Calculation of Tubing Critical Pump Rate while Fricturing by both Tubing and Casing with Packers

In order to prevent packers from moving in tubing and casing fracturing due to great piston force,the study on critical tubing pump rate which won’t cause packer motion was conducted.Through mechanical analysis of string,the calculation model of axial force for fracturing string was established,the anchoal force of packer rubber was simulated by using finite element software.So the calculation model of tubing critical pump rate which won’t cause packer motion was established according to the relationship of axial force and anchor force.The calculation results showed that critical pump rate of φ60.3 m,φ73.0 mm and φ88.9 mm tubings is 0.965 m3/min,0.810 m3/min and 0.470 m3/min respectively at well depth of 2 000 m and the fracturing pressure gradient of 2.1 MPa/100m,but at the depth of 3 000 m,the critical pump rate is 1.120 m3/min,0.985 m3/min and 0.680 m3/min respectively,which shows that the critical pump rate increases with well depth,and decreases with the increase of tubing size.Furthermore,when formation fracturing pressure gradient is 1.8 MPa/100m,the critical pump rate of φ88.9 mm tubing was the minimum value of 0.460 m3/min.It is concluded that only tubing injection pump rate higher than the critical value can the fracturing string be prevented from moving effectively, which is beneficial for insuring the accuracy of fractured interval and depth in the operation of tubing and casing fracturing.