The Calculation of Coal Rock Fracture Conductivity with Different Arrangements of Proppants

An accurate evaluation of coal rock fracture conductivity is an important prerequisite for predicting the productivity of CBM wells. Coal rock is soft and fragile, with low elastic modulus and high Poisson ratio. In the process of fracturing flowback, the contact deformation between proppant and fracture wall will affect the fracture conductivity when the proppant is embedded in the coal rock; thus the calculation method of plate fracture conductivity is no longer suitable for the evaluation of coal rock. Based on the contact deformation theory of elastic mechanics, a method for calculating contact deformation of proppant in fracture is proposed. Considering the effect of the deformation and embedded depth of proppant and the tortuosity of pore flow channel between proppant particles on fracture conductivity, a model for calculating fracture conductivity of coal rock fractures under three kinds of proppant arrangement (Model 4-1, Model 3-1, and Model 2-1) is established. Comparison of calculation results of theoretical model and experiments confirmed that the arrangement of proppant in coal rock fracture is closest to Model 3-1, and the influence of mechanical parameters of coal rock and proppant on fracture conductivity is calculated and analyzed by this theoretical model. The study shows that the coal rock fracture conductivity is affected little by Poisson’s ratio of coal rock and proppant, which is greatly influenced by the elastic modulus of them, and the effect of particle size of proppant is especially significant.