The course is designed to provide participants with principles of flow and transport in aquifers. Students will learn the way key physical, geo-chemical and hydrologic processes can be conceptualized and described to quantify flow dynamics in subsurface systems. They will also learn how to interpret laboratory and field scale tracer data and how to cope with the intrinsic uncertainty associated with the characterization of subsurface heterogeneous aquifers.

Students will develop the ability to investigate groundwater systems and to solve problems at laboratory and field scales. Lectures and practical exercise sessions will enable students to:

• be familiar with principles, approaches and techniques for aquifers characterization;
• learn about physical, chemical and hydrologic factors controlling dynamics of groundwater;
• understand the theory of flow and transport in heterogeneous porous media;
• effectively parameterize flow and transport models;
• solve flow and transport problems (including laboratory and field scales data interpretation);
• assess flow and transport model under uncertainty;
• learn key elements and tools of geostatistically-based aquifer characterization, flow and transport simulation.

Key processes that control fluid movement. Pore and continuum approach. Fluid flow in porous and fractured media. Mass balance equation. Permeability and conductivity. Deformable porous medium. Specific storativity. Darcy’s Law (phenomenology, theoretical derivation and range of validity). Anisotropic media and permeability tensor. Scale dependence of hydraulic properties and heterogeneity. Theoretical and empirical correlations between flow parameters (specific storage, porosity, permeability). Interpretation of laboratory scale flow experiments.

Groundwater circulation.  Three- and two-dimensional models for fluid flow in porous media. Initial and boundary conditions. Confined and Phreatic Aquifer (Dupuit assumption). Multilayered aquifer-aquitard system. Analytical solutions for homogeneous systems. Superimposition. Groundwater maps and streamlines. Groundwater flow and leakage. Regional Groundwater balance.

Well hydraulics and field tests interpretation. Hydraulic of pumping and recharging wells: Steady and unsteady flow to a well in a confined, phreatic and leaky aquifer. Partially penetrating wells. Multiple well systems. Wells near boundaries and method of images. Well losses and specific well discharge. Effect of wellbore storage. Pumping tests. Type curves. Analytical solution, including storage and non-linear effects at the well. Interpretation of well-interference testing in complex hydrogeological systems.

Solute transport processes. Contaminant fluxes: advective flux, diffusive flux, hydrodynamic dispersion, dispersive flux. Derivation of Advection-dispersion equation. Diffusion versus dispersion. Balance equation for multi- species. Condition for chemical equilibrium, chemical reactions, sorption, ion exchange, precipitation-dissolution. Initial and boundary conditions. Analytical solutions. Laboratory and field tests to determine dispersivity. Dispersivity tensor. Scale effect of dispersion. Double porosity models. Laboratory and field- scale tracer tests and their interpretation. Random Walk and continuous time random walk models. Multi-component reactive transport. Models of precipitation-dissolution, sorption and homogeneous reactions in porous media.

Data Integration and Inverse Modeling. Introduction and application of techniques aimed at incorporating available data (including pressure transient tests, tracer tests, geological information) into aquifer characterization models. General formulation of non-linear inverse problems in porous media. Model calibration and validation.

Modeling under uncertainty. Uncertainty quantification in the characterization of heterogeneous systems. Basic principles of geostatistics. Probabilistic approaches to flow and transport in heterogeneous aquifers. Stochastic processes. Ensemble statistics. Ergodicity. Tools for uncertainty analysis: geostatistics, Kriging, sensitivity analyses. Stochastic description of heterogeneity. Monte Carlo simulation, generation of (correlated) random fields. Effective and equivalent parameters.

Students should be familiar with principles of:  fluid mechanics, hydraulics, partial differential equations, basics of statistics.

The exam consists of two compulsory parts: a written and an oral test. Both parts must be successfully completed to pass the course.

The written test is structured across 3 exercises aimed at assessing the ability to:

• solve a flow problem
• solve a transport problem (interpret experimental data)
• reconstruct the heterogeneous distribution of aquifer properties

Marks of the written tests range among: A (Excellent), B (Good), C (Average, Fair), D (Poor, Pass), F (Failure)

The oral test can be undertaken only if the written test has been successful (minimum mark: D); it starts from the discussion of the written test and of the project (optional, developed during the practical classes) and aims at verifying the degree of understanding of all aspects (theoretical, conceptual, and operational) covered during the course. It brings the mark of the written part up to date to define the final grade.