Numerical Modeling Studies of The Dissolution-Diffusion-Convection ProcessDuring CO2 Storage in Saline Aquifers Page: 5 of 33
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where u = z/2 Dt is the similarity variable for the diffusion process, with z the distance from
the top boundary (measured positive downward), t the time, and D the diffusivity. erfc(u)
denotes the complementary error function, expressed in terms of the error function
erf(u) = exp(- ) d (2)
as erfc(u) = 1 - erf(u). The thickness of the diffusive boundary layer can be estimated as
Az = Dt , although it must be kept in mind that the diffusive profile is very broad, and
significant non-zero concentrations extend beyond /5 (see below). In some cases 2 Dt may
be a better measure of the diffusive boundary layer, but for simplicity we will generally use
D. A finite "incubation time" t1c must elapse before convection is initiated, estimated from
linear stability analysis by Ennis-King and Paterson (2003a, b) as
u2 2D
tinp = c )2g2k2 (3)
Here, p is the fluid viscosity, Ap the density increase due to CO2 dissolution, is porosity, k
permeability, and g acceleration of gravity. co is a numerical constant that was estimated as co
180 based on the critical Rayleigh number for onset of convective instability, while from
numerical simulations a value of co = 80-100 was obtained (Ennis-King and Paterson, 2003b).
Our simulations yield much larger values of co > 1,000, see below. The thickness of the diffusive
boundary layer at the onset time t1c of convective activity is given by
Linc = Dtinc = c (ADk (4)
From the expression for diffusive flux,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/m1/5/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.