Front Tracking Using a Hybrid Analytical Finite Element Approach for Two-Phase Flow Applied to Supercritical CO2 Replacing Brine in a Heterogeneous Reservoir and Caprock

2011 ◽  
Vol 90 (2) ◽  
pp. 545-573 ◽  
Author(s):  
Christopher I. McDermott ◽  
Alexander E. Bond ◽  
Wenqing Wang ◽  
Olaf Kolditz
Keyword(s):  
Finite Element ◽  
Supercritical Co2 ◽  
Two Phase Flow ◽  
Front Tracking ◽  
Phase Flow ◽  
Two Phase ◽  
Finite Element Approach ◽  
Heterogeneous Reservoir ◽  
Element Approach

Finite element implementation of an improved conservative level set method for two-phase flow

2014 ◽  
Vol 100 ◽  
pp. 138-154 ◽  
Author(s):  
Lanhao Zhao ◽  
Jia Mao ◽  
Xin Bai ◽  
Xiaoqing Liu ◽  
Tongchun Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Finite Element Implementation ◽  
Conservative Level Set

On convergent schemes for two-phase flow of dilute polymeric solutions

2018 ◽  
Vol 52 (6) ◽  
pp. 2357-2408 ◽  
Author(s):  
Stefan Metzger
Keyword(s):  
Finite Element ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Flow ◽  
Two Phase ◽  
Extra Stress Tensor ◽  
Spring Force ◽  
Polymeric Solutions ◽  
Fokker Planck

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grün, Metzger, M3AS 26 (2016) 823–866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.

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