Modelling multiphase flow through micro-CT images of the pore space

Department of Earth Science and Engineering

Imperial College Consortium on Pore-scale Modelling

Ali Raeini, Branko Bijeljic and Martin Blunt

Objective

Micro-CT image

Capillary pressure

Relative permeability

,= ,

x

PPkkq 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

image

Finite 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 Method

Capturing interface position: Volume of Fluid method

Surface 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

,)()()(

= ,

x

sPsPskku acaa

a

aara

Simulation time

2/1

4 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