Establishment and application of damage constitutive model for acid-etched coal mass in CO₂ foam fracturing fluid

Although CO₂ foam fracturing can effectively increase the permeability of coal seams and improve the air permeability of coal seams, there are still problems that make it difficult to accurately predict the fracturing range due to the unclear constitutive relationship of acidified coal damage. In order to explore the influence of acidification−fracturing on the constitutive relationship of coal, based on the CO₂ foam fracturing mechanics experimental system, the uniaxial compression test of coal body under different acid intrusion durations was carried out, and the characteristic parameters such as peak strength, residual strength, elastic modulus and brittleness index were quantitatively characterized, the gradual failure behavior of acidified coal during loading was analyzed, and a segmented constitutive model of coal and rock damage under acid−force compound action was constructed. The results show that the internal structure of the coal body is damaged under acid intrusion, resulting in a significant decrease in its peak strength and residual strength, but due to the difference in the bearing mechanism between the two, the residual strength mainly depends on the interaction between blocks, which is more sensitive to microstructure damage, so the decrease is large. Under the chemical-physical synergy of CO₂ foam fracturing fluid, the acidic substances quickly seep and diffuse into the coal body, reacting with carbonates and some clay cements, resulting in the evolution of the mechanical characteristics of the coal body from partial ductility to high brittleness, and the brittleness degree increases with the extension of acid invasion time. Based on the Lemaitre strain equivalence hypothesis and elastic damage mechanics, a segmented constitutive model of coal-rock damage is established, and the deformation laws of coal in the pre-peak stage, post-peak stress drop stage and residual stability stage are characterized by different constitutive relationships. In this model, the damage correction coefficient δ characterize the residual deformation characteristics of the material, while the damage constitutive coefficient λ controls the post-peak softening rate, which together dominate the overall constitutive relationship characteristics of the model. Compared with the traditional constitutive model, the proposed model can more accurately characterize the phased changes of coal mechanical properties under CO₂ foam fracturing, and the prediction accuracy of fracturing radius can be effectively improved based on the quantitative calculation of this model and the fracturing radius correction formula. Based on the results, the “diamond-shaped hole” method is proposed, which can achieve precise permeability enhancement of low permeability coal seams and improve the efficiency of gas extraction.