An analytic model of wellbore stability for coal drilling base on limit equilibrium method

An analytic model of coal wellbore stability under non-uniform in-situ stress and drilling fluid pressure is es- tablished with the consideration of the random distribution of coal cleat and crack,and the coal near wellbore cutting into blocks. In this paper,the authors consider coal bed near wellbore as quasi continuum,and get the stress distribu- tion of coal bed using continuum theory and rock fracture mechanics. The analytic formula of block sliding,which is considered as a limit condition of coal wellbore collapse,is deduced. Considering positions and area of coal sliding block as control conditions,the PFC software that is one of DEM software is used to verify the accuracy of the analyti- cal model. The results show that the bigger drilling fluid pressure is,the worse wellbore collapse is. Type I and type III block are extremely easy to slide,in contrast,type II block is not easy to slide and the sliding conditions of type II block is that the adjacent block should slide first. For the block that slide along the face cleat,the angle of internal friction and the cohesion of end cleat have little influence on block sliding. For the well named Qin 12 -10 -70 -X, when the drilling fluid pressure is about 9. 5 MPa,borehole collapse has the lowest level,and the increase or decrease of drilling fluid pressure can intensify borehole collapse.