Numerical Modeling Studies of The Dissolution-Diffusion-Convection ProcessDuring CO2 Storage in Saline Aquifers Page: 4 of 33
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constant during the convection-dominated period, apart from random fluctuations due to the
chaotic nature of the underlying processes. Ennis-King et al. (2008) compared DDC for
homogeneous media with simulations for heterogeneous media, that featured a random
distribution of shale bodies in a homogeneous sand background. Recently, laboratory studies are
being conducted that have confirmed qualitative and quantitative aspects of DDC (Yang and Gu,
2006; Kneafsey and Pruess, 2008).
This study explores quantitative aspects of CO2 dissolution. The DDC process begins on
small spatial scales and, after convection is initiated, continually grows to eventually encompass
the entire permeable interval. We employ high-resolution numerical simulation to examine the
onset of convective activity, and the rate at which this process removes CO2 from the dissolution
boundary. A first goal of our work is to achieve realistic numerical simulations of the DDC
process, in which space and time are resolved on the actual scale of the governing diffusive and
convective processes. A further goal, not addressed in this report, will be the design of sub-grid-
scale discretization methods that can achieve a satisfactory representation of the processes in a
field-scale modeling approach. In the context of this goal, we are primarily interested in CO2
dissolution rates for systems whose vertical thickness H is large in comparison to the thickness
L1nc of the diffusive boundary layer at onset of instability, H >> Linc. We focus on the earlier
portion of the convective period, before convection is affected by the presence of a lower
boundary. It is expected that late-stage convection, and systems with vertical thickness H ~ Linc,
can be treated adequately with the fairly coarse spatial resolutions that would be commonly
employed in field-scale models.
2. Molecular Diffusion
Stability analysis has shown that, in the early stages, DDC is entirely dominated by
molecular diffusion (Ennis-King and Paterson, 2003a, b). For a boundary concentration (CO2
mass fraction) Xo, applied at time t = 0 to a homogeneous domain with initial concentration X =
0, the concentration profile away from the boundary is given by the appropriate solution of the
diffusion equation OX/Ot = D a2X/at2 (Carslaw and Jaeger, 1959),
X(z,t) = Xo erfc(u) (1)
17 November 2008
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Pruess, Karsten & Zhang, Keni. Numerical Modeling Studies of The Dissolution-Diffusion-Convection ProcessDuring CO2 Storage in Saline Aquifers, report, November 17, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc898341/m1/4/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.