In the past few years, micromodels have become a useful tool for visualizing flow phenomena in porous media with pore structures, e.g., the multifluid dynamics in soils or rocks with fractures in natural geomaterials. Micromodels fabricated using glass or silicon substrates incur high material cost; in particular, the microfabrication-facility cost for making a glass or silicon-based micromold is usually high. This may be an obstacle for researchers investigating the two-phase-flow behavior of porous media. A rigid thermoplastic material is a preferable polymer material for microfluidic models because of its high resistance to infiltration and deformation. In this study, cyclic olefin copolymer (COC) was selected as the substrate for the micromodel because of its excellent chemical, optical, and mechanical properties. A delicate micromodel with a complex pore geometry that represents a two-dimensional (2D) cross-section profile of a fractured rock in a natural oil or groundwater reservoir was developed for two-phase-flow experiments. Using an optical visualization system, we visualized the flow behavior in the micromodel during the processes of imbibition and drainage. The results show that the flow resistance in the main channel (fracture) with a large radius was higher than that in the surrounding area with small pore channels when the injection or extraction rates were low. When we increased the flow rates, the extraction efficiency of the water and oil in the mainstream channel (fracture) did not increase monotonically because of the complex two-phase-flow dynamics. These findings provide a new mechanism of residual trapping in porous media.