Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-02-05T15:37:03.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Pore-scale modelling of multiphase reactive flow: application to mineral dissolution with production of $\text{CO}_{2}$

Published online by Cambridge University Press:  19 September 2018

Cyprien Soulaine Open the ORCID record for Cyprien Soulaine [Opens in a new window] ,
Sophie Roman ,
Anthony Kovscek  and
Hamdi A. Tchelepi
Cyprien Soulaine*
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 95305, USA
Sophie Roman
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 95305, USA Institut des Sciences de la Terre d’Orléans, UMR 7327, Université d’Orléans-CNRS-BRGM, 45071 Orléans CEDEX, France
Anthony Kovscek
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 95305, USA
Hamdi A. Tchelepi
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford, CA 95305, USA
*
†Email address for correspondence: csoulain@stanford.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale in the presence of multiple fluid phases. The approach employs an extended Darcy–Brinkman–Stokes formulation that accounts for the interfacial tension between the two immiscible fluid phases and the moving contact line at the mineral surface. The simulation framework is validated using an experimental microfluidic device that provides time-lapse images of the dissolution dynamics. The set-up involves a single-calcite crystal and the subsequent generation of $\text{CO}_{2}$ bubbles in the domain. The dissolution of the calcite crystal and the production of gas during the acidizing process are analysed. We then show that the production of $\text{CO}_{2}$ bubbles during the injection of acid in a carbonate formation may limit the overall dissolution rate and prevent the emergence of wormholes.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Low-Reynolds-number flows: Porous media Multiphase and Particle-laden Flows: Reacting multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 616 - 645
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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), 618–633.Google Scholar
Angot, P., Bruneau, C.-H. & Fabrie, P. 1999 A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81 (4), 497–520.Google Scholar
Bastami, A., Allahgholi, M. & Pourafshary, P. 2014 Experimental and modelling study of the solubility of CO2 in various CACL2 solutions at different temperatures and pressures. Petrol. Sci. 11 (4), 569–577.Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354.Google Scholar
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, 27–34.Google Scholar
Buchgraber, M., Al-Dossary, M., Ross, C. M. & Kovscek, A. R. 2012 Creation of a dual-porosity micromodel for pore-level visualization of multiphase flow. J. Petrol. Sci. Engng 86 (0), 27–38.Google Scholar
Békri, S., Thovert, J. F. & Adler, P. M. 1995 Dissolution of porous media. Chem. Engng Sci. 50 (17), 2765–2791.Google Scholar
Chen, L., Kang, Q., Mu, Y., He, Y.-L. & Tao, W.-Q. 2014a A critical review of the pseudopotential multiphase lattice Boltzmann model: methods and applications. Intl J. Heat Mass Transfer 76, 210–236.Google Scholar
Chen, L., Kang, Q., Robinson, B. A., He, Y.-L. & Tao, W.-Q. 2013 Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems. Phys. Rev. E 87, 043306.Google Scholar
Chen, L., Kang, Q., Tang, Q., Robinson, B. A., He, Y.-L. & Tao, W.-Q. 2015 Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation. Intl J. Heat Mass Transfer 85, 935–949.Google Scholar
Chen, L., Kang, Q., Viswanathan, H. S. & Tao, W.-Q. 2014b Pore-scale study of dissolution-induced changes in hydrologic properties of rocks with binary minerals. Water Resour. Res. 50 (12), 9343–9365.Google Scholar
Cohen, Y. & Rothman, D. H. 2015 Mechanisms for mechanical trapping of geologically sequestered carbon dioxide. Proc. R. Soc. Lond. A 471, 20140853.Google Scholar
Daccord, G. 1987 Chemical dissolution of a porous medium by a reactive fluid. Phys. Rev. Lett. 58 (5), 479–482.Google Scholar
Daccord, G. & Lenormand, R. 1987 Fractal patterns from chemical dissolution. Nature 325 (6099), 41–43.Google Scholar
Daccord, G., Lietard, O. & Lenormand, R. 1993 Chemical dissolution of a porous medium by a reactive fluid. II. Convection vs reaction, behavior diagram. Chem. Engng Sci. 48 (1), 179–186.Google Scholar
Damian, S. M.2013 An extended mixture model for the simultaneous treatment of short and long scale interfaces. PhD thesis, Facultad de Ingeniería y Ciencias Hídricas, Universidad Nacional del Litoral.Google Scholar
Deising, D., Marschall, H. & Bothe, D. 2016 A unified single-field model framework for volume-of-fluid simulations of interfacial species transfer applied to bubbly flows. Chem. Engng Sci. 139, 173–195.Google Scholar
Eddings, M. A., Johnson, M. A. & Gale, B. K. 2008 Determining the optimal PDMS–PDMS bonding technique for microfluidic devices. J. Micromech. Microengng 18, 067001–067004.Google Scholar
Fredd, C. N. & Fogler, H. S. 1998a Alternative stimulation fluids and their impact on carbonate acidizing. SPE J. 13 (1), 34–41.Google Scholar
Fredd, C. N. & Fogler, H. S. 1998b Influence of transport and reaction on wormhole formation in porous media. AIChE J. 44 (9), 1933–1949.Google Scholar
Garing, C., Gouze, P., Kassab, M., Riva, M. & Guadagnini, A. 2015 Anti-correlated porosity–permeability changes during the dissolution of carbonate rocks: experimental evidences and modeling. Trans. Porous Med. 107 (2), 595–621.Google Scholar
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, 213–254.Google Scholar
Graveleau, M., Soulaine, C. & Tchelepi, H. A. 2017 Pore-scale simulation of interphase multicomponent mass transfer for subsurface flow. Trans. Porous Med. 120 (2), 287–308.Google Scholar
Guibert, R., Nazarova, M., Horgue, P., Hamon, G., Creux, P. & Debenest, G. 2015 Computational permeability determination from pore-scale imaging: sample size, mesh and method sensitivities. Trans. Porous Med. 107 (3), 641–656.Google Scholar
Guo, D. Z., Sun, D. L., Li, Z. Y. & Tao, W. Q. 2011 Phase change heat transfer simulation for boiling bubbles arising from a vapor film by the VOSET method. Numer. Heat Transfer A 59 (11), 857–881.Google Scholar
Guo, J., Laouafa, F. & Quintard, M. 2016 A theoretical and numerical framework for modeling gypsum cavity dissolution. Intl J. Numer. Anal. Meth. Geomech. 40, 1662–1689.Google Scholar
Guo, J., Quintard, M. & Laouafa, F. 2015 Dispersion in porous media with heterogeneous nonlinear reactions. Trans. Porous Med. 109 (3), 541–570.Google Scholar
Haroun, Y., Legendre, D. & Raynal, L. 2010 Volume of fluid method for interfacial reactive mass transfer: application to stable liquid film. Chem. Engng Sci. 65 (10), 2896–2909.Google Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225.Google Scholar
Horgue, P., Prat, M. & Quintard, M. 2014 A penalization technique applied to the volume-of-fluid method: wettability condition on immersed boundaries. Comput. Fluids 100, 255–266.Google Scholar
Horgue, P., Soulaine, C., Franc, J., Guibert, R. & Debenest, G. 2015 An open-source toolbox for multiphase flow in porous media. Comput. Phys. Commun. 187 (0), 217–226.Google Scholar
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 Univ. (Natural Sciences) 47 (3), 235–251.Google Scholar
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), 109–130.Google Scholar
Issa, R. I. 1985 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62, 40–65.Google Scholar
Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine.Google Scholar
Juric, Damir & Tryggvason, Grétar 1998 Computations of boiling flows. Intl J. Multiphase Flow 24 (3), 387–410.Google Scholar
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, 1049–1055.Google Scholar
Kang, Q., Zhang, D. & Chen, S. 2003 Simulation of dissolution and precipitation in porous media. J. Geophys. Res. 108 (B10), 1–5.Google Scholar
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), 651–684.Google Scholar
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.Google Scholar
Li, L., Peters, C. A. & Celia, M. A. 2006 Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Resour. 29 (9), 1351–1370.Google Scholar
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), 2908–2923.Google Scholar
Lichtner, P. C. & Kang, Q. 2007 Upscaling pore-scale reactive transport equations using a multiscale continuum formulation. Water Resour. Res. 43 (12), W12S15.Google Scholar
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), 181–196.Google Scholar
Liu, X. & Ortoleva, P. 1996 A general-purpose, geochemical reservoir simulator. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.Google Scholar
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, 131–146.Google Scholar
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. 38, 1600–1616.Google Scholar
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), 913–932.Google Scholar
Maes, J. & Geiger, S. 2017 Direct pore-scale reactive transport modelling of dynamic wettability changes induced by surface complexation. Adv. Water Resour. 111, 6–19.Google Scholar
Maes, J. & Soulaine, C. 2018 A new compressive scheme to simulate species transfer across fluid interfaces using the volume-of-fluid method. Chem. Engng Sci. 190, 405–418.Google Scholar
Marschall, H., Hinterberger, K., Schüler, C., Habla, F. & Hinrichsen, O. 2012 Numerical simulation of species transfer across fluid interfaces in free-surface flows using OpenFOAM. Chem. Engng Sci. 78, 111–127.Google Scholar
Mauri, R. 1991 Dispersion, convection, and reaction in porous media. Phys. Fluids A 3 (5), 743–756.Google Scholar
McDonald, J. C., Duffy, D. C., Anderson, J. R., Chiu, D. T., Wu, H. K., Schueller, O. J. A. & Whitesides, G. M. 2000 Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21 (1), 27–40.Google Scholar
Molins, S., Trebotich, D., Miller, G. H. & Steefel, C. I. 2017 Mineralogical and transport controls on the evolution of porous media texture using direct numerical simulation. Water Resour. Res. 53 (5), 3645–3661.Google Scholar
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), 475–478.Google Scholar
Nogues, J. P., Fitts, J. P., Celia, M. A. & Peters, C. A. 2013 Permeability evolution due to dissolution and precipitation of carbonates using reactive transport modeling in pore networks. Water Resour. Res. 49 (9), 6006–6021.Google Scholar
Oltéan, C., Golfier, F. & Buès, M. A. 2013 Numerical and experimental investigation of buoyancy-driven dissolution in vertical fracture. J. Geophys. Res. 118 (5), 2038–2048.Google Scholar
Orgogozo, L., Renon, N., Soulaine, C., Hénon, F., Tomer, S. K., Labat, D., Pokrovsky, O. S., Sekhar, M., Ababou, R. & Quintard, M. 2014 An open source massively parallel solver for Richards equation: mechanistic modelling of water fluxes at the watershed scale. Comput. Phys. Commun. 185 (12), 3358–3371.Google Scholar
Ormond, A. & Ortoleva, P. 2000 Numerical modeling of reaction-induced cavities in a porous rock. J. Geophys. Res. 105 (B7), 16737–16747.Google Scholar
Ott, H. & Oedai, S. 2015 Wormhole formation and compact dissolution in single-and two-phase CO2 -brine injections. Geophys. Res. Lett. 42 (7), 2270–2276.Google Scholar
Parmigiani, A., Huber, C., Bachmann, O. & Chopard, B. 2011 Pore-scale mass and reactant transport in multiphase porous media flows. J. Fluid Mech. 686, 40.Google Scholar
Portier, S., Vuataz, F.-D., Nami, P., Sanjuan, B. & Gérard, A. 2009 Chemical stimulation techniques for geothermal wells: experiments on the three-well egs system at Soultz-sous-Forêts, France. Geothermics 38 (4), 349–359.Google Scholar
Prutton, C. F. & Savage, R. L. 1945 The solubility of carbon dioxide in calcium chloride-water solutions at 75, 100, 120 and high pressures. J. Am. Chem. Soc. 67 (9), 1550–1554.Google Scholar
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.Google Scholar
Roman, S., Abu-Al-Saud, M. O., Tokunaga, T., Wan, J., Kovscek, A. R. & Tchelepi, H. A. 2017 Measurements and simulation of liquid films during drainage displacements and snap-off in constricted capillary tubes. J. Colloid Interface Sci. 507, 279–289.Google Scholar
Roman, S., Lorthois, S., Duru, P. & Risso, F. 2012 Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients. Microvasc. Res. 84 (3), 249–261.Google Scholar
Roman, S., Soulaine, C., AlSaud, M. A., Kovscek, A. & Tchelepi, H. 2016 Particle velocimetry analysis of immiscible two-phase flow in micromodels. Adv. Water Resour. 95, 199–211.Google Scholar
Rudman, M. 1997 Volume-tracking methods for interfacial flow calculations. Intl J. Numer. Meth. Fluids 24 (7), 671–691.Google Scholar
Rusche, H.2003 Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial College London (University of London).Google Scholar
Scheibe, T. D., Perkins, W. A., Richmond, M. C., McKinley, M. I., Romero-Gomez, P. D. J., Oostrom, Mart, 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), 1023–1035.Google Scholar
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), 551–571.Google Scholar
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, 4382–4390.Google Scholar
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), 227–243.Google Scholar
Soulaine, C., Roman, S., Kovscek, A. & Tchelepi, H. A. 2017 Mineral dissolution and wormholing from a pore-scale perspective. J. Fluid Mech. 827, 457–483.Google Scholar
Soulaine, C. & Tchelepi, H. A. 2016a Micro-continuum approach for pore-scale simulation of subsurface processes. Trans. Porous Med. 113, 431–456.Google Scholar
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. 1–11. EAGE.Google Scholar
Starchenko, V., Marra, C. J. & Ladd, A. J. C. 2016 Three-dimensional simulations of fracture dissolution. J. Geophys. Res. 121, 6421–6444.Google Scholar
Steefel, C. I., Molins, S. & Trebotich, D. 2013 Pore scale processes associated with subsurface CO2 injection and sequestration. Rev. Mineral. Geochem. 77 (1), 259–303.Google Scholar
Swoboda-Colberg, N. G. & Drever, J. I. 1993 Mineral dissolution rates in plot-scale field and laboratory experiments. Chem. Geol. 105 (1–3), 51–69.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2004 Microscopic simulations of fracture dissolution. Geophys. Res. Lett. 31 (23), 1–4.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2009 Wormhole formation in dissolving fractures. J. Geophys. Res. 114 (B6), 1–22.Google Scholar
Tartakovsky, A. M., Meakin, P., Scheibe, T. D. & West, R. M. E. 2007 Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. J. Comput. Phys. 222 (2), 654–672.Google Scholar
Thompson, K. E. & Gdanski, R. D. 1993 Laboratory study provides guidelines for diverting acid with foam. SPE Prod. Facilities 8 (04), 285–290.Google Scholar
Trebotich, D. & Graves, D. 2015 An adaptive finite volume method for the incompressible Navier–Stokes equations in complex geometries. Commun. Appl. Maths Comput. Sci. 10 (1), 43–82.Google Scholar
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, 87–100.Google Scholar
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.Google Scholar
Voller, V. R. 2009 Numerical Methods for Phase-Change Problems, pp. 593–622. Wiley.Google Scholar
Wang, C.-Y. & Beckermann, C. 1993 A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media. I. Formulation. Intl J. Heat Mass Transfer 36, 2747–2747.Google Scholar
Welch, S. W. J. & Wilson, J. 2000 A volume of fluid based method for fluid flows with phase change. J. Comput. Phys. 160 (2), 662–682.Google Scholar
Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys. 12 (6), 620–631.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging, Theory and Applications of Transport in Porous Media. Kluwer Academic.Google Scholar
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.Google Scholar
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), 15–19.Google Scholar