Study on permeability-enhancing mathematical model of coal fracturing with borehole water injection and liquid nitrogen injection

In order to determine the design parameters of the cool fracturing and permeability improved seam with the water injection-liquid nitrogen injection in low water-content coal seam.A mathematical moistening model of the borehole water injection was established and a calculation formula of the water injection time and the moistened radius was provided. Based on the thermodynamics theory, a freezing mathematical model with a coal borehole liquid nitrogen injection was established. An analytic solution of the temperature filed evolution in the liquid nitrogen freezing seam was provided and the calculation formula of the fracturing and permeability enhancing radius by the liquid nitrogen injection was provided. The model established was applied to analyze the fracturing and permeability enhancing effect of the borehole water injection-liquid nitrogen injection. The results showed that when the water injection pressure was 8 MPa, with the reservoir pressure of 1.1 MPa,the water injection time was 8.7 h,and the moistened radius of the water injection could be 1.2 m. With the liquid nitrogen freezing time increasing, the freezing fracturing and permeability enhancing radius would be increased and but the increasing rate would be reduced. After 240 h of the liquid nitrogen freezing, even if the freezing time was increased and the freezing fracturing radius would not be varied basically.After liquid cooling for 180 h,the freezing radius was about 1.2 m.The research would help the design of the water injection-liquid nitrogen injection into coal seam to enhance the permeability.