Unlike conventional or tight gas reservoirs, shale gas or oil reservoirs have complex fracture networks that are often developed due to the interactions between natural and hydraulic fractures. Another major characteristic of shale reservoirs is that a good portion of shale gas can be in adsorbed state. In order to capture these characteristics of shale reservoirs numerically, PSU-SHALECOMP, a compositional dual-porosity, dual-permeability, multi-phase reservoir simulator is employed together with the implementation of stimulated reservoir volume (SRV) approach. In this approach, three of the reservoir parameters are altered to define hydraulic fractures in the form of SRV. These altered properties are SRV fracture permeability, SRV fracture porosity and SRV fracture spacing. In the validation phase of these computationally inexpensive SRV models, rock and fluid properties and reservoir conditions representative of a Marcellus shale reservoir and normalized field data from Marcellus shale wells to history-match the production performances were used. It is shown that the PSU-SHALECOMP simulator with the implementation of SRV model is capable of matching the historical data effectively and rapidly. In pursuit of successful validations of various production scenarios, several carbon dioxide injection scenarios were performed to see the performance of the PSU-SHALECOMP simulator in depleted Marcellus shale reservoirs.