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Natural gas in unconventional gas reservoirs typically contains multiple gas components. Existing models incorporate either the unique flow mechanisms in tight and shale gas reservoirs (slip flow) or multi-component sorption isotherm without combining them. In this work, we developed a compositional flow code incorporating slip flow and multi-component sorption using the extended Langmuir isotherm (EL). The model was discretized using finite volume method based on unstructured Perpendicular Bisection (PEBI) grids for their local orthogonality and flexibility in handling irregular shaped domain. The code was verified using ECLIPSE-CBM for multi-component sorption and using ECLIPSE with modified transmissibility for slip flow calculation. The model was further validated by reproducing the pressure build up data during well shut-in period in a tight gas reservoir in Xinjiang, China. The developed code was used to understand and quantify the importance of multi-component EL isotherm and slip flow. The evolution of the bottom-hole pressure (BHP), sorption volume, and gas composition was also simulated under various reservoir conditions including different initial gas compositions, sorption capacities, and reservoir sizes. The deviations caused by representing shale gas as pure methane using single-component Langmuir isotherm can reach as much as 90% for BHP and 45% for sorbed volume if the initial methane composition was 80%. The predicted produced gas composition with the EL isotherm showed a unique constant composition (CC) stage before the gas flow reached the domain boundary, indicating the potential use of gas composition as another type of data to infer reservoir boundary and flow regimes. The developed code offers a powerful tool to understand gas flow and sorption, as well as an analyzing tool to identify reservoir boundary and flow regimes compared to traditional well test method, which requires expensive measurements of BHP. [ABSTRACT FROM AUTHOR]