Abstract
Hydraulic fracturing, as a critical technology for reservoir stimulation, has functioned as a central stimulation technique in the large-scale development of shale gas and coalbed methane. During hydraulic fracturing operations, the movement and distribution of proppants within fractures serve as the key determinant of both fracture conductivity created by fracturing and long-term sustained production performance. Meanwhile, the settling and packing mechanisms of proppants greatly affects proppant transportation efficiency and distribution within fractures, which in turn determines the level of oil and gas production. However, current research on settling and packing mechanisms of proppants has primarily focused on spherical proppants, while some aspects of the non-spherical shaped proppants with different shapes and structures have not yet been fully considered. In this study, 3D printing technology was utilized to fabricate various non-spherical proppants, including cube, rhombohedron, tetrahedron, cuboid, and cylinder shapes. Compared to spherical proppants, these non-spherical counterparts were examined in terms of their settling, transport, and packing mechanisms using visualized proppant settling and transport setup. The result show that proppants with irregular shapes, such as rhombohedrons and tetrahedrons, experienced greater turbulent effects in the fluid, while proppants with regular shapes, such as cuboids, cubes, cylinders, and spheres, generated much less turbulence. For instance, under a low viscosity of 1 mPa·s, the settling velocity of spherical proppants was measured at 0.086 m/s, significantly higher than the 0.046 m/s for rhombohedron and 0.052 m/s for tetrahedron proppants. More importantly, the angle variation during the settlement process was much larger for the irregular-shaped proppants than for the regular ones. Moreover, the results also indicate that under low-viscosity conditions (< 3 mPa·s), non-spherical shape has a more significant effect on settling velocity. However, this effect becomes less apparent when the viscosity increases to the range of 6–9 mPa·s. Porosity measurements further revealed that rhombohedron and tetrahedron proppants achieved higher porosities (approximately 40–45%) compared to spheres and cubes (~ 35%), suggesting potential for enhanced fracture permeability. Finally, six new mathematical models were developed to predict the terminal settling velocity of different types of non-spherical shape proppants. The study of non-spherical proppants might provide a new idea for proppants application with new structures in the future.
Data availability
The data that support the findings of this study are available from the corresponding author [L J], upon reasonable request.
Abbreviations
- V:
-
Settling velocity of the non-spherical proppant, cm/s
- T40 :
-
The time of non-spherical or spherical shape proppants located 40 cm from the fracture model top, s
- T20 :
-
The time of non-spherical or spherical shape proppants located 20 cm from the fracture model top, s
- Q1 :
-
The pump rates in the field, m3/min
- Q2 :
-
The pump rates in the physical model, m3/min
- A1 :
-
The end fracture surface areas in the field, m2
- A2 :
-
The end fracture surface areas in the physical model, m2
- Re1 :
-
Reynolds numbers in the field
- Re2 :
-
Reynolds numbers in the physical model
- ρ1 :
-
Density of the fracturing fluid in the field, kg/m3
- ρ2 :
-
Density of the fracturing fluid in the physical model, kg/m3
- V1 :
-
Velocity of the fracturing fluid in the field, m/s
- V2,:
-
Velocity of the fracturing fluid in the physical model, m/s
- µ1 :
-
Viscosity of the fracturing fluid in the field, Pa·s
- µ2 :
-
Viscosity of the fracturing fluid in the physical model, Pa·s
- l1 :
-
The characteristic lengths of the fracture in the field, m
- l2 :
-
The characteristic lengths of the fracture in the physical models, m
- f :
-
The porosity of the non-spherical or spherical proppant, %
- V f :
-
The filling volume of non-spherical or spherical proppant, mL
- V r :
-
The total volume after adding water, mL
- k:
-
Shape factor of the non-spherical proppant
- \({S_{{\text{particle}}}}\) :
-
The surface area of the non-spherical proppant, m2
- \({S_{{\text{sphere}}}}\) :
-
The surface area of a sphere with the same volume, m2
- \({V_{{\text{particle}}}}\) :
-
The volume of the non-spherical proppant, m3
- \({V_{ps{\text{RE}}}}\) :
-
The predicted settling velocities of the cuboids, m/s
- \({V_{psS}}\) :
-
The predicted settling velocities of the spheres, m/s
- \({V_{psRH}}\) :
-
The predicted settling velocities of the rhombohedrons, m/s
- \({V_{psT}}\) :
-
The predicted settling velocities of the tetrahedrons, m/s
- \({V_{psCY}}\) :
-
The predicted settling velocities of the cylinders, m/s
- \({V_{psCU}}\) :
-
The predicted settling velocities of the cubes, m/s
- d :
-
The equivalent particle size of the proppant, m
- \({\rho _p}\) :
-
The density of the proppant, kg/m3
- \({\rho _f}\) :
-
The density of the fracturing fluid, kg/m3
- \(\mu\) :
-
The viscosity of the fracturing fluid, Pa·s
- \(\phi\) :
-
Gravitational acceleration, m/s2
- \(Valu{e_{act}}\) :
-
Experimental values of setting velocities, m/s
- \(Valu{e_{Cal}}\) :
-
Predicted values of setting velocities, m/s
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Funding
This work was sponsored by CNPC Innovation Fund (2024DQ02-0131) and the Entrepreneurship and Innovation Seedling Project of Sichuan Provincial Department of Science and Technology (2024JDRC0089).
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Supervision: [Jun Li]; Conceptualization: [Jun Li]; Methodology: [Jun Li, Siyuan He，Mingyi Wu]; Investigation: [Jun Li, Siyuan He，Mingyi Wu]; Data Curation: [Jun Li, Siyuan He，Mingyi Wu]; Formal Analysis: [Jun Li，Siyuan He，Mingyi Wu, Kewen Tang, Changyin Zhou]; Writing – Review & Editing: [Jun Li，Siyuan He，Mingyi Wu, Kewen Tang, Changyin Zhou]; Funding Acquisition: [Jun Li, Siyuan He].
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Li, J., He, S., Wu, M. et al. Experimental study on settling, transport, and packing mechanisms of proppants with different shapes in a physical model. Sci Rep (2026). https://doi.org/10.1038/s41598-026-40890-z
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DOI: https://doi.org/10.1038/s41598-026-40890-z
