The key parameters of proppant transport in complex fractures

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The proppant transport in complex fracture has been a hot area of research. Via optimizing the pumping parameters, like pump rate and proppant type, the proppant packing efficiency will be improved in the branch fractures, by which the stimulation results will be enhanced. The research work on proppant transportation has just started, and the laboratory physical simulation experiments are the main methods. The researchers from Katherine Thomas Technology Center and Colorado School of Mines have carried out proppant transporting experiments in complex fractures separately. The major finding is the mechanism that the proppant flows from the main fracture turning into the branches: (1) the gravity effects of the proppant bed; (2) the fluid drag effect under the critical flow rate. However, only the descriptive results were obtained from the experiments. The further numerical models and calculations based on the experimental findings still can’t be found in the current reports. This paper was aimed to reveal the proppant transporting in complex fractures using numerical methods. By literature surveys, the fractional flow of fracturing fluid and critical condition of proppant diversion were proposed to be the key parameters of proppant transport in complex fractures. The calculations of fluid fractional flow in complex fractures and the critical condition of proppant diversion were derived and verified in this paper. The fracture unit model was abstracted and used to describe the complex fractures, by using which the complex fractures could be simplified into the combination of superior fracture and sub-fracture. The fracture unit model was compared with the model of limited entry fracturing for the fluid flow, formation condition, flow friction, etc. A calculation of fracturing fluid fractional flow in complex fractures was built referring to the calculation of limited entry fracturing. Furthermore, an improved calculation of fracturing fluid fractional flow in complex fractures was derived based on the electricity flow principle in the parallel circuit, which was also the mechanism of the limited entry fracturing. The calculation results were verified by the fluent simulation results. The improved calculation was proved to be more accurate, which had the error of −2.76%. Hence, the improved calculation will be used for the fluid distribution in the proppant transport in the complex fractures. Based on the fractional flow calculation, the critical flow rate of proppant initiation was proposed to represent the critical condition of proppant diversion. The calculation of critical velocity of proppant diversion has been derived. The calculation results were tested by the Colorado School of Mines experimental results. The average error was 8.18%, which indicated that the calculation could predict the critical velocity of proppant diversion. By synthesizing the fractional flow calculation and the propapnt diversion calculation, the proppant transport in branch fractures was predicted. Using the calculation results, a chart was drawn, in which the critical proppant diversion conditions were compared with the branch fracture flow rates intuitively under the experimental conditions of Katherine Thomas Technology Center. The 100 mesh proppant was able to enter the secondary and tertiary fractures. The 20/40 mesh proppant needed higher flow rate in the main fracture to be transported into the secondary fracture. The predicted results were in accordance with the Katherine Thomas Technology Center experimental results. Therefore, the key parameters theory and their calculations have been verified and could be used for further studies and as the theoretical foundation of the fracture design.