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SUMMARY:From Pore to Porous Media: A Connected Hierarchy of Chaos
DTSTART;VALUE=DATE-TIME:20180517T133200Z
DTEND;VALUE=DATE-TIME:20180517T134700Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-914@events.interpore.org
DESCRIPTION:Speakers: Guy Metcalfe (Monash University)\n.\n\nhttps://event
s.interpore.org/event/2/contributions/914/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/914/
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SUMMARY:Lagrangian transport and chaotic advection in a class of (anisotro
pic) subsurface reservoirs
DTSTART;VALUE=DATE-TIME:20180517T150200Z
DTEND;VALUE=DATE-TIME:20180517T151700Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-913@events.interpore.org
DESCRIPTION:Speakers: Michel Speetjens (Eindhoven University of Technology
)\nSubsurface scalar transport of e.g. heat or chemicals by fluid flow is
key to problems as enhanced oil recovery\, enhanced geothermal systems\, c
arbon sequestration or in situ minerals mining. The Lagrangian transport p
roperties of the subsurface flow are crucial in such processes. For exampl
e\, recent studies in the literature on a two-dimensional (2D) unsteady Da
rcy flow in a circular reservoir driven by reoriented injection–extracti
on wells demonstrated that well configurations and pumping schemes designe
d via chaos theory enable efficient fluid distribution (for e.g. in situ m
ining) through the entire reservoir. Central to this is accomplishment of
chaotic advection\, i.e. the rapid dispersion and stretching of material f
luid elements\, by “proper” flow forcing. Problems as e.g. groundwater
remediation may\, on the other hand\, require targeted delivery (and subs
equent confinement) of fluid containing chemicals to designated regions of
the reservoir for local contaminant treatment. This may be achieved by sy
stematic creation and manipulation of Lagrangian transport barriers. \n\nT
he present study seeks to deepen insight into generic subsurface Lagrangia
n transport by investigating the formation of so-called Lagrangian coheren
t structures (LCSs) as e.g. the above transport barriers as well as the ac
complishment of (localised) chaotic advection. To this end theoretical and
computational analyses are performed for the above 2D circular reservoir.
This reveals that\, in general\, appropriate pumping schemes enable syste
matic and robust creation of various Lagrangian transport conditions for g
iven well configurations (e.g. confinement zones of controlled size embedd
ed in a chaotic environment). A key aspect is the impact of anisotropy in
the porous matrix. Such anisotropy generically eliminates key organizing m
echanisms\, viz. symmetries\, and thus tends to promote disorder and\, inh
erently\, chaotic advection at the expense of LCSs. However\, symmetries a
re partially preserved — and thus order and coherence partially restored
— for certain pumping schemes and well configurations aligned with the
anisotropy. Symmetry associated with well alignment in fact gives rise to
an intriguing “order within chaos” observed only in such cases: prolon
ged confinement of fluid to subregions of chaotic areas.\n\nhttps://events
.interpore.org/event/2/contributions/913/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/913/
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SUMMARY:Methods for extracting Lagrangian coherent structures from unstead
y velocity data
DTSTART;VALUE=DATE-TIME:20180517T144400Z
DTEND;VALUE=DATE-TIME:20180517T145900Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-916@events.interpore.org
DESCRIPTION:Speakers: Sanjeeva Balasuriya (University of Adelaide)\nThe fa
ct that examining Eulerian entities in unsteady velocity fields gives misl
eading information on Lagrangian coherence is now well-established. In th
is talk\, I will review a range of techniques which have been proposed to
extract coherent structures from given velocity data. These include the c
ommonly used finite-time Lyapunov exponents\, as well as methods such as c
urves/surfaces to which there is maximal attraction\, transfer (Perron-Fro
benius) operator methods for identifying sets which are coherent to transp
ort\, clustering methods which group similarly behaving particles\, Lagran
gian-averaged vorticity for identifying vortices in a frame-independent fa
shion\, and sets which are most susceptible to random perturbations. Each
seeks different characteristics\, and thus the appropriate method for a g
iven problem needs to be chosen carefully. These methods---not currently
well-known in the porous media community---may offer new approaches for ex
tracting coherence in porous flows.\n\nhttps://events.interpore.org/event/
2/contributions/916/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/916/
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SUMMARY:Use of Lagrangian coherent structures and angular multiscale stati
stics to assess turbulence in porous media
DTSTART;VALUE=DATE-TIME:20180517T142600Z
DTEND;VALUE=DATE-TIME:20180517T144100Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-917@events.interpore.org
DESCRIPTION:Speakers: Sourabh Apte (Oregon State University)\nTwo approach
es based on Lagrangian statistics of turbulent flow in porous media are in
vestigated. In the first approach\, usage of Lagrangian coherent structure
s (LCS) to understand barriers in transport and mixing in turbulent flows
is studied. The computation of LCS typically involves post processing of
experimentally or numerically obtained fluid velocity fields to obtain the
finite time Lyapunov exponent (FTLE) via a sequence of flow maps (vector
fields which describe fluid displacement patterns over a finite time inter
val). However\, this procedure can be prohibitively expensive for large-sc
ale complex flows of engineering interest. In this work\, an alternative a
nd efficient approach involving computation of the FTLE on the fly during
direct numerical simulation (DNS) of the 3D Navier-Stokes equations is dev
eloped. Spatio-temporal evolution of LCS in a turbulent flow in a randoml
y packed porous bed are computed\, and their role in identifying dead zone
s\, mixing length and time-scales are assessed. In the second approach\, L
agrangian statistics of scale dependent curvature angle and acceleration a
re calculated by tracking a large number of fluid particle trajectories fo
r turbulent flows in porous media over a range of Reynolds numbers (300-10
00). For an isotropic turbulence\, it has been shown that the mean curvatu
re angle varies linearly with time initially\, reaches an inertial range a
nd asymptotes to a value of $\\pi/2$ at long times\, corresponding to the
decorrelation and equipartition of the cosine of the curvature angle. Simi
lar trends are observed at early times for turbulence in porous medium\; h
owever\, the mean curvature angle asymptotes to a value larger than $\\pi/
2$. This is attributed to the effect of confinement on the fluid particle
trajectories that result in preferred directions at large times. The two L
agrangian approaches and their importance in analysing turbulence and tran
sport in porous media will be illustrated.\n\nhttps://events.interpore.org
/event/2/contributions/917/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/917/
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SUMMARY:The dynamics of fluid deformation in Darcy scale porous media and
impact on mixing
DTSTART;VALUE=DATE-TIME:20180517T135000Z
DTEND;VALUE=DATE-TIME:20180517T140500Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-915@events.interpore.org
DESCRIPTION:Speakers: Marco Dentz (IDAEA-CSIC)\nStretching and compression
of fluid elements is key for the understanding and quantification mixing
and reaction in heterogeneous porous media. We quantify the evolution of
the deformation tensor in 2 and 3 dimensional Darcy-scale porous media flo
ws using streamline coordinates. Thus\, we derive a stochastic process for
the stretching of a material strip in terms of a coupled continuous \ntim
e random walk which is parameterized by the statistical medium and flow pr
operties. The derived model is compared to direct numerical simulation of
flow\, particle motion and Lagrangian deformation. The impact on mixing is
studied for the evolution of a diffusive material blob in heterogeneous D
arcy scale flow.\n\nhttps://events.interpore.org/event/2/contributions/915
/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/915/
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SUMMARY:A Lagrangian scheme to model subgrid-scale mixing in heterogeneous
porous media
DTSTART;VALUE=DATE-TIME:20180517T140800Z
DTEND;VALUE=DATE-TIME:20180517T142300Z
DTSTAMP;VALUE=DATE-TIME:20210918T173646Z
UID:indico-contribution-175-919@events.interpore.org
DESCRIPTION:Speakers: Albert Valocchi (University of Illinois at Urbana-Ch
ampaign)\nSmall-scale heterogeneity of permeability plays a major role in
the spreading and mixing of contaminant plumes in groundwater systems. Spr
eading and mixing are interrelated because heterogeneity-induced spreading
leads to the stretching of interfaces of the contaminant plume\, while mi
xing across the interfaces is governed by local hydrodynamic dispersion. I
n many practical problems\, mixing is the key process since it controls pe
ak contaminant concentrations and overall rates of reaction during enginee
red or in-situ remediation. In spite of advances in high performance comp
uting\, it is still not possible to resolve all spatial heterogeneity scal
es in numerical simulation of conservative and reactive transport. We pr
opose a Lagrangian numerical approach to implement closure models to accou
nt for subgrid-scale spreading and mixing in Darcy-scale numerical simulat
ions of solute transport in mildly heterogeneous porous media. The novelty
of the proposed approach is that it considers two different dispersion co
efficients to account for advective spreading mechanisms and local scale d
ispersion. This technique considers fluid particles that carry solute mass
and whose locations evolve according to a deterministic component given b
y the grid-scale velocity and a stochastic component that corresponds to a
block-effective macro-dispersion coefficient. Mass transfer between parti
cles due to local-scale dispersion is approximated by a meshless method.\n
\nUsing results of benchmark numerical simulations\, we demonstrate that
the proposed approach is able to model subgrid-scale spreading and mixing
provided there is a correct choice of block-scale dispersion coefficient.
We assume for convenience the common adopted model that the hydraulic con
ductivity is a second-order stationary\, log-normally distributed random f
ield with exponential covariance. This allows use of the closed-form expr
essions for the block effective macro dispersion coefficient developed by
Rubin and co-workers [1] for the case of small variance. \nThe presentati
on will be based on our recently published paper [2].\n\nhttps://events.in
terpore.org/event/2/contributions/919/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/919/
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