A fractional poroelastic-fracture model for predicting crack initiation and propagation during CO2 foam fracturing in low-permeability coal seams

Low-permeability coal seams create serious difficulties for gas extraction. Safe mining operations and optimal use of coalbed methane resources both suffer as a result. This study takes the No. 2 coal seam of YUANZIGOU Coal Mine as a case example, aiming to reveal how borehole-surrounding coal fractures initiate and grow during CO 2 foam fracturing. A theoretical model was developed-combining poroelastic mechanics, fracture mechanics, and radial fracturing tests-to predict crack initiation pressure and propagation length. The model accounts for in-situ stress, pore pressure, phase-transition-induced thermal stress, foam quality, crack filtration loss, and joint roughness. Overall, the observed fracture evolution follows a distinct sequence: initiation, expansion, connection, then stabilization and adjustment. Raising foam quality from 0.4 to 0.7 lowers crack initiation pressure by 19.1–37.8% compared to conventional hydraulic fracturing. Theoretical calculations deviate from field measurements by less than 2.2% relative error-a fairly tight match. Under typical engineering conditions, fracture half-length reaches 1.67 m after 20 min of injection. That aligns well with predicted values (relative error range: 1.7–3.0%). Thirty days after fracturing, single-well gas extraction concentration jumps from 18.5 to 36.8%; gas flow rate climbs from 0.12 to 0.41 m 3 /min; and effective extraction radius expands from 1.2 to 2.8 m. The above results verify the high accuracy of the proposed fractional prediction model for CO 2 foam fracturing fracture evolution. It can therefore provide a solid theoretical basis for optimizing fracturing parameters and borehole layout to improve gas extraction efficiency in low-permeability coal seams.