Abstract: Under-balanced drilling technology for pinnate horizontal well is a new technology that has been widely used for enhancing the coal bed methane recovery of low permeability reservoirs and reducing the coal seam damage both home and abroad.In this paper，based on the characteristics of this new technology，the physical model is established，the mathematical models are optimized，and the solution to the models is also proposed.With the established models and the field case，by calculating and analyzing the bottom hole annular flow performance and annular gas-injection parameters，the authors conclude that the bottom hole pressure increases as the mud discharge rate increases.The larger the annular gas injection rate is，the lower the bottom hole pressure at the same mud discharge rate.The air voids and the fluid velocity in vertical well bole annulus increase slowly from the bottom to wellhead at first，but fall rapidly when the annular pressure drops to a certain extent，which is contrary to the distribution of the density of annular miscible liquid.The annular pressure decreases linearly from the bottom to wellhead.

Key words: coal bed methane, pinnate horizontal wells, under-balanced drilling, flow performance, annular pressure drop, bottom hole pressure, annular gas injection