# Course Information

 Duration (hours) 39 ECTs 5 Practice Simulation Instructor(s) Prof. Dionisios Christopoulos; Dr. Vasilis Gaganis; Prof. Pasadakis Nikolaos

# 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

 Week No. Topics Instructor 1 General statistics Prof. D. Christopoulos 2 Mathematics - Calculus Dr. V. Gaganis 3 Mathematics - Differential equationsin petroleum engineering Dr. V. Gaganis 4 Mathematics - Linear algebra Dr. V. Gaganis 5 Root finding & optimization Dr. V. Gaganis 6 Linear and non-linear regression & classification Dr. V. Gaganis 7 Data pretreatment, visualization & clustering Prof. N. Pasadakis 8 Data analysis in petroleum engineering Dr. V. Gaganis 9 Time series Prof. D. Christopoulos 10 Fourier analysis Prof. D. Christopoulos 11 Variograms Prof. D. Christopoulos 12 Kriging Prof. D. Christopoulos 13 Simulation Prof. D. Christopoulos

Detailed description:

General Statistics: Introduction; Random variables, time series, random fields; Conditional Probability and Bayes’ theorem; Distribution Functions; Statistical Moments; Common probability models; Measures of dependence; Estimation; Hypothesis testing; Regression

Mathematics - Calculus: Mathematical background for engineers. Functions, derivatives, integration, expansions, properties, multivariate calculus.

Mathematics - Differential equations in petroleum engineering: Definitions, methods, derivation of the single phaseflow differential equation for reservoir simulation

Mathematics - Linear algebra: Vectors, matrices, data storage, operators, invertibility, linear systems

Root finding & Optimization: Bracket methods, Newton-Raphson, solution of systems of equations. Optimization: criteria, closed form solutions, equality and inequality constraints, iterative methods

Linear and non-linear regression & classification: Single and multi- variable linear regression, regular and partial least squares, non-linear regression, linear-in-the-weights models, neural networks. Classification: least squares method, Fisher method, neural networks, support vector machines

Data pretreatment, visualization & clustering: Scaling, non-linear transformations, scatter plots, 3D, contours, outlier detection, moving average filters. Clustering: Definitions, k-means, hierarchical method, Principal Components Analysis

Data analysis in petroleum enginnering: Flash calculations, Rachford-Rice equation, reservoir pressure regime, PVT properties regression models development

Time series: Introduction, Correlation, Trends, Periodicities, Stationarity, Detrending, Normalizing Transforms,  Autoregressive models, Moving average models, Estimation, Prediction

Fourier Analysis: Introduction, Frequency space, Fourier series, Fourier integrals, Nyquist frequency, Power spectral density, Periodogram, Bias and Variance, Spectral leakage, Windowing

Variograms: Definition, Stationary vs. non-stationary models, permissibility theorems, variogram parameters, anisotropy. Regionalization, empirical variogram, method of moments estimation, theoretical models

Kriging: Principles of interpolation, best linear unbiased estimation, Simple kriging, ordinary kriging, regression kriging, kriging variance

Simulation: Random number generators, Monte Carlo, methods of unconditional simulation, methods of conditional simulation

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.