Title Model dvostruke poroznosti Author Ivana Radišić Mentor Mladen Jurak (mentor)Committee member Mladen Jurak (predsjednik povjerenstva)Committee member Eduard Marušić-Paloka (član povjerenstva)Committee member Josip Tambača (član povjerenstva)Committee member Andrej Dujella (član povjerenstva)Granter University of Zagreb Defense date and country 2014-09-24, Croatia Scientific / art field, NATURAL SCIENCES Abstract U ovom radu smo izveli model dvostruke poroznosti koji opisuje gibanje fluida kroz frakturiranu poroznu sredinu. Frakturirana porozna sredina
Ω je porozna sredina koja se sastoji od matrice poroznih blokova
Ω ε m , koja je okruzena sustavom fraktura
Ω ε f , gdje parametar
ε predstavlja veličinu matričnog bloka. U radu smo najprije opisali model jednofaznog toka fluida na mikroskopskoj skali. Dobili smo sljedeću inicijalno rubnu zadaću
... More { Φ ε ∂ ∂ t ρ ε − d i v ( K ε μ c ∇ ρ ε ) = f u Ω × ( 0 , T ) ρ ε = ρ b d na Γ D × ( 0 , T ) K ε μ c ∇ ρ ε ⋅ ν Ω = h na Γ N × ( 0 , T ) ρ ε = ρ i n i t na Ω × { 0 } , ρ ε Ω Φ ε K ε Φ ε ( x ) = { Φ ∗ x ∈ Ω ε f ϕ ε ( x ) x ∈ Ω ε m , K ε ( x ) = { K ∗ x ∈ Ω ε f ε 2 k ε ( x ) x ∈ Ω ε m , Φ ε K ε Φ H = | Y f | | Y | Φ ∗ K H = K ∗ 1 | Y | ∫ Y f ( ∇ y ω ( y ) + I ) d y , { Φ H ∂ t ρ 0 f − d i v ( K H μ c ∇ ρ 0 f ) = f − 1 | Y | ∫ Y m ϕ ( y ) ∂ t ρ 0 m d y u Ω × ( 0 , T ) ρ 0 f = ρ b d na Γ D × ( 0 , T ) K H μ c ∇ ρ 0 f ⋅ ν Ω = h na Γ N × ( 0 , T ) ρ 0 f = ρ i n i t f na Ω × { 0 } , { ϕ ( y ) ∂ t ρ 0 m ( x , y , t ) − d i v y ( k ( y ) μ c ∇ y ρ 0 m ( x , y , t ) ) = f ( x , t ) u Ω × Y m × ( 0 , T ) ρ 0 m ( x , y , t ) = ρ 0 f ( x , t ) na Ω × ∂ Y m × ( 0 , T ) ρ 0 m ( x , y , 0 ) = ρ i n i t m ( x ) na Ω × Y m . Ω ε ε Less Abstract (english) In this paper we derived double porosity model of flow in fractured porous media. Fractured porous media
Ω contains system of fracture planes
Ω ε f dividing the porous rock into collection of blocks
Ω ε m . In this paper we first have described model of single phase flow on a microscopic scale. Single phase flow is described by following equations \begin{align*} \begin{cases} \Phi^\varepsilon \frac{\partial}{\partial t}\rho^\varepsilon - div
... More \left( \frac{K^\varepsilon}{\mu c} \nabla \rho^\varepsilon \right)=f &\text{u } \Omega \times (0,T)\\ \rho^\varepsilon=\rho_{bd} &\text{na} \: \Gamma_D \times (0,T)\\ \frac{K\varepsilon}{\mu c} \nabla \rho^\varepsilon \cdot \nu_\Omega=h &\text{na } \Gamma_N \times (0,T)\\ \rho^\varepsilon=\rho^{init} &\text{na } \Omega \times \{0\}, \end{cases} \end{align*} where ρ ε Φ ε K ε Φ ε ( x ) = { Φ ∗ x ∈ Ω ε f ϕ ε ( x ) x ∈ Ω ε m , K ε ( x ) = { K ∗ x ∈ Ω ε f ε 2 k ε ( x ) x ∈ Ω ε m , Φ ε K ε Φ H = | Y f | | Y | Φ ∗ K H = K ∗ 1 | Y | ∫ Y f ( ∇ y ω ( y ) + I ) d y , { Φ H ∂ t ρ 0 f − d i v ( K H μ c ∇ ρ 0 f ) = f − 1 | Y | ∫ Y m ϕ ( y ) ∂ t ρ 0 m d y u Ω × ( 0 , T ) ρ 0 f = ρ b d na Γ D × ( 0 , T ) K H μ c ∇ ρ 0 f ⋅ ν Ω = h na Γ N × ( 0 , T ) ρ 0 f = ρ i n i t f na Ω × { 0 } , { ϕ ( y ) ∂ t ρ 0 m ( x , y , t ) − d i v y ( k ( y ) μ c ∇ y ρ 0 m ( x , y , t ) ) = f ( x , t ) u Ω × Y m × ( 0 , T ) ρ 0 m ( x , y , t ) = ρ 0 f ( x , t ) na Ω × ∂ Y m × ( 0 , T ) ρ 0 m ( x , y , 0 ) = ρ i n i t m ( x ) na Ω × Y m . ε ε Less Keywords
model dvostruke poroznosti
gibanje fluida kroz frakturiranu poroznu sredinu
DUNE software-a za rješavanje parcijalnih diferencijalnih jednadžbi
Keywords (english)
double porosity model
flow in fractured porous media
DUNE modular toolbox for solving partial differential equations
Language croatian URN:NBN urn:nbn:hr:217:628243 Study programme Title: Applied Mathematics Type of resource Text File origin Born digital Access conditions Access restricted to students and staff of home institution Terms of use Created on 2019-02-01 11:05:32
