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Onset of instability in CO2 sequestration into saline aquifer: scaling relationship and the effect of perturbed boundary

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Abstract

Storage and disposal of greenhouse gases in saline aquifers is an important solution for reduction of these gases from atmosphere. Understanding the concepts and mechanisms involved in the storage process, especially natural convection and their impact on long-term fate of injected CO2 are essential. Natural convection is an effective mechanism which increases solubility of carbon dioxide in the storage process. In this work, injection of carbon dioxide into aquifer is numerically simulated. First, numerical criteria are developed to provide numerical accuracy and stability by mesh resolution. Then, changes in input wave number in surface perturbation and order of element used in finite element method were analyzed. It was found that depending on Rayleigh number, there is a wave number at which instability occurs earlier and grows faster. Also, onset of CO2 convective mixing in saline aquifers was obtained and correlated for a number of field cases. Results show that onset of convection can be approximated by a scaling relationship for dimensionless time as a function of inverse square of Rayleigh number, Ra−2, for Rayleigh range used in this work. This scaling relationship provides a predictive tool for onset of convection and also long-term fate of disposed CO2 in large scale geological sequestration.

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Abbreviations

C:

CO2 concentration (mol/m3)

Ceq :

Constant interface concentration (mol/m3)

c1, c2 :

Correlation constants

Cr:

Courant number (−)

\(\overline{\text{c}}\) :

Fraction of ultimate CO2 dissolution (−)

C*:

Interface concentration due to imposed perturbation (mol/m3)

D:

Molecular diffusion coefficient (m2/s)

Err:

Numerical error in pure diffusion region (−)

FO, SO, TO:

First-order, second-order, and third-order elements

H:

Height of the porous medium (m)

k:

Permeability of the porous medium (m−2)

K:

Wave number

L:

Length of the porous medium (m)

n:

Summation index

N:

Number of elements

P:

Pressure (pa)

Pe:

Peclet number (−)

Ra :

Rayleigh number (−)

rand:

Random function

Sh :

Sherwood number (−)

t:

Time (s)

t>c :

Time of the onset of convection (s)

t>D :

Dimensionless time (−)

t>Dc :

Dimensionless time of the onset of convection (−)

U:

Darcy velocity in x-coordinate (m/s)

v:

Vector of Darcy velocity (m/s)

vl :

Grid Darcy’s velocity (m/s)

w:

Darcy velocity in z-coordinate (m/s)

x:

Dimensionless distance in x-coordinate

z:

Dimensionless distance in z-coordinate

∆l(l = x, z):

Grid sizes (L)

∆t:

Simulation time-step (s)

ρ>mix :

Mixture CO2-brine density (kg/m3)

ρ 0 :

Brine density (kg/m3)

∅:

Porosity of the porous medium (−)

∆ρ :

Density difference between CO2 saturated brine and fresh brine (kg/m3)

β :

Volumetric expansion factor (m3/mol)

μ :

Brine viscosity (kg/m s)

Nu:

Numerical solution

Pd-th:

Analytical solution in pure diffusion region

x:

Quantity in x-direction

z:

Quantity in z-direction

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Authors and Affiliations

  1. Department of Petroleum Engineering, Faculty of Oil, Gas, and Petrochemical Engineering, Persian Gulf University, 7516913817, Bushehr, Iran

    Reza Azin & Seyed Mostafa Jafari Raad

  2. Department of Chemical Engineering, Faculty of Oil, Gas, and Petrochemical Engineering, Persian Gulf University, 7516913817, Bushehr, Iran

    Shahriar Osfouri

  3. Department of Mechanical Engineering, Faculty of Engineering, Persian Gulf University, 7516913817, Bushehr, Iran

    Rooholla Fatehi

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  1. Reza Azin
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  2. Seyed Mostafa Jafari Raad
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  3. Shahriar Osfouri
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  4. Rooholla Fatehi
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Correspondence to Reza Azin.

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Azin, R., Raad, S.M.J., Osfouri, S. et al. Onset of instability in CO2 sequestration into saline aquifer: scaling relationship and the effect of perturbed boundary. Heat Mass Transfer 49, 1603–1612 (2013). https://doi.org/10.1007/s00231-013-1199-7

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  • DOI: https://doi.org/10.1007/s00231-013-1199-7

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