Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena

master's thesis

• Author: Manuela Koštroman
• Mentor: Mladen Jurak (mentor)
• Committee member: Mladen Jurak (predsjednik povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-04-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu smo proučavali model dvofaznog toka kroz heterogenu poroznu sredinu u slučaju kada su fluidi izotermni i inkompresibilni. U Poglavlju 1 opisujemo makroskopske jednadžbe za model jednofaznog toka. Uvođenjem pojmova zasićenja, kapilarnog tlaka i relativnih propusnosti, model jednofaznog toka smo lako poopćili na model dvofaznog toka. Iz generaliziranog Darcyjevog zakona i iz zakona sačuvanja mase dobivamo matematičke jednadžbe dvofaznog modela. Pokazujemo da je model dvofaznog toka paraboličko-eliptičkog tipa. Uvodimo formulaciju tlak-zasićenje. U Poglavlju 3 uvodimo diskretizaciju sustava u formulaciji tlak-zasićenje. Koristimo metodu konačnih volumena s implicitnom vremenskom derivacijom i upwind metodom. Upwind metodu smo koristili za stabilizaciju numeričkog modela. Na kraju smo napravili tri simulacijska primjera utoka jednog fluida u poroznu sredinu zasićenu drugim fluidom pomoću DUNE-a, software-a za rješavanje parcijalnih diferencijalnih jednadžbi.

Abstract (english)

In this diploma thesis we studied two-phase flow model through heterogeneous porous media under assumption of isothermal and incompressible fluids. In Chapter 1 we described macroscopic equations for a single-phase flow model. By introducing the concepts of saturation, capillary pressure and relative permeability, the single-phase flow model can be easily generalized to a two-phase flow model. Using generalized Darcy’s law and fluid mass conservation, we obtained mathematical equations for two-phase model. We showed that the two-phase flow model is of parabolic-elliptic type and introduced the pressure-saturation formulation. In Chapter 3 we introduced the discretization of the system in pressure-saturation formulation. We used the finite volume method with implicit time derivation and upwind method. Upwind method is used to stabilize the numerical model. In the end, we made three simulation examples of one fluid entering the porous media saturated by another fluid using DUNE, the software for solving partial differential equations.

• Keywords: model dvofaznog toka; heterogena porozna sredina; izotermni fluidi; inkompresibilni fluidi; generalizirani Darcyev zakon; upwind metoda; DUNE
• Keywords (english): two-phase flow; heterogeneous porous media; isothermal fluids; incompressible fluids; generalized DArcy's law; upwind method; DUNE
• Language: croatian
• URN:NBN: urn:nbn:hr:217:321479
• 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: 2019-02-15 12:45:20