# 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

| 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.