# ENERGY RESOURCES AND PETROLEUM ENGINEERING PROGRAM ACADEMICS

Faculty and students in the Energy Resources and Petroleum Engineering Program (ERPE) at KAUST engage in interdisciplinary research to understand and model hydro-chemo-thermo-mechanical coupled processes in the subsurface, with emphasis on multiphase and reactive fluid flow (oil, gas, brine, water and steam).

The Energy Resources and Petroleum Engineering Program focuses on modern reservoir description, engineering and management. Students in this program receive broad training in basic scientific concepts, geology, geophysical characterization, and reservoir engineering. Our Students participate in scientific research activities that may include mathematical analyses, computational modeling, and/or laboratory/field studies. Ph.D. candidates focus on original research driven to advance the boundaries of knowledge.

## Masters Assessment Test

Students are admitted to KAUST from a wide variety of programs and backgrounds. In order to facilitate the design of an appropriate study plan for each individual student, all MS and MS/PhD incoming students will be required to take an assessment during orientation week. There is no grade for the assessment. The purpose of the assessment is to determine whether students have mastered the prerequisites for undertaking graduate level courses taught in the program. The Advisor uses the results of the assessments to design, if necessary, a remedial study plan with a list of courses aimed at addressing content areas that may impede a student from successful completion of the degree requirements.

Students are encouraged to prepare for the assessment by refreshing the general knowledge gained from their undergraduate education before arriving at KAUST.**Earth Science and Engineering Assessment Test Subjects**Earth Science and Engineering students will be tested on the following subjects:**Basic Principles of Mechanics****Basic Principles of Physics****Engineering Mathematics****Linear Algebra****Ordinary Differential Equations**

**1. Basic Principles of Mechanics**Topics included in the Principles of Mechanics assessment test:- Solid Mechanics
- Fundamental Concepts: Units, Scalar & Vector
- Adding/resolving forces, moments, types of load/support
- Equilibrium of rigid bodies. Free body diagrams. Static determinacy
- Trusses: static determinacy, method of joints and method of sections
- Stress, strain, elastic constants, Hooke's law
- Beams: shear force and bending moment diagrams
- Engineer's Bending Theory. First and second moments of area
- Beam deflection due to bending, moment-curvature relationship
- Differential equation of the deflection curve. Solution by integration
- Shear stress in beams. Shear formula
- Torsion of circular section shafts, polar second moment of area
- Buckling of elastic struts. Concept of instability. Euler formula
- Stress, strain, elastic constants, thermal strain, Hooke's law (2D/3D)
- Stresses in thin-walled cylinders subject to internal pressure
- Two-dimensional analysis of stress
- Stress transformation using Mohr circles
- Principle stresses and strains
- Friction
- Stress-strain relationships of common structural materials
- Materials in Engineering: Metals, ceramics, polymers and composites
- Basic concepts of fluid Mechanics

Recommended References:- Roger T. Fenner and J.N. Reddy,
*Mechanics of Solids and Structures*, CRC Press – ISBN 9781439858141. - Online reference: “Engineering Mechanics of Solids” MIT.

**2. Basic Principles of Physics**Topics inluded in the Principles of Physics assessment test:- Newtonian Physics:
- Kinematics (motion with constant acceleration in one and two dimensions).
- Dynamics (Newton’s Laws of motion).
- Work-Energy theorem, potential energy and energy conservation.
- Momentum, impulse and collisions.
- Electromagnetism:
- Electric fields, Coulomb’s law, electric potential and potential energy, electric flux (Gauss’s law).
- Direct-current circuits, resistors and capacitors is series and in parallel, theory of metallic conduction, power distribution systems.
- Magnetic field, motion of charged particles within uniform magnetic fields, magnetic force on current-carrying conductors, forces between parallel conductors.
- Electromagnetic Induction: Faraday’s and Lenz’s Laws, motional electromotive force, induced electric fields.
- Quantum Physics:
- The photoelectric effect.
- Wave particle duality, probability and uncertainty.
- Electron waves, de Broglie wavelength.
- Atomic spectra, energy levels and the Bohr model of the atom.
- Wave function interpretation.
- Thermodynamics:
- Calorimetry and phase changes.
- Equations of state, molecular properties of matter.
- Kinetic-molecular model of an ideal gas.
- Work done during volume changes.
- Paths between thermodynamics states .
- Kinds of thermodynamic processes.
- 1st law of thermodynamics and Internal Energy.
- 2nd law of thermodynamics. Carnot cycle and entropy.
- Oscillations and Waves:
- Mathematical description of a wave.
- Energy in wave motion.
- Speed of waves.
- Superposition of waves.
- Standing waves.
- Reflection, Refraction, critical angle and total internal reflection.
- Diffraction from a single, double slits and around objects. Interference patterns including double-slit interference.

Recommended References:- Young, Hugh D., et al. University Physics with Modern Physics. Addison-Wesley, 2011 (or any undergraduate general physics textbook).
- Online Reference: Elert, Glenn. “Welcome.” Viscosity – ThePhysics Hypertextbook.

**3. Engineering Mathematics and Basic Calculus**Topics included in the Engineering Mathematics assessment test:- Functions and Models (including graphical representation of functions)
- Limits
- Derivatives (including graphical and physical interpretation of derivatives)
- Anti-derivatives and definite integrals.
- The classes of functions used to develop these concepts are: polynomial, rational, trigonometric exponential and logarithmic.
- Integration (by parts, substitutions, partial fractions, approximation of integrals and improper integrals)
- Infinite sequences and series
- Convergence tests
- Power series
- Taylor polynomials and series
- Taylor's Remainder Theorem
- Vector Calculus: Vector Fields, Divergence and Curl.

Recommended References:- Banner, Adrian. The Calculus Lifesaver: All the Tools You Need to Excel at Calculus. Princeton, NJ, USA: Princeton University Press, 2009, ISBN-13: 978-0691130880
- Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 2010, ISBN 978-09802327-4-5
- Zill, Dennis G., and Warren S. Wright. Advanced Engineering Mathematics. Burlington, Ma: Jones and Bartlett Learning, 2018, ISBN-13: 978-1284105902
- Stewart, James. Essential Calculus: Early Transcendentals. Australia: Brooks/Cole, 2013, ISBN-13: 978-1133112280

Online Recommended References:

Calculus: Early Transcendentals by James Stewart

**4. Linear Algebra**Topics included in the Linear Algebra assessment test:- Vector spaces and linear mappings between such spaces
- Introduction to vector spaces
- Basis and dimension
- Rank of a matrix
- Determinants
- Inverse of a matrix
- Eigenvalues and diagonalization
- Similarity
- Positive definite matrices
- Orthogonal and unitary matrices and transformations
- Orthogonal projections
- Gram-Schmidt procedure
- Solving systems of linear equations
- Applications of linear systems
- Cramer’s rule
- Linear transformations
- Isomorphism
- Parallelepipeds

Recommended References:- Linear Algebra and Its Applications, David C. Lay, Addison-Wesley/Pearson, ISBN: 978-0321385178.
- Linear Algebra: Concepts and Methods, Martin Anthony & Michele Harvey, Cambridge University Press, ISBN:978-0-521-27948-2.

Online Recommended References:

A First Course in Linear Algebra, by Robert A. Beezer

Introduction to Linear Algebra, by Gilbert Strang

**5. Vecot Analysis and Ordinary Differential Equations**Topics included in the ODE assessment test:- Direction Fields (visualize the solution(s) of an ordinary differential equation without actually solving the equation).
- Solving simple ordinary differential equations
- Classification by order
- Linearity and homogeneity
- Autonomous differential equations
- Asymptotic behavior
- Equilibrium points and stability
- Solutions by numerical schemes
- Euler’s method

Recommended References:- J. Robinson, An Introduction to Ordinary Differential Equations, Cambridge University Press, ISBN: 978-0521533911.
- J. Polking, A. Boggess, D. Arnold, Differential Equations with Boundary Value Problems, Pearson, ISBN: 978-0131862364.
- M. Tenenbaum, H. Pollard, Ordinary Differential Equations, Dover Publications, ISBN: 978-0486649405.
- J. Robinson, Differential Equations, Cambridge University Press, ISBN: 978-0521533911.

Online Recommended References:

Elementary Differential Equations with Boundary Values Problems, by William F. Trench

## Student Forms - Registrar's Office

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