Application of the building block approach to characterize the pressure loss of water and fracturing fluid in contraction-expansion pipe

Abstract

In the fracturing pipeline, the contraction-expansion pipe structure is various. Accurate calculation of pressure loss can provide a theoretical support for the design of high sand ratio fracturing process parameter and tools selection. In this paper, the building block approach is used to describe the general framework for calculating the pressure loss of water in contraction-expansion pipe [D1≠D2、Ld/(D1/2 + D2/2)＜2.00] and expansion-contraction pipe (d1≠d2、LD/D＜3.75). The drag ratio method was used to describe the pressure loss of the fracturing fluid based on the pressure loss of water in the contraction-expansion pipe and the expansion-contraction pipe. Finally, the calculation methods for the pressure loss of water and fracturing fluid were described. The data from the experimental test showed that the relative error was less than 15%. The experimental study of water in the contraction-expansion pipe showed that the pressure loss was positively correlated with the flow rate, but it was negatively correlated with the ratio of inlet-outlet diameter and the ratio of flow path length. And for the expansion-contraction pipe, pressure loss was positively correlated with the flow rate and ratio of flow path length. When the ratio of flow path length was close to 3.75, the ratio of inlet-outlet diameter was positively correlated with the pressure loss, and when the ratio of flow path length was close to 0.05, the ratio of inlet-outlet diameter was negatively correlated with the pressure loss. Analysis of fracturing fluid in contraction-expansion pipe and expansion-contraction pipe showed that the flow rate, proppant concentration and thickener concentration were positively correlated with pressure loss, and the drag rate of fracturing fluid reached 72%.