Abstract: While pipe replacement is performed for urgent repair of long-distance pipelines, tie-in operation is generally necessary, but it lasts long time with high difficulty. At present, there is no criterion for tie-in of different pipe diameters in China. Tie-in operation usually depends on plumbers' own work experience and traditional operation methods, so the operation errors are larger. In order to improve tie-in efficiency and quality of long-distance pipelines, all kinds of tie-in situations were analyzed, especially that with bifacial pipes. The computation formula for the material cutting of fixed nozzle was established by analyzing the plane projection of fixed nozzle and intermediate nipple assembly. The material cutting method for intermediate nipple was mainly analyzed by means of space analytic geometry. And finally, the material cutting calculation formula and operation method for intermediate nipple of tie-in were provided by mathematical modeling and parameterization equation. The research results improve the operation efficiency of pipe replacement in the urgent repair of long-distance pipelines and reduce the operation risks.