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Mineral dissolution and wormholing from a pore-scale perspective

  • Cyprien Soulaine (a1), Sophie Roman (a1), Anthony Kovscek (a1) and Hamdi A. Tchelepi (a1)

Abstract

A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy–Brinkman–Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian–Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.

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Corresponding author

Email address for correspondence: csoulain@stanford.edu

References

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Algive, L., Bekri, S. & Vizika, O. 2010 Pore-network modeling dedicated to the determination of the petrophysical-property changes in the presence of reactive fluid. SPE J. 15 (03), 618633.
Angot, P., Bruneau, C.-H. & Fabrie, P. 1999 A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81 (4), 497520.
Békri, S., Thovert, J. F. & Adler, P. M. 1995 Dissolution of porous media. Chem. Engng Sci. 50 (17), 27652791.
Bousquet-Melou, P., Goyeau, B., Quintard, M., Fichot, F. & Gobin, D. 2002 Average momentum equation for interdendritic flow in a solidifying columnar mushy zone. Intl J. Heat Mass Transfer 45 (17), 36513665.
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 2734.
Chen, L., Kang, Q., Viswanathan, H. S. & Tao, W.-Q. 2014 Pore-scale study of dissolution-induced changes in hydrologic properties of rocks with binary minerals. Water Resour. Res. 50 (12), 93439365.
Cohen, C. E., Ding, D., Quintard, M. & Bazin, B. 2008 From pore scale to wellbore scale: impact of geometry on wormhole growth in carbonate acidization. Chem. Engng Sci. 63 (12), 30883099.
Cohen, Y. & Rothman, D. H. 2015 Mechanisms for mechanical trapping of geologically sequestered carbon dioxide. Proc. R. Soc. Lond. A 471, 20140853.
Daccord, G. & Lenormand, R. 1987 Fractal patterns from chemical dissolution. Nature 325 (6099), 4143.
Daccord, G., Lietard, O. & Lenormand, R. 1993 Chemical dissolution of a porous medium by a reactive fluid – ii. Convection versus reaction, behavior diagram. Chem. Engng Sci. 48 (1), 179186.
Davarzani, H., Marcoux, M. & Quintard, M. 2010 Theoretical predictions of the effective thermodiffusion coefficients in porous media. Intl J. Heat Mass Transfer 53 (7), 15141528.
Edwards, D. A., Shapiro, M. & Brenner, H. 1993 Dispersion and reaction in two-dimensional model porous media. Phys. Fluids A 5 (4), 837848.
Emmanuel, S. & Berkowitz, B. 2005 Mixing-induced precipitation and porosity evolution in porous media. Adv. Water Resour. 28 (4), 337344.
Fredd, C. N. & Fogler, H. S. 1998a Alternative stimulation fluids and their impact on carbonate acidizing. SPE J. 13 (1), 3441.
Fredd, C. N. & Fogler, H. S. 1998b Influence of transport and reaction on wormhole formation in porous media. AIChE J. 44 (9), 19331949.
Golfier, F., Zarcone, C., Bazin, B., Lenormand, R., Lasseux, D. & Quintard, M. 2002 On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium. J. Fluid Mech. 457, 213254.
Guo, J., Laouafa, F. & Quintard, M. 2016a A theoretical and numerical framework for modeling gypsum cavity dissolution. Int. J. Numer. Anal. Meth. Geomech. 40, 16621689.
Guo, J., Quintard, M. & Laouafa, F. 2015 Dispersion in porous media with heterogeneous nonlinear reactions. Trans. Porous Med. 109 (3), 541570.
Guo, J., Veran-Tissoires, S. & Quintard, M. 2016b Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions. J. Comput. Phys. 305, 942963.
Hsu, C. T. & Cheng, P. 1990 Thermal dispersion in a porous medium. Intl J. Heat Mass Transfer 33 (8), 15871597.
Huang, H. & Li, X. 2011 Pore-scale simulation of coupled reactive transport and dissolution in fractures and porous media using the level set interface tracking method. J. Nanjing University (Natural Sciences) 47 (3), 235251.
Huber, C., Shafei, B. & Parmigiani, A. 2014 A new pore-scale model for linear and non-linear heterogeneous dissolution and precipitation. Geochim. Cosmochim. Acta 124 (0), 109130.
Issa, R. I. 1985 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62, 4065.
Kalia, N. & Balakotaiah, V. 2007 Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks. Chem. Engng Sci. 62, 919928.
Kang, Q., Chen, L., Valocchi, A. J. & Viswanathan, H. S. 2014 Pore-scale study of dissolution-induced changes in permeability and porosity of porous media. J. Hydrol. 517, 10491055.
Kang, Q., Zhang, D. & Chen, S. 2003 Simulation of dissolution and precipitation in porous media. J. Geophys. Res. 108 (B10), 15.
Khadra, K., Angot, P., Parneix, S. & Caltagirone, J.-P. 2000 Fictitious domain approach for numerical modelling of Navier–Stokes equations. Intl J. Numer. Meth. Fluids 34 (8), 651684.
Kim, D., Peters, C. A. & Lindquist, W. B. 2011 Upscaling geochemical reaction rates accompanying acidic CO2 -saturated brine flow in sandstone aquifers. Water Resour. Res. 47 (1), W01505.
Landrot, G., Ajo-Franklin, J. B., Yang, L., Cabrini, S. & Steefel, C. I. 2012 Measurement of accessible reactive surface area in a sandstone, with application to CO2 mineralization. Chem. Geol. 318, 113125.
Li, L., Peters, C. A. & Celia, M. A. 2006 Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Resour. 29 (9), 13511370.
Li, X., Huang, H. & Meakin, P. 2010 A three-dimensional level set simulation of coupled reactive transport and precipitation/dissolution. Intl J. Heat Mass Transfer 53 (13), 29082923.
Lichtner, P. C. 1988 The quasi-stationary state approximation to coupled mass transport and fluid–rock interaction in a porous medium. Geochim. Cosmochim. Acta 52 (1), 143165.
Liu, X., Ormond, A., Bartko, K., Ying, L. & Ortoleva, P. 1997 A geochemical reaction-transport simulator for matrix acidizing analysis and design. J. Petrol. Sci. Engng 17 (1), 181196.
Liu, X. & Ortoleva, P. 1996 A general-purpose, geochemical reservoir simulator. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
Luo, H., Laouafa, F., Debenest, G. & Quintard, M. 2015 Large scale cavity dissolution: from the physical problem to its numerical solution. Eur. J. Mech. (B/Fluids) 52, 131146.
Luo, H., Laouafa, F., Guo, J. & Quintard, M. 2014 Numerical modeling of three-phase dissolution of underground cavities using a diffuse interface model. Intl J. Numer. Anal. Meth. Geomech. 38, 16001616.
Luo, H., Quintard, M., Debenest, G. & Laouafa, F. 2012 Properties of a diffuse interface model based on a porous medium theory for solid–liquid dissolution problems. Comput. Geosci. 16 (4), 913932.
Mauri, R. 1991 Dispersion, convection, and reaction in porous media. Phys. Fluids A 3 (5), 743756.
Molins, S., Trebotich, D., Yang, L., Ajo-Franklin, J. B., Ligocki, T. J., Shen, C. & Steefel, C. I. 2014 Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments. Environ. Sci. Technol. 48 (13), 74537460.
Neale, G. & Nader, W. 1974 Practical significance of Brinkman’s extension of Darcy’s law: coupled parallel flows within a channel and a bounding porous medium. Can. J. Chem. Engng 52 (4), 475478.
Noiriel, C., Luquot, L., Madé, B., Raimbault, L., Gouze, P. & van der Lee, J. 2009 Changes in reactive surface area during limestone dissolution: an experimental and modelling study. Chem. Geol. 265 (1–2), 160170; CO $_{2}$ geological storage: integrating geochemical, hydrodynamical, mechanical and biological processes from the pore to the reservoir scale.
Noiriel, C., Madé, B. & Gouze, P. 2007 Impact of coating development on the hydraulic and transport properties in argillaceous limestone fracture. Water Resour. Res. 43 (9), 116.
Oltéan, C., Golfier, F. & Buès, M. A. 2013 Numerical and experimental investigation of buoyancy-driven dissolution in vertical fracture. J. Geophys. Res. 118 (5), 20382048.
Ormond, A. & Ortoleva, P. 2000 Numerical modeling of reaction-induced cavities in a porous rock. J. Geophys. Res. 105 (B7), 1673716747.
Panga, M. K. R., Ziauddin, M. & Balakotaiah, V. 2005 Two-scale continuum model for simulation of wormholes in carbonate acidization. AIChE J. 51 (12), 32313248.
Rathnaweera, T. D., Ranjith, P. G. & Perera, M. S. A. 2016 Experimental investigation of geochemical and mineralogical effects of CO2 sequestration on flow characteristics of reservoir rock in deep saline aquifers. Sci. Rep. 6, 19362.
Roman, S., Soulaine, C., Abu AlSaud, M., Kovscek, A. & Tchelepi, H. 2016 Particle velocimetry analysis of immiscible two-phase flow in micromodels. Adv. Water Resour. 95, 199211.
Scheibe, T. D., Perkins, W. A., Richmond, M. C., McKinley, M. I., Romero-Gomez, P. D. J., Oostrom, M., Wietsma, T. W., Serkowski, J. A. & Zachara, J. M. 2015 Pore-scale and multiscale numerical simulation of flow and transport in a laboratory-scale column. Water Resour. Res. 51 (2), 10231035.
Shapiro, M. & Brenner, H. 1988 Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium. Chem. Engng Sci. 43 (3), 551571.
Song, W., de Haas, T. W., Fadaei, H. & Sinton, D. 2014 Chip-off-the-old-rock: the study of reservoir-relevant geological processes with real-rock micromodels. Lab on a Chip 14, 43824390.
Soulaine, C., Gjetvaj, F., Garing, C., Roman, S., Russian, A., Gouze, P. & Tchelepi, H. 2016 The impact of sub-resolution porosity of x-ray microtomography images on the permeability. Trans. Porous Med. 113 (1), 227243.
Soulaine, C., Quintard, M., Allain, H., Baudouy, B. & Weelderen, R. V. 2015 A piso-like algorithm to simulate superfluid helium flow with the two-fluid model. Comput. Phys. Commun. 187 (0), 2028.
Soulaine, C. & Tchelepi, H. A. 2016a Micro-continuum approach for pore-scale simulation of subsurface processes. Trans. Porous Med. 113, 431456.
Soulaine, C. & Tchelepi, H. A. 2016b Micro-continuum formulation for modelling dissolution in natural porous media. In ECMOR XV – 15th European Conference on the Mathematics of Oil Recovery 29 August–1 September 2016, Amsterdam, Netherlands, pp. 111. EAGE.
Starchenko, V., Marra, C. J. & Ladd, A. J. C. 2016 Three-dimensional simulations of fracture dissolution. J. Geophys. Res. Solid Earth 121, 64216444.
Steefel, C. I., Molins, S. & Trebotich, D. 2013 Pore scale processes associated with subsurface CO2 injection and sequestration. Rev. Mineralogy Geochem. 77 (1), 259303.
Swoboda-Colberg, N. G. & Drever, J. I. 1993 Mineral dissolution rates in plot-scale field and laboratory experiments. Chem. Geol. 105 (1–3), 5169.
Szymczak, P. & Ladd, A. J. C. 2004 Microscopic simulations of fracture dissolution. Geophys. Res. Lett. 31 (23), 14.
Szymczak, P. & Ladd, A. J. C. 2009 Wormhole formation in dissolving fractures. J. Geophys. Res. 114 (B6), 122.
Trebotich, D. & Graves, D. 2015 An adaptive finite volume method for the incompressible Navier–Stokes equations in complex geometries. Commun. Appl. Math. Comput. Sci. 10 (1), 4382.
Vafai, K. & Tien, C. L. 1981 Boundary and inertia effects on flow and heat transfer in porous media. Intl J. Heat Mass Transfer 24 (2), 195203.
Vafai, K. & Tien, C. L. 1982 Boundary and inertia effects on convective mass transfer in porous media. Intl J. Heat Mass Transfer 25 (8), 11831190.
Varloteaux, C., Békri, S. & Adler, P. M. 2013a Pore network modelling to determine the transport properties in presence of a reactive fluid: from pore to reservoir scale. Adv. Water Resour. 53, 87100.
Varloteaux, C., Vu, M. T., Békri, S. & Adler, P. M. 2013b Reactive transport in porous media: pore-network model approach compared to pore-scale model. Phys. Rev. E 87 (2), 023010.
Wakao, N. & Smith, J. M. 1962 Diffusion in catalyst pellets. Chem. Engng Sci. 17 (11), 825834.
Whitaker, S. 1999 The Method of Volume Averaging. Kluwer Academic.
Williams, B. B., Gidley, J. L. & Schechter, R. S. 1979 Acidizing Fundamentals.; Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME.
Xu, Z., Huang, H., Li, X. & Meakin, P. 2012 Phase field and level set methods for modeling solute precipitation and/or dissolution. Comput. Phys. Commun. 183 (1), 1519.
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