Modelling multiphase flow through micro-CT images of the pore space
Department of Earth Science and EngineeringImperial College Consortium on Pore-scale Modelling
Ali Raeini, Branko Bijeljic and Martin Blunt
Objective
Micro-CT image
Capillary pressure
Relative permeability
,= ,
xPPkk
q ca
a
ara
Macroscopic description of the flow
Direct numerical simulation
Microscopic description of flow
Capillary pressure
Relative permeability
Previous studies
Pore network model
Pore network
modelling
Micro-CT
image
Capillary pressure
Relative permeability
Methodology
Numerical
Simulation
Micro-CT
imageFinite
volume mesh
Governing equations
Capillary pressure equation
Mass balance
Momentum balance
Advection of indicator function
Numerical code
OpenFOAM: open source CFD toolbox
interFOAM code:Discretisation of PDEs: Finite Volume MethodCapturing interface position: Volume of Fluid methodSurface tension forces: Continuous Surface Force (CSF) model
(Brackbill et al., 1992)
www.openfoam.com
+ our modifications ......
Test cases Modelling a static droplet
Initial conditionEquilibrium
solution
Test cases Modelling a static droplet Original CSF formulation
(m/s)
Presence of spurious velocities in CSF formulation makes the simulations impossible at low capillary numbers
Test cases Modelling a static droplet
Sharp Surface Force (SSF) formulation
(m/s)(Pa)
Test cases Modelling a static droplet CSF vs. SSF results
Capillary waves Spurious currents
Jagged solid walls
Test cases Droplet in contact with a flat plate
Smooth solid walls
solid wall
(m/s)
Non-physical velocities are generated close to the jagged solid walls in both CSF and SSF formulations
Test cases Droplet in contact with a flat plate
Filtering capillary forces parallel to the interface
(m/s)(Pa)
CSF formulationSSF formulation
Test cases Steady movement of a micro-scale droplet
Filtering capillary fluxes
Test cases Steady movement of a micro-scale droplet
Filtering is necessary to obtain accurate results for the velocity field
Novel contributions in this study
Filtering capillary forces parallel to the interface
Filtering capillary fluxes
Sharp Surface Force formulation
.....
Primarily pore-scale simulations Transient drainage experiment
,)()()(= ,
xsPsPskk
u acaa
a
aara
Simulation time
2/14 1
xuNt
dsim
4Ntsim High Capillary Numbers
Low Capillary Numbers
3Ntsim Single-phase flow
(>10-7)
(Pa)
(Pa)
Future work
Pd
Obtaining Capillary pressure and relative permeability curves from transient experiments
Improving the efficiency of the numerical model for low capillary numbers
Pc
Future work
Steady two-phase flow experiments, using cyclic boundary conditions
Multiphase micro-CT images
Transient experiments
Thanks to:
oStephen Neethling, Peyman Mostaghimi, Christopher Pentland
and many other colleagues, for useful discussions
o Sponsors of the project:DTI, EPSRC, ENI, Saudi Aramco, BG, BHP,JOGMEC, Schlumberger, Shell, Statoil and Total
and Thank you for your attention
References
Brackbill, J. U., Kothe, D. B., and Zemach, C. A continuum method for modeling surface tension. J. Comput. Phys., 100(2):335–354, 1992