Course Information

Duration (hours)   
39
ECTs5
PracticeSimulation
Instructor(s)

Prof. Dionisios Christopoulos; Dr. Paris Stratis

Description

This course introduces the use of statistical tools for modeling field- and production-related data. Data mining, regression, classification, clustering and geostatistical methods (variogram, kriging interpolation, simulation) are covered.

Syllabus

 

 

  

1st Lecture

Basic calculus I: Single and multidimensional functions. Function examples. Implicit functions. Plots, 2D plots, contours.

2nd Lecture

Basic calculus II: Derivatives, gradient, Hessian. Expansions, Taylor series. Coordinate systems.

3rd Lecture

Basic linear algebra I: Scalars, vectors, matrices, vector and matrix operations. Data matrices. Scalar-matrix analogs. 

4th Lecture

Basic linear algebra II: Linear systems of equations. Setup and solution. Eigenvalues, eigenvectors, eigen-decomposition. Non-linear equations.

5th Lecture

Root finding: Exact vs numerical methods, classic methods, Newton-Raphson, extend to systems of equations.

6th Lecture

Optimization: Classic optimization, optimality conditions, equality & inequality constraints. Numerical methods for linear, quadratic and non-linear optimization.

7th Lecture

Data and its properties: Descriptive statistics, probability distributions, hypothesis testing

8th Lecture

Exploratory data analysis I: Unsupervised learning, factor analysis, cluster analysis.

9th Lecture

Regression I: Single and multiple variable linear regression. Closed form solutions. Residual analysis.

10th Lecture

Regression II: Single and multiple variable non-linear regression. Numerical solutions. Neural nets and relevant models.

11th Lecture

Classification & clustering: Discriminating functions. Class probabilities. Deterministic and statistical methods.

12th Lecture

Geostatistics: Spatial analysis, kriging

13th  Lecture

Differential equations: Setup of ODEs and PDEs for various engineering problems

 

 

 

 

 

 

 

 

 

 

 

 

Petroleum Engineering postgraduate program of the Technical University of Crete is a one-year, full-time program, designed to provide students with a scientific background in hydrocarbon exploration and skills in the practical aspects of petroleum engineering. The program begins in October, and leads to a Master of Science (MSc) degree. The program is run by the School of Mineral Resources Engineering.