Scaling behavior of convective mixing, with application to geological storage of CO₂

Abstract

in Wiley InterScience (www.interscience.wiley.com).CO 2 storage in deep saline aquifers is considered a possible option for mitigation of greenhouse gas emissions from anthropogenic sources. Understanding of the underlying mechanisms, such as convective mixing, that affect the long-term fate of the injected CO 2 in deep saline aquifers, is of prime importance. We present scaling analysis of the convective mixing of CO 2 in saline aquifers based on direct numerical simulations. The convective mixing of CO 2 in aquifers is studied, and three mixing periods are identified. It is found that, for Rayleigh numbers less than 600, mixing can be approximated by a scaling relationship for the Sherwood number, which is proportional to Ra 1/2 . Furthermore, it is shown that the onset of natural convection follows t Dc ;Ra À2 and the wavelengths of the initial convective instabilities are proportional to Ra. Such findings give insight into understanding the mixing mechanisms and long term fate of the injected CO 2 for large scale geological sequestration in deep saline aquifers. In addition, a criterion is developed that provides the appropriate numerical mesh resolution required for accurate modeling of convective mixing of CO 2 in deep saline aquifers.

Convective shutdown in a porous medium at high Rayleigh number

“…Once this dense fluid reaches the upper boundary, the dynamics of the system change and the convective flux begins to decrease. The qualitative behaviour of the flux in this 'shutdown' regime has been observed in numerical simulations by Hassanzadeh et al (2007) for Ra < 1000, although they provided no theoretical analysis of the system. Slim et al (2013) presented experimental results in this regime for 100 < Ra < 1700, and derived a phenomenological model that describes the evolution of the flux based on an ad hoc parametrization of the typical boundary-layer depth.…”

“…The system evolves independently of the depth of the domain until the largest plumes reach the lower boundary. There have been a number of numerical studies for Ra O(10 3 ) that examine the evolution of the dynamics and the merging of descending plumes before they interact with the lower boundary (Hassanzadeh et al 2007;Pau et al 2010). Slim et al (2013) performed experiments in a Hele-Shaw cell for 100 < Ra < 1700, and categorized the evolution of the system from the onset of convection in detail.…”

“…Many previous studies of one-sided convective systems have focused on the conditions required for the onset of convection, which presents significant theoretical challenges because the diffusive base state is both time-dependent and nonlinear. Various theoretical studies (Hassanzadeh, Pooladi-Darvish & Keith 2006;Riaz et al 2006;Xu, Chen & Zhang 2006;Slim & Ramakrishnan 2010) have been complemented by direct numerical investigations (Riaz et al 2006;Hassanzadeh, Pooladi-Darvish & Keith 2007) and laboratory experiments (Fernandez et al 2002;Backhaus, Turitsyn & Ecke 2011;Slim et al 2013) that explore the onset of convection.…”

An empirical theory for gravitationally unstable flow in porous media

“…The increase of the mass-transfer rate is equivalent to a dissolution of a larger amount of CO 2 in a shorter period of time and faster propagation of CO 2 in porous media (aquifers and hydrocarbon reservoirs) [33,34,38]. The large volume of dissolved CO 2 remains permanently in the liquid (at least as long as the pressure remains unchanged) and poses no threat of leakage, which is favorable for geological storage of CO 2 [23].…”

Insights from a pseudospectral approach to the Elder problem

“…[2] The simulation of buoyancy driven flow (BDF) is frequently required in many areas of hydrology including saline contamination [Zimmermann et al, 2006;Bolster et al, 2007;Narayan et al, 2007;Lin et al, 2009] and more recently carbon sequestration [Riaz et al, 2006;Farajzadeh et al, 2007;Hassanzadeh et al, 2007]. A major issue in BDF modeling is the problem of benchmarking [Simpson and Clement, 2003;Simmons, 2005;Goswami and Clement, 2007].…”