Predicting the radial heat transfer in the wellbore of cryogenic nitrogen fracturing: Insights into stimulating underground reservoir

Cryogenic nitrogen fracturing is an attractive method for stimulating underground reservoir, since it could favorably induce complex fracture due to the huge temperature difference with lower injection pressure and with the replacement of current water-based fracturing fluid. However, the concern about whether cryogenic nitrogen would be overheated remains unrevealed in the engineering environment with large wellbore length. In addition, reservoir stimulation results are also related with the pressure state at bottom hole. Therefore, in this study, a mathematical model was proposed to predict the radial heat transfer and its influence on vertical pressure transmission in the wellbore with cryogenic nitrogen as fracturing fluid. The model fully couples the heat transfer, hydraulics, and the compressibility of nitrogen, and then, the calculation results were presented and analyzed through a case study. According to the results, the temperature of nitrogen increases too fast under conventional engineering conditions, and it changes into gaseous state at the depth lower than 100 m. Finally, the temperature difference between nitrogen and formation rock becomes too minimal to induce thermal stress at bottom hole. Due to the fast temperature increase, the density of nitrogen decreases too much, and the vertical pressure increasing rate by liquid nitrogen (1.66 MPa/km) is merely 18.2% that in carbon dioxide fracturing (9.13 MPa/km). The results indicate that utilization of special casing with much larger thermal resistance is an indispensable approach to realize the feasibility and advantages of cryogenic nitrogen fracturing.