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(Draft — 31 August 2009) Petroleum Engineering 620
Fluid Flow in Petroleum Reservoirs
Syllabus and Administrative Procedures — Fall 2009
Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs
Syllabus and Administrative Procedures
Fall 2009
Petroleum Engineering 620 Instructor: Dr. Tom Blasingame Co-Instructor: Dilhan Ilk
Texas A&M University Office: Richardson 815/TBA Office: Richardson 821/TBA
College of Engineering TL: +1.979.845.2292 TL: +1.979.845.4064
TR 08:10.-09:15 RICH 208 EM: EM:
Required Texts/Resources: (*Book must be purchased. #Out of Print/Public Domain — Electronic file to be made available by instructor.)
*1. Advanced Mathematics for Engineers and Scientists, M.R. Spiegel, Schaum's Series (1971).
*2. Conduction of Heat in Solids, 2nd edition, H. Carslaw and J. Jaeger, Oxford Science Publications (1959).
#3. Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, Dover Pub. (1972).
#4. Table of Laplace Transforms, G.E. Roberts and H. Kaufman, W.B. Saunder, Co. (1964).
#5. Numerical Methods, R.W. Hornbeck, Quantum Publishers, Inc., New York (1975).
#6. Approximations for Digital Computers: Hastings, C., Jr., et al, Princeton U. Press, Princeton, New Jersey (1955).
#7. Handbook for Computing Elementary Functions: L.A. Lyusternik, et al, Pergamon Press, (1965).
Optional Texts/Resources: (+Special order at MSC Bookstore or check TAMU library. #Local bookstores)
#1. Calculus, 4th edition: Frank Ayres and Elliot Mendelson, Schaum's Outline Series (1999) (Remedial text)
#2. Differential Equations, 2nd edition: Richard Bronson, Schaum's Outline Series (1994) (Remedial text)
#3. Laplace Transforms, M.R. Spiegel, Schaum's Outline Series (1965) (Remedial text)
#4. Numerical Analysis, F. Scheid, Schaum's Outline Series, McGraw-Hill Book Co, New York (1968). (Remedial text)
+5. The Mathematics of Diffusion, 2nd edition, J. Crank, Oxford Science Publications (1975). (important/historical)
+6. Table of Integrals, Series, and Products, I.S. Gradshteyn and I.M. Ryzhik, Academic Press (1980). (very important/historical)
+7. Methods of Numerical Integration, P.F. Davis and P. Rabinowitz, Academic Press, New York (1989). (perhaps useful for research)
+8. An Atlas of Functions, J. Spanier and K. Oldham, Hemisphere Publishing (1987). (perhaps useful for research)
+9. Adv. Math. Methods for Eng. and Scientists, 2nd edition, C.M. Bender and S.A. Orsag, McGraw-Hill (1978). (excellent text)
+10. Asymptotic Approximations of Integrals, R. Wong, Academic Press (1989). (perhaps useful for research)
+11. Asymptotics and Special Functions, F.W.J. Olver, Academic Press (1974). (perhaps useful for research)
Course and Reference Materials:
The course materials for this course are located at:
http://www.pe.tamu.edu/blasingame/data/P620_09C/
Basis for Grade: [Grade Cutoffs (Percentages) → A: < 90 B: 89.99 to 80 C: 79.99 to 70 D: 69.99 to 60 F: < 59.99]
Assignments 90 percent
Class Participation 10 percent
Total = 100 percent
Policies and Procedures:
1. Students are expected to keep pace in the course — DO NOT FALL BEHIND IN THE LECTURES OR YOUR ASSIGNMENTS.
2. Policy on Grading
a. All work in this course is graded on the basis of answers only — any partial credit is at the discretion of the instructor.
b. All work requiring calculations shall be properly and completely documented for credit.
c. All grading shall be done by the instructor, or under his direction and supervision, and the decision of the instructor is final.
3. Policy on Regrading
a. Only in very rare cases will exams be considered for regrading — partial credit (if any) is not subject to appeal.
b. Work which, while possibly correct, but cannot be followed, will be considered incorrect.
c. Grades assigned to homework problems will not be considered for regrading.
d. If regrading is necessary, the student is to submit a letter to the instructor explaining the situation that requires consideration for regrading, the material to be regraded must be attached to this letter. The letter and attached material must be received within one week from the date returned by the instructor.
4. The grade for a late assignment is zero. Homework will be considered late if it is not turned in at the start of class on the due date. If a student comes to class after homework has been turned in and after class has begun, the student's homework will be considered late and given a grade of zero. Late or not, all assignments must be turned in. A course grade of Incomplete will be given if any assignment is missing, and this grade will be changed only after all required work has been submitted.
5. Each student should review the University Regulations concerning attendance, grades, and scholastic dishonesty. In particular, anyone caught cheating on an examination or collaborating on an assignment where collaboration is not specifically authorized by the instructor will be removed from the class roster and given an F (failure grade) in the course.
Course Description
Graduate Catalog: Analysis of fluid flow in bounded and unbounded reservoirs, wellbore storage, phase redistribution, finite and infinite conductivity vertical fractures, dual-porosity systems.
Translation: Development of skills required to derive "classic" problems in reservoir engineering and well testing from the fundamental principles of mathematics and physics. Emphasis is placed on a mastery of fundamental calculus, analytical and numerical solutions of 1st and 2nd order ordinary and partial differential equations, as well as extensions to non-linear partial differential equations that arise for the flow of fluids in porous media.
Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs
Course Outline/Topics
Fall 2009
Course Outline/Topics:
Advanced Mathematics Relevant to Problems in Engineering: (used throughout assignments)
l Approximation of Functions
n Taylor Series Expansions and Chebyshev Economizations
n Numerical Differentiation and Integration of Analytic Functions and Applications
n Least Squares
l First-Order Ordinary Differential Equations
l Second-Order Ordinary Differential Equations
l The Laplace Transform
n Fundamentals of the Laplace Transform
n Properties of the Laplace Transform
n Applications of the Laplace Transform to Solve Linear Ordinary Differential Equations
n Numerical Laplace Transform and Inversion
l Special Functions
Petrophysical Properties:
l Porosity and Permeability Concepts
l Correlation of Petrophysical Data
l Concept of Permeability — Darcy's Law
l Capillary Pressure
l Relative Permeability
l Electrical Properties of Reservoir Rocks
Fundamentals of Flow in Porous Media:
l Steady-State Flow Concepts: Laminar Flow
l Steady-State Flow Concepts: Non-Laminar Flow
l Material Balance Concepts
l Pseudosteady-State Flow in a Circular Reservoir
l Development of the Diffusivity Equation for Liquid Flow
l Development of the Diffusivity Equations for Gas Flow
l Development of the Diffusivity Equation for Multiphase Flow
Classical Reservoir Flow Solutions:
l Dimensionless Variables and the Dimensionless Radial Flow Diffusivity Equation
l Solutions of the Radial Flow Diffusivity Equation — Infinite-Acting Reservoir Case
l Laplace Transform (Radial Flow) Solutions — Bounded Circular Reservoir Cases
l Real Domain (Radial Flow) Solutions — Bounded Circular Reservoir Cases
l Linear Flow Solutions: Infinite and Finite-Acting Reservoir Cases
l Solutions for a Fractured Well — High Fracture Conductivity Cases
l Dual Porosity Reservoirs — Pseudosteady-State Interporosity Flow Behavior
l Direct Solution of the Gas Diffusivity Equation Using Laplace Transform Methods
l Convolution and Concepts and Applications in Wellbore Storage Distortion
Advanced Reservoir Flow Solutions: (Possible Coverage)
l Multilayered Reservoir Solutions
l Dual Permeability Reservoir Solutions
l Horizontal Well Solutions
l Radial Composite Reservoir Solutions
l Models for Flow Impediment (Skin Factor)
Applications/Extensions of Reservoir Flow Solutions: (Possible Coverage)
l Oil and Gas Well Flow Solutions for Analysis, Interpretation, and Prediction of Well Performance
l Low Permeability/Heterogeneous Reservoir Behavior
l Macro-Level Thermodynamics (coupling PVT behavior with Reservoir Flow Solutions)
l External Drive Mechanisms (Water Influx/Water Drive, Well Interference, etc.).
l Hydraulic Fracturing/Solutions for Fractured Well Behavior
l Analytical/Numerical Solutions of Various Reservoir Flow Problems.
l Applied Reservoir Engineering Solutions — Material Balance, Flow Solutions, etc.
Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs
Tentative Course Schedule
Fall 2009
Date / TopicSeptember 01 T Course Introduction — Review of the Syllabus
03 R Course Introduction — Review of the Syllabus
08 T Lecture 01: [Mod1_ML_01] Review of Functions
10 R Lecture 02: [Mod1_ML_02] Approximation of Functions
15 T Lecture 03: [Mod1_ML_03] First Order Ordinary Differential Equations
17 R Lecture 04: [Mod1_ML_04] Second Order Ordinary Differential Equations
22 T Lecture 05: [Mod1_ML_05] The Laplace Transform
24 R Lecture 06: [Mod1_ML_06] Introduction to Special Functions
29 T Lecture 07: [Mod2_PtrPhy_01] Introduction to Porosity and Permeability Concepts
October 01 R Lecture 08: [Mod2_PtrPhy_02] Correlation of Petrophysical Data
06 T Lesson 09: [Mod2_PtrPhy_03] Empirical Development of Permeability: Darcy's Law
08 R Lesson 10: [Mod2_PtrPhy_04] Capillary Pressure
13 T Lesson 11: [Mod2_PtrPhy_05] Relative Permeability
15 R Lesson 12: [Mod2_PtrPhy_06] Electrical Properties of Reservoir Rocks
20 T Lesson 13: [Mod3_FunFld_01] Single-Phase, Steady-State Flow in Porous Media
22 R Lesson 14: [Mod3_FunFld_02] Non-Laminar Flow in Porous Media
27 T Lesson 15: [Mod3_FunFld_03] Material Balance Concepts
29 R Lesson 16: [Mod3_FunFld_04] Pseudosteady-State Flow in a Circular Reservoir
November 03 T Lesson 17: [Mod3_FunFld_05] Development of the Diffusivity Equation for Liquid Flow
05 R Lesson 18: [Mod3_FunFld_06] Development of the Diffusivity Equations for Gas Flow
10 T Lesson 19: [Mod3_FunFld_07] Development of the Diffusivity Equation for Multiphase Flow
12 R Lesson 20: [Mod4_ResFlw_01] Dimensionless Variables/Radial Flow Diffusivity Equation
17 T Lesson 21: [Mod4_ResFlw_02] Solutions of the Radial Flow Diffusivity Equation
19 R Lesson 22: [Mod4_ResFlw_03] Linear Flow Solutions: Infinite and Finite-Acting Reservoir Cases
24 T Lesson 23: [Mod4_ResFlw_04] Solutions for a Fractured Well — High Fracture Conductivity Cases
26 R Lesson 24: [Mod4_ResFlw_05] Dual Porosity Reservoirs — PSS Interporosity Flow Behavior
December 01 T Lesson 25: [Mod4_ResFlw_06] Direct Solution of the Gas Diffusivity Equation
03 R Lesson 26: [Mod4_ResFlw_07] Convolution
08 T Lesson 27: [Mod4_ResFlw_08] Wellbore Storage
14 M Any/all remaining assignments due on 14 December 2009 — by 5 p.m.
(Final Exam date per University Calendar (for classes on TR 8-9:15 a.m.))
16 W Final grades for all students GRADUATING in Fall 2009 term.
21 M Final grades for all students.
Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs
Homework Topics and Format Guidelines
Fall 2009
Homework Topics: (These are intended topics, addition and/or deletion of certain problems may occur as other problems become available. Multiple assignments from each topic are likely.)
l Analytical and numerical problems in calculus.
l Laplace transform methods — analytical and computational considerations.
l Special functions — analytical and computational considerations.
l Development of steady-state flow equations from physical principles.
l Development of pseudosteady-state flow equations from the diffusivity equation.
l Development and solution of diffusion-type partial differential equations.
l Development and application of various well/reservoir/production solutions.
Computing Topics: Students will be asked to make numerical computations for certain problems — in such cases the student will generally be allowed to select the computational product for their work.
Homework Format Guidelines:
1. General Instructions: You must use engineering analysis paper or lined notebook paper, and this paper must measure 8.5 inches in width by 11 inches in height
a. You must only write on the front of the page!
b. Number all pages in the upper right-hand corner and staple all pages together in upper left-hand corner. You must also put your name (or initials) in the upper right corner of each page next to the page number (e.g. John David Doe (JDD) page 4/6).
c. Place the following identification on a cover page: (Do not fold)
Name: (printed)
Course: Petroleum Engineering 620
Date: Day-Month-Year
Assignment: (Specific)
2. Outline of Assignment Format
a. Given: (Base Data)
b. Required: (Problem Objectives)
c. Solution: (Methodology)
l Sketches and Diagrams
l Assumption, Working Hypotheses, References
l Formulas and Definitions of Symbols (Including Units)
l Calculations (Including Units)
d. Results
e. Conclusions: Provide a short summary that discusses the problem results.
3. Guidelines for Paper Reviews
For each paper you are to address the following questions: (Type or write neatly)
l Problem:
— What is/are the problem(s) solved?
— What are the underlying physical principles used in the solution(s)?
l Assumptions and Limitations:
— What are the assumptions and limitations of the solutions/results?
— How serious are these assumptions and limitations?
l Practical Applications:
— What are the practical applications of the solutions/results?
— If there are no obvious "practical" applications, then how could the solutions/results be used in practice?
l Discussion:
— Discuss the author(s)'s view of the solutions/results.
— Discuss your own view of the solutions/results.
l Recommendations/Extensions:
— How could the solutions/results be extended or improved?
— Are there applications other than those given by the author(s) where the solution(s) or the concepts used in the solution(s) could be applied?
Petroleum Engineering 620 — Fluid Flow in Petroleum Reservoirs
Course Objectives
Fall 2009
Learning Objectives
The student should be able to demonstrate mastery of objectives in the following areas:
l Module 1 — Advanced Mathematics Relevant to Problems in Engineering
l Module 2 — Petrophysical Properties
l Module 3 — Fundamentals of Flow in Porous Media
l Module 4 — Reservoir Flow Solutions
l Module 5 — Applications/Extensions of Reservoir Flow Solutions
Considering these modular topics, we have the following catalog of course objectives:
Module 1: Advanced Mathematics Relevant to Problems in Engineering
l Fundamental Topics in Mathematics:
n Work fundamental problems in algebra and trigonometry, including partial fractions and the factoring of equations.
n Perform elementary and advanced calculus: analytical integration and differentiation of elementary functions (polynomials, exponentials, and logarithms), trigonometric functions (sin, cos, tan, sinh, cosh, tanh, and combinations), and special functions (Error, Gamma, Exponential Integral, and Bessel functions).
n Derive the Taylor series expansions and Chebyshev economizations for a given function.
n Derive and apply formulas for the numerical differentiation and integration of a function using Taylor series expansions. Specifically, be able to derive the forward, backward, and central "finite-difference" relations for differentiation, as well as the "Trapezoidal" and "Simpson's" Rules for integration.