Ductile failure seepage coupling constitutive equations of broken soft coal and its verification in indirect fracturing engineering

Indirect fracturing is one of the new technologies to improve the output of coal bed methane (CBM) in surface wells in broken soft and low-permeability coal bed.The key to its success lies in whether hydraulic fractures (HFs) in roof can effectively penetrate the coal rock interface and enter the coal seam.And the core factor is the coupled response characteristics of ductile failure and seepage for the coal.The Park Paulino Roesler potential energy function of the twodimensional problem is extended to the three dimensional stress space,combining with the cubic law,the ductile fracture tangential seepage relationship of coal discontinuities is obtained.The Helmholtz free energy expression considering coal plastic deformation,tensile and compressive damage is constructed,combining with Darcy’s law,the permeability coefficient (or filtration coefficient) expression of the coal matrix under the influence of plastic deformation and tensile damage variables is derived.In the numerical calculation,the mechanical properties of coal matrix and discontinuities are assigned to the solid elements and the zero thickness cohesive elements,respectively,and they are connected by sharing nodes to realize the stress seepage coupling.The fracture mechanics experiment is used to identify the material parameters,and the rationality of the ductile failure seepage (DF-S) coupled constitutive equations of the coal is verified by experiments of fracture mechanics and hydraulic fracturing.On this basis,the process of HFs extending from the roof to the coal bed under the influence of multiple factors are simulated,including the distance between the horizontal well and the interface D,the difference between vertical and minimum horizontal in situ stress Δσ,and the coal rock interface friction coefficient fc,r.The results show that:① DF-S constitutive equations can well reflect the ductile failure seepage coupling response characteristics of the coal during indirect fracturing;② The coal rock interface will hinder the HFs expansion,and the mechanism of this phenomenon lies in the hydraulic energy dissipation caused by the ductile fracture of the coal discontinuities,plastic damage of the coal matrix,and the leakage of fracturing fluid,resulting in a minimum of 2% of hydraulic energy used for HFs propagation;③ Under numerical simulation conditions,the critical fc,r for HFs to penetrate the coal rock interface is positively correlated with D,and negatively correlated with Δσ.D has a greater impact on the critical fc,r,and 18%-30% of hydraulic energy is used for HFs propagation if D is controlled within 1 m,thus increasing the success rate of indirect fracturing technology.The critical D,Δσ,fc,r condition of HFs penetrating the coal rock interface has been applied in Zhaozhuang mine of Jincheng,so as to improve the CBM production of surface wells in broken soft and low-permeability coal seam,which provides theoretical support for indirect fracturing design.