An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

Cheng, Hanz Martin; Droniou, Jérôme

doi:10.1016/j.petrol.2018.08.062

Cited by 7 publications

(1 citation statement)

References 40 publications

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“…where (x n , y n ) are the particle location in the Cartesian space at time nδt , n refers to the current time step, n + 1 is the succeeding time step, N (0, 1) is a random selection from the standard normal distribution with zero mean and unit variance, and D m is the molecular diffusion coefficient. Within grid cells, the mean flow velocity v is derived from linear interpolations in both directions, as it is the sole interpolation scheme that verifies the continuity equation [68][69][70][71][72]. N p particles are injected in an injection window of size 0.8 L y , orthogonal to the flow direction and located at least five correlation lengths λ downstream from the side of the system (see Figure 2).…”

Section: Particle Tracking Simulationmentioning

confidence: 99%

Impact of the fracture contact area on macro-dispersion in single rough fractures

Beaudoin¹,

Farhat²

2021

Comptes Rendus. Mécanique

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In the scientific literature, the study of the impact of the fracture contact area on macro-dispersion in single rough fractures is still an open question. In this work, we study numerically the combined effects of the fracture roughness and the fracture contact area on the non-Fickian transport in single rough fractures. In particular, we quantify the contribution of the fracture contact area on macro-dispersion. These objectives are achieved by estimating the macro-dispersion coefficient from Monte Carlo parallel numerical simulations in pure advection and advection-diffusion cases. When the fractional void S O is equal to 1 (i.e., for σ lnb < 0.25), the Monte Carlo simulations show that macro-dispersion results of two contributions, dispersion caused by the heterogeneity of fracture apertures that induces a channelization of flow paths and molecular diffusion, as shown by the analytical solution proposed by Gelhar in 1993. When the fraction void S O is different from 1 (i.e., for σ lnb > 0.25), a third mechanism plays in macro-dispersion. The presence of contacts or obstacles causes a disruption of flow paths. This mechanism is identical to that induced by the fracture roughness with a lower amplitude. Its amplitude is the function of the fractional void S O .

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