Knowledge and ability to understand: learn the basics
of the equations describing the flow of fluids (in particular
in porous media) and of the advective transport of contaminants.
Knowledge and understanding skills applied: ability to read
and understand how to apply the theoretical knowledge acquired to examples
of the modeled case studies.
Making judgments: knowing how to evaluate the content of
innovation present in the examples of case studies based on the
acquired theoretical knowledge.
Communication skills: knowing how to present and organize the exposition
of a specialized subject based on the developed topics.
Ability to learn: to learn more about a topic starting
from previous knowledge applied to similar examples and applications
of modeling a fluids flow problem.
Course contents summary
The course intends to provide on one side, an
overview of mathematical models describing the flow of fluids
(especially in porous media) and the advective transport
and to the equations describing these phenomena.
On the other hand, it intends to provide numerical calculation tools for
modeling and forecasting in time and space using
examples of real case studies.
Fundamentals of modeling (knowledge and understanding)
Darcy's law. Generalization in three dimensions.
Equations that describe the single-phase flow in porous media.
Flow equation in the presence of external sources (knowledge and
ability to understand).
Equations describing the immiscible two-phase flow. Differential equations
written in terms of pressure and saturation.
Equations in transitory and stationary regime.
Classification of differential equations. Boundary conditions:
Dirichlet, Neumann and mixed (knowledge and understanding).
Solution of the steady-state flow equation, in one media
isotropic and homogeneous. Laplace equation.
Examples of analytical models and solution (knowledge and ability of
Introduction to the finite difference method. Examples of approximate solutions.
Discretization of the grid and boundary conditions.
Numerical methods. Implementation for some case studies (knowledge and ability of
Equations of the transport of contaminants in a single-phase fluid.
Transport of multicomponents in a single phase fluid.
Example of analytical solutions (knowledge and understanding).
Application to case studies using a numerical program, for example MODFLOW
(autonomy of judgment).
Simulation application of interdisciplinary studies for the solution
of a real problem (communication skills).
Applied Groundwater Modeling, Simulation of Flow and Advective Transport.
Mary P. Anderson, William W. Woessner, Randall J. Hunt.
Computational Methods for Multiphase Flows in Porous Media.
Zhangxin Chen, Guanren Huan, Yuanle Ma.
Material supplied by the teacher.
Lectures and activities in the laboratory of modeling and
simulations of case studies and real cases.
Assessment methods and criteria
Informal checks in the classroom and oral exam. For foreign students
the English language is used.