Limited attempts have been made to model shale gas reservoirs on a compositional basis. Multiple distinct physical phenomena influence the behavior of reservoir fluids in shale, resulting in measurable compositional changes in the produced gas over time. These phenomena include differential desorption, fractionation via phase change, and preferential diffusion. To address these phenomena, we have developed a compositional numerical model which describes the coupled processes of diffusion and desorption. We have also developed a tool for generating simulation grids capturing fracture geometries of realistic complexity. By combining the physics of flow in complex fractures with diffusion through nanopores, we show how gas composition changes during production. We identify and illustrate signature trends in the flowing gas composition according to our model. In addition, we present a workflow for the integration of measured gas composition data into traditional production data analysis. We prove that the onset of various transient flow regimes that are unique to shale gas reservoir systems can be identified in the model-based flowing composition data. For example, the transition from fracture-drainage to matrix-drainage can be identified by a characteristic trend in flowing gas composition. Some reservoir properties can be determined through analysis of the compositional shift in the flowing gas. This work expands the current understanding of well performance for shale gas to include physical phenomena that lead to compositional changes for realistic fracture configurations. This work can be used to optimize fracture and completion design, improve well performance analysis and provide more accurate reserves estimation. In this work we develop a numerical model which captures multicomponent desorption, diffusion, and phase behavior in ultra-tight rocks, we present a grid generation technique which captures the complexity of shale system fractures, and we validation of our interpretations of diagnostic trends.