InterPore2018 New Orleans

Numerical modeling and simulation of two-phase flow problems in heterogeneous porous media with gravity and dynamic capillary pressure

16 May 2018, 16:34

15m

New Orleans

Oral 20 Minutes MS 2.08: Recent Advances in Multiscale Methods and Uncertainty Quantification Parallel 8-H

Speaker

Eduardo Abreu (University of Campinas, Sao Paulo, Brazil)

Description

Numerical simulations of immiscible two-phase flow in porous
media with dynamic capillary pressure and gravity interactions in
heterogeneous porous media are presented with a novel computational
method based on ideas introduced in [1]. We formulate and test
numerically a new two-dimensional fully coupled and implicit procedure
for numericaly solving two-phase transport problems of
pseudo-parabolic nature, see [1,2,3]. For the parameter range considered,
immiscible viscous fingers are found to undergo interaction with
dynamic capillary pressure and gravity effects for typical flow path
situations in porous media transport problems. The dominant feature
for these flows is the saturation overshoot under non-equilibrium
effects in the capillarity pressure [2,3]. Our numerical experiments
demonstrate the viability of the proposed procedure for multiscale
problems in heterogeneous high contrast media.

[1] E. Abreu and J. Vieira, Computing numerical solutions of the pseudo-parabolic Buckley-Leverett equation with dynamic capillary pressure. Mathematics and Computers in Simulation 137 (2017) 29-48.

[2] C.J.van Duijn, K. Mitra and I.S.Pop, Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure, Nonlinear Analysis: Real World Applications 41 (2018) 232-268.

[3] S.M. Hassanizadeh and W.G. Gray, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res., 29(10) (1993) 3389-3405.

References

[1] E. Abreu and J. Vieira, Computing numerical solutions of the pseudo-parabolic Buckley-Leverett equation with dynamic capillary pressure. Mathematics and Computers in Simulation 137 (2017) 29-48.

[2] C.J.van Duijn, K. Mitra and I.S.Pop, Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure, Nonlinear Analysis: Real World Applications 41 (2018) 232-268.

[3] S.M. Hassanizadeh and W.G. Gray, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res., 29(10) (1993) 3389-3405.