  A deep understanding of two-phase displacement in porous media with
permeability contrast is essential for the design and optimisation of enhanced
oil recovery processes. In this paper, we investigate the forced imbibition
behaviour in two dual-permeability geometries that are of equal permeability
contrast. First, a mathematical model is developed for the imbibition in a pore
doublet, which shows that the imbibition dynamics can be fully described by the
viscosity ratio $\lambda$ and capillary number $Ca_m$ which creatively
incorporates the influence of channel width and length. Through the finite
difference solution of the mathematical model, a $\lambda-Ca_m$ phase diagram
is established to characterise the imbibition preference in the pore doublet.
We then investigate the imbibition process in a dual-permeability pore network
using a well-established lattice Boltzmann method, focusing on the competition
between the viscous and capillary forces. Like in the pore doublet, the
preferential imbibition occurs in high permeability zone at high $Ca_{m}$ but
in low permeability zone at low $Ca_{m}$. When $Ca_m$ is not sufficiently high,
an oblique advancing pattern is observed which is attributed to non-trivial
interfacial tension. Thanks to the newly defined capillary number, the critical
$Ca_{m}$ curve on which the breakthrough simultaneously occurs in both
permeability zones, is found to match perfectly with that from the pore doublet
and it is the optimal condition for maximising the imbibition efficiency in the
entire pore network.

Fluid Dynamics;Soft Condensed Matter