Optimal Search Strategy for the Definition of a DNAPL Source

Summary Contamination created by dense non-aqueous phase liquids (DNAPLs) is a serious threat to the quality of the groundwater supply; thus, delineating and removing the DNAPL source is an essential step in a successful remediation strategy. The goal of this work is to create an optimal search strategy that identifies a DNAPL source using the least number of water quality samples. The search strategy includes a Monte Carlo stochastic groundwater flow and transport model, a predetermined set of potential source locations and a Kalman filter that updates the simulated contaminant concentration field using contaminant concentration data. The updated plume is compared to the concentration fields that emanate from each individual potential source using a technique rooted in fuzzy set theory. The comparison provides weights that reflect the degree of truth regarding the location of the source at the selected potential source locations. The steps described above are repeated until the weights stabilize and the optimal source location is determined. This paper presents the various mathematical tools employed in the search algorithm and their modifications for incorporation into the proposed methodology. The algorithm’s effectiveness in identifying a DNAPL source is shown using a synthetic example.

[1]  Jon C. Helton,et al.  An Approach to Sensitivity Analysis of Computer Models: Part II - Ranking of Input Variables, Response Surface Validation, Distribution Effect and Technique Synopsis , 1981 .

[2]  M. W. Davis,et al.  Production of conditional simulations via the LU triangular decomposition of the covariance matrix , 1987, Mathematical Geology.

[3]  E. Todini,et al.  A solution to the inverse problem in groundwater hydrology based on Kalman filtering , 1996 .

[4]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[5]  Yingqi Zhang,et al.  Least cost design of groundwater quality monitoring networks , 2005 .

[6]  Amvrossios C. Bagtzoglou,et al.  Mathematical Methods for Hydrologic Inversion: The Case of Pollution Source Identification , 2005 .

[7]  Jon C. Helton,et al.  Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems , 2002 .

[8]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[9]  Roseanna M. Neupauer,et al.  Backward probability model using multiple observations of contamination to identify groundwater contamination sources at the Massachusetts Military Reservation , 2005 .

[10]  Mustafa M. Aral,et al.  Identification of Contaminant Source Location and Release History in Aquifers , 2001 .

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

[12]  Wendy D. Graham,et al.  Forecasting piezometric head levels in the Floridan Aquifer: A Kalman Filtering Approach , 1993 .

[13]  Amvrossios C. Bagtzoglou,et al.  A computationally attractive approach for near real-time contamination source identification , 2004 .

[14]  T. Skaggs,et al.  Limitations in recovering the history of a groundwater contaminant plume , 1998 .

[15]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[16]  G. Finder,et al.  Cost-effective Groundwater Quality Sampling Network Design , 1998 .

[17]  Harald Kunstmann,et al.  Conditional first‐order second‐moment method and its application to the quantification of uncertainty in groundwater modeling , 2002 .

[18]  T. Skaggs,et al.  Recovering the History of a Groundwater Contaminant Plume: Method of Quasi‐Reversibility , 1995 .

[19]  Allan L. Gutjahr,et al.  Cross‐correlated random field generation with the direct Fourier Transform Method , 1993 .

[20]  Amvrossios C. Bagtzoglou,et al.  Pollution source identification in heterogeneous porous media , 2001 .

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

[22]  Amvrossios C. Bagtzoglou,et al.  Near real-time atmospheric contamination source identification by an optimization-based inverse method , 2005 .

[23]  William P. Ball,et al.  Application of inverse methods to contaminant source identification from aquitard diffusion profiles at Dover AFB, Delaware , 1999 .

[24]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[25]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[26]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[27]  Michel Grabisch.  A graphical interpretation of the Choquet integral , 2000, IEEE Trans. Fuzzy Syst..

[28]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[29]  Francois Alabert,et al.  The practice of fast conditional simulations through the LU decomposition of the covariance matrix , 1987 .

[30]  Bithin Datta,et al.  Optimal Monitoring Network and Ground-Water–Pollution Source Identification , 1997 .

[31]  Amvrossios C. Bagtzoglou,et al.  Probabilistic Simulation for Reliable Solute Source Identification in Heterogeneous Porous Media , 1991 .

[32]  George F. Pinder,et al.  Latin hypercube lattice sample selection strategy for correlated random hydraulic conductivity fields , 2003 .

[33]  Thomas P. McWilliams.  Sensitivity analysis of geologic computer models: A formal procedure based on Latin hypercube sampling , 1987 .

[34]  P. Domenico,et al.  Physical and chemical hydrogeology , 1990 .

[35]  Brian Borchers,et al.  Comparison of inverse methods for reconstructing the release history of a groundwater contamination source , 2000 .

[36]  Ashu Jain,et al.  Identification of Unknown Groundwater Pollution Sources Using Artificial Neural Networks , 2004 .

[37]  M. Grabisch.  The application of fuzzy integrals in multicriteria decision making , 1996 .

[38]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[39]  Amvrossios C. Bagtzoglou,et al.  Marching‐jury backward beam equation and quasi‐reversibility methods for hydrologic inversion: Application to contaminant plume spatial distribution recovery , 2003 .

[40]  A. Bárdossy,et al.  Kriging with imprecise (fuzzy) variograms. I: Theory , 1990 .

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

[42]  A. Bárdossy,et al.  Kriging with imprecise (fuzzy) variograms. II: Application , 1990 .

[43]  G. Matheron.  The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

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

[45]  T. Ulrych,et al.  Minimum Relative Entropy Inversion: Theory and Application to Recovering the Release History of a Groundwater Contaminant , 1996 .

[46]  George J. Klir,et al.  Constructing fuzzy measures in expert systems , 1997, Fuzzy Sets Syst..

[47]  M. Eppstein,et al.  SIMULTANEOUS ESTIMATION OF TRANSMISSIVITY VALUES AND ZONATION , 1996 .

[48]  Z. J. Kabala,et al.  Recovering the release history of a groundwater contaminant using a non-linear least-squares method. , 2000 .

[49]  Roseanna M. Neupauer,et al.  Backward probabilistic model of groundwater contamination in non-uniform and transient flow , 2002 .

[50]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[51]  Krishan Rana,et al.  An Optimization Approach , 2004 .

[52]  Robert D. Morrison,et al.  Application of Forensic Techniques for Age Dating and Source Identification in Environmental Litigation , 2000 .

[53]  Didier Dubois,et al.  Fuzzy information engineering: a guided tour of applications , 1997 .

[54]  A. Bagtzoglou,et al.  State of the Art Report on Mathematical Methods for Groundwater Pollution Source Identification , 2001 .

[55]  Roko Andričević,et al.  Coupled withdrawal and sampling designs for groundwater supply models , 1993 .

[56]  Bithin Datta,et al.  Identification of Pollution Sources in Transient Groundwater Systems , 2000 .

[57]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[58]  A. Parr,et al.  Optimal Estimation of Two‐Dimensional Contaminant Transport , 1995 .

[59]  D. Rizzo,et al.  An Adaptive Long-Term Monitoring and Operations System (aLTMOs TM ) for Optimization in Environmental Management , 2000 .

[60]  M. Heidari,et al.  Optimal estimation of contaminant transport in ground water , 1989 .

[61]  R. Neupauer,et al.  Adjoint‐derived location and travel time probabilities for a multidimensional groundwater system , 2001 .

[62]  Roseanna M. Neupauer,et al.  Adjoint method for obtaining backward‐in‐time location and travel time probabilities of a conservative groundwater contaminant , 1999 .

[63]  WU Jian-feng.  CONTAMINANT MONITORING NETWORK DESIGN:RECENT ADVANCES AND FUTURE DIRECTIONS , 2004 .

[64]  George F. Pinder,et al.  Space‐time optimization of groundwater quality sampling networks , 2005 .

[65]  G. Mahinthakumar,et al.  Hybrid Genetic Algorithm—Local Search Methods for Solving Groundwater Source Identification Inverse Problems , 2005 .

[66]  Didier Dubois,et al.  On the use of aggregation operations in information fusion processes , 2004, Fuzzy Sets Syst..

[67]  C. Stroet,et al.  Using Kalman Filtering to Improve and Quantify the Uncertainty of Numerical Groundwater Simulations: 2. Application to Monitoring Network Design , 1991 .

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

[69]  F. C. van Geer,et al.  Applications of Kalman filtering in the analysis and design of groundwater monitoring networks , 1987 .

[70]  J. R. Macmillan,et al.  Stochastic analysis of spatial variability in subsurface flows: 2. Evaluation and application , 1978 .

[71]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .