46 research outputs found
From arteries to boreholes: Steady-state response of a poroelastic cylinder to fluid injection
The radially outward flow of fluid into a porous medium occurs in many
practical problems, from transport across vascular walls to the pressurisation
of boreholes. As the driving pressure becomes non-negligible relative to the
stiffness of the solid structure, the poromechanical coupling between the fluid
and the solid has an increasingly strong impact on the flow. For very large
pressures or very soft materials, as is the case for hydraulic fracturing and
arterial flows, this coupling can lead to large deformations and, hence, to
strong deviations from a classical, linear-poroelastic response. Here, we study
this problem by analysing the steady-state response of a poroelastic cylinder
to fluid injection. We consider the qualitative and quantitative impacts of
kinematic and constitutive nonlinearity, highlighting the strong impact of
deformation-dependent permeability. We show that the wall thickness (thick vs.
thin) and the outer boundary condition (free vs. constrained) play a central
role in controlling the mechanics
Impact of pressure dissipation on fluid injection into layered aquifers
Carbon dioxide (CO2) capture and subsurface storage is one method for
reducing anthropogenic CO2 emissions to mitigate climate change. It is well
known that large-scale fluid injection into the subsurface leads to a buildup
in pressure that gradually spreads and dissipates through lateral and vertical
migration of water. This dissipation can have an important feedback on the
shape of the CO2 plume during injection, and the impact of vertical pressure
dissipation, in particular, remains poorly understood. Here, we investigate the
impact of lateral and vertical pressure dissipation on the injection of CO2
into a layered aquifer system. We develop a compressible, two-phase model that
couples pressure dissipation to the propagation of a CO2 gravity current. We
show that our vertically integrated, sharp-interface model is capable of
efficiently and accurately capturing water migration in a layered aquifer
system with an arbitrary number of aquifers. We identify two limiting cases ---
`no leakage' and `strong leakage' --- in which we derive analytical expressions
for the water pressure field for the corresponding single-phase injection
problem. We demonstrate that pressure dissipation acts to suppress the
formation of an advancing CO2 tongue during injection, resulting in a plume
with a reduced lateral extent. The properties of the seals and the number of
aquifers determine the strength of pressure dissipation and subsequent coupling
with the CO2 plume. The impact of pressure dissipation on the shape of the CO2
plume is likely to be important for storage efficiency and security
Fluid-driven deformation of a soft granular material
Compressing a porous, fluid-filled material will drive the interstitial fluid
out of the pore space, as when squeezing water out of a kitchen sponge.
Inversely, injecting fluid into a porous material can deform the solid
structure, as when fracturing a shale for natural gas recovery. These
poromechanical interactions play an important role in geological and biological
systems across a wide range of scales, from the propagation of magma through
the Earth's mantle to the transport of fluid through living cells and tissues.
The theory of poroelasticity has been largely successful in modeling
poromechanical behavior in relatively simple systems, but this continuum theory
is fundamentally limited by our understanding of the pore-scale interactions
between the fluid and the solid, and these problems are notoriously difficult
to study in a laboratory setting. Here, we present a high-resolution
measurement of injection-driven poromechanical deformation in a system with
granular microsctructure: We inject fluid into a dense, confined monolayer of
soft particles and use particle tracking to reveal the dynamics of the
multi-scale deformation field. We find that a continuum model based on
poroelasticity theory captures certain macroscopic features of the deformation,
but the particle-scale deformation field exhibits dramatic departures from
smooth, continuum behavior. We observe particle-scale rearrangement and
hysteresis, as well as petal-like mesoscale structures that are connected to
material failure through spiral shear banding
Wettability control on multiphase flow in patterned microfluidics
Multiphase flow in porous media is important in many natural and industrial processes, including geologic CO₂ sequestration, enhanced oil recovery, and water infiltration into soil. Although it is well known that the wetting properties of porous media can vary drastically depending on the type of media and pore fluids, the effect of wettability on multiphase flow continues to challenge our microscopic and macroscopic descriptions. Here, we study the impact of wettability on viscously unfavorable fluid–fluid displacement in disordered media by means of high-resolution imaging in microfluidic flow cells patterned with vertical posts. By systematically varying the wettability of the flow cell over a wide range of contact angles, we find that increasing the substrate’s affinity to the invading fluid results in more efficient displacement of the defending fluid up to a critical wetting transition, beyond which the trend is reversed. We identify the pore-scale mechanisms—cooperative pore filling (increasing displacement efficiency) and corner flow (decreasing displacement efficiency)—responsible for this macroscale behavior, and show that they rely on the inherent 3D nature of interfacial flows, even in quasi-2D media. Our results demonstrate the powerful control of wettability on multiphase flow in porous media, and show that the markedly different invasion protocols that emerge—from pore filling to postbridging—are determined by physical mechanisms that are missing from current pore-scale and continuum-scale descriptions.United States. Department of Energy (DE-SC0003907)United States. Department of Energy (DE-FE0009738
Migration, trapping, and venting of gas in a soft granular material
Gas migration through a soft granular material involves a strong coupling
between the motion of the gas and the deformation of the material. This process
is relevant to a variety of natural phenomena, such as gas venting from
sediments and gas exsolution from magma. Here, we study this process
experimentally by injecting air into a quasi-2D packing of soft particles and
measuring the morphology of the air as it invades and then rises due to
buoyancy. We systematically increase the confining pre-stress in the packing by
compressing it with a fluid-permeable piston, leading to a gradual transition
in migration regime from fluidization to pathway opening to pore invasion. We
find that mixed migration regimes emerge at intermediate confinement due to the
spontaneous formation of a compaction layer at the top of the flow cell. By
connecting these migration mechanisms with macroscopic invasion, trapping, and
venting, we show that mixed regimes enable a sharp increase in the average
amount of gas trapped within the packing, as well as much larger venting
events. Our results suggest that the relationship between invasion, trapping,
and venting could be controlled by modulating the confining stress
Flow and deformation due to periodic loading in a soft porous material
Soft porous materials, such as biological tissues and soils, are exposed to
periodic deformations in a variety of natural and industrial contexts. The
detailed flow and mechanics of these deformations have not yet been
systematically investigated. Here, we fill this gap by identifying and
exploring the complete parameter space associated with periodic deformations in
the context of a 1D model problem. We use large-deformation poroelasticity to
consider a wide range of loading periods and amplitudes. We identify two
distinct mechanical regimes, distinguished by whether the loading period is
slow or fast relative to the characteristic poroelastic timescale. We develop
analytical solutions for slow loading at any amplitude and for infinitesimal
amplitude at any period. We use these analytical solutions and a full numerical
solution to explore the localisation of the deformation near the permeable
boundary as the period decreases and the emergence of nonlinear effects as the
amplitude increases. We show that large deformations lead to asymmetry between
the loading and unloading phases of each cycle in terms of the distributions of
porosity and fluid flux
Gas compression systematically delays the onset of viscous fingering
Using gas to drive liquid from a Hele-Shaw cell leads to classical viscous
fingering. Strategies for suppressing fingering have received substantial
attention. For steady injection of an incompressible gas, the intensity of
fingering is controlled by the capillary number Ca. Here, we show that gas
compression leads to an unsteady injection rate controlled primarily by a
dimensionless compressibility number C. Increasing C systematically delays the
onset of fingering at high Ca, highlighting compressibility as an overlooked
but fundamental aspect of gas-driven fingering
Compression-driven viscous fingering in a radial Hele-Shaw cell
The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a
classical problem. The gas-liquid interface is hydrodynamically unstable,
forming striking finger-like patterns that have attracted research interest for
decades. Generally, both the gas and liquid phases are taken to be
incompressible, with the capillary number being the key parameter that
determines the severity of the instability. Here, we consider a radially
outward displacement driven by the steady compression of a gas reservoir. The
associated gas-injection rate is then unsteady due to the compressibility of
the gas. We identify a second nondimensional parameter, the compressibility
number, that plays a strong role in the development of the fingering pattern.
We use an axisymmetric model to study the impact of compressibility number on
the unsteady evolution of injection rate and gas pressure. We use linear
stability analysis to show that increasing the compressibility number delays
the onset of finger development relative to the corresponding incompressible
case. Finally, we present and compare a series of experiments and fully
nonlinear simulations over a broad range of capillary and compressibility
numbers. These results show that increasing the compressibility number
systematically decreases the severity of the fingering pattern at high
capillary number. Our results provide an unprecedented comparison of
experiments with simulations for viscous fingering, a comprehensive
understanding of the role of compressibility in unstable gas-liquid
displacement flows, and insight into a new mechanism for controlling the
development of fingering patterns
Capillary pinning and blunting of immiscible gravity currents in porous media
Gravity-driven flows in the subsurface have attracted recent interest in the context of geological carbon dioxide (CO2) storage, where supercritical CO2 is captured from the flue gas of power plants and injected underground into deep saline aquifers. After injection, the CO2 will spread and migrate as a buoyant gravity current relative to the denser, ambient brine. Although the CO2 and the brine are immiscible, the impact of capillarity on CO2 spreading and migration is poorly understood. We previously studied the early time evolution of an immiscible gravity current, showing that capillary pressure hysteresis pins a portion of the macroscopic fluid-fluid interface and that this can eventually stop the flow. Here we study the full lifetime of such a gravity current. Using tabletop experiments in packings of glass beads, we show that the horizontal extent of the pinned region grows with time and that this is ultimately responsible for limiting the migration of the current to a finite distance. We also find that capillarity blunts the leading edge of the current, which contributes to further limiting the migration distance. Using experiments in etched micromodels, we show that the thickness of the blunted nose is controlled by the distribution of pore-throat sizes and the strength of capillarity relative to buoyancy. We develop a theoretical model that captures the evolution of immiscible gravity currents and predicts the maximum migration distance. By applying this model to representative aquifers, we show that capillary pinning and blunting can exert an important control on gravity currents in the context of geological CO2 storage