Liquid-filled corners and capillary bridges can establish networks connecting seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these networks constitutes a secondary drainage mechanism that can significantly affect fluid configurations and residual saturations. In order to investigate the prevalence of this drainage mechanism, we propose a quasi-static pore-network model based on modifying the trapped-cluster-identification algorithm in an invasionpercolation model. With the modification, wetting-phase connectivity is provided by direct successions of pores and throats, represented by sites and bonds, as well as by chains of interconnected capillary bridges. The advancement of the fluid interface in the porous matrix is determined by the bonds' invasion thresholds and local capillary pressure values, calculated taking into consideration gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media are reproduced, showing good qualitative agreement.