Study On The Constitutive Equation Of The Cohesive Crack In Coals And Its Application In Fracturing Engineering

As an important source of clean energy,coalbed methane?CBM?has received considerable attention in recent decades.The main technique to enhance the recovery of CBM is hydraulic fracturing in coals.The crack propagation behavior of hydraulic fracturing in coal seam will directly affect the exploitation of coalbed methane,which requires a deep understanding of the fracture behaviors of coals.Linear elastic fracture mechanics?LEFM?has become an enormously successful theory framework in characterizing crack propagation in a wide range of solid materials.For linear elastic rock fracture mechanics,rocks is generally simplified to brittle materials,in which the fracture process zone?FPZ?,i.e.the region ahead of the crack tip where micro-cracks initiate and coalesce,is small compared to the size of the crack and the size of the specimen.On the other hand,coals usually exhibit quasi-brittle failure behaviors,characterized by a strain softening regime after the peak stress.For the quasi-brittle material,the size of FPZ is considerably large and has strong impact on the fracture behavior,and thus the theory of LEFM no longer apply to study the crack propagation behavior in coals.The cohesive zone model?CZM?has proven a useful theoretical tool to describe the fracture behavior in the FPZ of quasi-brittle materials.In the theory of CZM,the FPZ in front of the real crack tip is lumped hypothetically into a discrete line or plane corresponding to two-dimensional or three-dimensional cases,respectively,and the nonlinear behavior occurring in the FPZ is represented by a constitutive equation that relates the cohesive stresses to the displacement jump across this line or plane.In this research,we carried out tests to establish the constitutive equation of cohesive crack in different rank coals,and the constitutive relationships were incorporated into numerical modeling to predict the fluid-driven crack propagation procedure in coals.Furthermore,the fracturing experimental results of coals are compared with the numerical simulation results based on the CZM and LEFM,respecively.The main contents and results are as follows:?1?The mode I constitutive relationships of CZMs for the five different rank coals have been determined by the disk-shaped compact tension?DC?T??tests.With the coal rank rising,the initial stiffness and peak loads increase,and the critical crack separation displacement reduces.Meanwhile the shape of the post-peak softening curves tends to be linear and the failure mode becomes more brittle.Moreover,as the coal rank rises,the average mode I fracture energy decreases,and the coefficient of variation?CVs?of fracture energy increases.For the lower rank coals,the crack propagation paths are more tortuous,and the roughness coefficients?R_s?of the fracture are larger.More importantly,to arrive at a general form of CZM,the Karihaloo's polynomial cohesion-separation law was applied,which shows the best fitting degree for all the coal materials,and such is selected as the final CZM model for the coals.Furthermore,the mode I SENB tests were carried out with different rank coals,and the corresponding numerical simulation was conducted by means of the cohesive element method which utilized the Karihaloo's polynomial cohesion-separation laws with the fitting parameters obtained from DC?T?tests.The comparison between the test results and the numerical simulation results was carried out,the established CZMs have been verified to be applicable to characterize the mode I crack propagation in coals..?2?The mixed mode I/II PPR constitutive relationships of CZM for the different rank coals have been determined by DC?T?tests and the punch-through shear?PTS?tests.For the PTS tests,with the coal rank rising,the initial stiffness and peak loads increase,and the maximum crack tangential displacement reduces,meanwhile the average mode II fracture energy decreases.Furthermore,the mixed mode I/II SENB tests were carried out with different rank coals,and the corresponding numerical simulation was also conducted by means of the cohesive element method which utilized the PPR constitutive equation obtained from DC?T?and PTS tests.The comparison between the test results and the numerical simulation results was carried out,and it is verified that the mixed mode I/II established-CZMs are applicable to describe the crack propagation behavior in coals.?3?Hydraulic fracturing experiments were carried out on the different rank coals,including weakly caking coal,fat coal and anthracite.Meanwhile,the liquid CO₂ fracturing experiment and the supercritical CO₂ fracturing experiment were also performed on the coal samples.The experimental results show that:with the coal rank rising,the initiation pressure increases and the fracturing time gradually decreases.Compared with the hydraulic fracturing,the initiation pressure of waterless fracturing significantly decreases.And the initiation pressure for ScCO₂ fractruing in fat coals,anthracite and mudstone is about 30.42%,33.95%and 35.68%smaller than that for hydraulic fracturing.Moreover,the number of crack after the waterless fracturing are significantly more than that induced by the water,for the ScCO₂ fracturing,the interlaced crack networks appeared in the fractured coal specimens.?4?The hydraulic fracturing numerical simulations of the different rank coals were carried out by means of the cohesive element method which utilized the constitutive equation obtained from DC?T?and PTS tests.And the numerical simulation results agree well with the experimental results of hydraulic fracturing for the different rank coals.In comparison with the simulation based on the CZMs of coals,the numerical simulation results based on LFEM deviate significantly from the test results.Therefore,the CZMs obtained from tests are more suitable to describe the crack propagation of hydraulic fracturing in coals.In addition,the numerical simulation of multi-crack propagation was implemented for the different fluid fracturing in the coal seam by using zero-thickness cohesive element.