An analytical model of coal wellbore stability based on block limit equilibrium considering irregular distribution of cleats

An analytical model of coal wellbore stability is established based on the block limit equilibrium method, taking the irregular distribution of cleats into account. Because coal seam is cut into discontinuous blocks with different shapes and sizes, block slip can be treated as the symbol of coal wellbore instability. According to the geometric characteristic of blocks, blocks surrounding the wellbore can be divided into 3 categorizes: type I, type II and type III. To evaluate the block slip, the stress distribution near the wellbore is determined based on the continuous medium mechanics and the fracture mechanics. Using Mohr-Coulomb criterion and limit equilibrium method, the critical conditions of block slip are derived by defining the failure coefficient, including type I, type II and type III. The proposed model is verified by comparison of the obtained results from the proposed analytical method with the discrete element method as well as the actual drilling. It can be proved that the proposed model can predict accurately block slip. Additionally, the effect of drilling fluid pressures on the wellbore stability is specially investigated. The results show that with the increasing of drilling fluid pressure, the degree of wellbore collapse may be more severe. Meanwhile, the analysis method of reasonable drilling fluid pressure for coal drilling is proposed based on the interval theory, combining the slip area of blocks. Finally, the parametric study is focused on investigating the effects of the internal friction angle of face cleats, the cohesion of face cleats and the tensile strength of butt cleats on the failure coefficients of blocks.