• A mathematical model is developed for penetration lengths in a pore doublet with arbitrary initial interface location. • The effects of initial interface location, capillary number, viscosity ratio and width ratio are investigated. • Phase diagrams are presented for the occurrence of backflow in a pore doublet. • The capillary valve effect is found to inhibit backflow in pore networks. Backflow is a typical flow phenomena in two-phase displacement, but it is rarely studied in the forced imbibition and it remains unknown if the backflow occurs in forced imbibition into a porous medium. In this paper, we focus on the forced imbibition and investigate the backflow behavior in pore doublet (PD) models and in dual-permeability pore networks. Inspired by Gu et al. (2021) and Shan et al. (2023), a general mathematical model is first developed to predict the evolution of the penetration length of wetting fluid in a PD with arbitrary initial interface locations. Based on the analytical predictions and numerical simulations, we then study the influence of initial interface location, capillary number, viscosity ratio, and channel width ratio on the backflow. Results show that the backflow in a PD is mainly attributed to high flow rate in narrow channel, driven by the dominant capillary force. To supplement the insufficiency of inlet flow rate, the fluid in wide channel has to flow backwards to fill the narrow channel. The backflow strengthens with the decrease of capillary number or viscosity ratio, but it exhibits non-monotonic variation with initial interface location and channel width ratio. Moreover, the phase diagrams showing the critical conditions for the occurrence of backflow are established in terms of capillary number, viscosity ratio and channel width ratio. Finally, numerical simulations are conducted to explore the occurrence of backflow in three different dual-permeability pore networks. It is found that the backflow does not occur in dual-permeability pore networks due to the low flow rate caused by overlap event and pronounced tortuosity in the low permeability zone, or occurs only in the early stage when the capillary valve effect does not work. [Display omitted] [ABSTRACT FROM AUTHOR]