Metoda konačnih volumena za dvofazni tok kroz poroznu sredinu

master's thesis

• Title (english): Finite volume method for two-phase flow through a porous medium
• Author: Donata Borić
• Mentor: Mladen Jurak (mentor)
• Committee member: Mladen Jurak (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskome radu je uveden model dvofaznog toka kroz poroznu sredinu te je opisana metoda konačnih volumena za njegovo rješavanje. U prvom poglavlju je opisana porozna sredina te su uvedena osnovna svojstva toka fluida koji njome prolazi. U drugom poglavlju je uvedena jednadžba sačuvanja mase na makroskali pomoću koje možemo predvidjeti transport mase unutar sustava. U trećem poglavlju je opisan Darcyjev zakon te makroskopska svojstva fluida i porozne sredine. Uparivanjem jednadžbe sačuvanja mase te Darcyjevog zakona, četvrto poglavlje uvodi dvofazni tok nemješivog fluida. Također, u istome poglavlju je izvedena 1D Buckley-Leverettova jednadžba. Peto poglavlje se bavi opisom mogućih numeričkih načina rješavanja uvedenog modela. Preciznije, za metodu konačnih volumena opisane su neke od njezinih verzija (TPFA, MPFA te Box metoda). Nakon odabira jedne od njih, korištenjem IMPES algoritma model je moguće efikasno riješiti. Šesto poglavlje pruža rezultate te opis tri numeričke simulacije od različitih dvofaznih nemješivih modela. Simulacije su napravljene u programskoj biblioteci DuMu\(^x\).

Abstract (english)

In this thesis, a model of two-phase flow through a porous medium is introduced and the finite volume method for its solution is described. The first chapter describes the porous medium and introduces the basic properties of the fluid flow that passes through it. In the second chapter, the mass conservation equation on the macroscale is introduced, by which we can predict the transport of mass within the system. The third chapter describes Darcy’s law and some additional macroscopic properties of fluids and porous media. Using the mass conservation equation and Darcy’s law, the fourth chapter introduces a two-phase flow of an immiscible fluid. Also, the 1D Buckley-Leverett equation is derived in the same chapter. The fifth chapter deals with the description of possible numerical ways for solving the introduced model. More precisely, for the finite volume method some of its versions (TPFA, MPFA and Box method) are described. After selecting one of them, using the IMPES algorithm the model can be solved efficiently. The sixth chapter provides the results and a description of three numerical simulations from different two-phase immiscible models. Simulations were made in the program library DuMu\(^x\).

• Keywords: tok fluida; Darcyjev zakon; 1D Buckley-Leverettova jednadžba; IMPES algoritam; DuMu\(^x\)
• Keywords (english): fluid flow; Darcy’s law; 1D Buckley-Leverett equation; IMPES algorithm; DuMu\(^x\)
• Language: croatian
• URN:NBN: urn:nbn:hr:217:222170
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-09-13 08:24:59