Lectures delivered by Prof. Shaul Sorek (MODULES 1-3
).INTRODUCTION TO MODELING TRANSPORT PHENOMENA IN HETEROGENEOUS MEDIAAims:
Introduction to physical concepts for mathematical modeling of transport phenomena through unsaturated/saturated porous/fractured media. Formulation of balance equations concerning multi-phase flow and multi-component transport through heterogeneous media. The knowledge obtained will enable students further to continue and direct the running of commercialized computer codes to specific physics associated with the characteristics of the studied field problem.Prerequisite:
Linear algebra; Integration and differentiation calculus; Fluid mechanics.Course contents:MODULE 1 . Lumped Parameter Models.
The three-dimensional investigated domain is discretized by a network of finite compartments, of identifiable physical space(s) characterized by lumped (i.e. not a function of space) parametersSpecific topics - Fluid mass balance; Fluid momentum balance; Solute mass balance; Unknown flow direction; Fluid diffusion flux; Solute diffusion flux.
Each compartment can account for multi-fluids comprised of multi-components. The regional flow regime and transport pattern is expressed by fluxes crossing compartments boundaries and formalized by a set of balance equations of fluids mass and momentum and solutes mass, accumulated over the entire compartmental setup.
Examples of model constructions include: Filtering system; Flow through a pins matrix; Flow through fractured networks.
MODULE 2 . Continuum Models.
On the basis of continuum mechanics we formulate the Eulerian or Lagrangian forms of the general balance equation for any extensive quantity (mass, volume, momentum and energy) of a phase.
Specific topics - Solute mass balance; Fluid mass balance; Momentum balance of a phase; Dimensionality and units; Boundary conditions; Continuum to lumped.
The general balance equation presents a recipe for constructing the solute mass balance equation. Using the notion of a phase we expand the equation of solute mass balance into that of a fluid mass balance. We construct the phase momentum balance equation and present constitutive laws for diffusion fluxes of solute mass balance and phase momentum balances.
The continuum transport equation for two spatial directions and the general balance equation are transformed to the equivalent lumped parameter equations. In doing so we identify the parameters affiliated with continuum models that are associated with lumped parameters models.
MODULE 3. Macroscopic Models.
Accounting for the uncertainty of the porous matrix geometry, we use continuum mechanics concepts and average the microscopic balance equations on the basis of a Representative Elementary Volume (REV) and obtain its corresponding macroscopic balance equations.
Specific topics - Averaging rules over the REV; Phase mass balance; Solute mass balance; Momentum balance of a phase.
Examples of model constructions include: Stresses in a saturated porous matrix; Mass transport of a single fluid flowing through a saturated deformable porous matrix.
Lectures delivered by Prof. Giuseppe Gambolati (MODULES 4-5).
MODULE 4 . Finite Element Method (FEM). Introduction. Variational Principles. FEM of Ritz and Galerkin. Piecewise interpolation. 2D finite elements.
Introduction to FEM. Functionals and functional minimization. Euler’s equation. Example of the flow equation in porous media. Piecewise interpolation over triangular, bilinear, biquadratic, bicubic and serendipity finite elements. Application of FEM to the solution of the flow and transport equation in porous media (with triangular finite elements).
MODULE 5. Solution to FEM with Conjugate Gradient Like Methods. Preconditioners. Convergence. Examples of FEM in Civil and Environmental Engineering.
Projective or conjugate gradient like methods for symmetric and positive definite FEM applications. Convergence profile. Acceleration of convergence by precontioning. Example of FEM applications to simulate and predict anthropogenic land subsidence (uplift) of Venice and saltwater intrusion in the aquifer system of Recanati.
Lectures delivered by Prof. M. Hassanizadeh (MODULES 7-10).
The subsurface environment plays an important role in many human activities as well as in natural systems. Both soil and groundwater are valuable natural resources for human beings. Moreover, the subsurface is frequently used for storage of mass (toxic and otherwise) and energy, and construction of certain facilities and infrastructure. For a sustainable use of the subsurface and its resources, it is extremely important to understand and predict various processes that occur in the subsurface. In particular, knowledge of the flow of water and the movement of dissolved components is essential for the design of various activities occurring in the subsurface. These modules relate to the understanding and description of processes affecting the fate of dissolved components of groundwater.
In these modules, we learn to study the fate of pollutants in the subsurface (the unsaturated soil and the groundwater zone as well as deeper layers) in a systematic manner and in a quantitative way. The fate of pollutants that enter the subsurface is determined by physical, chemical, and biological processes. Depending on the relative significance of these processes, the pollutants may spread in the subsurface (mixing by advection and dispersion), may be kept in place and rendered immobile (e.g. due to adsorption, precipitation) and/or may be transformed into other (less harmful) substances (e.g. due to radioactive decay, biodegradation, inactivation). We will introduce these processes, explain their physical basis, describe their effects, provide governing equations, and develop solutions for simple situations. Some web-based models will be introduced and used.
The knowledge obtained in this course will be also relevant to the study of transport of solutes in general porous media, such as human tissues, plants, ceramics, concrete and other construction materials, food, paper, and other industrial materials.
MODULE 7. Mass transfer processes
In soils and aquifers, in addition to water and solid grains, other phases may be present. These include gases (e.g., air) and non-aqueous liquids (such as oil). Solutes dissolved in water may be exchanged with other phases through various processes. These include volatilization, adsorption, dissolution, and precipitation. Within the water phrase, solutes may appear and disappear due to chemical reactions, radioactive decay, and biodegradation. In this module, we present mathematical descriptions of these processes for a batch system. Linear and nonlinear as well as equilibrium and kinetic models will be discussed.
MODULE 8. Transport processes: Advection and hydrodynamic dispersion
Solutes are transported in soil and groundwater by diffusion, advection, and dispersion. In this module, governing equations for these processes are introduced, typical initial and boundary conditions are defined, and analytical solutions for some typical situations are given. Also, the combination of transport and mass transfer processes are modelled and analytical solutions for some typical cases are given.
MODULE 9. Two-phase flow
Two-phase flow is of great significance in many industrial porous media, in oil and gas production, and in CO2 sequestration. In this module, main concepts of two-phase flow, such as wettability, capillarity, Extended Darcy’s law, and relative permeability, are introduced. Also, unsaturated zone hydrology will be discussed and special aspects of solute transport in unsaturated zone will be explained.
MODULE 10. Special topics in mass transport in porous media
In this module, some advanced topics will be discussed. This will include virus and colloid transport, density-dependent flow and transport, solute transport in structured porous media, and disposal radioactive waste in geological formations. Based on interest of participants, other special topics may be introduced.
Lectures delivered by Dr. Rudy Rossetto (MODULE 11).
MODULE 11. Introduction to the FEFLOW GUI. Application of the FEFLOW code to a groundwater flow and solute transport problem.
Students will be introduced to the main functionalities of the FEFLOW GUI by means of the implementation of a groundwater flow and solute transport problem. This module is preparatory to the subsequent ones in order to familiarise the students with the code used in the following tutorials. This lecture and the following will be given in a fully equiped computer room.
Lectures delivered by Dott. Claudio Gallo (MODULES 12-15).
The aim of these lessons is to go deeper into the problem of numerical modelling of flow and transport phenomena. Although numerical discretization notions will be recalled, the focus will be on “what is not written on books”, namely, which problems are encountered when running a commercial code. The objective is twofold: passing from theory to experience for application problems from small to large scale; achieving the basic sensitivity in the response a numerical simulator/commercial package will give when certain kinds of inputs are setup. The experience teaches that the user should know what is inside the simulator in order to realize when the results provided by the computer is not valid.
MODULE 12. Flow and transport equations: equations and boundary conditions.
In this section we review the major equations used in groundwater/vadose zone modelling together with their boundary conditions. However, we are not supposed to discuss them from the mathematical point of view, but on the basis of the implications that using such a boundary condition have when flagged on in an application. In particular, the focus will be on nonlinear boundary conditions (rain, seepage face), diffusive/total flux, Dirichlet boundary conditions and how these impact on the results.
MODULE 13. Testing the numerical simulators: what should be tested for achieving a feeling.
Compared to 15 years ago numerical simulators have been improved quite a lot and they are provided with nice user interfaces, capability to make 3D images with contouring, etc. Furthermore the computational capability has increased of 2 order of magnitudes thus calculations are not currently a problem unless we go to very large scale simulations with half a million nodes. However, we should keep in mind what we are calculating and the demo cases always works perfectly. The focus on this section will be on classical issues that can cause a strong “headache” to the simulator and, as a consequence, to the user. Advection dominated problems, peclet/courant constraints, anisotropy/heterogeneity, rainfall etc are just a few examples of a wide variety of issues that can be discussed. Firstly the mathematical numerical problems will be discussed at the blackboard, and the the direct implications will be test by the participants on FEFLOW on some ad-hoc test cases.
MODULE 14. Simulation of reactive transport: how to formulate equilibria, competitive and chain reaction. Numerical solution techniques and implications on computational time. Impact on mass balances.
Reactive transport is a complicated matter to be treated. On the one hand, we have to cope with the complexity of chemical reactions (competitive, chain, auto-catalytic, adsorption, biological, etc.) and equilibria; on the other hand, we have to deal with the computational burden associated with the numerical solution (analytic solution is obviously not conceivable). In many cases the computational time required by the “chemistry” is much higher than that related to the fluid dynamics. In this lecture we make an overview on the main classes of reaction we may be concerned with when considering geochemical characteristics of contamination problems. Then, we focus on the possible troubles we may face when included in our simulations: in easy words, we will try to understand what we may expect in the quality of the results, especially when dealing with nonlinearities.
MODULE 15. Discussion on test cases and on reliability of results.
Problems to be solved are the logical consequence of modelling issues. The importance of the experience in applied modelling is often overlooked: modelling results are considered the dirty-work that should be made by technicians. This is a big mistake, since in many cases only a deep knowledge of the whole matter can help us in analyze, schematizing, modelling and simulating a scenario with the tools that are available to us. This final lecture will focus on some real-scenario cases, on various caveats regarding modelling and results reliability and, finally, a general discussion regarding on the top-bottom procedure one may follows when dealing with brand new modelling scenario.
Lectures delivered by Dott.ssa Claudia Cherubini (MODULES 16-18).
MODULE 16. Fractured aquifers: Classification, parameters, saturated groundwater flow and contaminant transport.
- Classification of fractured aquifers;
- Key physical parameters governing groundwater flow and the relations existing among them;
- Methods of estimating hydraulic properties of rocks (Laboratory methods, hydraulic testing of fractured rocks, pumping tests);
- Laws governing groundwater flow in fractures;
- The parallel plate model and how it oversimplifies the system in case of pronounced anisotropy;
- The applicability of the Darcy law in presence of fractured aquifers.
MODULE 17. Contaminant transport in fractured aquifers.
- Overview of the mechanisms of solute transport in fractured rock;
- Hydrodynamic dispersion;
- Matrix diffusion and channeling phenomena;
- Equations for diffusion;
- Effects of diffusion.
- Transport by advection and diffusion in fractured aquifers;
- Mathematical modelling of transport in the fractured media.
MODULE 18. Unsaturated fracture flow. Modeling approaches for fractured aquifers.
- Key physical processes governing seepage in fractured formations;
- Relations existing between moisture content, relative permeability and degree of saturation for fractures and the matrix;
- Fractures sandy soil behavior (gravity dominated system) versus matrix to clayey soils behavior (capillarity dominated system);
- Capillary barrier phenomena in unsaturated conditions, drift shadow, influence of the nature of the system of fractures on the failure of the capillary barrier or on the contrary the flow diversion.
Detailed overview on all the modeling approaches used for fractured aquifers:
- The Discrete Approach (Discrete Fracture Network Approach–DFN, Discrete Channel Network Approach DCN) that considers the flow within individual fractures or conduits.
- The Continuum Approach (Single Continuum Approach, Double Continuum Approach, Multiple Interacting Continua) that treats heterogeneities in terms of effective model parameters and their spatial distribution.
- The Hybrid Approach (Combined Discrete-Continuum Approach-CDC) that combines a continuum dominium with a discrete network of fractures.
Lectures delivered by Dott.ssa Giuditta Lecca (MODULES 19-20).
MODULE 19. Modeling Seawater Intrusion in Coastal Aquifers.
The module describes the simulation of seawater intrusion phenomena in coastal aquifers using density-dependent variably saturated coupled groundwater flow and contaminant transport models. Special attention is devoted to the set-up, development and operational use of large and complex 3D groundwater models.
MODULE 20. Online real world applications.
The module concerns the application of the CODESA-3D model to a series of real world case studies, including the discussion of automatic model calibration and probabilistic analysis issues. The simulations selected will be carried out in the online AQUAGRID problem solving platform (.crs4.it:8080/enginframe/aquagrid/index.xml) oriented to the development of hydrogeological and geochemical applications, hosted on the GRIDA3 computing portal.