Analytical method for parameter optimization in hydraulic fracturing

An analytical method for optimizing fracture geometry size was presented,which can obtain the maximal dimensionless productivity idex(PI) considering the limited proppant mass.The analytical expression considering the dimensionless PI,dimensionless fracture conductivity and fracture length was given,by which the optimal fracture length and the maximal dimensionless PI can be calculated.This method is more simple,more convenient and faster than simulation.The calculated results show that there is only one optimal fracture length corresponding to the maximal dimensionless PI when the mass of injected proppant is fixed in known formation.