31 May 2021 to 4 June 2021
Europe/Berlin timezone

From the non-linear Darcy law for immiscible two-phase flow in porous media to constitutive equations for each fluid species

2 Jun 2021, 19:50
15m
Oral Presentation (MS6-A) Physics of multi-phase flow in diverse porous media MS6-A

Speaker

Alex Hansen (NTNU)

Description

There is growing evidence that the flow velocity vp of an immiscible fluid mixture flowing in a porous medium depends on the local pressure gradient to a power in the range 1.5 to 2 when capillary and viscous forces compete [1]. The relative permeability equations relate the flow velocity of each immiscible fluid species, vw and vn, to a gradient in the corresponding pressure field. These equations allow the mapping (vw,vn)vp. However, the opposite mapping, vp(vw,vn) is not unique. Hence, attempts at generalizing the relative permeability equations to account for the non-linear behavior of vp cannot use vp as a starting point. Hansen et al. [2] have defined a co-moving velocity vm which is related to but not equal to the velocity difference between the two fluid species and provided a transformation (vp,vm)(vw,vn), making it possible relate the non-linear behavior of vp to non-linearities in the behavior of vw and vn. We use a dynamic network model [3] and relative permeability data from the literature to explore this mapping and what it means.

References

[1] Tallakstad, K. T., Knudsen, H. A., Ramstad, T., Løvoll, G., Måløy, K. J., Toussaint, R., and Flekkøy, E. G., Phys. Rev. Lett., 102, 074502 (2009); Tallakstad, K. T., Løvoll, G., Knudsen, H. A., Ramstad, T., Flekkøy, E. G., and Måløy, K. J., Phys. Rev. E, 80, 036308 (2009); Sinha, S. and Hansen, A., EPL, 99, 44004 (2012); Roy, S., Hansen, A. and Sinha, S., Front. Phys. 7, 92 (2020).Aursj{\o}, O., Erpelding, M., Tallakstad, K. T., Flekkøy, E. G., Hansen, A., and Måløy, K. J., Front. Phys. 2, 63 (2014); Sinha, S., Bender, A.T., Danczyk, M., Keepseagle, K., Prather, C.A., Bray, J.M., Thrane, L.W., Seymour, J.D., Codd, S.L. and Hansen, A., Transport Por. Media, 119, 77 (2017); Gao, Y., Lin, Q., Bijeljic, B. and Blunt, M. J., Water Resources Research, 53, 10274 (2017); Gao, Y., Lin, Q., Bijeljic, B. and Blunt, M. J., Phys. Rev. Fluids, 5, 013801 (2020); Zhang, Y., Bijeljic, B., Gao, Y., Lin, Q. and Blunt, M. J., eartharXiv, https://doi.org/10.31223/osf.io/2rxbn (2020).
[3] Hansen, A., Sinha, S., Bedeaux, D., Kjelstrup, S., Gjennestad, M. A., and Vassvik, M. Transp. Porous Media, 125, 565 (2018).}
[4] Sinha, S., Gjennestad, M. Aa., Vassvik, M. and Hansen, A., arXiv:1907.12842 (2019).

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Primary authors

Dr Subhadeep Roy (PoreLab) Mr Håkon Pedersen (PoreLab) Santanu Sinha (Beijing Computational Science Research Center, 10 East Xibeiwang Road, Haidian District, Beijing 100193, China.) Alex Hansen (NTNU)

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