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Abstract
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The conventional advection-dispersion equation (ADE) with constant coefficients often fails to capture the spatial variability that characterizes flow velocity and dispersion in river systems, thus necessitating the use of models with spatially variable coefficients (SVC-ADE). This study proposes a new analytical solution for the SVC-ADE that successfully fills the current void in modeling sudden pollutant releases with linear velocity (u = k1 x) and quadratic dispersion (D = k2 x2) variation. Through Laplace transform and variable transformation techniques, the solution was verified with Conococheague Creek field data. The effects of coefficients (k1, k2, k, C0) on breakthrough curve (BC) shapes were explored with similarities to classical ADE but with greater accuracy for spatial variability. Spatial moments decreased exponentially, and temporal moments increased as power functions with distance, while dispersivity increased linearly and maximum concentration decreased nonlinearly. Nonlinear relationships were established between SVC-ADE and conventional ADE parameters. Model performance (RMSE = 0.038–0.045 ppm, DC = 0.93) confirms its utility for environmental management.
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