Calculation methods for pressure drop along downhole bending section of coiled tubing

With the development of fracturing technologies, fracturing process and string structures become more and more complicated, especially the curvature radius of pipe string in downhole bending section is varying from a few meters to thousands of meters. The numerical simulation model for straight pipes and bends was established by means of numerical simulation based on the geometric characteristics of coiled tubing. Then, the on-way pressure drop in different working conditions was calculated and compared with the theoretical calculation result. It is verified that the numerical model is accurate with the error of bend and straight pipe lower than 5% and 6% respectively. The pressure drop along the bend with curvature radius of 1.25-1 280 m was calculated and then compared with the numerical simulation result. It is shown that the numerical simulation result coincides well with the theoretical calculation result when the curvature radius of bend is shorter than a certain critical value which is related to fluid medium and displacement. When the curvature radius of bend is longer than the certain critical value, the theoretical calculation result of bend is lower, and even lower than the pressure drop of straight pipe. Finally, the theoretical pressure drop formula of bend was corrected according to the numerical simulation results. It broadens the calculation range of pressure drop calculation formula of bends, and provides the reliable calculation formula for the pressure drop of bent structures, such as coiled tubing.