Analytical Solution for Determining Fracture Attenuation

This work is devoted to the analytical solution of the damping of the fracture of the hydraulic fracturing. A solution is obtained for changing the dimensionless conductivity of the crack due to a decrease in the conductivity of the proppant and its removal from the crack. The considered crack geometry corresponds to the Perkins-Kern analytical model, which allows us to take into account the change in the crack width depending on its length. To calculate the proppant conductivity, laboratory studies were used, the data of which were extrapolated in order to predict the destruction of proppant balls during the operation of a well with a fractured hydraulic fracturing.