Field transport of reactive solute species is investigated through a class of stochastic models, here termed mass response functions (MRFs), which incorporate simplified concepts of chemical/physical nonequilibrium kinetics in the formulation of transport by travel time distributions. MRFs are probability density functions (pdfs) associated with solute particles' travel time within transport volumes. The theory hinges on recent advances in modeling transport of solutes in groundwater and in basin scale transport volumes and links the approaches of surface hydrologists with recent subsurface transport models. The relationship between MRFs and the theory of solute transport by continuous motions is investigated. It is found that MRFs extend the basic formulation of transport of inert solutes to a particular case of sorption process. The relationship between MRFs and the basic differential convection-dispersion equation incorporating linear sorption is also investigated. It is found here that not only are transfer functions of solutes consistent with any mechanistic three-dimensional (3-D) model of convection dispersion, but also that they are, under limit conditions, the product of the travel time distribution of the carrier flow with a bounded continuous function. The latter is the solution to an initial value problem which results from solving the general 3-D differential equations of convection dispersion with sorption under some simplifying assumptions, and formally coincides with the resident concentration included (as an assumption) in the original MRF formulation. Travel time distributions and MRFs underlain by statistical constraints rather than by dynamical models are proposed. Non-Gaussian distributions are studied by statistical-mechanical tools and are found to represent the norm, rather than the exception, in this formulation of transport of reactive solutes. The concepts are applied to a field study and are shown to yield reliable models of solute migration in nonpoint pollution problems.
On Mass- Response Functions / A., Rinaldo; M., Marani; Bellin, Alberto. - In: WATER RESOURCES RESEARCH. - ISSN 0043-1397. - STAMPA. - 25:7(1989), pp. 1603-1617. [10.1029/WR025i007p01603]
On Mass- Response Functions
Bellin, Alberto
1989-01-01
Abstract
Field transport of reactive solute species is investigated through a class of stochastic models, here termed mass response functions (MRFs), which incorporate simplified concepts of chemical/physical nonequilibrium kinetics in the formulation of transport by travel time distributions. MRFs are probability density functions (pdfs) associated with solute particles' travel time within transport volumes. The theory hinges on recent advances in modeling transport of solutes in groundwater and in basin scale transport volumes and links the approaches of surface hydrologists with recent subsurface transport models. The relationship between MRFs and the theory of solute transport by continuous motions is investigated. It is found that MRFs extend the basic formulation of transport of inert solutes to a particular case of sorption process. The relationship between MRFs and the basic differential convection-dispersion equation incorporating linear sorption is also investigated. It is found here that not only are transfer functions of solutes consistent with any mechanistic three-dimensional (3-D) model of convection dispersion, but also that they are, under limit conditions, the product of the travel time distribution of the carrier flow with a bounded continuous function. The latter is the solution to an initial value problem which results from solving the general 3-D differential equations of convection dispersion with sorption under some simplifying assumptions, and formally coincides with the resident concentration included (as an assumption) in the original MRF formulation. Travel time distributions and MRFs underlain by statistical constraints rather than by dynamical models are proposed. Non-Gaussian distributions are studied by statistical-mechanical tools and are found to represent the norm, rather than the exception, in this formulation of transport of reactive solutes. The concepts are applied to a field study and are shown to yield reliable models of solute migration in nonpoint pollution problems.File | Dimensione | Formato | |
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