1. Effects of Pore-Scale Chemical Heterogeneities on Continuum- Scale Rates of Anorthite and Kaolinite Reactions Li Li, Catherine A. Peters, Michael A. Celia EEWR/CEE, Princeton University Nov. 9, GSA 2004 Funding:

2. Motivation  Chemical heterogeneities of porous media exist in a range of length scales.  Reactive transport modeling: - Spatially-averaged properties used at the grid block scale - Geochemical reaction rates calculated from uniform concentrations - Captures the heterogeneities at scales larger than the grid block scale  Previous results: importance of pore-scale chemical heterogeneities in determining continuum-scale reaction rates

3. Motivation Objective Purpose : identify the conditions under which pore-scale chemical heterogeneities are important  Reactive minerals: anorthite and kaolinite  Non-reactive mineral: sandstone  Spatial distribution This presentation: what are effects of the reactive cluster size on the continuum-scale reaction rates?

4. Kinetic Reactions and Rate Laws Anorthite reaction: Kaolinite reaction:

5. Pore-scale network modeling Pore-scale network :  Captures the characteristics of porous media at the continuum scale  Incorporates details at the pore scale  Spatial distribution of reactive minerals  Network : Reactive minerals: 12.5%  Reactive cluster size: 1  1  1, 2  2  2, …, 10  10  10

6. Reactive Transport Equations at the Pore Scale  Reactions: anorthite and kaolinite dissolution/ppt (kinetic), aqueous reactions (instantaneous)  Species (14): Ca 2+, H +, OH -, H 2 CO 3 *, HCO 3 -, CO 3 2-, H 4 SiO 4, H 3 SiO 4 -, H 2 SiO 4 2-, Al 3+, AlOH 2+, Al(OH) 2 +, Al(OH) 3, Al(OH) 4 -  Mass balance equations for Ca 2+, C T, H T, Al T, Si T:  Output : Concentrations of each species in each pore at each time step

7. The continuum-scale reaction rates R C :The continuum model - Maintains the same continuum-scale properties - Ignores details at the pore scale The comparison provides insights into the effects of pore-scale heterogeneities. R N : T he network model: (”true” reaction rate)

8. Simulation Conditions Relevant to CO 2 sequestration: High T, P, salinity  Initial: brine in equilibrium with reactive minerals, pH 7.5  Boundary conditions: brine in equilibrium with P CO2 = 100 atm, pH 2.9

9. Dynamics of Reactive Transport Processes

10. Concentration Fields and Distributions log[Ca 2+ ] pH 111111 444444 10  10  10 log[Ca 2+ ] pH

11. Concentration Distributions in Reactive Pores 111111 444444 10  10  10 log[Ca 2+ ] pH

12. Distributions of Pore-Scale Reaction Rates Anorthite Kaolinite RNRN RCRC 111111 444444 10  10  10

13. Difference Between Continuum-Scale Rates as a Function of Reactive Cluster Size AA KK

14. Conclusions  Reactive cluster size affects the distributions of concentrations and reaction rates. Large cluster size: skewed distributions, smaller r A, larger r K  Effects of reactive cluster size on continuum-scale rates are significant. Large cluster size: smaller anorthite dissolution rates, larger kaolinite ppt rates.  The continuum model can not capture the spatial variability at the pore scale. Single rate; overestimation of anorthite dissolution rate, underestimation of kaolinite ppt rate  The error associated with the rates from the continuum model increases with reactive cluster size.