ACCRETE can easily be coupled to multiphase flow simulators. (e.g., Utsira 1944 grid 3D reactive transport simulations run with the Athena multiphase flow ...
An explicit and efficient algorithm to solve kinetically constrained CO2-water-rock interactions
Helge Hellevang Bjørn Kvamme* *presenting author
Department of Physics and Technology University of Bergen, Norway
CO2 storage
Storage of CO2 in saline aquifers is one option to reduce atmospheric emissions (e.g. the Utsira Sand, North Sea). To understand the long-term reactivity of injected CO2 (thousands of years), both fast reactions between injected CO2 and the aqueous phase, as well as slow mineral reactions must be included in numerical models. Most mineral reactions approach a non-equilibrim steady-state, and must be modelled as kinetically constrained reactions.
The ACCRETE code
ACCRETE solves CO2-water-rock interactions including: – – –
Consumption of CO2(g,liq) into saline aqueous solutions. Speciation of carbon in the aqueous solution. Kinetically constrained mineral reactions.
Number of mineral reactions solved simultaneously is currently 16, which can easily be expanded. Mineral reactions included are a minimum of what is expected important for CO2 storage settings. Number of aqueous components are currently 15, sufficient for describing the aqueous carbon equilibrium in a seawarer-like solutions and the mineral reactions. ACCRETE can easily be coupled to multiphase flow simulators (e.g., Utsira 1944 grid 3D reactive transport simulations run with the Athena multiphase flow code).
Athena/ACCRETE simulations
3x3x0.25 km3 of the sand simulated Low-permeable clayey horizons included as suggested by gamma-logs from the reservoir.
Fig. 2, Paper D (Modified from Chadwick et al., 2004).
Fig. 3, Paper D.
Athena/ACCRETE simulations pH
Immiscible CO2 Volume frac.
ACCRETE – activity and fugacity calculations
Non-ideality of aqueous species in saline solutions are quantified through activity coefficients:
ai = [i ]⋅ γ i
Activity coefficients for charged species are calculated according to the Truesdell-Jones model* –
This model is appropriate for up to 2M NaCl dominated solutions.
Activity of water (H2O) estimated in accordance with the b-dot equations of Helgeson** The CO2,aq activity coefficient is calculated after Drummond et al.*** Neutral species like SiO2,aq and NaHCO3 are assumed to have activity coefficients of 1 i.e., ai = [i]. *Truesdell and Jones, 1974. J. Res., U.S. Geological Survey, 2, 233-274. **Helgesson, 1969. Am. J. Sci., 267, 729-804. ***Drummond et al., 1981. Ph.D. thesis, The Pennsylvania State University, University Park, Pennsylvania.
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ACCRETE – Aqueous carbon speciation
Dissolved CO2 reacts with water and produces carbonic acid The carbonic acid dissociates into bicarbonate and carbonate ions releasing H+. The elevated H+ activity (lower pH*) results in instability of minerals and a higher reactivity of the reservoir sand.
Reactions:
CO2,aq + H 2 O ↔ H 2 CO3
H 2 CO3 ↔ HCO3− + H + HCO3− ↔ CO32− + H + Na + + HCO3− ↔ NaHCO3
* pH = − log(a + ) H
ACCRETE – Reaction rates Kinetic expression:
The reaction rate of individual minerals is calculated from their kinetic constants (experimental determined or based on similar minerals), their reactive surface area, and their distance from equilibrium.
ξi ∆t
= ki Si {Ω − 1}
Ωk = qk =
qk Kk
∏ aν
i
i ,k
i
∏a
vj j ,k
j
Reactive surface area: Stot = 10
−4
∑ i
S prec = ϖ ⋅ S tot
(
ni M i β i 1 − xCO2
ρi
)
Stiffness problems
The thermodynamic stability of aluminosilicates and their reaction rates are sensitive to the concentration of aluminium. Aluminium is at steady-state at such a low concentration that even small time increments may lead to instabilities – This occurs if the total change in aluminium over a time increment approach the initial aluminium concentration (Fig.)
Total change aluminium caused by min. reac. Al at time t0.
Stiffness problems Short timesteps (slow simulation) – no problems
Longer timesteps (faster simulation) – stiffness problems in Al!
Stiffness problems Solid carbonates formed for the stable (left) and unstable (right) simulations:
Solution – Constant aluminium
Simulations ran at short time increments suggest that at a given chemistry and physical conditions, aluminium approach a steady concentration over long time intervals (hundreds to thousands of years). This suggests that using a constant aluminium value obtained from small stable simulations may provide fast reliable simulations. Alternatively, the variable aluminium is replaced by a non-constant function also obtained from preliminary simulations.
Solution – Constant aluminium Total stored carbon for Stable vs. Constant aluminium runs.
Summary
Solving CO2-water-rock interactions involves solving a stiff system of equations. The stiffness is mainly cused by a low steady-state aluminium concentration. Replacing the variable aluminium in the mineral reaction rate expressions by a constant value or a simple function found from preliminary studies is suggested. 1000 years simulations of a system that resembles the Utsira Sand in the North Sea, suggest that an approximation using constant aluminium provides results that, for most of the time, is indistinguishable from the true stable solution. A full multigrid simulation can by done in a few seconds using this approximation.
