Transport in Porous Media

, Volume 89, Issue 3, pp 459–473 | Cite as

Dependence of Pore-to-Core Up-scaled Reaction Rate on Flow Rate in Porous Media

  • D. Kim
  • W. B. LindquistEmail author


Due to inherent heterogeneities in structure, mineral placement and fluid velocity in rock, bulk reaction rates realized during reactive flow through porous media may differ significantly from that predicted by laboratory-measured rate laws. In particular, rate laws determined in batch reactor experiments do not capture any of the flow dependence that will be experienced in the porous medium. Based on network flow model simulations of anorthite and kaolinite reactions in two sandstone pore networks under acidic conditions commensurate with CO2 sequestration, we compute up-scaled reaction rates at the core scale and investigate the dependence of the observed reaction rates on flow rate. For the anorthite reaction which, under these acidic conditions is far from equilibrium and dominated by pH, we find a power law dependence of reaction rate on flow rate. For the kaolinite reaction, which is near equilibrium, a more complex dependence emerges, with the up-scaled rate tending to rapidly increasing net precipitation at low-flow rates, then reversing and tending toward net dissolution at high-flow rates.


Up-scaling Reactive flow CO2 sequestration Network flow models Porous media 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amrhein C., Suarez D.L.: The use of a surface complexation model to describe the kinetics of ligand-promoted dissolution of anorthite. Geochim. Cosmochim. Acta 52(12), 2785–2793 (1988)CrossRefGoogle Scholar
  2. Benjamin M.M.: Water Chemistry. McGraw-Hill Series in Water Resources and Environmental Engineering. McGraw-Hill, New York (2002)Google Scholar
  3. Brady P.V., Walther J.V.: Controls on silicate dissolution rate in neutral and basic pH solutions at 25°C. Geochim. Cosmochim. Acta 53(11), 2823–2830 (1989)CrossRefGoogle Scholar
  4. Carroll S.A., Walther J.V.: Kaoliniate dissolution at 25°C, 60°C, and 80°C. Am. J. Sci. 290(7), 797–810 (1990)CrossRefGoogle Scholar
  5. Ganor J., Mogollon J.L., Lasaga A.C.: The effect of pH on kaolinite dissolution rates and on activation-energy. Geochim. Cosmochim. Acta 59(6), 1037–1052 (1995)CrossRefGoogle Scholar
  6. Helgeson H.C., Murphy W.M., Aagaard P.: Thermodynamics and kinetic constraints on reaction-rates among minerals and aqueous-solutions. 2. Rate constants, effective surface-area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta 48(12), 2405–2432 (1984)CrossRefGoogle Scholar
  7. Johnson J.W., Oelkers E.H., Helgeson H.C.: SUPCRT92: a software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000°C. Comput. Geosci. 18(7), 899–947 (1992)CrossRefGoogle Scholar
  8. Kim D.: Scale-up of Reactive Flow Through Network Flow Modeling. Stony Brook University, Stony Brook, NY (2008)Google Scholar
  9. Kim, D., Peters, C.A., Lindquist, W.B.: Up-scaling geochemical reaction rates accompanying acidic CO2- saturated brine flow in sandstone aquifers. Water Resour. Res. 47(1), WO1505 (2011)Google Scholar
  10. Li L., Peters C.A., Celia M.A.: Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Resour. 29(9), 1357–1370 (2006)CrossRefGoogle Scholar
  11. Li L., Peters C.A., Celia M.A.: Effects of mineral spatial distribution on reaction rates in porous media. Water Resour. Res. 43(1), W01419 (2007a)CrossRefGoogle Scholar
  12. Li L., Peters C.A., Celia M.A.: Applicability of averaged concentrations in determining geochemical reaction rates in heterogeneous porous media. Am. J. Sci. 307(10), 1146–1166 (2007b)CrossRefGoogle Scholar
  13. Lichtner P.C.: Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochim. Cosmochim. Acta 49(3), 779–800 (1985)CrossRefGoogle Scholar
  14. Lichtner P.C.: Continuum formulation of multicomponent-multiphase reactive transport. In: Lichtner, P.C., Steefel, C.I., Oelkers , E.H. (eds) Reviews in Mineralogy, vol. 34, pp. 1–81. Mineralogical Society of America, Washington, DC (1996)Google Scholar
  15. Lindquist W.B., Venkatarangan A., Dunsmuir J., Wong T.-f.: Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones. J. Geophys. Res. 105(B9), 21508–21528 (2000)CrossRefGoogle Scholar
  16. Lorensen W.E., Cline H.E.: Marching cubes: a high resolution 3-D surface construction. ACM Comput. Graph. 21(4), 163–169 (1987)CrossRefGoogle Scholar
  17. Morel F., Hering J.G.: Principles and Applications of Aquatic Chemistry. Wiley, New York (1993)Google Scholar
  18. Nagy K.L., Lasaga A.C.: Simultaneous precipitation kinetics of kaolinite and gibbsite at 80°C and pH 3. Geochim. Cosmochim. Acta 57(17), 4329–4335 (1993)CrossRefGoogle Scholar
  19. Nagy K.L., Blum A.E., Lasaga A.C.: Dissolution and precipitation of kaolinite at 80°C and pH 3—the dependence on solution saturation state. Am. J. Sci. 291(7), 649–686 (1991)CrossRefGoogle Scholar
  20. Oelkers E.H., Schott J.: Experimental study of anorthite dissolution and the relative mechanism of feldspar hydrolysis. Geochim. Cosmochim. Acta 59(24), 5039–5053 (1995)CrossRefGoogle Scholar
  21. Oh W., Lindquist W.B.: Image thresholding by indicator kriging. IEEE Trans. Pattern Anal. Mach. Intell. 21(7), 590–602 (1999)CrossRefGoogle Scholar
  22. Patzek T.W.: Verification of a complete pore network simulator of drainage and imbibition. SPE J. 6(2), 144–156 (2001)Google Scholar
  23. Peters C.A.: Accessibilities of reactive minerals in consolidated sedimentary rock: an imaging study of three sandstones. Chem. Geol. 265(1-2), 198–208 (2009)CrossRefGoogle Scholar
  24. Quinn M.J.: Parallel Programming in C with MPI and OPENMP. McGraw-Hill, New York (2003)Google Scholar
  25. Shin H., Lindquist W.B., Sahagian D.L., Song S.R.: Analysis of the vesicular structure of basalts. Comput. Geosci. 31(4), 473–487 (2005)CrossRefGoogle Scholar
  26. Sholokova Y., Kim D., Lindquist W.B.: Network flow modeling via lattice-Boltzmann based channel conductance. Adv. Water Resour. 32(2), 205–212 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA

Personalised recommendations