Natural gas hydrate (NGH) has the advantages of wide distribution and large reserves, and has attracted extensive attention from the international community. Researchers have conducted quantitative microscopic pore-scale simulations, exploitation surveys, laboratory tests, and numerical simulations, but commercial development is still a long way off. In view of the existing problem of insufficient productivity, enlarged permeable well wall technology is studied in this paper, which is a method to improve reservoir productivity by changing well conditions. There is a free gas zone in the Class 1 reservoir and no free gas zone in the Class 3 reservoir; the structural differences lead to different multiphase seepage processes, and the mechanisms of stimulation are also different. In order to further improve productivity and understand the production difference between the two reservoirs, this paper selects Class 1 and Class 3 reservoirs, establishes the numerical simulation model of NGH extraction by the depressurization method, analyzes the influence of well radius and permeability on productivity, and compares the influence of this technology on the two reservoirs. The results show that (1) the productivity of Class 1 and Class 3 reservoirs is significantly increased under this technology. The same well adjustment has a better effect on Class 3 reservoirs. (2) When the radius is 1 m, the best stimulation effect is shown; the radius enlarges from 0.1 to 1 m, and the V P of Class 1 and Class 3 reservoirs is increased by 19.70 and 17.06%, respectively. (3) When permeability is 1 × 10–7 m2, the best stimulation effect is shown; the permeability is increased from 1 × 10–9 to 1 × 10–7 m2, and V P is increased by 35.50 and 115.35%, respectively. (4) Changing the radius and permeability at the same time can better improve the productivity of the two reservoirs, and has a synergistic effect on Class 3 reservoirs.