  Bundle-of-tubes model was previously used to understand the flow behaviour in
a porous medium. The interacting nature of the pores within a porous medium can
be well depicted by an interacting capillary model. However, the arrangement of
pores is crucial in understanding the flow behaviour in an interacting
capillary system, which also leads to different governing equations of
spontaneous imbibition. To this end, in the present work, we first develop a
generalized one-dimensional lubrication approximation model to predict the
imbibition behaviour in an interacting multi-capillary system. Using our
generalized model, we observe that the flow dynamics, the capillary having the
leading meniscus and the breakthrough time are governed by the contrast in the
radii and the arrangement of the capillaries. We also show that during
breakthrough, the saturation of the multi-capillary system depends on the
arrangement of the capillaries. We show that the breakthrough in the
bundle-of-tubes model occurs at a dimensionless time of $0.5$, while the
breakthrough in the interacting capillary system occurs between the
dimensionless times $0.31$ and $0.42$, for the capillary system considered in
this study. Comparing the interacting multi-capillary system with the
bundle-of-tubes model, we present substantial deviations and show that the
interacting capillary system is closer to the real porous medium.
