Convective stability of carbon sequestration in anisotropic porous media

© 2014 The Author(s) Published by the Royal Society. All rights reserved. The stability of convection in an anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction, is studied. This is a simplified model for the interactions between carbon dioxide and brine in underground aquifers; the instability of which is essential in reducing reservoir mixing times. The key purpose of this paper is to explore the role porous media anisotropy plays in convective instabilities. It is shown that varying the ratio of horizontal to vertical solutal diffusivites does not significantly affect the behaviour of the instability. This is also the case for changes of permeability when the diffusion rate dominates the solute reaction rate. However, interestingly, when the solute reaction rate dominates the diffusion rate a change in the permeability of the porous material does have a substantial effect on the instability of the system. The region of potential subcritical instabilities is shown to be negligible, which further supports the novel instability behaviour

Thermal convection with a Cattaneo heat flux model

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one

Bidispersive thermal convection with relatively large macropores

We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the macropores. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. The coincidence of the linear and nonlinear stability boundaries is established under general thermal boundary conditions

Christov-Morro theory for non-isothermal diffusion

We propose a theory for diffusion of a substance in a body allowing for changes in temperature. The key aspect is that the body is allowed to deform although we restrict our attention to the case where the velocity field is known. In accordance with recent developments in the literature, we concentrate on a situation where diffusion and temperature diffusion are governed by equations which have more of a hyperbolic nature than parabolic. Since this involves relaxation time equations for both the heat flux and the solute flux the fact that the body can deform necessitates the use of appropriate objective time derivatives. In this regard our work is based on recent work of Christov and Morro on heat transport in a moving body. An analysis of well posedness of the theory is commenced in that we establish the uniqueness of a solution to the boundary-initial value problem, and continuous dependence on the initial data for the same. (C) 2011 Elsevier Ltd. All rights reserved

Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations. Consequently, we provide a complete characterization of the group and phase velocities for these two cases, together with some non-trivial remarks on the nature of wave dispersion in fractional models.Comment: 18 pages, 7 figure

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

A Noninvasive Method to Detect Mexican Wolves and Estimate Abundance

Monitoring wolf abundance is important for recovery efforts of Mexican wolves (Canis lupus baileyi) in the Blue Range Wolf Recovery Area in Arizona and New Mexico, USA. Although radiotelemetry has been a reliable method, collaring and tracking wolves in an expanding population will be prohibitively expensive and alternative methods to estimate abundance will become necessary. We applied 10 canid microsatellite loci to 235 Mexican wolf samples, 48 coyote (C. latrans) samples, and 14 domestic dog (C. lupus familiaris) samples to identify alleles that provide reliable separation of these species. We then evaluated an approach for prescreening, noninvasively collected DNA obtained from fecal samples to identify Mexican wolves. We generated complete genotypes for only those samples identified as probable Mexican wolves. We used these genotypes to estimate mark–recapture population estimates of Mexican wolves and compared these to known numbers of wolves in the study area.We collected fecal samples during 3 sampling periods in 2007–2008 and used Huggins-type mark–recapture models to estimate Mexican wolf abundance. We were able to generate abundance estimates with 95% confidence for 2 of 3 sampling periods. We estimated abundance to be 10 (95% Cl = 6–34) during one sampling period when the known abundance was 10 and we estimated abundance to be 9 (95% CI = 6 –30) during the other sampling period when the known abundance was 10. The application of this noninvasive method to estimate Mexican wolf abundance provides an alternative monitoring tool that could be useful for long-term monitoring of this and other recovering populations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA

A Noninvasive Method to Detect Mexican Wolves and Estimate Abundance

Monitoring wolf abundance is important for recovery efforts of Mexican wolves (Canis lupus baileyi) in the Blue Range Wolf Recovery Area in Arizona and New Mexico, USA. Although radiotelemetry has been a reliable method, collaring and tracking wolves in an expanding population will be prohibitively expensive and alternative methods to estimate abundance will become necessary. We applied 10 canid microsatellite loci to 235 Mexican wolf samples, 48 coyote (C. latrans) samples, and 14 domestic dog (C. lupus familiaris) samples to identify alleles that provide reliable separation of these species. We then evaluated an approach for prescreening, noninvasively collected DNA obtained from fecal samples to identify Mexican wolves. We generated complete genotypes for only those samples identified as probable Mexican wolves. We used these genotypes to estimate mark–recapture population estimates of Mexican wolves and compared these to known numbers of wolves in the study area.We collected fecal samples during 3 sampling periods in 2007–2008 and used Huggins-type mark–recapture models to estimate Mexican wolf abundance. We were able to generate abundance estimates with 95% confidence for 2 of 3 sampling periods. We estimated abundance to be 10 (95% Cl = 6–34) during one sampling period when the known abundance was 10 and we estimated abundance to be 9 (95% CI = 6 –30) during the other sampling period when the known abundance was 10. The application of this noninvasive method to estimate Mexican wolf abundance provides an alternative monitoring tool that could be useful for long-term monitoring of this and other recovering populations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA