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Considering that fractures arising from fracturing systems have bifurcation characteristics, mathematical models for single- and two-phase flow in porous media with a bifurcated fracture (BFPM) were established. The phase-field method was adopted to trace the oil–water interface, and the influence of fracture morphology, boundary conditions, gravity, and wettability on imbibition in BFPM was discussed. The results are as follows: (1) during single-phase flow in BFPM, the velocity in the bifurcated fracture was several orders of magnitude greater than that in the matrix. (2) Imbibition in BFPM includes countercurrent imbibition and the combination of co-current and countercurrent imbibition. The bifurcated fracture produces an increase in matrix pores that participate in imbibition, thus increasing the oil recovery factor by approximately 30% during simulation. (3) Closing an outlet of the bifurcated fracture has minimal effect on imbibition during the early stage (approximately the first 6 s) and an inhibitory effect during the middle and late stages (after 6 s), which leads to a decrease in oil recovery factor. (4) When the surface tension value is low (0.1 and 1 mN/m), disregarding the effect of gravity during imbibition results in an overestimated oil recovery factor value, while a large surface tension value (20 and 25 mN/m) produces the opposite effect. (5) Similar to the laws followed in porous media with pure pores and a single fracture, improving BFPM wettability increases the oil recovery factor value. This study can provide guidance for the production of low-permeability reservoirs.

The fracture-control matrix unit (F-CMU) is a special body present in low-permeability fractured reservoirs that can be distinguished by a fracture system and a matrix system. The imbibition phenomenon of the F-CMU provides the possibility for secondary development of low-permeability fractured reservoirs because of the driving force including capillary force and gravity. However, the F-CMU is difficult to obtain during the field core drilling, which has limited the development for laboratory dynamic imbibition tests. Therefore, a new F-CMU reconstruction method is proposed in this study. According to the geometry and parameters, combining laser engraving technology, the fracture system is designed and engraved. Then, the F-CMU is established using a three-dimensional (3D) printed material called polyvinyl alcohol (PVA) as fracture support material which has a faster dissolution rate and causes less damage to the core due to water being the solvent. Finally, the porosity, permeability, and wettability of the matrix system and the T2 spectra from nuclear magnetic resonance (NMR) before and after reconstruction are measured. In addition, numerical simulation calculation of F-CMU permeability is performed. The results show that the characteristic parameters of the matrix system hardly change, indicating low damage to the core. The reconstructed fracture system is found on the T2 spectra, and the fracture permeability is consistent by comparing with the experimental and numerical simulation results. The permeability of the fracture system is about 104 orders of magnitude of the matrix system, which is closer to real core and meets the requirements needed for dynamic permeability experiments.