Pollution source identification in heterogeneous porous media

Abstract

Abstract. The reliable assessment of hazards or risks arising from water contamination problems and the design of efficient and effective techniques to mitigate these problems require the capability to predict the behavior of chemical contaminants in flowing water. Most attempts at quantifying contaminant transport have relied on a solution of some form of the advection-dispersion-reaction equation. In this paper, the Backward Beam Equation (BBE) method is studied and enhanced to solve the Advection-Dispersion Equation (ADE) within a contaminant source identification context. Even though the BBE has been applied successfully to parabolic problems before, it has never been applied to solving the ADE with heterogeneous parameters. The BBE employed in this work is capable of recovering the time history and spatial distribution of a groundwater contaminant plume from measurements of its current position. Using examples involving deterministic heterogeneous dispersion coefficients, we show that the method is robust enough to handle heterogeneous parameters. By altering the method, to produce a hybrid between a marching and a jury method called the Marching-Jury Backward Beam Equation (MJBBE), we were also able to make the problem practical to solve. IntroductionGroundwater amounts to about half of the U. Furthermore, by accurately identifying pollution sources, the time and cost requirements associated with the complex and lengthy process of remediation can be dramatically reduced. Most attempts at quantifying contaminant transport have relied on solving some form of a well-known governing equation referred to as advection-dispersion-reaction equation. In identifying the source of pollution we have to solve the governing equations backward in time. Modeling contaminant transport using reverse time is an ill-posed problem since the process, being dispersive, is irreversible. Because of this illposedness, the problems have discontinuous dependence on data and are sensitive to the errors in data. A problem is categorized as a well-posed problem if (1) the solution exists, (2) the solution is unique, and (3) the problem is stable [Tikhonov and Arsenin, 1977]. Problems that do not satisfy these criteria are called ill-posed. For the groundwater contamination problem the plume has to have originated from someplace, therefore, physically, the plume exists. However, in mathematically rigorous terms, the fact that we have a presentday plume concentration does not necessarily mean that we satisfy the existence criterion. The solution exists only when we have perfect and consistent model and data that satisfy extremely restrictive conditions. Meeting the stability criterion is a difficult task to accomplish since numerical schemes that are 2113

Estimation of river pollution source using the space-time radial basis collocation method

“…[9]. Commonly employed techniques include the Tikhonov regularization method [38], the nonlinear optimization model [2], particlebased methods [1,7], the backward beam equation method [3,4,8] and geostatistical based methods [6,32]. Some other newly emerged techniques have also been under intensive investigation, such as artificial neural networks [37], a global search algorithm with a constrained least squares estimator [40], geostatistical kriging [36] and iterative regularization [23].…”

An Effective Kalman Filter-Based Method for Groundwater Pollution Source Identification and Plume Morphology Characterization

“…A significant number of statistical and deterministic methods have been proposed to solve this inverse problem considering the hydrogeological conditions known [5][6][7][8][9][10]. Extensive reviews on the identification methods of pollution source characteristics and the applications of various inverse modeling techniques in pollution source identification have been described in past research [11][12][13][14]. Since the inverse problem possesses an ill-posed nature, linked simulation-optimization methodology has been widely used [5,15].…”

Solving the backward heat equation on the unit sphere

“…In hydrologic inversion [1], sources of groundwater pollution are sought by reconstructing the contaminant history. Kovasznay and Joseph [6] proposed the use of a backward diffusion equation to restore blurred images.…”