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Constitutive Relations for Reactive Transport Modeling: Effects of Chemical Reactions on Multi-phase Flow Properties

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Abstract

The relationship between flow properties and chemical reactions is the key to modeling subsurface reactive transport. This study develops closed-form equations to describe the effects of mineral precipitation and dissolution on multi-phase flow properties (capillary pressure and relative permeabilities) of porous media. The model accounts for the fact that precipitation/dissolution only takes place in the water-filled part of pore space. The capillary tube concept was used to connect pore-scale changes to macroscopic hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and consequently in the pore size distribution. The updated pore size distribution is converted back to a new capillary pressure–water saturation relation from which the new relative permeabilities are calculated. Pore network modeling is conducted on a Berea sandstone to validate the new continuum-scale relations. The pore network modeling results are satisfactorily predicted by the new closed-form equations.

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Abbreviations

\({\bar{S}}\) :

Effective water saturation

\(\beta \) :

Ratio of pore volume after reactions to before reactions

\(\phi \) :

Porosity after reactions

\(\phi _0\) :

Initial porosity

\(\tau \) :

Tortuosity

h :

Capillary pressure head

K :

Permeability after reactions

\(K_0\) :

Initial permeability

\(K_{\mathrm{g}0}\) :

Initial gas permeability

\(k_{\mathrm{g}0}\) :

Initial gas relative permeability

\(K_{\mathrm{g}}\) :

Gas permeability after reactions

\(k_{\mathrm{g}}\) :

Gas relative permeability after reactions

\(K_{\mathrm{w}0}\) :

Initial water permeability

\(k_{\mathrm{w}0}\) :

Initial water relative permeability

\(K_{\mathrm{w}}\) :

Water permeability after reactions

\(k_{\mathrm{w}}\) :

Water relative permeability after reactions

m :

Empirical parameter in the van Genuchten h–S relation

r :

Radius of capillary tube

\(r^*\) :

Radius after reactions

\(r_\mathrm{p}\) :

Maximum radius up to which pores are water-filled

S :

Water saturation

\(S_\mathrm{p}\) :

Water saturation when mineral reaction occurs

\(S_\mathrm{r}\) :

Residual water saturation

References

  • Algive, L., Békri, S., Nader, F.H., Lerat, O., Vizika, O.: Impact of diagenetic alterations on the petrophysical and multiphase flow properties of carbonate rocks using a reactive pore network modeling approach. Oil Gas Sci. Technol. 67(1), 147–160 (2012)

    Article  Google Scholar 

  • Bjørkum, P.A., Nadeau, P.H.: Temperature controlled porosity/permeability reduction, fluid migration, and petroleum exploration in sedimentary basins. APPEA J. 38(Part 1), 452–464 (1998)

    Google Scholar 

  • Blunt, M.J.: Flow in porous media—pore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6(3), 197–207 (2001)

    Article  Google Scholar 

  • Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Article  Google Scholar 

  • Brace, W.: Permeability from resistivity and pore shape. J. Geophys. Res. 82(23), 3343–3349 (1977)

    Article  Google Scholar 

  • Carman, P.C.: Flow of Gases Through Porous Media. Academic Press, London (1956)

    Google Scholar 

  • Ginn, T.R., Wood, B.D., Nelson, K.E., Scheibe, T.D., Murphy, E.M., Clement, T.P.: Processes in microbial transport in the natural subsurface. Adv. Water Resour. 25(8), 1017–1042 (2002)

    Article  Google Scholar 

  • Hiorth, A., Cathles, L., Madland, M.: The impact of pore water chemistry on carbonate surface charge and oil wettability. Transp. Porous Media 85(1), 1–21 (2010)

    Article  Google Scholar 

  • Kozeny, J.: Über kapillare Leitung des Wassers im Boden: (Aufstieg. Hölder-Pichler-Tempsky, Versickerung und Anwendung auf die Bewässerung) (1927)

  • Larson, R., Scriven, L., Davis, H.: Percolation theory of two phase flow in porous media. Chem. Eng. Sci. 36(1), 57–73 (1981)

    Article  Google Scholar 

  • Li, L., Peters, C.A., Celia, M.A.: Upscaling geochemical reaction rates using pore-scale network modeling. Adv. Water Resour. 29(9), 1351–1370 (2006)

    Article  Google Scholar 

  • Liu, H.-H., Zhang, G., Yi, Z., Wang, Y.: A permeability-change relationship in the dryout zone for \(\text{ CO }_2\) injection into saline aquifers. Int. J. Greenh. Gas Control 15, 42–47 (2013)

    Article  Google Scholar 

  • Mavis, F., Wilsey, E.: Filter sand permeability studies. Eng. News Rec. 118, 299–300 (1937)

    Google Scholar 

  • Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(3), 513–522 (1976)

    Article  Google Scholar 

  • Nogues, J.P., Fitts, J.P., Celia, M.A., Peters, C.A.: Permeability evolution due to dissolution and precipitation of carbonates using reactive transport modeling in pore networks. Water Resour. Res. 49(9), 6006–6021 (2013)

    Article  Google Scholar 

  • Ott, H., Roels, S., De Kloe, K.: Salt precipitation due to supercritical gas injection: I. Capillary-driven flow in unimodal sandstone. Int. J. Greenh. Gas Control 43, 247–255 (2015)

    Article  Google Scholar 

  • Panda, M.N., Lake, L.W.: A physical model of cementation and its effects on single-phase permeability. AAPG Bull. 79(3), 431–443 (1995)

    Google Scholar 

  • Pruess, K., Müller, N.: Formation dry-out from CO\(_{2}\) injection into saline aquifers: 1. Effects of solids precipitation and their mitigation. Water Resour. Res. 45(3) (2009). doi:10.1029/2008WR007101

  • Raoof, A., Nick, H., Hassanizadeh, S., Spiers, C.: Poreflow: a complex pore-network model for simulation of reactive transport in variably saturated porous media. Comput. Geosci. 61, 160–174 (2013)

    Article  Google Scholar 

  • Ritter, H., Drake, L.: Pressure porosimeter and determination of complete macropore-size distributions. Pressure porosimeter and determination of complete macropore-size distributions. Ind. Eng. Chem. Anal. Ed. 17(12), 782–786 (1945)

    Article  Google Scholar 

  • Ryazanov, A., Van Dijke, M., Sorbie, K.: Two-phase pore-network modelling: existence of oil layers during water invasion. Transp. Porous Media 80(1), 79–99 (2009)

    Article  Google Scholar 

  • Schäfer, D., Schäfer, W., Kinzelbach, W.: Simulation of reactive processes related to biodegradation in aquifers: 1. Structure of the three-dimensional reactive transport model. J. Contam. Hydrol. 31(1), 167–186 (1998)

    Article  Google Scholar 

  • Schechter, R., Gidley, J.: The change in pore size distribution from surface reactions in porous media. AIChE J. 15(3), 339–350 (1969)

    Article  Google Scholar 

  • Steefel, C.I., DePaolo, D.J., Lichtner, P.C.: Reactive transport modeling: an essential tool and a new research approach for the earth sciences. Earth Planet. Sci. Lett. 240(3), 539–558 (2005)

    Article  Google Scholar 

  • Taylor, S.W., Jaffé, P.R.: Biofilm growth and the related changes in the physical properties of a porous medium: 1. Experimental investigation. Water Resour. Res. 26(9), 2153–2159 (1990)

    Google Scholar 

  • Van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980)

    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 

  • Verma, A., Pruess, K.: Thermohydrological conditions and silica redistribution near high-level nuclear wastes emplaced in saturated geological formations. J. Geophys. Res. Solid Earth (1978–2012) 93(B2), 1159–1173 (1988)

    Article  Google Scholar 

  • Xie, M., Mayer, K.U., Claret, F., Alt-Epping, P., Jacques, D., Steefel, C., Chiaberge, C., Simunek, J.: Implementation and evaluation of permeability–porosity and tortuosity–porosity relationships linked to mineral dissolution–precipitation. Comput. Geosci. 19(3), 655–671 (2015)

  • Zhang, S, Liu, H.-H.: Porosity-permeability relationships in modeling salt precipitation during CO\(_2\) sequestration: review of conceptual models and implementation in numerical simulations. Int. J. Greenh. Gas Control 52, 24–31 (2016)

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Authors and Affiliations

  1. Aramco Research Center-Houston, 16300 Park Row Dr., Houston, TX, 77084, USA

    Shuo Zhang, Hui-Hai Liu & Susan M. Agar

  2. Heriot-Watt University, Edinburgh, EH14 4AS, UK

    Marinus I. J. van Dijke & Sebastian Geiger

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  1. Shuo Zhang
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  2. Hui-Hai Liu
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  3. Marinus I. J. van Dijke
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  4. Sebastian Geiger
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  5. Susan M. Agar
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Correspondence to Shuo Zhang.

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Zhang, S., Liu, HH., van Dijke, M.I.J. et al. Constitutive Relations for Reactive Transport Modeling: Effects of Chemical Reactions on Multi-phase Flow Properties. Transp Porous Med 114, 795–814 (2016). https://doi.org/10.1007/s11242-016-0744-5

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