Optimal design of pump-and-treat systems under uncertain hydraulic conductivity and plume distribution.

In this work, we present a stochastic optimal control framework for assisting the management of the cleanup by pump-and-treat of polluted shallow aquifers. In the problem being investigated, hydraulic conductivity distribution and dissolved contaminant plume location are considered as the uncertain variables. The framework considers the subdivision of the cleanup horizon in a number of stress periods over which the pumping policy implemented until that stage is dynamically adjusted based upon new information that has become available in the previous stages. In particular, by following a geostatistical approach, we study the idea of monitoring the cumulative contaminant mass extracted from the installed recovery wells, and using these measurements to generate conditional realizations of the hydraulic conductivity field. These realizations are thus used to obtain a more accurate evaluation of the initial plume distribution, and modify accordingly the design of the pump-and-treat system for the remainder of the remedial process. The study indicates that measurements of contaminant mass extracted from pumping wells retain valuable information about the plume location and the spatial heterogeneity characterizing the hydraulic conductivity field. However, such an information may prove quite soft, particularly in the instances where recovery wells are installed in regions where contaminant concentration is low or zero. On the other hand, integrated solute mass measurements may effectively allow for reducing parameter uncertainty and identifying the plume distribution if more recovery wells are available, in particular in the early stages of the cleanup process.

[1]  David E. Goldberg,et al.  Risk‐based in situ bioremediation design using a noisy genetic algorithm , 2000 .

[2]  O. V. Stryk,et al.  DERIVATIVE-FREE OPTIMIZATION METHODS FOR HANDLING FIXED COSTS IN OPTIMAL GROUNDWATER REMEDIATION DESIGN , 2006 .

[3]  Domenico Baù,et al.  Data-worth analysis for multiobjective optimal design of pump-and-treat remediation systems , 2007 .

[4]  Brian J. Wagner,et al.  Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling , 1992 .

[5]  Joel Massmann,et al.  Hydrogeological Decision Analysis: 2. Applications to Ground‐Water Contamination , 1991 .

[6]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[7]  K. R. Fowler,et al.  Approaching the Groundwater Remediation Problem Using Multifidelity Optimization. , 2006 .

[8]  Jeffrey Horn,et al.  Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA) , 2002 .

[9]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[10]  C. Shoemaker,et al.  Dynamic optimal control for groundwater remediation with flexible management periods , 1992 .

[11]  Cass T. Miller,et al.  Optimal design for problems involving flow and transport phenomena in saturated subsurface systems , 2002 .

[12]  G. Marsily.  Quantitative Hydrogeology: Groundwater Hydrology for Engineers , 1986 .

[13]  T. Skaggs,et al.  Recovering the release history of a groundwater contaminant , 1994 .

[14]  S. Gorelick,et al.  Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design , 1989 .

[15]  Brian J. Wagner,et al.  Evaluating data worth for ground-water management under uncertainty , 1999 .

[16]  P. Kitanidis.  Quasi‐Linear Geostatistical Theory for Inversing , 1995 .

[17]  Mario Putti,et al.  A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems , 1994 .

[18]  P. Kitanidis,et al.  Optimization of the pumping schedule in aquifer remediation under uncertainty , 1990 .

[19]  S. Gorelick,et al.  Identifying sources of groundwater pollution: An optimization approach , 1983 .

[20]  S. Gorelick,et al.  Optimal groundwater quality management under parameter uncertainty , 1987 .

[21]  W. G. Gray,et al.  Computational methods in water resources X , 1994 .

[22]  James R. Craig,et al.  Pump-and-treat optimization using analytic element method flow models , 2006 .

[23]  J. Philip,et al.  Theory of Infiltration , 1969 .

[24]  Joel Massmann,et al.  Hydrogeological Decision Analysis: 1. A Framework , 1990 .

[25]  Domenico Baù,et al.  Stochastic management of pump-and-treat strategies using surrogate functions , 2006 .

[26]  Hamid R. Nemati,et al.  Groundwater quality management under uncertainty: stochastic programming approaches and the value of information , 1992 .

[27]  T. Ptak,et al.  Monitoring groundwater contamination and delineating source zones at industrial sites: uncertainty analyses using integral pumping tests. , 2005, Journal of contaminant hydrology.

[28]  Cass T. Miller,et al.  Solution of a Well-Field Design Problem with Implicit Filtering , 2004 .

[29]  T. Ptak,et al.  Average contaminant concentration and mass flow in aquifers from time‐dependent pumping well data: Analytical framework , 2004 .

[30]  David W. Watkins,et al.  Finding Robust Solutions to Water Resources Problems , 1997 .

[31]  Charles Audet,et al.  Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems , 2008 .

[32]  C. Shoemaker,et al.  DYNAMIC OPTIMAL CONTROL OF IN-SITU BIOREMEDIATION OF GROUND WATER , 1998 .

[33]  P. Huyakorn,et al.  Techniques for Making Finite Elements Competitve in Modeling Flow in Variably Saturated Porous Media , 1984 .

[34]  A. Bagtzoglou,et al.  Application of particle methods to reliable identification of groundwater pollution sources , 1992 .

[35]  David E. Dougherty,et al.  Design Optimization for Multiple Management Period Groundwater Remediation , 1996 .

[36]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[37]  R. Allan Freeze,et al.  Convergence of Stochastic Optimization and Decision Analysis in the Engineering Design of Aquifer Remediation , 1999 .

[38]  Christopher E. Kees,et al.  A hydraulic capture application for optimal remediation design , 2004 .

[39]  J. Bear.  Hydraulics of Groundwater , 1979 .

[40]  Oskar von Stryk,et al.  A mixed-integer simulation-based optimization approach with surrogate functions in water resources management , 2008 .

[41]  P. Kitanidis,et al.  A method for enforcing parameter nonnegativity in Bayesian inverse problems with an application to contaminant source identification , 2003 .

[42]  P. Kitanidis,et al.  A geostatistical approach to contaminant source identification , 1997 .

[43]  A.F.B. Tompson,et al.  Numerical simulation of solute transport in randomly heterogeneous porous media: Motivation, model development, and application , 1987 .