Backward location and travel time probabilities for a decaying contaminant in an aquifer.

Backward location and travel time probabilities can be used to determine the prior position of contamination in an aquifer. These probabilities, which are related to adjoint states of concentration, can be used to improve characterization of known sources of groundwater contamination, to identify previously unknown contamination sources, and to delineate capture zones. The first contribution of this paper is to extend the adjoint model to the case of a decaying solute (first-order decay), and to describe two different interpretations of backward probabilities. The conventional interpretation accounts for the probability that a contaminant particle could decay before reaching the detection location. The other interpretation is conditioned on the fact that the detected contaminant particle actually reached the detection location, despite this possibility of decay. In either case, travel time probabilities are skewed toward earlier travel times, relative to a conservative solute. The second contribution of this paper is to verify the load term for a monitoring well observation. We provide examples using one-dimensional models and hypothetical aquifers. We employ an infinite domain in order to verify the monitoring well load. This new but simple one-dimensional adjoint solution can also be used to verify higher-dimensional numerical models of backward location and travel time probabilities. We employ a semi-infinite domain to illustrate the effect of decay on backward models of pumping well probabilistic capture zones. Decay causes the capture zones to fall closer to the well.

[1]  An asymptotic method for predicting the contamination of a pumping well , 1995 .

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

[3]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[4]  J. W. Mercer,et al.  Contaminant transport in groundwater. , 1992 .

[5]  D. A. Barry,et al.  On the Dagan Model of solute transport in groundwater: Foundational aspects , 1987 .

[6]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[7]  Gedeon Dagan,et al.  Theory of Solute Transport by Groundwater , 1987 .

[8]  G. Dagan Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 2. The solute transport , 1982 .

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

[10]  J. V. Kooten Groundwater contaminant transport including adsorption and first order decay , 1994 .

[11]  David A. Chin,et al.  Risk Management in Wellhead Protection , 1994 .

[12]  M. V. Genuchten,et al.  Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport , 1984 .

[13]  Chia-Shyun Chen,et al.  Analytical solution for aquifer decontamination by pumping , 1988 .

[14]  W. Kinzelbach,et al.  Computation of stochastic wellhead protection zones by combining the first-order second-moment method and Kolmogorov backward equation analysis , 2000 .

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

[16]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[17]  Kurt Roth,et al.  Transfer Functions and Solute Movement Through Soil: Theory and Applications , 1991 .

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

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

[20]  R. Andricevic,et al.  Radionuclide migration using a travel time transport approach and its application in risk analysis , 1994 .

[21]  A. Zuber,et al.  On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions , 1978 .

[22]  E. Frind,et al.  Delineation of Three‐Dimensional Well Capture Zones for Complex Multi‐Aquifer Systems , 2002, Ground water.

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