer management tools.
Groundwater management models fall in two general categories: hydraulics
or policy evaluation and water allocation. Groundwater hydraulic
management models enable the determination of optimal locations and
pumping rates of numerous wells under a variety of restrictions placed
upon local drawdown, hydraulic gradients, and water production targets.
Groundwater policy evaluation and allocation models can be used to study
the influence upon regional groundwater use of institutional policies
such as taxes and quotas. Furthermore, fairly complex
groundwater-surface water allocation problems can be handled using
system decomposition and multilevel optimization. Experience from the
few real world applications of groundwater optimization-management
techniques is summarized. Classified separately are methods for
groundwater quality management aimed at optimal waste disposal in the
subsurface. This classification is composed of steady state and
transient management models that determine disposal patterns in such a
way that water quality is protected at supply locations. Classes of
research missing from the literature are groundwater quality management
models involving nonlinear constraints, models which join groundwater
hydraulic and quality simulations with political-economic management
considerations, and management models that include parameter
uncertainty.
Optimal annual operation of a coastal aquifer is determined by using a multiple objective linear programing model based on a multicell model of the aquifer and a network representation of the hydraulic distribution system. The decision variables are pumping and/or recharge quantities in each cell. Four objective functions are based on (1) a desired ground water surface map, (2) a desired location of the sea water-fresh water interface toe in each coastal cell, (3) a desired concentration map of a selected conservative contaminant, and (4) minimization of the energy for pumping and recharge. An approximate linearized expression of the location of the interface has been developed to enable the use of linear programing as the optimization method. A trade-off procedure is employed for identifying the most desirable solution. The model is applied to a segment of the coastal aquifer in Israel (a 44-km strip along the coast with a width of 7 to 15 km) and results are discussed.
A large-scale field experiment on natural gradient transport of solutes in groundwater has been conducted at a site in Borden, Ontario. Well-defined initial conditions were achieved by the pulse injection of 12 m3 of a uniform solution containing known masses of two inorganic tracers (chloride and bromide) and five halogenated organic chemicals (bromoform, carbon tetrachloride, tetrachloroethylene, 1,2-dichlorobenzene, and hexachloroethane). A dense, three-dimensional array of over 5000 sampling points was installed throughout the zone traversed by the solutes. Over 19,900 samples have been collected over a 3-year period. The tracers followed a linear horizontal trajectory at an approximately constant velocity, both of which compare well with expectations based on water table contours and estimates of hydraulic head gradient, porosity, and hydraulic conductivity. The vertical displacement over the duration of the experiment was small. Spreading was much more pronounced in the horizontal longitudinal than in the horizontal transverse direction; vertical spreading was very small. The organic solutes were retarded in mobility, as expected.
To date optimization models for groundwater quality management give no assurance that water quality standards will be met. This is in part because they ignore errors in hydraulic heads, flows, and solute concentrations due to flow and transport model parameter uncertainty. Here we explicitly incor-porate parameter estimation and estimate uncertainties into a model for the optimal design of an aquifer remediation scheme. Parameter uncertainty is incorporated into the decision-making process. The objec-tive is to identify the best remediation strategies (well site selection and pumping-recharge rates) so that water quality standards are met at a specified reliability level. The procedure couples three methods: (1) a finite element flow and transport simulation model combined with nonlinear least squares multiple regression for simultaneous flow and transport parameter estimation; (2) first-order first-and second-moment analysis to transfer the information about the effects of parameter uncertainty to the manage-ment model; and (3) nonlinear chance-constrained stochastic optimization combined with flow and transport simulation for optimal decision making. This joint approach enables one to estimate unknown aquifer parameters, quantify the uncertainty of the parameter estimates, simulate flow and transport responses, and automatically account for parameter uncertainty in the decision-making process through the simulation management model. Results show that remediation requirements can increase dramati-cally due to parameter uncertainty. Risk-averse design solutions automatically provide insurance by "overdesigning" the strategy relative to the risk-neutral case. The approach is fairly general and is applicable to a variety of groundwater management problems. The influence on design solutions of the reliability level and verification of the underlying statistical assumptions of the first-order analysis are explored in a sensitivity study and 2000 Monte Carlo simulations, respectively.
The problem of where to drill wells, how many to drill, and how to pump them in order to maintain low water levels in an excavation most economically is formulated as a fixed-charge problem. The cost to be minimized includes fixed installation costs and the variable costs of pumping. The governing ground-water equations in numerical form are included as constraints. The solution includes optimal well locations, costs, steady-state discharge schedules, and hydraulic head distributions.
The problem dealt with herein is to determine the optimal operation of production wells in a multilayered groundwater reservoir. The aquifer is assumed to be divided by interlying a relatively thin aquitard. Namely, the upper aquifer is regarded as a phreatic leaky aquifer while the lower aquifer as a confined leaky aquifer (see Fig.1). Hereafter, the water-table aquifer and the confined aquifer are referred to as I-layer and III-layer respectively. The aquitard is called II-layer. It is also assumed that some wells penetrate the I-layer only, some have screens only in the III-layer and some completely penetrate both I- and III-layers.
The problem of where to drill wells, how many to drill, and how to pump them in order to maintain low water levels in an excavation most economically is formulated as a fixed-charge problem. The cost to be minimized includes fixed installation costs and the variable costs of pumping. The governing ground-water equations in numerical form are included as constraints. -from ASCE Publications Abstracts
Nonlinear optimization models are presented for the optimal operation of
an unconfined aquifer system. The aquifer's response equations are
developed using finite difference methods, quasilinearization, and
matrix calculus. The optimization model, which is structured as a
discrete time optimal control problem, identifies the optimal pumping
pattern necessary to satisfy an exogenous water demand. A
quasilinearization optimization algorithm and projected Lagrangian
methods are used for the solution of the planning model. Example
problems are presented which demonstrate the viability of the approach
for nonlinear, nonconvex groundwater management problems.
An optimization approach to designing contaminated groundwater aquifer remediation systems is described and used to analyze alternate hypothetical remediation strategies at a Superfund site in Woburn, Massachusetts. The methodology combines two-dimensional convective-dispersive transport simulation, nonlinear optimization, and sensitivity theory. Remediation strategies are generated based on different design criteria as represented by two alternate optimization formulations. It is demonstrated that field scale simulation models can be successfully incorporated into a nonlinear optimization framework to solve important design problems. Through the use of sensitivity theory for the transport simulation model it is possible to solve field scale problems with at least an order of magnitude less computational effort than when using perturbation methods.
In many cases, mitigation of the impact of localized groundwater contamination can be achieved, or enhanced, by using groundwater withdrawal and/or injection to control plume migration. However, for complicated flow domains, where multiple wells are required, the determination of the pumping rates necessary to achieve a specific plume manipulation objective is nontrivial. A relatively simple and flexible methodology is presented for initial screening estimation of pumping rates that will achieve plume manipulation objectives. Plume manipulation objectives are formulated as unconstrained nonlinear minimization problems using penalty function methods. For solution, a nonlinear mathematical programming algorithm is loosely coupled to a finite difference simulator of the hydraulic response of the flow domain to pumping and a numerical integration routine for plume tracking.
A three-dimensional finite element model combined with an optimization approach based on linear mixed integer programming is developed and applied to assist in the design of the dewatering system for the electronuclear plant to be built by the Italian Electric Agency (ENEL) in Trino Vercellese, northwestern Italy. The foundations site is encompassed by a 25- to 35-m deep plastic wall with the purpose of protecting the unconfined aquifer from the significant water table lowering required by the construction project. To reduce further the propagation of the depression cone a large amount of the water pumped out is reinjected through ad hoc recharge ditches. The finite element optimization model includes both the natural and the artificial constraints and provides several optimal withdrawal strategies for the dewatering system design concerning the distribution of the abstraction wells and the corresponding pumping rates. Physical and economical objective functions are explored and the related solutions are discussed.
Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities.
Groundwater simulation modeling, mathematical programing, and decision
theory are combined to plan and manage an irrigated farm, subject to
variation in economic factors such as pumping costs and crop prices, in
hydrologic factors such as transmissivity and storage coefficient, and
in physical factors such as the choice of a physical model of the
groundwater system. Those factors that are most critical to planning and
managing the farm are identified and analyzed. The results of the
analysis are a decision on cropping and pumping patterns over a design
period, a choice of a physical model of the groundwater system that
meets the needs of the farm, a ranking of data by the worth to the farm
(worth being related to the regret incurred by the farm when an
undesirable decision is made), and a ranking of data by priority for
further data collection activities.
A stochastic groundwater management model for a confined, homogenous, and nonuniform aquifer is developed using the concept of response function in the linear system theory. The Cooper-Jacob equation is used to develop the unit response function. The model explicitly considers the random nature of transmissivity and storage coefficient, which enables the determination of optimal pumping pattern in a well field subject to a specified system performance reliability requirement. A hypothetical example is utilized to demonstrate applicability of the model. Model results affected by reliability requirement and.uncertainty level of aquifer parameters were examined. A post-optimality simulation is conducted to examine the performance of the model and to further assess its usefulness.
The objective of this paper is to review the state of the art of systems analysis and optimization techniques developed in the field of water resources for the planning and management of a ground-water system. The areas reviewed include the following: ground-water management models, inverse solution techniques for parameter identification, and optimal experimental design methods. Emphasis is placed upon ground-water supply management models, as opposed to models used for ground-water quality management. The techniques that have been used in the optimization of ground-water management include: linear programming, mixed-integer and quadratic programming, differential dynamic programming, nonlinear programming, and simulation. The inverse problem of parameter identification pertains the optimal determination of model parameters using historical input and output observations. Because of data limitation in both quantity and quality, the inverse problem is inherently ill posed. This paper summarizes recent advances made in the inverse procedures and methods developed to alleviate the problems of instability ard nonuniqueness of the identified parameters. The optimal experimental design problem addresses the issue of data requirements and optimal sampling strategies for the purpose of parameter identification. A criterion must be established for the optimal design of a pumping test. The fundamental concept of optimal experimental design and various criteria used for optimization are reviewed.
Although available technology may be inadequate for the complete remediation of certain contaminated ground water-sites, hydraulic control can be used to reduce the extent of, and contain, ground-water contaminants until adequate technology can be developed. The design of such a remediation system can be viewed as a two-stage process. A first stage is the achievement of a reduction of the extent of the contaminant, and a second stage is the maintenance of the contaminant at this reduced areal extent. Viewed in this light, alternative pump staging criteria can be considered within the design process. Triese criteria can include allowing the well location and pumping rate to change during the remediation effort. This paper analyzes the economic significance of incorporating increasing complexity of pump-stage criteria into the design process. The analysis is conducted using numerical simulation and a new multistage optimization formulation. The analysis concludes that while different pumping strategies should be used in each stage of remediation, it is generally unnecessary to consider the impact of the pumping strategy in the first stage on the remediation cost in the second stage.
A successive approximation linear quadratic regulator (SALQR) method with management periods is combined with a finite element groundwater flow and transport simulation model to determine optimal time-varying groundwater pump-and-treat reclamation policies. Management periods are groups of simulation time steps during which the pumping policy remains constant. In an example problem, management periods reduced the total computational demand, as measured by the CPU time, by as much as 85% compared to the time needed for the SALQR solution without management periods. Conversely, the optimal costs increased as the number of times that the control can change is reduced. With two simulation periods per management period, the optimal cost increased by less than 1% compared to the optimal cost with no management periods, yet the computational work was reduced by a third. The optimal policies, including the number and locations of wells, changed significantly with the number of management periods. Complexity analysis revealed that the SALQR algorithm with management periods can significantly reduce the computational requirements for nonsteady optimization of groundwater reclamation and other management applications.
Attempts to store fluids in confined aquifers will sometimes be frustrated by regional groundwater flow and/or by buoyancy drift due to density differences between the stored fluid and the native groundwater. Such effects can largely be overcome through the use of gradient control wells. A procedure based on linear programing can be used for the initial design of a well field that will create a zero gradient or a finite gradient in a given region. The finite difference form of the steady state groundwater equation provides one set of constraints, while the gradient condition in the storage region provides a second set. A standard linear programing solution routine is then used to provide the minimum pumping rates and head distribution consistent with the constraints and the chosen well array.
Distributed parameter groundwater simulation models are difficult to couple explicitly with management models that seek to optimize an economic objective. For a groundwater system whose drawdown in response to pumping was modeled by a two-dimensional linear partial differential equation, an algebraic technological function was produced that related seasonal pumping at wells in the system to drawdown at those wells. The algebraic technological function allowed an explicit coupling of the groundwater model with a quadratic programing management model.
A three-dimensional groundwater flow management model for making decisions on the design of hydrodynamic control of a groundwater flow system using a combination of extraction and/or injection wells is developed. The model takes into account constraints imposed on the system to stop the horizontal spread of contaminants and to ensure a net upward flow in areas where downward vertical gradients exist. The mathematical formulation of the groundwater remediation problem as a mixed-integer model and the strategy for solving the model are presented. Numerical results are presented for the Toms River Plant site, which is modeled as a five-layer aquifer system with interconnecting aquitards. A sensitivity analysis on the relative magnitude of the continuous operating costs and the fixed-charge costs is also presented.
The equations of transient and steady-state flow in two-dimensional artesian aquifers are approximated using finite differences. The resulting linear difference equations, combined with other linear physical and management constraints and a linear objective function, comprise a linear programming (LP) formulation. Solutions of such LP models are used to determine optimal well distributions and pumping rates to meet given management objectives for a hypothetical transient problem and for a steady-state field problem.
This study considers the design and analysis of nonpumped well systems to provide pressure relief in the Cochrane aquifer, which is hydraulically connected to the Waterton Reservoir, Analyses of the relief well management problem are performed with a management model formulated by the combined simulation-optimization approach. The model determines active relief well sites and their optimal discharge schedules. The existing relief wells are inadequate to provide the desirable pressure relief. The locations and design capacities of two new relief well systems are determined by the management model. The relationships between reservoir level and well discharge are estimated for these two well systems.
A ground-water-management model was developed to investigate the best management options for the containment of an oil-field-brine plume in the Equus Beds aquifer in south-central Kansas. The main purpose of the management model was to find the optimal locations and minimum rates of pumpage of a set of plume-interception wells, to successfully reverse the velocity vectors at observation wells located along the plume front, and also to satisfy freshwater demands from supply wells. The effects of the calculated minimum withdrawals from the interception wells on the migration of contaminants throughout the ground-water system were evaluated utilizing a solute-transport model. This latter analysis was carried out to ensure the containment of the plume. Whereas application of the management model to the study area achieves the management objectives, the implementation of the results is believed to be impractical and expensive. This is because a considerable amount of water must be pumped out to reverse the velocity vectors in the vicinity of the plume. In general, the proposed technique of pollutant containment may be effective when applied to aquifers having low hydraulic gradients and/or to aquifers with hazardous plumes whose containment is not subject to economic constraints.
ABSTRACTA groundwater hydraulic management model is used to identify the optimal strategy for allocating limited fresh-water supplies and containing wastes in a hypothetical aquifer affected by brine contamination from surface disposal ponds. The present cost of pumping from a network of potential supply and interception wells is minimized over a five-year planning period, subject to a set of hydraulic, institutional, and legal constraints. Hydraulic constraints are formulated using linear systems theory to describe drawdown and velocity variables as linear functions of supply and interception well discharge decision variables. Successful validation of the optimal management strategy suggests that the model formulation can feasibly be applied to define management options for locally contaminated aquifer systems which are used to fulfill fresh-water demands.
This paper describes the formulation and application of a ground-water hydraulic management model to determine the optimal development and operating policies of a regional aquifer in the Eastern Province of Saudi Arabia. The hydraulic response of the aquifer system is represented by a simulation model that is linked to an optimization management model using response functions. Yearly optimal ground-water extraction rates over a planning horizon of 15 years are determined for four scenarios, each reflecting alternative ground-water development policies. The results are presented in the form of tradeoff curves, relating drawdowns to optimal pumpage, which may enhance the decisionmaker's ability to select the best development policy from a set of alternatives. The results illustrate how various optimal management schemes can be devised to increase the total withdrawal from the aquifer while preventing excessive de-watering.
A new computational methodology for capture zone design for contaminated ground-water remediation is described. This method has been implemented in a computer model which utilizes both simulation and optimization techniques. The procedure determines the well locations and pump rates which will produce a desired ground-water flow field at minimum cost. In this paper, the design procedure is described along with an example of its use on a hypothetical aquifer system. Numerical experiments are presented which determine the effect on remediation cost of alternate well locations. It is found that different well locations can have a major impact on the overall cost of remediation.
1. AbstractA hydraulic control optimization model is applied to the conceptual and implementation analysis of a ground-water remediation system in coastal New Jersey. The site is modeled using a distributed parameter finite-difference model containing 36,000 nodes within five layers. The conceptual problem is to determine the feasibility of producing a capture zone which encompasses the entire existing plume while recharging all extracted water within property boundaries in such a way that the recharged water satisfies criteria on its fate. The conceptual analysis problem is formulated as a linear program in which the total extraction pumping is minimized, and requirements are placed on hydraulic heads and gradients in both horizontal and vertical directions. A requirement is also made that all extracted water be recharged to the subsurface. The model is used for determination of the feasibility of the remediation concept. Details of constructing constraints for a large-scale formulation are presented. The concept of constraint calibration, using particle tracking to insure that constraints are producing desired results, is introduced and demonstrated. The optimization formulation is used for detailed implementation analysis of the remediation system. A number of techniques for modifying elements of the conceptual model results, such as unrealistically small pump rates, are described. The optimization approach is found to be useful for determining the feasibility of the remedial strategy at this site and for producing results which can be used as a starting point for detailed analysis of the remediation strategy.
The Blue Lake aquifer is an unconfined sloping aquifer in Northern California traversed by the Mad River which is regulated by Ruth Reservoir. High pumpage from the existing six wells operated by Humboldt Bay Municipal Water District (HBMWD) of the order of a few million gallons per day (MGD) causes appreciable drawdown compared to the saturated thickness of the aquifer. Additionally, HBMWD also proposed another set of ten wells for meeting an anticipated daily demand of 23 MG of the Humboldt County. Therefore reduction of the governing nonlinear groundwater flow equation into a linear equation was not considered appropriate. An existing explicit scheme coded by previous workers for this project was found most suitable for the solution of inherent nonlinear equations. However, many modifications in the existing algorithm were required before a groundwater balance was obtained for the Blue Lake Aquifer.HBMWD wanted to minimise pumping cost for lifting the proposed 23 MGD from the ten wells. This required the simulation of a groundwater management model of the aquifer involving the principles of nonlinear optimisation. A recent Modified Embedded Approach was used to solve the problem incorporating the appropriate constraints based upon the real system and on the optimisation requirements. It was estimated that HBMWD could have an annual saving of $20,000 by implementing the annual optimal pumping policy (involving monthly planning periods as listed in the Appendix) compared to nonoptimised policy (equal pumping of 2.3 MGD from ten wells).
The problem of locating pumps and setting pump rates to most effectively stabilize and remove a plume of contaminated groundwater at a hazardous waste site is examined. Nonlinear optimization methods are combined with convective-disperisve transport simulation in a unit response matrix type of optimization formulation.Constraints are used which guarantee that the contaminant plume is removed by limiting the concentrations at nodal points in the domain at a future time. Additional constraints explicitly require that concentrations not increase in the area outside the initial plume boundary. The effectiveness of alternative formulations are examined by performing numerical experiments using a hypothetical aquifer.The experiments show that computational costs are dominated by the repeated simulations required for computation of constraint gradients and are proportional to the number of pump sites under consideration. This characteristic of the formulation and algorithm used, limits the use of the approach to problems where the number of potential pump sites is relatively small.
The paper describes an optimization method for the solution of groundwater management problems. The method consists of a combination of the computation of horizontal plane groundwater flow with a free surface (finite element method) and a linear optimization procedure (simplex algorithm). Considering the special structure of data which result form computing the groundwater flow with the finite element method, and modifying the simplex algorithm, the solution of management problems with complex groundwater flow is realized without any difficulties. Compared to a flow computation alone the additional effort of the optimization (computer time and scope for data storage) is only small.
The Rocky Mountain Arsenal near Denver, Colorado, U.S.A., is used as a realistic setting for a hypothetical test of a procedure that plans the hydraulic stabilization and removal of a groundwater contaminant plume. A two-stage planning procedure successfully selects the best wells and their optimal pumping/recharge schedules to contain the plume while a well or system of wells within the plume removes the contaminated water. In stage I, a combined groundwater flow and solute transport model is used to simulate contaminant removal under an assumed velocity field. The result is the approximated plume boundary location as a function of time. In stage II, a linear program, which includes a groundwater flow model as part of the set of constraints, determines the optimal well selection and their optimal pumping/recharge schedules by minimizing total pumping and recharge. The simulation—management model eliminates wells far from the plume perimeter and activates wells near the perimeter as the plume decreases in size. This successfully stablizes the hydraulic gradient during aquifer cleanup.
A natural gradient experiement of solute transport in sand aquiferA mixed integer programming model for three-dimensional ground-water remediation designScreening method for contaminant plume control
- P V Roberts
- D M Mackay
- Conn
- J M Sharer
- L W Vail
Roberts, P. V., and MacKay, D. M. (1986). "A natural gradient experiement of solute transport in sand aquifer." Tech. Rep. No. 292, Dept. of Cir. Engrg., Stanford University, Stanford, Calif. Sawyer, C. S. (1992). "A mixed integer programming model for three-dimensional ground-water remediation design," PhD dissertation, University of Connecticut, Storrs, Conn. Sharer, J. M., and Vail, L. W. (1987). "Screening method for contaminant plume control." J. Water Resour. Ptng. Mgmt., ASCE, 113(3), 336-352.
Groundwater systems planning and management
- R Willis
- W. W-G Yeh
Willis, R., and Yeh, W. W-G. (1987). Groundwater systems planning and manage-ment. Prentice-Hall, Inc., Englewood Cliffs, N.J.
Optimal Operation of Wells in a Multilayer Leaky AquiferRapid removal of a ground-water contaminant plume Groundwater contamination and reclamation
- T Kawatani
- Hannover
- Germany
- L J Lefkoff
- S M Gorelick
Kawatani, T. (1982). "Optimal Operation of Wells in a Multilayer Leaky Aquifer," Proc. 4th Int. Conf. on Finite Elements in Water Resour., Hannover, Germany. Lefkoff, L. J., and Gorelick,-S. M. (1985). "Rapid removal of a ground-water contaminant plume." Groundwater contamination and reclamation, 125-131, American Water Resources Association, 125-131.
Demonstrative model for identifying ground-water-management options in a contaminated aquifer
- S J Colarullo
- M Heidari
- Iii T Maddock
Colarullo, S. J., Heidari, M., Maddock III, T. (1985). "Demonstrative model for identifying ground-water-management options in a contaminated aquifer." Groundwater Ser. 8, Kansas Geological Survey, Lawrence, Karts. Culver, T. B., and Shoemaker, C. A. (1992). "Dynamic optimal control for ground-water remediation with flexible management periods." Water Resour. Res., 28(3), 629-641.
Cost minimization of ground-water pump and treat systems
- L Deschaine
Deschaine, L. (1992). "Cost minimization of ground-water pump and treat systems," MS thesis, University of Connecticut, Storrs, Conn.
Linear and nonlinear programmingManagement model as a tool for studying the worth of data
- D G Luenberger
Luenberger, D. G. (1984). Linear and nonlinear programming. Addison-Wesley Publishing Co., Reading, Mass. Maddock III, T. (1973). "Management model as a tool for studying the worth of data." Water Resour. Res., 9(3), 270-280.
Physical and chemical hydrogeologyOptimal dewatering schemes in the foun-dation design of an electronuclear plant
- P A Domenico
- F W Y Schwartz
- G Galeati
- G Gambolati
Domenico, P. A., and Schwartz, F. W. (1990). Physical and chemical hydrogeology. John Wiley and Sons, Inc., New York, N.Y. Galeati, G., and Gambolati, G. (1988). "Optimal dewatering schemes in the foun-dation design of an electronuclear plant." Water Resour. Res., 24(4), 541-552.
Rapid removal of a ground-water contaminant plume
- L J Lefkoff
- S M Gorelick
A modular three-dimensional finite-difference ground-water flow model.” Techniques of water-resources investigations of the United States Geological Survey
- M G Mcdonald
- A W Harbaugh
Design methodology for efficient aquifer remediation using pump and treat systems
- D C Mckinney
- M D Lin