Using the method of moments to analyze three‐dimensional diffusion‐limited solute transport from temporal and spatial perspectives

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Abstract
This paper focuses on the analysis and application of an analytical model that incorporates solute diffusion within immobile regions into the three‐dimensional advection/dispersion solute transport equation. The diffusion term of the model is formulated using either a first‐order rate expression or an expression assuming Fickian diffusion into spherical, cylindrical, or rectangular immobile regions. In order to assist in the analysis of solute transport behavior by means of the models, a modified form of Aris's method of moments is developed, which permits the calculation of the spatial and temporal moments of solute distributions simulated using the three‐dimensional diffusion models, without having to invert the Laplace‐ or Fourier‐transformed solutions. By using this method, the moments of the diffusion models are compared with one another, with the moments of a model that assumes equilibrium advective/dispersive transport, and with the moments of a model that assumes that a first‐order rate law governs mass transfer between the mobile and immobile regions. The method of moments also is used to assess the differences in the spatial and temporal moment behavior of each transport model under discussion.