With the increase in energy consumption, new oil and gas extraction methods in unconventional resources have been explored. Hydraulic fracturing creates fractures to produce and make low permeability reservoirs economically profitable. Hydraulic fractures are also caused unintentionally by the uncontrolled injection in secondary recovery projects or CO2 geological storage. During proppant placement and CO2 injection, the permeability is reduced near the wellbore region due to pore clogging and mineral precipitation. The generated fractures act as high conductivity conduits that increase the capacity of flow in the reservoir. The fracture conductivity is strictly related to its geometry and hydraulic properties. However, these tend to degrade as pressure decreases. The current models do not consider fracture width change in the diffusivity inside the fracture. Additionally, the effect of fracture face skin in fracture closure has not been incorporated. This work focuses on the identification of fracture closure in fractured wells using Pressure Transient data. A semi-analytical model was developed for including the effects of fracture closure, fracture face skin, and complex fracture geometries. The matrix and fracture systems are coupled by pressure continuity at the interface. Fracture face skin is added, assuming a thin layer surrounding the fracture. The model is solved in Laplace space using a semi-analytical approach. The results are validated using a commercial simulator (CMG) and previous models. The pressure response in fractured wells with stress-sensitive fractures is analyzed at early, middle, and late times. In each time period, we identify pressure signals to detect fracture closure by incorporating effective fracture compressibility and fracture conductivity reduction. By incorporating the effective fracture compressibility, the model can reproduce a high storage capacity fracture signal. This signal occurs at early times and can help in post-fracture analysis. The fracture face skin creates an additional pressure drop in the fracture system, triggering conductivity reduction earlier than an undamaged fracture. We proposed a semi-log approach to identify fracture closure for slow rates of fracture closure and the pseudo-radial simplification to generate late time response curves instead of the complete solution for the model.