Mathematical modeling of CO2 -storage MatMoRA M.T. Elenius H. K. Dahle, J. M. Nordbotten, K.-A. Lie University of Bergen Centre for Integrated Petroleum Research SINTEF ICT

Climit PhD seminar 2010, Oslo 1-2 November

Personnel

Institution

Senior personnel

Researchers/PhD/postdocs.

UiB

Helge K. Dahle Jan M. Nordbotten

Paulo Herrera (postdoc) Leonid Vasilyev (PhD) Maria Elenius (PhD) Trine Mykkeltvedt (PhD) Elsa du Plessis (PhD)

Uni Research

Klaus Johannsen Karsten Pruess (adjoint) Ivar Aavatsmark Jan Tveranger

Martha Lien Geir T. Eigestad Eirik Keilegavlen

SINTEF ICT

Knut-Andreas Lie

Halvor M. Nilsen (postdoc) Meisam Ashraf (PhD) Ingeborg S. Ligaarden

Stuttgart

Rainer Helmig Holger Class

Princeton

Michael A. Celia

Steering committee: Benedicte Kvalheim (Statoil), Martin Iding (Statoil), Jostein Haga (Norske Shell), Roger Bjørgan (SINTEF), Ivar Aavatsmark (Uni Research/UiB), Aage Stangeland (Forskningsrådet/Climit, observatør)

Leakage pathways and storage mechanisms The CO2 is injected as a supercritical fluid which is buoyant relative to the resident water. A caprock with low permeability is therefore needed. Possible leakage pathways include,

fractures and faults, abandoned wells, and disappearance of the caprock. Picture courtesy Statoil.

In time, the CO2 is trapped by hydrodynamic trapping, capillary trapping, dissolution trapping and mineral trapping. It is important to understand and quantify the time- and length scales of the flow and trapping mechanisms as well as the effects of geological variation.

Capillary- and dissolution trapping in a sloping aquifer High resolution simulations are performed in collaboration with Stanford University to understand and quantify trapping of a CO2 plume. This can then be used as input in upscaled models.

CO2 phase saturation with and without dissolution.

Dissolution- and capillary trapping are both important for safe storage of CO2 . The saturations in the plume correspond to pressures consistent with vertical equilibrium.

Dissolution trapping Water density increases with dissolved CO2 content, and eventually the diffusive boundary layer under the plume becomes unstable. This enhances the dissolution rate.

Mass fraction of CO2 in the water at the advancing tip.

Leonid Vasilyev’s work addresses parameters that are important in this context.

Dissolution trapping The capillary transition zone takes part in the convective mixing. Water ’meandering’ might decrease the plume speed.

Mass fraction of CO2 in the water phase 200 m behind the tip, 500 years.

The capillary transition zone and convective mixing We perform linear stability analysis and numerical simulations to study the effect of the capillary transition zone on the onset and evolution of the convective mixing.

Upscaled Convective Mixing

Preuss, et.al. 2009

Hypothesis: Earlier onset → larger dissolution rate.

Vertical Equilibrium (VE) Models Assume vertical equilibrium across the aquifer: ∇⊥ pα = ρα g⊥

Vertical Equilibrium (VE) Models Assume vertical equilibrium across the aquifer: ∇⊥ pα = ρα g⊥

Vertical Equilibrium: Upscaling Variables

Fine-scale variables pn − pw = pc (sn ), krα = krα (sn ), λα =

krα µα

Coarse-scale variables Z Z H 1 1 H φdz, Sα = φsα dz Φ= H 0 ΦH 0 Z Z 1 H 1 H H K= kH dz, Uα = uα dz H 0 H 0 Z H K−1 1 K rα = · krα kH dz, Λα = K rα H µα 0

Vertical Equilibrium Models: Effect of Capillary Fringe

Nordbotten, Dahle, WRR 2010, CMWR 2010

Ex: Johansen Formation (Cross Section) z−dim = 5, relative error: 0.74

z−dim = 10, relative error: 0.45

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Eksempel: Matching Data Using VE-model Reproducing seismic data using VE-simulator

Seismiske data (2006) / 3D simulering (tough2)

Chadwick, Noy, Arts & Eiken: Latest time-lapse seismic data from Sleipner yield new insights into CO2 -plume development, Energy Procedia (2009), 2103–2110.

VE simulering

Impact of Geological Uncertainty Lobosity (depositional curve)

Geological parameters:

Barriers (thin clay layers)

Progradation

Lobosity – flat, one-lobe, two-lobe Barriers – small, average, high Aggradation – small, average, high Progradation – up and down Faults – Open or closed

Aggradation Faults (sealing/nonsealing)

Impact of Geological Uncertainty

Preliminary conclusions: Viscous forces dominate over gravity segregation during this early period. Some features like aggradation, faults and barriers enhance the lateral flow during injection which increases the sweep efficiency. Large variations in the results show the importance of reducing the uncertainty in the geological modelling. Plans: Larger domains/later times will be studied with vertical equilibrium methods.

Summary

Both capillary- and dissolution trapping control the long-term fate of CO2 plumes. Dissolution trapping is controlled by convective mixing. Linear stability analysis shows that convective mixing is affected by the capillary transition zone. Vertical Equilibrium models may be very efficient and capture the migration of the CO2 -plume better than traditional 3D reservoir-models. Geological patterns have a large impact on the trapping of CO2 . Different barriers enhance lateral flow which increases the sweep efficiency and thereby e.g. the capillary trapping.

Thank You!