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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 $λ$ 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 $λ-Ca_m$ 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.