Numerical investigation for the effect of deformation and dynamic pressure on the fast drainage of porous materials

References

• Abidoye, L. K., & Das, D. B. (2014). Scale dependent dynamic capillary pressure effect for two-phase flow in porous media. Advances in Water Resources, 74, 212–230. https://doi.org/10.1016/j.advwatres.2014.09.009
   Web of Science ®Google Scholar
• Barenblatt, G. I., & Gil'man, A. A. (1987). Nonequilibrium counterflow capillary impregnation. Journal of Engineering Physics, 52(3), 335–339. https://doi.org/10.1007/BF00872519
   Google Scholar
• Barenblatt, G., Patzek, T. W., & Silin, D. (2003). The mathematical model of nonequilibrium effects in water-oil displacement. SPE Journal, 8(04), 409–416. https://doi.org/10.2118/87329-PA
   Google Scholar
• Berentsen, C., Hassanizadeh, S., Bezuijen, A., & Oung, O. (2006). Modelling of two-phase flow in porous media including non-equilibrium capillary pressure effects. Proceedings of the XVI International Conference on Computational Methods in Water Resources, Tech. Univ. of Denmark Copenhagen (pp. 1–11).
   Google Scholar
• Biot, M., & Willis, D. (1957). The elastic coefficients of the theory of consolidation. Journal of Applied Mechanics, 24(4), 594–601. https://doi.org/10.1115/1.4011606
   Google Scholar
• Bottero, S. (2009). Advances in the theory of capillarity in porous media. Wöhrmann Print Service.
   Google Scholar
• Bottero, S., Hassanizadeh, S. M., Kleingeld, P., & Heimovaara, T. (2011). Nonequilibrium capillarity effects in two-phase flow through porous media at different scales. Water Resources Research, 47(10), WR010887. https://doi.org/10.1029/2011WR010887
   Google Scholar
• Bouadjila, K., Mokrane, A., Saad, A. S., & Saad, M. (2018). Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure. Computers & Mathematics with Applications, 75(10), 3614–3631. https://doi.org/10.1016/j.camwa.2018.02.021
   Web of Science ®Google Scholar
• Bourgeat, A., & Panfilov, M. (1998). Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects. Computational Geosciences, 2(3), 191–215. https://doi.org/10.1023/A:1011502303588
   Web of Science ®Google Scholar
• Camps-Roach, G., O'Carroll, D. M., Newson, T. A., Sakaki, T., & Illangasekare, T. H. (2010). Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling. Water Resources Research, 46(8). https://doi.org/10.1029/2009WR008881
   Google Scholar
• Cao, X., & Pop, I. (2016). Degenerate two-phase porous media flow model with dynamic capillarity. Journal of Differential Equations, 260(3), 2418–2456. https://doi.org/10.1016/j.jde.2015.10.008
   Web of Science ®Google Scholar
• Carman, P. C. (1939). Permeability of saturated sands, soils and clays. The Journal of Agricultural Science, 29(2), 262–273. https://doi.org/10.1017/S0021859600051789
   Google Scholar
• Corey, A. T. (1978). Mechanic of heterogeneous fluids in porous media. Soil Science, 125(5), 331.
   Google Scholar
• Coussy, O. (2011). Mechanics and physics of porous solids. John Wiley & Sons.
   Google Scholar
• Coussy, O., Dangla, P., Lassabatère, T., & Baroghel-Bouny, V. (2004). The equivalent pore pressure and the swelling and shrinkage of cement-based materials. Materials and Structures, 37(1), 15–20. https://doi.org/10.1007/BF02481623
   Google Scholar
• Dahle, H. K., Celia, M. A., & Hassanizadeh, S. M. (2005). Bundle-of-tubes model for calculating dynamic effects in the capillary-pressure-saturation relationship. Transport in Porous Media, 58(1-2), 5–22. https://doi.org/10.1007/s11242-004-5466-4
   Web of Science ®Google Scholar
• Das, D. B., & Mirzaei, M. (2012). Dynamic effects in capillary pressure relationships for two-phase flow in porous media: Experiments and numerical analyses. AIChE Journal, 58(12), 3891–3903. https://doi.org/10.1002/aic.13777
   Web of Science ®Google Scholar
• Diamantopoulos, E., & Durner, W. (2012). Dynamic nonequilibrium of water flow in porous media: A review. Vadose Zone Journal, 11(3), vzj2011.0197. https://doi.org/10.2136/vzj2011.0197
   Web of Science ®Google Scholar
• Elzeftawy, A., & Mansell, R. (1975). Hydraulic conductivity calculations for unsaturated steady-state and transient-state flow in sand. Soil Science Society of America Journal, 39(4), 599–603. https://doi.org/10.2136/sssaj1975.03615995003900040013x
   Web of Science ®Google Scholar
• Friedman, S. P. (1999). Dynamic contact angle explanation of flow rate-dependent saturation-pressure relationships during transient liquid flow in unsaturated porous media. Journal of Adhesion Science and Technology, 13(12), 1495–1518. https://doi.org/10.1163/156856199X00613
   Web of Science ®Google Scholar
• Fučík, R., Mikyška, J., Sakaki, T., Beneš, M., & Illangasekare, T. H. (2010). Significance of dynamic effect in capillarity during drainage experiments in layered porous media. Vadose Zone Journal, 9(3), 697–708. https://doi.org/10.2136/vzj2009.0106
   Web of Science ®Google Scholar
• Genuchten, V., & Th, M. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44(5), 892–898.
   Web of Science ®Google Scholar
• Ghorbani, J., Nazem, M., & Carter, J. (2016). Numerical modelling of multiphase flow in unsaturated deforming porous media. Computers and Geotechnics, 71, 195–206. https://doi.org/10.1016/j.compgeo.2015.09.011
   Web of Science ®Google Scholar
• Ghourchian, S., Wyrzykowski, M., & Lura, P. (2018). A poromechanics model for plastic shrinkage of fresh cementitious materials. Cement and Concrete Research, 109, 120–132. https://doi.org/10.1016/j.cemconres.2018.04.013
   Web of Science ®Google Scholar
• Goel, G., Abidoye, L. K., Chahar, B. R., & Das, D. B. (2016). Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect. Environmental Fluid Mechanics, 16(5), 945–963. https://doi.org/10.1007/s10652-016-9459-y
   Web of Science ®Google Scholar
• Goel, G., & O'Carroll, D. M. (2011). Experimental investigation of nonequilibrium capillarity effects: Fluid viscosity effects. Water Resources Research, 47(9), WR009861. https://doi.org/10.1029/2010WR009861
   Google Scholar
• Grondin, F., Bouasker, M., Mounanga, P., Khelidj, A., & Perronnet, A. (2010). Physico-chemical deformations of solidifying cementitious systems: Multiscale modelling. Materials and Structures, 43(1-2), 151–165. https://doi.org/10.1617/s11527-009-9477-z
   Web of Science ®Google Scholar
• Hassanizadeh, S. M. (2015). Advanced theories of two-phase flow in porous media. In J. Prieur Du Plessis, Editor, Handbook of porous media (pp. 47–62). Computational Mechanics Publications.
   Google Scholar
• Hassanizadeh, S. M., Celia, M. A., & Dahle, H. K. (2002). Dynamic effect in the capillary pressure–saturation relationship and its impacts on unsaturated flow. Vadose Zone Journal, 1(1), 38–57. https://doi.org/10.2136/vzj2002.0038
   Web of Science ®Google Scholar
• Hassanizadeh, S. M., & Gray, W. G. (1990). Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Advances in Water Resources, 13(4), 169–186. https://doi.org/10.1016/0309-1708(90)90040-B
   Web of Science ®Google Scholar
• Hassanizadeh, S. M., & Gray, W. G. (1993). Thermodynamic basis of capillary pressure in porous media. Water Resources Research, 29(10), 3389–3405. https://doi.org/10.1029/93WR01495
   Web of Science ®Google Scholar
• Hillel, D. (2003). Introduction to environmental soil physics. Elsevier.
   Google Scholar
• Hilpert, M. (2012). Velocity-dependent capillary pressure in theory for variably-saturated liquid infiltration into porous media. Geophysical Research Letters, 39(6). https://doi.org/10.1029/2012GL051114
   Google Scholar
• Holt, E., & Leivo, M. (2004). Cracking risks associated with early age shrinkage. Cement and Concrete Composites, 26(5), 521–530. https://doi.org/10.1016/S0958-9465(03)00068-4
   Web of Science ®Google Scholar
• Hou, L., Chen, L., & Kibbey, T. C. (2012). Dynamic capillary effects in a small-volume unsaturated porous medium: Implications of sensor response and gas pressure gradients for understanding system dependencies. Water Resources Research, 48(11), WR012434. https://doi.org/10.1029/2012WR012434
   Google Scholar
• Joekar-Niasar, V., & Hassanizadeh, S. (2011). Specific interfacial area: The missing state variable in two-phase flow equations? Water Resources Research, 47(5), WR009291. https://doi.org/10.1029/2010WR009291
   Google Scholar
• Kalaydjian, F.-M. (1992). Dynamic capillary pressure curve for water/oil displacement in porous media: Theory vs. experiment. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
   Google Scholar
• Kunz, P., Zarikos, I. M., Karadimitriou, N. K., Huber, M., Nieken, U., & Hassanizadeh, S. M. (2016). Study of multi-phase flow in porous media: Comparison of SPH simulations with micro-model experiments. Transport in Porous Media, 114(2), 581–600. https://doi.org/10.1007/s11242-015-0599-1
   Web of Science ®Google Scholar
• Li, Y., & Li, J. (2014). Capillary tension theory for prediction of early autogenous shrinkage of self-consolidating concrete. Construction and Building Materials, 53, 511–516. https://doi.org/10.1016/j.conbuildmat.2013.12.010
   Web of Science ®Google Scholar
• Lo, W., Yang, C., Hsu, S., Chen, C., Yeh, C., & Hilpert, M. (2017). The dynamic response of the water retention curve in unsaturated soils during drainage to acoustic excitations. Water Resources Research, 53(1), 712–725. https://doi.org/10.1002/2016WR018833
   Web of Science ®Google Scholar
• Manthey, S., Hassanizadeh, S. M., Oung, O., & Helmig, R. (2004). Dynamic capillary pressure effects in two-phase flow through heterogeneous porous media (Vol. 55). Elsevier.
   Google Scholar
• Mikelić, A. (2010). A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure. Journal of Differential Equations, 248(6), 1561–1577. https://doi.org/10.1016/j.jde.2009.11.022
   Web of Science ®Google Scholar
• Morel-Seytoux, H. J., Meyer, P. D., Nachabe, M., Tourna, J., Genuchten, M. v., & Lenhard, R. J. (1996). Parameter equivalence for the Brooks-Corey and van Genuchten soil characteristics: Preserving the effective capillary drive. Water Resources Research, 32(5), 1251–1258. https://doi.org/10.1029/96WR00069
   Web of Science ®Google Scholar
• Peszynska, M., & Yi, S.-Y. (2008). Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media. International Journal of Numerical Analysis & Modeling, 5, 126–149.
   Web of Science ®Google Scholar
• Qin, C.-Z., Guo, B., Celia, M., & Wu, R. (2019). Dynamic pore-network modeling of air-water flow through thin porous layers. Chemical Engineering Science, 202, 194–207.
   Web of Science ®Google Scholar
• Sakaki, T., O'Carroll, D. M., & Illangasekare, T. H. (2010). Direct quantification of dynamic effects in capillary pressure for drainage–wetting cycles. Vadose Zone Journal, 9(2), 424–437. https://doi.org/10.2136/vzj2009.0105
   Web of Science ®Google Scholar
• Samouh, H., Rozière, E., & Loukili, A. (2017). The differential drying shrinkage effect on the concrete surface damage: Experimental and numerical study. Cement and Concrete Research, 102, 212–224. https://doi.org/10.1016/j.cemconres.2017.09.016
   Web of Science ®Google Scholar
• Shahbodagh-Khan, B., Khalili, N., & Esgandani, G. A. (2015). A numerical model for nonlinear large deformation dynamic analysis of unsaturated porous media including hydraulic hysteresis. Computers and Geotechnics, 69, 411–423. https://doi.org/10.1016/j.compgeo.2015.06.008
   Web of Science ®Google Scholar
• Smiles, D., Vachaud, G., & Vauclin, M. (1971). A test of the uniqueness of the soil moisture characteristic during transient, nonhysteretic flow of water in a rigid soil. Soil Science Society of America Journal, 35(4), 534–539. https://doi.org/10.2136/sssaj1971.03615995003500040018x
   Google Scholar
• Smith, D., Scherer, G., & Anderson, J. (1995). Shrinkage during drying of silica gel. Journal of Non-Crystalline Solids, 188(3), 191–206. https://doi.org/10.1016/0022-3093(95)00187-5
   Web of Science ®Google Scholar
• Stauffer, F. (1978). Time dependence of the relations between capillary pressure, water content and conductivity during drainage of porous media. IAHR Symposium on Scale Effects in Porous Media, Thessaloniki, Greece (Vol. 29, pp. 3–35).
   Google Scholar
• Szymkiewicz, A. (2012). Modelling water flow in unsaturated porous media: Accounting for nonlinear permeability and material heterogeneity. Springer Science & Business Media.
   Google Scholar
• Terzaghi, K. (1951). Theoretical soil mechanics. Chapman and Hall, Limited.
   Google Scholar
• Vachaud, G., Vauclin, M., & Wakil, M. (1972). A study of the uniqueness of the soil moisture characteristic during desorption by vertical drainage. Soil Science Society of America Journal, 36(3), 531–532. https://doi.org/10.2136/sssaj1972.03615995003600030044x
   Google Scholar
• Vlahinić, I., Jennings, H. M., & Thomas, J. J. (2009). A constitutive model for drying of a partially saturated porous material. Mechanics of Materials, 41(3), 319–328. https://doi.org/10.1016/j.mechmat.2008.10.011
   Web of Science ®Google Scholar
• Wang, S., Yu, C., Sang, G., Yu, R., & Cheng, F. (2020). An oil–water two-phase reservoir numerical simulation coupled with dynamic capillary force based on the full-implicit method. Computers & Mathematics with Applications, 79(9), 2527–2549. https://doi.org/10.1016/j.camwa.2019.11.013
   Web of Science ®Google Scholar
• Wang, X., & Nackenhorst, U. (2020). A coupled bio-chemo-hydraulic model to predict porosity and permeability reduction during microbially induced calcite precipitation. Advances in Water Resources, 140, 103563. https://doi.org/10.1016/j.advwatres.2020.103563
   Web of Science ®Google Scholar
• Weitz, D., Stokes, J., Ball, R., & Kushnick, A. (1987). Dynamic capillary pressure in porous media: Origin of the viscous-fingering length scale. Physical Review Letters, 59(26), 2967–2970. https://doi.org/10.1103/PhysRevLett.59.2967
   PubMed Web of Science ®Google Scholar
• Wen, T., Shao, L., & Guo, X. (2019). Effect of hysteresis on hydraulic properties of soils under multiple drying and wetting cycles. European Journal of Environmental and Civil Engineering, 1–13. https://doi.org/10.1080/19648189.2019.1600037
   Google Scholar
• Wheeler, S., Sharma, R., & Buisson, M. (2003). Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils. Géotechnique, 53(1), 41–54. https://doi.org/10.1680/geot.2003.53.1.41
   Web of Science ®Google Scholar
• Wildenschild, D., Hopmans, J., Rivers, M., & Kent, A. (2005). Quantitative analysis of flow processes in a sand using synchrotron-based X-ray microtomography. Vadose Zone Journal, 4(1), 112–126. https://doi.org/10.2113/4.1.112
   Web of Science ®Google Scholar
• Wildenschild, D., Hopmans, J., & Simunek, J. (2001). Flow rate dependence of soil hydraulic characteristics. Soil Science Society of America Journal, 65(1), 35–48. https://doi.org/10.2136/sssaj2001.65135x
   Web of Science ®Google Scholar
• Wittmann, F. (1976). On the action of capillary pressure in fresh concrete. Cement and Concrete Research, 6(1), 49–56. https://doi.org/10.1016/0008-8846(76)90050-8
   Google Scholar
• Zhou, A., Wu, S., Li, J., & Sheng, D. (2018). Including degree of capillary saturation into constitutive modelling of unsaturated soils. Computers and Geotechnics, 95, 82–98. https://doi.org/10.1016/j.compgeo.2017.09.017
   Web of Science ®Google Scholar
• Zhou, C., & Ng, C. W. W. (2014). A new and simple stress-dependent water retention model for unsaturated soil. Computers and Geotechnics, 62, 216–222. https://doi.org/10.1016/j.compgeo.2014.07.012
   Web of Science ®Google Scholar
• Zhuang, L., Hassanizadeh, S. M., Qin, C. Z., & de Waal, A. (2017). Experimental investigation of hysteretic dynamic capillarity effect in unsaturated flow. Water Resources Research, 53(11), 9078–9088. https://doi.org/10.1002/2017WR020895
   PubMed Web of Science ®Google Scholar