*KAUST, Fall 2010 *

**ErSE 305:**** Multiphase Flows in Porous Media **

*Course Syllabus*

**Meeting Time and Location**:

2:30-4:00pm Saturdays and Tuesdays in Room 2132, Building 9

**Instructor**:

Prof. Shuyu Sun Telephone: +966 2808-0342 Email: shuyu.sun@kaust.edu.sa

**Teaching Assistant: **

Dr. Kai Bao Email: kai.bao@kaust.edu.sa

**Office Hours**:

9:00-10:30am Sundays and Tuesdays (no appointment needed during office hours)

Location: Dr. SunŐs office at Building 1, Room 4417

**Goals and Objectives: **The aim of this course is to
introduce the basic theory and computational techniques for modeling multiphase
flow in subsurface porous media, especially as applied to petroleum reservoir
simulation. At the end of the
course students will be able to construct conceptual and mathematical models
that represent simplified scenarios of petroleum reservoir, and students are
expected to be able to implement the mathematical models into numerical
simulators using a high-level programming language such as MATLAB.

**Course Description:
**

Understanding and modeling of multiphase flow in geological formation is required for making decisions associated with the management of petroleum reservoir. This course will cover the basic theory and numerical computation of multiphase flow in porous media. In the class, we present not only the models that describe phenomena of multiphase flow in porous media, but also to emphasize the theoretical foundation and the various assumptions that simplify the complex reality to the extent that it can be described by rather simple and solvable models. We will pay particular attention to the following two models: 1) incompressible two-phase immiscible flow and 2) compressible compositional multiphase flow. To make this course an introductory one accessible to students without any previous porous media flow knowledge, we will also go over subsurface single-phase flow in the beginning of this course.

We will first provide basic physical laws governing flow and transport in porous media, and then we discuss rock and fluid properties. Then derivation of mathematical models for multiphase flow in subsurface porous media will be covered. Since the equations governing a mathematical model of a reservoir cannot be solved by analytical methods in general, we will focus on numerical solution approaches. Finite difference methods, especially the mass-conservative block-centered finite difference scheme, will be formulated and discussed in details for the pressure equation and the saturation equation (for immiscible flow) or the species transport equation (for compositional flow). If time allows, toward the end of the semester we will gently and briefly touch upon a number of important finite volume and finite element approaches for the numerical modeling of groundwater flow and species transport. Implementation of numerical simulators, especially of block-centered finite difference oil-water two-phase flow simulators, is one focus of this course. Students will have opportunities to earn hands-on experiences of developing their own numerical reservoir simulators using MATLAB (or a language of your choice with consent of instructor).

**Prerequisite: **Basic numerical PDE course and basic
programming skills in MATLAB, or consent of instructor

**Text: **

1) *Reservoir Simulation: Mathematical Techniques in
Oil Recovery (CBMS-NSF Regional Conference Series in Applied Mathematics)*, by Zhangxin
Chen. Published by Society for Industrial and Applied Mathematics. 1 edition
(October 31, 2007). ISBN: 978-0898716405.

2) *Principles of Applied Reservoir Simulation*, by John R.
Fanchi. Published by Gulf Professional Publishing. Third Edition (December 22,
2005). ISBN: 978-0750679336.

**Recommended
References: **

1) *Computational Methods for Multiphase Flows in
Porous Media* (Computational Science and Engineering), by Zhangxin Chen. Published by
Society for Industrial and Applied Mathematics. 1^{st} edition (March
30, 2006). ISBN: 978-0898716061.

2) *Thermodynamics of Hydrocarbon Reservoirs, *by Abbas
Firoozabadi. Published by McGraw-Hill Professional. 1^{st} edition
(January 1, 1999). ISBN: 978-0070220713

**Grading Policy: **

- Your final grade will be determined as follows:

Three computational projects: 20% each

Semester project (including presentation and final report): 40%

- The letter grades will be assigned according to:

*A*: 95–100; *A-*:
90–94; *B+*: 85–89;

*B*: 80–84; *B-*: 75–79; *C+*: 70–74;

*C*: 65–69; C-: 60–64; *D+*: 55–59;

*D*: 50–54; *D-*:* *45–49; *F*:
0–44.

- In borderline cases, the instructor reserves the right to subjectively determine grades based on class attendance, class participation, quality of work, etc.

**Attendance: **Regular and punctual attendance is
necessary for each student to maximize his/her understanding of the material.
Students are expected to wait 15 minutes before leaving if the instructor is
not present at the scheduled start time of the class. Excused absences include
official university business and personal emergencies (medical, legal, death in
the family, etc). It is the studentŐs responsibility to contact the instructor
prior to the absence (when possible) and provide the documentation required for
excused absences. It is the
studentŐs responsibility to make up any deficiency resulting from class absence
in a timely manner, including getting class notes (from other students) and
assignments. Please carefully read
the university attendance policy for additional specifics. **Students who have more than 5 unexcused absences are subject to being
dropped from the course. **

**Academic Integrity: **As members of the KAUST
community, we have a mutual commitment to truthfulness, honor, and
responsibility, without which we cannot earn the trust and respect of
others. Furthermore, we recognize
that academic dishonesty detracts from the value of a KAUST degree. Therefore,
we shall not tolerate lying, cheating, or stealing in any form.

**Note: The
instructor reserves the right to make changes to this syllabus as necessary. **