Pollutant dynamics in water bodies is a teaching aimed at providing a deep knowledge on transport phenomena of active and passive, conservative and reactive pollutants, in natural water bodies, and at giving their mathematical formulation. The course also aims at consolidating the skills required for the developments of numerical models for the solution of the mathematical models introduced during the teaching.
The teaching belongs to the “Ingegneria Civile Per la Protezione dai Rischi Naturali” master course, which aims at training engineers towards high professional levels in the fields of the protection of both environment and civil infrastructures from hydrogeological and seismic hazards.
In such framework the teaching aims at defining conceptual models with increasing complexity for the representation of advective/diffusive/reactive transport phenomena in water.
Upon successful completion of the course, students will be able to: 1) examine a practical case of propagation of a pollutant in a water body; 2) verify the availability of existing formulations for a proper modelling of the phenomenon at hand; when this is not the case, they will be able to formulate a new one; 3) design and/or interpret experiments and dye studies aimed at determining values for the parameters of the derived model; 4) numerically solve the model, explicitly accounting for sources of uncertainty and their weight on the final result.
The teaching belongs to the “Ingegneria Civile Per la Protezione dai Rischi Naturali” master course, which aims at training engineers towards high professional levels in the fields of the protection of both environment and civil infrastructures from hydrogeological and seismic hazards.
In such framework the teaching aims at defining conceptual models with increasing complexity for the representation of advective/diffusive/reactive transport phenomena in water.
Upon successful completion of the course, students will be able to: 1) examine a practical case of propagation of a pollutant in a water body; 2) verify the availability of existing formulations for a proper modelling of the phenomenon at hand; when this is not the case, they will be able to formulate a new one; 3) design and/or interpret experiments and dye studies aimed at determining values for the parameters of the derived model; 4) numerically solve the model, explicitly accounting for sources of uncertainty and their weight on the final result.
teacher profile teaching materials
- definition of quantities involved
- dimensional analysis and Buckingham theorem
- "Fickian" diffusion
- diffusion coefficients
- 1D and 2D DE, and some analytical solutions:
i) instantaneous point source
ii) instantaneous uniform source
iii) constant point source
- impervious boundary conditions
Advection-Diffusion Equation (ADE) :
- Advection and diffusion spatial and temporal scales
- some analytical solutions for 1D ADE:
i) instantaneous point source
ii) instantaneous uniform source
iii) constant point source
Turbulent Diffusion (TD)
- TD in rivers:
i) longitudinal and transverse TD
ii) longitudinal dispersion: Taylor-Elder theory
- how to quantify longitudinal dispersion:
i) semi-empirical formulae
ii) method of moments
iii) tracers
Reacting solutes
- kinetic temporal scale vs convective ones
- first and second order
- ADE with homogeneous and heterogeneous reactions
- heterogeneous reactions:
i) air-water interface : Streeter-Phelps equation
ii) sediment-water interface: adsorption
Water quality models
- how to choose a model
- CSTR, PLug-flow
excercises
Programme
Diffusion Equation (DE):- definition of quantities involved
- dimensional analysis and Buckingham theorem
- "Fickian" diffusion
- diffusion coefficients
- 1D and 2D DE, and some analytical solutions:
i) instantaneous point source
ii) instantaneous uniform source
iii) constant point source
- impervious boundary conditions
Advection-Diffusion Equation (ADE) :
- Advection and diffusion spatial and temporal scales
- some analytical solutions for 1D ADE:
i) instantaneous point source
ii) instantaneous uniform source
iii) constant point source
Turbulent Diffusion (TD)
- TD in rivers:
i) longitudinal and transverse TD
ii) longitudinal dispersion: Taylor-Elder theory
- how to quantify longitudinal dispersion:
i) semi-empirical formulae
ii) method of moments
iii) tracers
Reacting solutes
- kinetic temporal scale vs convective ones
- first and second order
- ADE with homogeneous and heterogeneous reactions
- heterogeneous reactions:
i) air-water interface : Streeter-Phelps equation
ii) sediment-water interface: adsorption
Water quality models
- how to choose a model
- CSTR, PLug-flow
excercises
Core Documentation
Socolofsky, Jirka - Special Topics in Mixing and Transport Processes in the Environment - 5th Edition, 2005Type of delivery of the course
The course is made of theoretical and practical classes. There is at least one practical exercise dedicated to each theoretical macro-topic. Exercises require the knowledge of one tool of numerical calculus. The student can choose any tool he prefers. The teacher spends one or two classes to a short introduction to Matlab. The teacher offers supports to students employing Matlab or Mathematica to carry out the exercises.Type of evaluation
Oral exam consists of three questions. One of them is the discussion of one of the practical exercises carried out during the course.