Skip to main content
Log in

Large-Scale Model for the Dissolution of Heterogeneous Porous Formations: Theory and Numerical Validation

Transport in Porous Media Aims and scope Submit manuscript


In this paper, we study the dissolution of a porous formation made of soluble and insoluble materials with various types of Darcy-scale heterogeneities. Based on the assumption of scale separations, i.e., the convective and diffusive Damköhler numbers are smaller than certain limits which are documented in the paper, we apply large-scale upscaling to the Darcy-scale model to develop large-scale equations, which are used to describe the dissolution of porous formations with Darcy-scale heterogeneities. History-dependent closure problems are provided to get the effective parameters in the large-scale model. The large-scale model validity is tested by comparing numerical results for a 1D flow problem in a stratified system and a 2D flow problem in a nodular system to the Darcy-scale ones. The good agreement between results at Darcy and large scales shows the robustness of the large-scale model in representing the Darcy-scale results for the stratified system, even when the dissolution front is very sharp. Large-scale results for the nodular system represent satisfactorily the averaged Darcy-scale behaviors when the dissolution front is relatively thick, i.e., when model assumptions are satisfied, while there may be as expected some discrepancy generated between direct numerical simulations and large-scale results in the case of thin dissolution front. Overall, this study demonstrates the possibility of building a fully homogenized large-scale model incorporating dissolution history effects, and that the resulting large-scale model is capable to catch the main features of the Darcy-scale results within its applicability domain.

Article highlights

  • Large-scale model is developed for the dissolution of heterogeneous porous media, taking dissolution history effect into account.

  • A sequential algorithm is proposed for the solution of effective mass exchange coefficient and effective permeability tensor.

  • The large-scale model is validated for stratied and nodular systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


\(\mathbf {b}\) :

Mapping vector, m

\(c_{eq}\) :

Thermodynamic equilibrium concentration of the dissolved solid, \(\mathrm {kg}\,\mathrm {m}^{-3}\)

\(C_{l}\), \(C_{l}^{*}\) :

Darcy- and large-scale intrinsic average concentration of the dissolved solid, respectively, \(\mathrm {kg}\,\mathrm {m}^{-3}\)

\(\tilde{C}_{l}\) :

Large-scale concentration deviation, \(\mathrm {kg}\,\mathrm {m}^{-3}\)

D :

Diameter of the inclusions in the 2D geometry, \(\mathrm {m}\)

\(\mathrm {Da}\), \(\mathrm {Da}_{M}\) :

Micro- and macroscale Damköhler number, respectively, dimensionless

\(D_{r}\) :

Reference diffusion coefficient, \(\mathrm {m}^{2}\,\mathrm {s}^{-1}\)

\(\mathbf {D}_{l}\) :

Darcy-scale dispersion tensor, \(\mathrm {m}^{2}\,\mathrm {s}^{-1}\)

\(\mathbf {g}\) :

Gravitational acceleration, \(\mathrm {m}\,\mathrm {s}^{-2}\)

H :

Height of the 2D unit cell, \(\mathrm {m}\)

\(K_{l}\) :

Permeability, \(\mathrm {m}^{2}\)

\(K_{0}\) :

Permeability constant, \(\mathrm {m}^{2}\)

\(K_{s}\) :

Mass exchange of the dissolving solid, kg \(\mathrm {m}^{-3}\,\mathrm {s}^{-1}\)

\(\mathbf {K}_{l}\), \(\mathbf {K}_{l}^{*}\) :

Darcy- and large-scale permeability tensor, respectively, \(\mathrm {m}^{2}\)

\(\ell _{d}\) :

Thickness of dissolution front, m

\(\ell _{h}\) :

Characteristic length of heterogeneity, m

\(\ell _{i}\), \(\ell _{l}\), \(\ell _{s}\) :

Pore-scale characteristic lengths, m

\(\ell _{\omega }\) , \(\ell _{\eta }\) :

Darcy-scale characteristic length, m

L :

Large-scale characteristic length, m

\(P_{l}\), \(P_{l}^{*}\) :

Darcy- and large-scale intrinsic average pressure, respectively, Pa

\(P_{e}\) :

Pressure at the inlet of the 2D nodular system, Pa

\(\mathrm {Pe}_{M}\) :

Macroscale Péclet number, dimensionless

\(r_{0}\), \(R_{0}\) :

Characteristic length of the REV used to define Darcy- and large-scale variables, respectively, m

\(\mathbf {r}\) :

Position vector, m

S, \(S^{*}\) :

Darcy- and large-scale solid mineral saturation, respectively, dimensionless

\(\widehat{S}\), \(\widehat{S^{*}}\) :

Domain average of S and \(S^{*}\), respectively, dimensionless

\(\tilde{S}\) :

Large-scale soluble solid saturation deviation, dimensionless

t :

time, s

\(U_{r}\) :

Reference velocity, \(\mathrm {m}\,\mathrm {s}^{-1}\)

\(\mathbf {U}_{l}\), \(\mathbf {U}_{l}^{*}\) :

Darcy- and large-scale intrinsic average liquid velocity, respectively, \(\mathrm {m}\,\mathrm {s}^{-1}\)

\(\mathcal {V}\), \(\mathcal {V}_{\infty }\) :

Total volume of REV for the Darcy- and large-scale volume averaging, respectively, \(\mathrm {m}^{3}\)

\(\mathcal {V}_{l}\), \(\mathcal {V}_{i}\), \(\mathcal {V}_{s}\) :

Volume of the liquid phase, the insoluble solid and the soluble solid within an REV, \(\mathrm {m}^{3}\)

\(\mathbf {V}_{l}\),\(\mathbf {V}_{l}^{*}\) :

Darcy- and large-scale superficial average liquid velocity, \(\mathrm {m}\,\mathrm {s}^{-1}\)

\(\alpha\), \(\alpha ^{*}\) :

Darcy- and large-scale mass exchange coefficient, \(\mathrm {s}^{-1}\)

\(\alpha _{0}\), \(\alpha _{0,\eta }\), \(\alpha _{0,\omega }\) :

Mass exchange coefficient constant, \(\mathrm {s}^{-1}\)

\(\widehat{\alpha }_{0}\) :

Averaged mass exchange coefficient constant within an REV, \(\mathrm {s}^{-1}\)

\(\varepsilon _{l}\), \(\varepsilon _{i}\), \(\varepsilon _{s}\) :

Volume fraction of the liquid phase, the insoluble solid and the soluble solid, respectively, dimensionless

\(\varepsilon _{T}\), \(\varepsilon _{T}^{*}\) :

Darcy- and large-scale total porosity, respectively, dimensionless

\(\mu _{l}\) :

Dynamic viscosity, Pa s

\(\rho _{l}\), \(\rho _{s}\) :

Density of the liquid phase and the soluble solid, respectively, \(\mathrm {kg\,m}^{-3}\)

\(\varphi\) :

Volume fraction of each region within a unit cell, dimensionless


  • Abriola, L., Pinder, G.F.: A multiphase approach to the modeling of porous media contaminated by organic compounds -1. Equation development. Water Resour. Res. 21(1), 11–18 (1985)

    Article  Google Scholar 

  • Agartan, E., Trevisan, L., Cihan, A., Birkholzer, J., Zhou, Q., Illangasekare, T.H.: Experimental study on effects of geologic heterogeneity in enhancing dissolution trapping of supercritical \({\text{CO}}_{2}\). Water Resour. Res. 51(3), 1635–1648 (2015)

    Article  Google Scholar 

  • Ahmadi, A., Quintard, M., Whitaker, S.: Transport in chemically and mechanically heterogeneous porous media \(\rm V\): two-equation model for solute transport with adsorption. Adv. Water Resour. 22(1), 59–86 (1998)

    Article  Google Scholar 

  • Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 235(1200), 67–77 (1956)

  • Banwart, S.A.: Assessing the scale-dependence of mineral weathering rates at the Aitik waste rock deposit in Northern \(\rm S\)weden. Mineral. Mag. 62A(1), 108–109 (1998)

    Article  Google Scholar 

  • Békri, S., Renard, S., Delprat-Jannaud, F.: Pore to core scale simulation of the mass transfer with mineral reaction in porous media. Oil Gas Sci. Technol. Revue d’IFP Energies Nouvelles 70(4), 681–693 (2015)

    Article  Google Scholar 

  • Békri, S., Thovert, J.F., Adler, P.M.: Dissolution of porous media. Chem. Eng. Sci. 50, 2765–2791 (1995)

    Article  Google Scholar 

  • Bourgeat, A.: Homogenized behavior of two-phase flows in naturally fractured reservoirs with uniform fractures distribution. Comput. Methods Appl. Mech. Eng. 47(1–2), 205–216 (1984)

    Article  Google Scholar 

  • Bousquet-Melou, P., Neculae, A., Goyeau, B., Quintard, M.: Averaged solute transport during solidification of a binary mixture: active dispersion in dendritic structures. Metall. Mater. Trans. B 33(3), 365–376 (2002)

    Article  Google Scholar 

  • Brenner, H., Stewartson, K.: Dispersion resulting from flow through spatially periodic porous media. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 297(1430), 81–133 (1980)

  • Chabanon, M., Valdés-Parada, F.J., Ochoa-Tapia, J.A., Goyeau, B.: Large-scale model of flow in heterogeneous and hierarchical porous media. Adv. Water Resour. 109, 41–57 (2017)

    Article  Google Scholar 

  • Chastanet, J., Wood, B.D.: Mass transfer process in a two-region medium. Water Resour. Res. 44(5), W05413 (2008)

    Article  Google Scholar 

  • Chen, L., Kang, Q., Carey, B., Tao, W.: Pore-scale study of diffusion-reaction processes involving dissolution and precipitation using the lattice Boltzmann method. Int. J. Heat Mass Trans. 75, 483–496 (2014)

    Article  Google Scholar 

  • Cherblanc, F., Ahmadi, A., Quintard, M.: Two-medium description of dispersion in heterogeneous porous media: calculation of macroscopic properties. Water Resour. Res. 39(6), 1154 (2003)

    Article  Google Scholar 

  • Cherblanc, F., Ahmadi, A., Quintard, M.: Two-domain description of solute transport in heterogeneous porous media: Comparison between theoretical predictions and numerical experiments. Adv. Water Resour. 30(5), 1127–1143 (2007)

    Article  Google Scholar 

  • Christ, J.A., Lemke, L.D., Abriola, L.M.: The influence of dimensionality on simulations of mass recovery from nonuniform dense non-aqueous phase liquid (\(\rm DNAPL\)) source zones. Adv. Water Resour. 32(3), 401–412 (2009)

    Article  Google Scholar 

  • Cohen, C., Ding, D., Quintard, M., Bazin, B.: From pore scale to wellbore scale: Impact of geometry on wormhole growth in carbonate acidization. Chem. Eng. Sci. 63, 3088–3099 (2008)

    Article  Google Scholar 

  • Cooper, A.: Halite karst geohazards (natural and man-made) in the United Kingdom. Environ. Geol. 42(5), 505–512 (2002)

    Article  Google Scholar 

  • Coutelieris, F.A., Kainourgiakis, M.E., Stubos, A.K., Kikkinides, E.S., Yortsos, Y.C.: Multiphase mass transport with partitioning and inter-phase transport in porous media. Chem. Eng. Sci. 61(14), 4650–4661 (2006)

    Article  Google Scholar 

  • Dagan, G.: Flow and Transport in Porous Formations. Springer (1989)

  • Davit, Y., Quintard, M.: Technical notes on volume averaging in porous media I: How to choose a spatial averaging operator for periodic and quasiperiodic structures. Trans. Porous Media 119(3), 555–584 (2017)

    Article  Google Scholar 

  • Eidsath, A., Carbonell, R.G., Whitaker, S., Herrmann, L.R.: Dispersion in pulsed systems - \(\rm III\): comparison between theory and experiments for packed beds. Chem. Eng. Sci. 38(11), 1803–1816 (1983)

    Article  Google Scholar 

  • Farthing, M.W., Seyedabbasi, M.A., Imhoff, P.T., Miller, C.T.: Influence of porous media heterogeneity on nonaqueous phase liquid dissolution fingering and upscaled mass transfer. Water Resour. Res. 48(8), W08507 (2012)

    Article  Google Scholar 

  • Gelhar, L.W., Welty, C., Rehfeldt, K.R.: A critical review of data on field-scale dispersion in aquifers. Water Resour. Res. 28(7), 1955–1974 (1992)

    Article  Google Scholar 

  • Golfier, F., B. Bazin, R..L.., Quintard, M.: Core-scale description of porous media dissolution during acid injection - Part I: theoretical development. Comput. Appl. Math. 23, 173–194 (2004)

    Article  Google Scholar 

  • Golfier, F., Quintard, M., Bazin, B., Lenormand, R.: Core-scale description of porous media dissolution during acid injection - Part II: calculation of the effective properties. Comput. Appl. Math. 25, 55–78 (2006)

    Google Scholar 

  • Golfier, F., Quintard, M., Cherblanc, F., Zinn, B.A., Wood, B.D.: Comparison of theory and experiment for solute transport in highly heterogeneous porous medium. Adv. Water Resour. 30(11), 2235–2261 (2007)

    Article  Google Scholar 

  • Golfier, F., Zarcone, C., Bazin, B., Lenormand, R., Lasseux, D., Quintard, M.: 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 (2002)

    Article  Google Scholar 

  • Gray, W.G., Leijnse, A., Kolar, R.L., Blain, C.A.: Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems. CRC Press, Boca Raton, FL (1993)

    Google Scholar 

  • Guibert, R., Horgue, P., Debenest, G., Quintard, M.: A comparison of various methods for the numerical evaluation of porous media permeability tensors from pore-scale geometry. Math. Geosci. 48(3), 329–347 (2016)

    Article  Google Scholar 

  • Guo, J., Laouafa, F., Quintard, M.: A theoretical and numerical framework for modeling gypsum cavity dissolution. Int. J. Num. Anal.l Methods Geomech. 40, 1662–1689 (2016)

    Article  Google Scholar 

  • Guo, J., Quintard, M., Laouafa, F.: Dispersion in porousmedia with heterogeneous nonlinear reactions. Trans. Porous Media 109(3), 541–570 (2015)

    Article  Google Scholar 

  • Gvirtzman, H., Paldor, N., Magaritz, M., Bachmat, Y.: Mass exchange between mobile freshwater and immobile saline water in the unsaturated zone. Water Resour. Res. 24(10), 1638–1644 (1988)

    Article  Google Scholar 

  • Gwo, J.P., Jardine, P.M., Wilson, G.V., Yeh, G.T.: Using a multiregion model to study the effects of advective and diffusive mass transfer on local physical nonequilibrium and solute mobility in a structured soil. Water Resour. Res. 32(3), 561–570 (1996)

    Article  Google Scholar 

  • Hao, Y., Smith, M., Carroll, S.: Multiscale modeling of \(\rm CO_{2}\)-induced carbonate dissolution: from core to meter scale. Int. J. Greenhouse Gas Control 88, 272–289 (2019)

    Article  Google Scholar 

  • Hao, Y., Smith, M., Sholokhova, Y., Carroll, S.: \({\rm CO}_{2}\)-induced dissolution of low permeability carbonates. part II: numerical modeling of experiments. Adv. Water Resour. 62, 388–408 (2013)

    Article  Google Scholar 

  • Kalia, N., Balakotaiah, V.: Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks. Chem. Eng. Sci. 62(4), 919–928 (2007)

    Article  Google Scholar 

  • Kalia, N., Balakotaiah, V.: Effect of medium heterogeneities on reactive dissolution of carbonates. Chem. Eng. Sci. 64(2), 376–390 (2009)

    Article  Google Scholar 

  • Kang, Q., Chen, L., Valocchi, A., Viswanathan, H.: Pore-scale study of dissolution-induced changes in permeability and porosity of porous media. J. Hydrol. 517, 1049–1055 (2014)

    Article  Google Scholar 

  • Kang, Q., Zhang, D., Chen, S., He, X.: Lattice Boltzmann simulation of chemical dissolution in porous media. Phys. Rev. E 65, 036318 (2002)

    Article  Google Scholar 

  • Kitanidis, P.K.: Prediction by the method of moments of transport in a heterogeneous formation. J. Hydrol. 102, 453–473 (1988)

    Article  Google Scholar 

  • Laouafa, F., Prunier, F., Daouadji, A., Al Gali, H., Darve, F.: Stability in geomechanics, experimental and numerical analyses. Int. J. Num. Anal. Methods Geomech. 35(2), 112–139 (2011)

    Article  Google Scholar 

  • Liu, P., Yan, X., Yao, J., Sun, S.: Modeling and analysis of the acidizing process in carbonate rocks using a two-phase thermal-hydrologic-chemical coupled model. Chem. Eng. Sci. 207, 215–234 (2019)

    Article  Google Scholar 

  • Luo, H., Laouafa, F., Guo, J., Quintard, M.: Numerical modeling of three-phase dissolution of underground cavities using a diffuse interface model. Int. J. Num. Anal. Methods Geomech. 38, 1600–1616 (2014)

    Article  Google Scholar 

  • Luo, H., Quintard, M., Debenest, G., Laouafa, F.: Properties of a diffuse interface model based on a porous medium theory for solid-liquid dissolution problems. Comput.l Geosci. 16(4), 913–932 (2012)

    Article  Google Scholar 

  • Luquot, L., Gouze, P.: Experimental determination of porosity and permeability changes induced by injection of \(\rm CO_{2}\) into carbonate rocks. Chem. Geol. 265, 148–159 (2009)

    Article  Google Scholar 

  • Mabiala, B., Tathy, C., Quintard, M.: NAPL dissolution in heterogeneous systems: Large-scale analysis for stratified system. In: HEFAT 2003, 2nd International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, vol. paper MB3. Victoria Falls, Zambia (2003)

  • Marle, C.M.: On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media. Int. J. Eng. Sci. 20(5), 643–662 (1982)

    Article  Google Scholar 

  • Mei, C.C.: Method of homogenization applied to dispersion in porous media. Trans. Porous Media 9(3), 261–274 (1992)

    Article  Google Scholar 

  • Olsson, E., Kreiss, G.: A conservative level set method for two phase flow. J. Comput. Phys. 210(1), 225–246 (2005)

    Article  Google Scholar 

  • Olsson, E., Kreiss, G., Zahedi, S.: A conservative level set method for two phase flow \(\rm II\). J. Comput. Phys. 225, 785–807 (2007)

    Article  Google Scholar 

  • Panga, M.K.R., Ziauddin, M., Balakotaiah, V.: Two-scale continuum model for simulation of wormholes in carbonate acidization. AIChE J. 51(12), 3231–3248 (2005)

    Article  Google Scholar 

  • Parker, J., Park, E.: Modeling field-scale nonaqueous phase dissolution kinetics in heterogeneous aquifers. Water Resour. Res. 40, W05109 (2004)

    Article  Google Scholar 

  • Prunier, F., Laouafa, F., Darve, F.: 3D bifurcation analysis in geomaterials: investigation of the second order work criterion. Eur. J. Environ. Civ. Eng. 13(2), 135–147 (2009)

    Article  Google Scholar 

  • Prunier, F., Nicot, F., Darve, F., Laouafa, F., Lignon, S.: Three-dimensional multiscale bifurcation analysis of granular media. J. Eng. Mech. 135(6), 493–509 (2009)

    Article  Google Scholar 

  • Quintard, M., Whitaker, S.: Ecoulement monophasique en milieu poreux: effet des hétérogénéités locales. J. Theor. Appl. Mech. 6(5), 691–726 (1987)

    Google Scholar 

  • Quintard, M., Whitaker, S.: Two-phase flow in heterogeneous porous media: the method of large-scale averaging. Trans. Porous Media 3, 357–413 (1988)

    Article  Google Scholar 

  • Quintard, M., Whitaker, S.: Convection, dispersion, and interfacial transport of contaminants: homogeneous porous media. Adv. Water Resources 17, 221–239 (1994)

    Article  Google Scholar 

  • Quintard, M., Whitaker, S.: Transport in ordered and disordered porous media I: the cellular average and the use of weighting functions. Trans. Porous Media 14, 163–177 (1994)

    Article  Google Scholar 

  • Quintard, M., Whitaker, S.: Dissolution of an immobile phase during flow in porous media. Ind. Eng. Chem. Res. 38(3), 833–844 (1999)

    Article  Google Scholar 

  • Renard, P., de Marsily, G.: Calculating equivalent permeability: a review. Adv. Water Resour. 20(5), 253–278 (1997)

    Article  Google Scholar 

  • Säez, A.E., Otero, C.J., Rusinek, I.: The effective homogeneous behavior of heterogeneous porous media. Transp. Porous Media 4, 213–238 (1989)

    Article  Google Scholar 

  • Sánchez-Vila, X., Girardi, J.P., Carrera, J.: A synthesis of approaches to upscaling of hydraulic conductivities. Water Resour. Res. 31(4), 867–882 (1995)

    Article  Google Scholar 

  • Soulaine, C., Roman, S., Kovscek, A., Tchelepi, H.A.: Mineral dissolution and wormholing from a pore-scale perspective. J. Fluid Mech. 827, 457–483 (2017)

    Article  Google Scholar 

  • Soulaine, C., Roman, S., Kovscek, A., Tchelepi, H.A.: Pore-scale modelling of multiphase reactive flow: application to mineral dissolution with production of \(\text{ CO}_{2}\). J. Fluid Mech. 855, 616–645 (2018)

    Article  Google Scholar 

  • Starchenko, V., Marra, C.J., Ladd, A.J.C.: Three-dimensional simulations of fracture dissolution. J. Geophys. Res. Solid Earth 121(9), 6421–6444 (2016)

    Article  Google Scholar 

  • Szymczak, P., Ladd, A.J.C.: Instabilities in the dissolution of a porous matrix. Geophys. Res. Lett. 38, L07403 (2011)

    Article  Google Scholar 

  • Taylor, G.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 219(1137), 186–203 (1953)

  • Taylor, G.: The dispersion of matter in turbulent flow through a pipe. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 223(1155), 446–468 (1954)

  • Tran Ngoc, T..D., Le, N..H..N., Tran, T..V., Ahmadi, A., Bertin, H.: Homogenization of solute transport in unsaturated double-porosity media: model and numerical validation. Trans. Porous Media 132(1), 53–81 (2020)

    Article  Google Scholar 

  • Varloteaux, C., Békri, S., Adler, P.M.: 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 (2013)

    Article  Google Scholar 

  • Vignoles, G.L., Aspa, Y., Quintard, M.: Modelling of carbon-carbon composite ablation in rocket nozzles. Compos. Sci. Technol. 70(9), 1303–1311 (2010)

    Article  Google Scholar 

  • Whitaker, S.: Flow in porous media I: a theoretical derivation of Darcy’s law. Trans. Porous Media 1(1), 3–25 (1986)

    Article  Google Scholar 

  • Whitaker, S.: The Method of, vol. Averaging. Kluwer Academic Publishers, Dordrecht, The Netherlands (1999)

  • White, A.F., Brantley, S.L.: The effect of time on the weathering of silicate minerals: Why do weathering rates differ in the laboratory and field? Chem. Geol. 202(3–4), 479–506 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Jianwei Guo or Farid Laouafa.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 432 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, J., Laouafa, F. & Quintard, M. Large-Scale Model for the Dissolution of Heterogeneous Porous Formations: Theory and Numerical Validation. Transp Porous Med 144, 149–174 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: