Num. simulation in reserv. Engineering

Semester: 1

· Teaching Unit: UEF 1.1 (Fundamental Teaching Unit 1.1)

· Subject 4: Reservoir Simulation

· Total Weekly Hours (VHS): 45h00 (1h30 Lecture, 1h30 Tutorial)

· Credits: 4

· Coefficient: 2 

Professor: Dr. Mohamed DOUAK

1-Module Objectives
The main objective of teaching this module is to provide a foundation for first-year Master's students in production to simulate various physical phenomena, particularly in the oil industry. It also aims to develop students' skills in using modeling techniques for their final-year Master's theses. 

2-Recommended Prerequisites
Skills acquired during the Bachelor's degree in production (years 2 and 3), specifically in the modules of computer science and numerical methods. 

3-Module Content 

  • Chapter I: Classification of Partial Differential Equations
    • I.1 Elliptic problems
    • I.2 Parabolic problems
    • I.3 Hyperbolic problems
  • Chapter II: Method of Separation of Variables (Fourier Method)
    • II.1. Definition
    • II.2. Solving elliptic problems
    • II.3. Solving parabolic problems
    • II.4. Solving hyperbolic problems
  • Chapter III: Finite Difference Methods
    • III.1. The Taylor expansion
    • III.2. Finite difference methods
      • Expression of first derivatives
      • Expression of second derivatives
    • III.3. Procedure for solving boundary value problems
    • III.4. Solving elliptic problems
      • The Dirichlet problem
      • The Neumann problem
    • III.5. Solving parabolic problems
      • Formulation of the parabolic problem
      • Meshing
      • The explicit method
      • The implicit method
      • The Crank-Nicholson method
    • III.6. Solving hyperbolic problems
      • Formulation of the parabolic problem
      • Meshing
      • The explicit method
      • The implicit method
  • Chapter IV: Finite Volume Method
    • IV.1. Definition
    • IV.2. Solving elliptic problems
    • IV.3. Solving parabolic problems
    • IV.4. Solving hyperbolic problems

4-Assessment Method
Written assessment (exams) and continuous assessment (presentations, quizzes). 

5-Bibliographical References 

  1. Jean-Pierre NOUGIER, Méthodes de calcul numérique (Numerical Calculation Methods), MASSON, Paris 1991.
  2. M. MOKHTARI, A. MESBAH, Apprendre et Maîtriser MATLAB (Learning and Mastering MATLAB), 1997, Springer.

J. TAINE, J. P. PETIT, Transferts thermiques (Mécaniques des fluides