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master's thesis
Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:321479
Koštroman, Manuela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Koštroman, M. (2015). Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:321479

Koštroman, Manuela. "Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:321479

Koštroman, Manuela. "Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:321479

Koštroman, M. (2015). 'Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 July 2024, https://urn.nsk.hr/urn:nbn:hr:217:321479

Koštroman M. Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 July 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:321479

M. Koštroman, "Dvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:321479

Metadata
TitleDvofazni tok fluida kroz heterogenu poroznu sredinu. Uvjeti na granici različitih tipova stijena
AuthorManuela Koštroman
MentorMladen Jurak (mentor)
Committee memberMladen Jurak (predsjednik povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-04-23, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:321479
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-15 12:45:20