Modeling transient pressure behavior of a fractured well for shale gas reservoirs based on the properties of nanopores

Shale gas sources are abundant in China, but gas flow in reservoir cannot be simply represented by Darcy equation anymore and the natural productivity is ultra-low owing to numerous nanoscale pores in shale, so how to model gas flow in nanopores and couple it with hydraulic fracturing become important. This paper developed a dual-porosity model to simulate naturally fractured reservoir based on the research of hydraulic fracturing in which desorption, diffusion and slippage flow in nanopores were considered. The analytical solution of a fractured well in 3D reservoir simulator with laterally closed, infinite and constant pressure boundaries is obtained in Laplace space by employing point source function, and type curves of transient pressure and rate decline behaviors are plotted with Stehfest numerical inversion algorithm. Influence factors have been analyzed combined with the data of shale gas reservoirs. Results show that six flow regimes are recognized for transient pressure behavior. Gas desorbed from pore walls, Knudsen diffusion and slip flow in nanopores have great effect on type curves: the bigger the desorption coefficient is, the smaller the wellbore pressure drop is and the well produces longer; the bigger the diffusion coefficient and slippage factor are, the higher the production rate is and the transition regime finished earlier. Besides, capacitance coefficient, transfer coefficient and boundary also have influence on transient pressure and rate decline behaviors of fractured well.