Numerous reservoirs that play a significant role in worldwide petroleum production and reserves contain fractures. Typically, the fractures must form a connected network for a reservoir to be classified as naturally fractured. Characterizing the reservoir with a focus on its fracture network is crucial for modeling and predicting production performance. To simplify the solution, dual-continuum modeling techniques are commonly employed. However, to use continuum-scale approaches, properties such as the average aperture, permeability, and matrix fracture interaction parameters must be assigned, making it necessary to improve the fracture depiction and modeling methods. This study investigated a fractured reservoir with a low matrix permeability and a well-connected fracture network. The focus was on the impact of the hierarchical fracture network on the production performance of gas-based enhanced oil recovery methods. The discrete fracture network (DFN) model was utilized to create comprehensive two-dimensional models for three processes: gas injection (GI), water alternating gas (WAG), and foam-assisted water alternating gas (FAWAG). Moreover, dimensionless numbers were employed to establish connections between properties across the entire fracture hierarchy, spanning from minor to major fractures and encompassing the fracture intensity. The results indicate that the FAWAG process was more sensitive to fracture types and networks than the WAG and GI processes. Hence, the sensitivity of the individual EOR method to the fracture network requires a respective depth of description of the fracture network. However, other factors, such as reservoir fluid properties and fracture properties, might influence the recovery when the minor fracture networks are excluded. This study determined that among the enhanced oil recovery (EOR) techniques examined, the significance of the hierarchical depth of fracture networks diminished as the ratio of major (primary fracture) aperture to the aperture of medium and minor fractures increased. Additionally, the impact of the assisted-gravity drainage method was greater with increased reservoir height; however, as the intensity ratio increased, the relative importance of the medium and minor fracture networks decreased.