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
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
A homogenised model for flow, transport and sorption in a heterogeneous porous medium
A major challenge in flow through porous media is to better understand the
link between microstructure and macroscale flow and transport. For idealised
microstructures, the mathematical framework of homogenisation theory can be
used for this purpose. Here, we consider a two-dimensional microstructure
comprising an array of obstacles of smooth but arbitrary shape, the size and
spacing of which can vary along the length of the porous medium. We use
homogenisation via the method of multiple scales to systematically upscale a
novel problem involving cells of varying area to obtain effective continuum
equations for macroscale flow and transport. The equations are characterised by
the local porosity, a local anisotropic flow permeability, an effective local
anisotropic solute diffusivity, and an effective local adsorption rate. These
macroscale properties depend nontrivially on the two degrees of microstructural
geometric freedom in our problem: obstacle size, and obstacle spacing. We
exploit this dependence to construct and compare scenarios where the same
porosity profile results from different combinations of obstacle size and
spacing. We focus on a simple example geometry comprising circular obstacles on
a rectangular lattice, for which we numerically determine the macroscale
permeability and effective diffusivity. We investigate scenarios where the
porosity is spatially uniform but the permeability and diffusivity are not. Our
results may be useful in the design of filters, or for studying the impact of
deformation on transport in soft porous media
Discovery of Very High Energy Gamma-Ray Emission from the BL Lac Object H2356-309 with the H.E.S.S. Cherenkov Telescopes
The extreme synchrotron BL Lac object H2356-309, located at a redshift of z =
0.165, was observed from June to December 2004 with a total exposure of approx.
40 h live-time with the H.E.S.S. (High Energy Stereoscopic System) array of
atmospheric-Cherenkov telescopes (ACTs). Analysis of this data set yields, for
the first time, a strong excess of 453 gamma-rays (10 standard deviations above
background) from H2356-309, corresponding to an observed integral flux above
200 GeV of I(>200GeV) = (4.1+-0.5) 10^12 cm^-2.s^-1 (statistical error only).
The differential energy spectrum of the source between 200 GeV and 1.3 TeV is
well-described by a power law with a normalisation (at 1 TeV) of N_0 = (3.00 +-
0.80_stat +- 0.31_sys) 10^-13 cm^-2.s^-1.TeV^-1 and a photon index of Gamma =
3.09 +- 0.24_stat +- 0.10_sys. H2356-309 is one of the most distant BL Lac
objects detected at very-high-energy gamma-rays so far. Results from
simultaneous observations from ROTSE-III (optical), RXTE (X-rays) and NRT
(radio) are also included and used together with the H.E.S.S. data to constrain
a single-zone homogeneous synchrotron self-Compton (SSC) model. This model
provides an adequate fit to the H.E.S.S. data when using a reasonable set of
model parameters.Comment: 7 pages, 4 figures, accepted for publication in Astronomy and
Astrophysics (05/07/2006
MATLAB files from From arteries to boreholes: steady-state response of a poroelastic cylinder to fluid injection
A suite of MATLAB functions that implement the analytical and numerical steady-state solutions described in the manuscrip
The lifetime of carbon capture and storage as a climate-change mitigation technology
In carbon capture and storage (CCS), CO[subscript 2] is captured at power plants and then injected underground into reservoirs like deep saline aquifers for long-term storage. While CCS may be critical for the continued use of fossil fuels in a carbon-constrained world, the deployment of CCS has been hindered by uncertainty in geologic storage capacities and sustainable injection rates, which has contributed to the absence of concerted government policy. Here, we clarify the potential of CCS to mitigate emissions in the United States by developing a storage-capacity supply curve that, unlike current large-scale capacity estimates, is derived from the fluid mechanics of CO[subscript 2] injection and trapping and incorporates injection-rate constraints. We show that storage supply is a dynamic quantity that grows with the duration of CCS, and we interpret the lifetime of CCS as the time for which the storage supply curve exceeds the storage demand curve from CO[subscript 2] production. We show that in the United States, if CO[subscript 2] production from power generation continues to rise at recent rates, then CCS can store enough CO[subscript 2] to stabilize emissions at current levels for at least 100 y. This result suggests that the large-scale implementation of CCS is a geologically viable climate-change mitigation option in the United States over the next century.United States. Dept. of Energy (Grant DE-FE0002041)MIT Energy InitiativeReed Research FundMartin Family Society of Fellows for SustainabilityAtlantic Richfield Company (ARCO