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

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Abstract

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.

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Abbreviations

\(\mathbf {b}\) :

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

References

  • 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 

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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). https://doi.org/10.1007/s11242-021-01623-0

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