Reservoir Simulation

Semester 1

Teaching Unit : UEF 1.1

Material 4: Reservoir simulation

VHS: 67h30 (Lectures: 3h00, Tutorials: 1h30)

Credits: 6

Coefficient: 3

 

1- Teaching Objectives

 

The objective is to simulate some physical phenomena, especially in the petroleum sector, and also to develop students' skills in modeling topics for their final year Master's theses.

2-Recommended prior knowledge

 

Skills acquired during his bachelor's degree training in production 2 and 3; the modules: computer science and numerical methods.

 

3-Content of the material

 

Chapter I: Classification of Partial Differential Equations

 

I.1 Elliptic Problem

I.2 Parabolic Problem

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. Taylor's Development

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.
  • Neumann's problem.

III.5. Solving parabolic problems.

  • Formulation of the parabolic problem
  • The mesh.
  • The explicit method.
  • The implicit method.
  • Crank -Nicholson method .

III.6. Solving hyperbolic problems.

  • Formulation of the parabolic problem
  • The mesh.
  • 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-Evaluation Method

 

Written assessment (exams) and continuous assessment (presentations, quizzes) .

 

5-Bibliographical References

 

1- Jean-Pierre NOUGIER, Numerical Calculation Methods, MASSON, Paris 1991.

2- M.MOKHTARI, A.MESBAH, Learning and Mastering MATLAB, 1997, Springer.

3- J.TAINE , J. P.PETIT , Heat transfer ( Mechanics of anisothermal fluids ), 1989 ; Dunod university.

4- I. POPA, Numerical modeling of heat transfer, finite volume method , Universitaria , Craiova, 20