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Cabinet:216
E-mail: dragan.stankov@rgf.bg.ac.rs

Mathematical Models , Numerical Algorithms and Computer Technology

Course Description

Study program: Petroleum Engineering (VIII semester -OAS)

Name of subject: Mathematical Models , Numerical Algorithms and Computer Technology

Instructors: Dr Dragan Stankov

Status: Optional

ECTS: 5

Prerequisites: -

Course Objectives: Introducing students with numerical analysis methods and their application in solving specific tasks. Introducing students with the software that is now applied in the petroleum industry in the world and in our country (PipeSim, Eclipse, Petrel).

Learning Outcomes: Introduction of students with numerical analysis methods in solving specific tasks. Software mastering in the petroleum industry (PipeSim, Eclipse, Petrel).

Content:

Theory teaching
Recording of an approximate number, significant, secure digits, rounding rules. Absolute error, relative error and their boundaries. Function error and reverse error problem. Isolation of the real solution of the equation f (x) = 0 (analytical and graphical). Solving the equation f (x) = 0, methods: interval of interval, iteration, cuttings (regula falsi), Newton’s method (tangents), combined. Solving the system of linear equations: Gaussian, iterative method, Gauss–Seidel method. Solving the non-linear equations system: iterative method, Newton’s, gradient method. Interpolation: Lagrange interpolation polynomial, finite difference of a function, Newton’s interpolation polynomials, inverse interpolation. Differentiation. Integration: Methods of Rectangles and Trapezes, Simpson’s Method. Numerical solving of differential equations: Picard, Euler and Runge-Kutta methods. Network methods for partial equations of an elliptic, parabolic and hyperbolic type. PipeSim features, application possibilities. Eclipse-characteristics, application capabilities. Petrel-characteristics, application possibilities.

Practical teaching
Applying the numerical analysis methods specified in the content of the subject to solve tasks. PipeSim-application. Simulation of flow (oil and / or gas and / or water) through perforations, borehole, nozzle, piping. Separation. Integral flow simulation through out the entire production system. Dimensioning of production equipment (number of perforations, tubing diameter, nozzle diameter, piping diameter, separation conditions). Eclipse. Modeling of the ore deposit. Simulation. Estimation of the ore reserve. Petrel

Suggested Reading List

  1. Милош Миличић, Нада Миличић, Драган Станков: Елементи нумеричке анализе

Fund Hours:

Lectures Exercises Other forms of teaching Study research
2 2 0 0

Conduct of the Course: Classical lectures followed by contemporary visual presentations and practical examples.

AssessmentОцена знања:

Final Exam ECTS
Oral Exam 25
Classwork Assessment ECTS
Class Participation 10
Seminars 15

Additional Assessment Criteria -