A new optimal method on artificial fracture parameter with long-term conductivity taken into account

Artificial fracture parameter optimization with dimensionless proppant index method is an analytical approach widely used, but the effect of long-term artificial fracture conductivity performance change with time on the well productivity have not been taken into account. The optimization results by dimensionless proppant index method are not the best one in the view of practical production of stimulation wells. In this paper, combined with the experimental results of long-term proppant conductivity, transferring the fracture width and permeability in dimensionless proppant index method into the functions of time, the dimensionless cumulative productivity index has been presented though the integral of dimensionless proppant index with respect to time. And this result will serve as the optimal fracture parameter. Because of variable time being introduced into the formula and considering the change of proppant conductivity performance with time, the calculating method is more suitable in practice and more reasonable comparing to dimensionless proppant index method. The numerical solutions show that greater fracture width and higher concentration of proppant should be reached for low and extra-low permeability reservoirs with long-term conductivity taken into account in order to get more cumulative production. The views of lower demand artificial fracture conductivity and longer fracture for low and extra-low permeability reservoirs should be changed. This method can prolong the validity period of post-treatment production increase for single well and is of significance to evaluate operation effect. It is suggested that the influence of proppant concentration on long-term conductivity should be developed pertinently for certain areas, which could provides reliable reference for the application of dimensionless cumulative production index method.