14th International Symposium on Particle Image Velocimetry

Intermittency effects in single- and multi-phase flow and anomalous
transport in heterogeneous porous media

Zoë Penko1, Yaofa Li1,2, Diogo Bolster1,3, and Kenneth T. Christensen1,3,4

1University of Notre Dame, Department of Aerospace and Mechanical Engineering
2Now at Montana State University, Department of Mechanical and Industrial Engineering

3University of Notre Dame, Department of Civil and Environmental Engineering and Earth Sciences
4Now at Illinois Institute of Technology, Armour College of Engineering

Introduction

Multi-phase flow and transport in porous media

is prevalent in a wide range of challenging fluid

mechanics problems related to sustainability, energy,

and the environment. Accurate prediction of the

displacement and interaction of such flows is vital

in addressing these problems. In particular it is

critical to understand the small- or pore-scale flow

and its spatial and temporal evolution, which can

impact behaviors at system scales in a nontrivial

manner. Intermittency is a phenomenon currently

observed in numerical and experimental studies of

single-phase flow (Anna et al., n.d.; Morales et

al., n.d.), but the case of multi-phase flow has yet

to receive much study due to challenges faced in

both simulations and experiments. The underlying

physics of spreading, mixing, and interfacial processes

must be understood for accurate predictions of

transport in multi-phase flow systems. Therefore,

a comprehensive understanding of multi-phase flow

at these very small scales is necessary in the

development of accurate system-scale prediction

models. We present results from a coordinated

numerical and experimental study of intermittency

effects over a range of viscous and inertial flow

regimes in single- and multi-phase flows in 2D

heterogeneous micromodels to quantify Lagrangian

flow statistics to better inform pore-scale models.

The applicability of different modeling frameworks

such as the correlated-continuous time random walk

is tested by studying statistics of particle trajectories

obtained by particle tracking velocimetry (PTV)

measurements and Lattice Boltzmann simulations

from single- and multi-phase flows. The results make

particular note of the influence of the pore Reynolds

number (Re) and inertial effects on intermittency,

and compare these effects in the two flow regimes.

Methods

Experiments are conducted in the University of

Notre Dame MicroPIV Laboratory for Energy and

the Environment. A PTV approach utilizing small,

neutrally-buoyant (to serve as true tracers), and

low-density seeded particles illuminated by laser

light pulses synced to a camera by a synchronizer

that captures images of the fluoresced light to

reconstruct particle trajectories of single particles is

used. Volume illumination is employed to excite the

fluorescent tracer particles seeded in the flow and the

particle trajectories are imaged in a plane-defined 2D

micromodel depth. Figure 1 presents homogeneous

and heterogeneous 2D porous models that are

fabricated using established silicon microfabrication

methods (Kazemifar, 2020), where the top of the

micromodel is formed by anodic bonding of a glass

wafer to provide optical access to the flow in the 2D

porous matrix.

Some limitations exist in collecting quality

experimental data, as higher Re flow experiments

pose challenges due to the inherent trade-off between

spatial resolution and the physical size of the field

of view (FOV), image acquisition rate limitation

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Figure 1: (top) Homogeneous 2D porous micromodel;
(bottom) Heterogeneous 2D porous micromodel.

by data transfer bandwidth, and the record length

limitation by the on-board memory size for a given

resolution. Such limitations can be addressed by

a Lattice Boltzmann method (LBM) simulation

approach to numerically simulate multi-phase flow in

the same porous media and complement experiments

by broader parameter space exploration, an approach

used on a 2D micromodel of water (wetting phase)

being displaced by CO2 (non-wetting phase) by Li et

al. (n.d.).

Future Work

A coordinated simulation and experimental study of

intermittency effects in multi-phase flow spanning

flow regimes from viscous to inertial in 2D and

3D porous media is underway in an effort to

quantify Lagrangian flow statistics and accurately

model the pore-scale behavior, thereby advancing

the fundamental understanding of such behavior.

These data will be used to (1) calculate statistics

of particle trajectories and intermittency for single-

phase flow in 2D porous micromodels to test

the applicability of different modeling frameworks,

(2) study intermittency and dispersion with the

addition of a second, immiscible fluid and the

presence of trapped ganglia, (3) study the effect

of Re and inertia on intermittency in multi-phase

porous media flow, and (4) compare these effects

in single- and multi-phase flow in homogeneous and

heterogeneous porous models. This analysis will form

the basis of the final paper. The development of

a more general and robust modeling approach that

is fully validated by experiments and simulations

will allow better prediction of the spreading, mixing,

and interfacial processes that occur in natural and

engineered environments.

References

Anna, P. de, Le Borgne, T., Dentz, M., et al. (n.d.).

Flow Intermittency, Dispersion, and Correlated

Continuous Time Random Walks in Porous Media.

Physical Review Letters 110, (), 184502.

Kazemifar, F. (2020). An experimental study of

supercritical CO2 flow in pipes and porous micro-

models for carbon sequestration applications ().

url: https://core.ac.uk/reader/29175208

(visited on 07/16/2020).

Li, Y., Kazemifar, F., Blois, G., and Christensen,

K. T. (n.d.). Micro-PIV measurements of

multiphase flow of water and liquid CO2 in

2-D heterogeneous porous micromodels. Water

Resources Research 53, (), 6178–6196. issn:

00431397.

Morales, V. L., Dentz, M., Willmann, M., and

Holzner, M. (n.d.). Stochastic dynamics of

intermittent pore-scale particle motion in three-

dimensional porous media: Experiments and

theory. Geophysical Research Letters 44, (), 9361–

9371. issn: 0094-8276.

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