Abstract: The scale of shale pore diameter is usually under the magnitude of nanometers, and the gas transport mechanisms existed in the nano-pores make the traditional methods based on Darcy's flow law unsuitable to describe the flow in tight-and shale-gas reservoirs. Navier-Stokes equations with slippery velocity boundary condition are usually used to expand the extent of Darcy's law, which make permeability formulas stress-related (called "apparent permeability"). Therefore, the permeability correction method becomes a hotspot of shale gas research. A general form of permeability correction method is deduced from second-order slip model of equation, and an Ng apparent permeability correlation is proposed based on apparent permeability Ng slip velocity model equations. The Ng formula can describe slip flow, transition flow, and free molecular flow (Kn < 88), and is concise and easy to use. According to the actual shale reservoir parameters and pore distribution system, the Kn range is calculated, which indicates that slip flow, transition flow, and free molecular flow exists in the shale gas flow. Based on the general form of permeability correction model, a comparison run is conducted. The results show that differences of permeability correction factor under di erent slip models increase with the increase of Kn. Beskok model and Ng model can both describe free molecular regime, however, the two models result in di erent well bottom hole pressure with shale of 10nm radius, and the difference becomes more apparent with shale of 1nm radius.