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