  A numerical study of yield-stress fluids flowing in porous media is
presented. The porous media is randomly constructed by non-overlapping
mono-dispersed circular obstacles. Two class of rheological models are
investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic
fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham
numbers is studied at three different levels of porosities of the media. The
emphasis is on revealing some physical transport mechanisms of yield-stress
fluids in porous media when the elastic behaviour of this kind of fluids is
incorporated. Thus, computations of elastoviscoplastic fluids are performed and
are compared with the viscoplastic fluid flow properties. At a constant
Weissenberg number, the pressure drop increases both with the Bingham number
and the solid volume fraction of obstacles. However, the effect of elasticity
is less trivial. At low Bingham numbers, the pressure drop of an
elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at
high Bingham numbers we observe drag reduction by elasticity. At the yield
limit (i.e. infinitely large Bingham numbers), elasticity of the fluid
systematically promotes yielding: elastic stresses help the fluid to overcome
the yield stress resistance at smaller pressure gradients. We observe that
elastic effects increase with both Weissenberg and Bingham numbers. In both
cases, elastic effects finally make the elastoviscoplastic flow unsteady, which
consequently can result in chaos and turbulence. Keywords: Yield-stress fluids;
Viscoplastic fluids; Elastoviscoplastic fluids; Porous media
