Formations with interconnected pathways of fractures (or high permeability regions) between the production and injection wells suffer from early breakthrough and low cumulative recovery during gas injection process due to the contrast in the capillary pressure of matrix and fractures. A methodology is developed to modify the production well by a high breakthrough capillary pressure skin and by controlling the injection pressure. Consequently, the liquid recovery at the gas breakthrough is significantly enhanced. This flow manipulation prevents the gas pressure to exceed the breakthrough capillary pressure plus pressure drop of the skin. The experiments are conducted in a sintered heterogeneous glass bead model using air-liquid (e.g., water and CMC solutions) systems. Tests are initially performed without the pressure control to obtain the injection pressure at which the gas breakthrough occurs. In the experiments, the gas injection flow rate is reduced to half successively, whenever the gas injection pressure reaches within 10% of the skin breakthrough capillary pressure. We continuously measure the cumulative liquid production weight and the gas injection pressure over time; pictures are continuously captured from the process to track the advancement of air-liquid interface in matrix, fracture, and skin. The effects of flow rate, drainage direction (vertical or horizontal), and fluid viscosity on the process performance are investigated. Without the use of a skin and pressure control, the recovery at breakthrough from the horizontal model is only limited to that from the fracture which is about 9% of the pore volume. The overall recovery increases to more than 90% in the presence of the skin and injection pressure control. The recovery in the vertical gas injection benefits from additional driving force provided by gravity; the recovery factors (RF) as high as 93% are achieved in the vertical drainage tests using the skin, and even without the pressure control. The proposed methodology is successfully tested, implying its promising features such as delayed gas breakthrough in a highly heterogeneous porous medium where fractures interconnect the injection and production wells. This method has potential applications in enhanced oil recovery, remediation of contaminated porous media, and membrane separation processes.