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

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

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs     

Analytical and Semi‐Analytical Tools for the Design of Oscillatory Pumping Tests

Oscillatory pumping tests—in which flow is varied in a periodic fashion—provide a method for understanding aquifer heterogeneity that is complementary to strategies such as slug testing and constant‐rate pumping tests. During oscillatory testing, pressure data collected at non‐pumping wells can be processed to extract metrics, such as signal amplitude and phase lag, from a time series. These metrics are robust against common sensor problems (including drift and noise) and have been shown to provide information about aquifer heterogeneity. Field implementations of oscillatory pumping tests for characterization, however, are not common and thus there are few guidelines for their design and implementation. Here, we use available analytical solutions from the literature to develop design guidelines for oscillatory pumping tests, while considering practical field constraints. We present two key analytical results for design and analysis of oscillatory pumping tests. First, we provide methods for choosing testing frequencies and flow rates which maximize the signal amplitude that can be expected at a distance from an oscillating pumping well, given design constraints such as maximum/minimum oscillator frequency and maximum volume cycled. Preliminary data from field testing helps to validate the methodology. Second, we develop a semi‐analytical method for computing the sensitivity of oscillatory signals to spatially distributed aquifer flow parameters. This method can be quickly applied to understand the “sensed” extent of an aquifer at a given testing frequency. Both results can be applied given only bulk aquifer parameter estimates, and can help to optimize design of oscillatory pumping test campaigns.     

Cost Optimization of DNAPL Remediation at Dover Air Force Base Site

This study investigates stochastic optimization of dense nonaqueous phase liquid (DNAPL) remediation design at Dover Air Force Base Area 5 using emulsified vegetable oil (EVO) injection. The Stochastic Cost Optimization Toolkit (SCOToolkit) is used for the study, which couples semianalytical DNAPL source depletion and transport models with parameter estimation, error propagation, and stochastic optimization modules that can consider multiple sources and remediation strategies. Model parameters are calibrated to field data conditions on prior estimates of parameters and their uncertainty. Monte Carlo simulations are then performed to identify optimal remediation decisions that minimize the expected net present value (NPV) cleanup cost while maintaining concentrations at compliance wells under the maximum contaminant level (MCL). The results show that annual operating costs could be reduced by approximately 50% by implementing the identified optimal remediation strategy. We also show that recalibration and reoptimization after 50 years using additional monitoring data could lead to a further 60% reduction in annual operating cost increases the reliability of the proposed remediation actions.     

Parameter identification for leaky aquifers using global optimization methods

In the past, graphical or computer methods were usually employed to determine the aquifer parameters of the observed data obtained from field pumping tests. Since we employed the computer methods to determine the aquifer parameters, an analytical aquifer model was required to estimate the predicted drawdown. Following this, the gradient‐type approach was used to solve the nonlinear least‐squares equations to obtain the aquifer parameters. This paper proposes a novel approach based on a drawdown model and a global optimization method of simulated annealing (SA) or a genetic algorithm (GA) to determine the best‐fit aquifer parameters for leaky aquifer systems. The aquifer parameters obtained from SA and the GA almost agree with those obtained from the extended Kalman filter and gradient‐type method. Moreover, all results indicate that the SA and GA are robust and yield consistent results when dealing with the parameter identification problems. Copyright © 2006 John Wiley & Sons, Ltd.     

A simulation-based fuzzy chance-constrained programming model for optimal groundwater remediation under uncertainty

In this study a simulation-based fuzzy chance-constrained programming (SFCCP) model is developed based on possibility theory. The model is solved through an indirect search approach which integrates fuzzy simulation, artificial neural network and simulated annealing techniques. This approach has the advantages of: (1) handling simulation and optimization problems under uncertainty associated with fuzzy parameters, (2) providing additional information (i.e. possibility of constraint satisfaction) indicating that how likely one can believe the decision results, (3) alleviating computational burdens in the optimization process, and (4) reducing the chances of being trapped in local optima. The model is applied to a petroleum-contaminated aquifer located in western Canada for supporting the optimal design of groundwater remediation systems. The model solutions provide optimal groundwater pumping rates for the 3, 5 and 10 years of pumping schemes. It is observed that the uncertainty significantly affects the remediation strategies. To mitigate such impacts, additional cost is required either for increased pumping rate or for reinforced site characterization.     

Geologic heterogeneity and a comparison of two geostatistical models: Sequential Gaussian and transition probability-based geostatistical simulation

A covariance-based model-fitting approach is often considered valid to represent field spatial variability of hydraulic properties. This study examines the representation of geologic heterogeneity in two types of geostatistical models under the same mean and spatial covariance structure, and subsequently its effect on the hydraulic response to a pumping test based on 3D high-resolution numerical simulation and field data. Two geostatistical simulation methods, sequential Gaussian simulation (SGS) and transition probability indicator simulation (TPROGS) were applied to create conditional realizations of alluvial fan aquifer systems in the Lawrence Livermore National Laboratory (LLNL) area. The simulated K fields were then used in a numerical groundwater flow model to simulate a pumping test performed at the LLNL site. Spatial connectivity measures of high-K materials (channel facies) captured connectivity characteristics of each geostatistical model and revealed that the TPROGS model created an aquifer (channel) network having greater lateral connectivity. SGS realizations neglected important geologic structures associated with channel and overbank (levee) facies, even though the covariance model used to create these realizations provided excellent fits to sample covariances computed from exhaustive samplings of TPROGS realizations. Observed drawdown response in monitoring wells during a pumping test and its numerical simulation shows that in an aquifer system with strongly connected network of high-K materials, the Gaussian approach could not reproduce a similar behavior in simulated drawdown response found in TPROGS case. Overall, the simulated drawdown responses demonstrate significant disagreement between TPROGS and SGS realizations. This study showed that important geologic characteristics may not be captured by a spatial covariance model, even if that model is exhaustively determined and closely fits the exponential function.     

Performance comparison of multiple and single surrogate models for pumping optimization of coastal aquifers

Single and multiple surrogate models were compared for single-objective pumping optimization problems of a hypothetical and a real-world coastal aquifer. Different instances of radial basis functions and kriging surrogates were utilized to reduce the computational cost of direct optimization with variable density and salt transport models. An adaptive surrogate update scheme was embedded in the operations of an evolutionary algorithm to efficiently control the feasibility of optimal solutions in pumping optimization problems with multiple constraints. For a set of independent optimization runs, results showed that multiple surrogates, either by selecting the best or by using ensembles, did not necessarily outperform the single surrogate approach. Nevertheless, the ensemble with optimal weights produced slightly better results than selecting only the best surrogates or applying a simple averaging approach. For all cases, the computational cost, by using single or multiple surrogate models, was reduced by up to 90% of the direct optimization.     

Using Alternate Pumping and Cooperative Game Theory to Reduce Sea Water Intrusion

In this article, alternate pumping is studied as a means used to reduce the salinity concentration in coastal aquifers, pumped using a system of wells. This approach has been applied to a hypothetical confined coastal aquifer. Flow has been modeled, using SEAWAT. Two strategies are proposed based on cooperative game theory, to promote alternate pumping. In both strategies an external player will compensate the users that will pump during an unpopular pumping period. In the first strategy it is supposed that this external player aims at protecting a critical well, e.g. a municipal well, reducing its maximum salinity concentration by pumping alternately. In the second strategy proposed, the target is to reduce the overall salinity of the water pumped by the wells. In applying the cooperative game theory, the Shapley value is used to distribute the benefits of cooperation between the players (well users), according to their marginal contribution. Overall, well users can reduce sea water intrusion by cooperatively changing their pumping time schedules. The game theoretical model developed is a useful tool to promote cooperation toward this direction. The methods applied in the hypothetical aquifer, can be tested in actual aquifers to reduce sea water intrusion.     

Stochastic management of pump-and-treat strategies using surrogate functions

Typical pump-and-treat (PAT) optimization problems involve design of pumping schemes, while minimizing cost and meeting a set of constraints. Due to scarcity of information about the hydrogeological system, stochastic modeling approaches can be used to assess tradeoffs between optimality and reliability. Using a stochastic approach, the constrained, single-objective problem may be turned into a multiobjective problem by substituting constraint inequalities with an additional objective function (OF) that accounts for the reliability of the PAT process. In this work, two approaches are analyzed: in one case, the additional OF consists of the probability of failure of a given remediation policy; in another, the OF additional is represented by the recourse, namely the penalty cost induced by the violation of constraints. In order to overcome the overwhelming computational cost required by stochastic simulation, surrogate forms of the OFs are introduced. In the test case under investigation, such functions are estimated by a kriging interpolation of the OF over a series of data points obtained from stochastic simulations of flow and transport, and calibrated against stochastic optimization solutions. The analysis of the two approaches for addressing the tradeoff of cost vs. reliability indicates that recourse accounts not only for the frequency of constraint violations, as the probability of failure does, but also for the intensity with which these occur. Ultimately, the recourse method allows considering less restrictive policies, although these may be highly sensitive to the choice of penalty functions.     

Optimal Decision Making Algorithm for Managed Aquifer Recharge and Recovery Operation Using Near Real‐Time Data: Benchtop Scale Laboratory Demonstration

Aquifers show troubling signs of irreversible depletion as climate change, population growth, and urbanization lead to reduced natural recharge rates and overuse. One strategy to sustain the groundwater supply is to recharge aquifers artificially with reclaimed water or stormwater via managed aquifer recharge and recovery (MAR) systems. Unfortunately, MAR systems remain wrought with operational challenges related to the quality and quantity of recharged and recovered water stemming from a lack of data‐driven, real‐time control. This paper presents a laboratory scale proof‐of‐concept study that demonstrates the capability of a real‐time, simulation‐based control optimization algorithm to ease the operational challenges of MAR systems. Central to the algorithm is a model that simulates water flow and transport of dissolved chemical constituents in the aquifer. The algorithm compensates for model parameter uncertainty by continually collecting data from a network of sensors embedded within the aquifer. At regular intervals the sensor data is fed into an inversion algorithm, which calibrates the uncertain parameters and generates the initial conditions required to model the system behavior. The calibrated model is then incorporated into a genetic algorithm that executes simulations and determines the best management action, for example, the optimal pumping policy for current aquifer management goals. Experiments to calibrate and validate the simulation‐optimization algorithm were conducted in a small two‐dimensional synthetic aquifer under both homogeneous and heterogeneous packing configurations. Results from initial experiments validated the feasibility of the approach and suggested that our system could improve the operation of full‐scale MAR facilities.     

Conventional and combined pump-and-treat systems under nonuniform background flow

We investigate the performance of vertical hydraulic barriers in combination with extraction wells for the partial hydraulic isolation of contaminated aquifer areas. The potential advantage of such combinations compared to a conventional pump-and-treat system has already been demonstrated in a previous study. Here we extend the scope of the performance analysis to the impact of uncertainty in the regional flow direction as well as to highly heterogeneous aquifer transmissivity distributions. In addition, two new well-barrier scenarios are proposed and analyzed. The hydraulic efficiency of the scenarios is rated based on the expected (mean) reduction of the pumping rate that is required to achieve downgradient contaminant capture. The uncertain spatial distribution of aquifer transmissivity is considered by means of unconditioned Monte Carlo simulations. The significance of uncertain background flow conditions is incorporated by computing minimized pumping rates for deviations of the regional flow direction up to 30 degrees from a normative base case. The results give an answer on how pumping rates have to be changed for each barrier-well combination in order to achieve robust systems. It is exposed that in comparison to installing exclusively wells, the barrier-supported approach generally yields savings in the (average) pumping rate. The particular efficiency is shown to be highly dependent on the interaction of variance and integral scale of transmissivity distribution, well and barrier position, as well as direction of background flow.     

A Potential-Based Inversion of Unconfined Steady-State Hydraulic Tomography

The importance of estimating spatially variable aquifer parameters such as transmissivity is widely recognized for studies in resource evaluation and contaminant transport. A useful approach for mapping such parameters is inverse modeling of data from series of pumping tests, that is, via hydraulic tomography. This inversion of field hydraulic tomographic data requires development of numerical forward models that can accurately represent test conditions while maintaining computational efficiency. One issue this presents is specification of boundary and initial conditions, whose location, type, and value may be poorly constrained. To circumvent this issue when modeling unconfined steady-state pumping tests, we present a strategy that analyzes field data using a potential difference method and that uses dipole pumping tests as the aquifer stimulation. By using our potential difference approach, which is similar to modeling drawdown in confined settings, we remove the need for specifying poorly known boundary condition values and natural source/sink terms within the problem domain. Dipole pumping tests are complementary to this strategy in that they can be more realistically modeled than single-well tests due to their conservative nature, quick achievement of steady state, and the insensitivity of near-field response to far-field boundary conditions. After developing the mathematical theory, our approach is first validated through a synthetic example. We then apply our method to the inversion of data from a field campaign at the Boise Hydrogeophysical Research Site. Results from inversion of nine pumping tests show expected geologic features, and uncertainty bounds indicate that hydraulic conductivity is well constrained within the central site area.     

The value of subsidence data in ground water model calibration

The accurate estimation of aquifer parameters such as transmissivity and specific storage is often an important objective during a ground water modeling investigation or aquifer resource evaluation. Parameter estimation is often accomplished with changes in hydraulic head data as the key and most abundant type of observation. The availability and accessibility of global positioning system and interferometric synthetic aperture radar data in heavily pumped alluvial basins can provide important subsidence observations that can greatly aid parameter estimation. The aim of this investigation is to evaluate the value of spatial and temporal subsidence data for automatically estimating parameters with and without observation error using UCODE-2005 and MODFLOW-2000. A synthetic conceptual model (24 separate cases) containing seven transmissivity zones and three zones each for elastic and inelastic skeletal specific storage was used to simulate subsidence and drawdown in an aquifer with variably thick interbeds with delayed drainage. Five pumping wells of variable rates were used to stress the system for up to 15 years. Calibration results indicate that (1) the inverse of the square of the observation values is a reasonable way to weight the observations, (2) spatially abundant subsidence data typically produce superior parameter estimates under constant pumping even with observation error, (3) only a small number of subsidence observations are required to achieve accurate parameter estimates, and (4) for seasonal pumping, accurate parameter estimates for elastic skeletal specific storage values are largely dependent on the quantity of temporal observational data and less on the quantity of available spatial data.     

A two‐dimensional inverse model to identify transmissivity in an anisotropic aquifer

This study suggested a numerical model using the Tabu search algorithm along with the Adjoint State method to identify the hydrogeological characteristics of an anisotropic groundwater aquifer. The Tabu search algorithm was applied to identify the anisotropic transmissivity components to avoid a local optimum. Then, the Adjoint State method was used to calculate the sensitivity of the parameters in order to increase the efficiency of the optimization. For an anisotropic and homogeneous aquifer, results showed that the optimal procedure presented combining the Tabu search algorithm and the Adjoint State method might successfully identify the values of the transmissivity components. If the duration of the pumping test was long enough (12‐h pumping test), the value of the transmissivity components could be optimized with type‐curve, straight‐line, and Tabu search methods, along with the Adjoint State methods. If the duration of the pumping test was short (0·5‐h pumping test), the Tabu search method, along with the Adjoint State method proposed herein, might successfully optimize the transmissivity components. For an anisotropic but heterogeneous aquifer, results showed that the suggested optimal procedure still successfully identified the values of the transmissivity components. Copyright © 2008 John Wiley & Sons, Ltd.     

A GENERAL PURPOSE MICROCOMPUTER AQUIFER TEST EVALUATION TECHNIQUE

Abstract. Although determination of aquifer characteristics from pumping test data is generally carried out using type curves or other graphical techniques, a number of computer methods have been developed recently for this purpose. Based on the principle of least squares, these methods of nonlinear regression analysis can be applied to any flow system for which analytical expressions of the drawdown distribution are known. In view of the growing general interest in the application of microcomputers in ground-water hydrology, a BASIC routine has been developed for estimating any number of aquifer parameters. The least squares solution is calculated by Marquardt's algorithm, using the singular-value decomposition of the Jacobian matrix. The robust computing method obtained can be applied to all kinds of pumping tests. Aquifer characteristics as well as their standard deviations are computed with optimal speed and accuracy. The technique is demonstrated by a simple application to steady flow in a leaky aquifer and an example is provided. Other applications are easily implemented and programs for unsteady-state aquifer tests, recovery tests and multiple aquifer tests are available.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

Optimizing separate phase light hydrocarbon recovery from contaminated unconfined aquifers

A modeling approach is presented that optimizes separate phase recovery of light non-aqueous phase liquids (LNAPL) for a single dual-extraction well in a homogeneous, isotropic unconfined aquifer. A simulation/regression/optimization (S/R/O) model is developed to predict, analyze, and optimize the oil recovery process. The approach combines detailed simulation, nonlinear regression, and optimization. The S/R/O model utilizes nonlinear regression equations describing system response to time-varying water pumping and oil skimming. Regression equations are developed for residual oil volume and free oil volume. The S/R/O model determines optimized time-varying (stepwise) pumping rates which minimize residual oil volume and maximize free oil recovery while causing free oil volume to decrease a specified amount. This S/R/O modeling approach implicitly immobilizes the free product plume by reversing the water table gradient while achieving containment. Application to a simple representative problem illustrates the S/R/O model utility for problem analysis and remediation design. When compared with the best steady pumping strategies, the optimal stepwise pumping strategy improves free oil recovery by 11.5% and reduces the amount of residual oil left in the system due to pumping by 15%. The S/R/O model approach offers promise for enhancing the design of free phase LNAPL recovery systems and to help in making cost-effective operation and management decisions for hydrogeologists, engineers, and regulators.     

Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities

In many fields of study, and certainly in hydrogeology, uncertainty propagation is a recurring subject. Usually, parametrized probability density functions (PDFs) are used to represent data uncertainty, which limits their use to particular distributions. Often, this problem is solved by Monte Carlo simulation, with the disadvantage that one needs a large number of calculations to achieve reliable results. In this paper, a method is proposed based on a piecewise linear approximation of PDFs. The uncertainty propagation with these discretized PDFs is distribution independent. The method is applied to the upscaling of transmissivity data, and carried out in two steps: the vertical upscaling of conductivity values from borehole data to aquifer scale, and the spatial interpolation of the transmissivities. The results of this first step are complete PDFs of the transmissivities at borehole locations reflecting the uncertainties of the conductivities and the layer thicknesses. The second step results in a spatially distributed transmissivity field with a complete PDF at every grid cell. We argue that the proposed method is applicable to a wide range of uncertainty propagation problems.     

Data-worth analysis for multiobjective optimal design of pump-and-treat remediation systems

The design and the management of pump-and-treat (PAT) remediation systems for contaminated aquifers under uncertain hydrogeological settings and parameters often involve decisions that trade off cost optimality against reliability. Both design objectives can be improved by planning site characterization programs that reduce subsurface parameter uncertainty. However, the cost for subsurface investigation often weighs heavily upon the budget of the remedial action and must thus be taken into account in the trade-off analysis. In this paper, we develop a stochastic data-worth framework with the purpose of estimating the economic opportunity of subsurface investigation programs. Since the spatial distribution of hydraulic conductivity is most often the major source of uncertainty, we focus on the direct sampling of hydraulic conductivity at prescribed locations of the aquifer. The data worth of hydraulic conductivity measurements is estimated from the reduction of the overall management cost ensuing from the reduction in parameter uncertainty obtained from sampling. The overall cost is estimated as the expected value of the cost of installing and operating the PAT system plus penalties incurred due to violations of cleanup goals and constraints. The crucial point of the data-worth framework is represented by the so-called pre-posterior analysis. Here, the tradeoff between decreasing overall costs and increasing site-investigation budgets is assessed to determine a management strategy proposed on the basis of the information available at the start of remediation. The goal of the pre-posterior analysis is to indicate whether the proposed management strategy should be implemented as is, or re-designed on the basis of additional data collected with a particular site-investigation program. The study indicates that the value of information is ultimately related to the estimates of cleanup target violations and decision makers’ degree of risk-aversion.