Paper has a porous structure, and fluid imbibition in a paper channel is possible passively through the hydrophilic surfaces by capillary action, so it can be an appropriate substrate in the field of microfluidics. To realize the fluid behavior in a paper-based microchannel, there is a need to obtain a model for fluid flow. In this study, the capillary-driven flow in a porous structure was simulated, and the effect of geometrical and physical parameters on the wetted length and average fluid pressure was investigated. Geometric parameters are pores’ shape and size, channel dimensions, and porosity, while the investigated physical parameters were the contact angle, surface tension coefficient, and viscosity. According to the results, geometric parameters influenced the capillary pressure through the capillary surface and channel resistance variation, and physical parameters directly impacted the capillary pressure. Considering the wetted length results, the fluid imbibition velocity was fast at the beginning of the simulation and reached a constant value over time due to the increase in the flow resistance. The pressure drop was observed in the liquid phase suggesting the fluid flow from the higher pressure to the lower. The wetted-length equation was obtained based on geometrical and physical parameters. Finally, the proposed equation can be used to design and predict the liquid imbibition in porous channels.