In order to predict sand transport in the fracture, the velocity of sand settling under horizontal shear flow (dynamics settling) was quantified for a variety of high viscosity friction reducers (HVFRs). Correlations between the dynamic settling velocity and rheological properties of the viscosifiers are reported.
The dynamic settling velocity was obtained by processing video images of sand flow in a slot with a gap of 0.25”, height of 12”, and length of 96”. The time evolution of the sand bed was obtained by an image processing algorithm. The dynamic sand settling velocity was then obtained from the rate of sand bed growth. The static settling velocity after the flow was stopped was also measured using the same method. Rheological properties including the shear viscosity profile, elastic and loss moduli under oscillatory shear, and first normal stress difference in steady shear were measured using a rheometer.
The average dynamic settling velocity measured for 2 lbs. per gallon 40-70 mesh sand suspended in HVFR fluids ranges from 0.4 to 6 mm/s under shear rate range comparable to that in the fracture. The settling velocity does not show strong correlation with most rheological parameters measured at any single shear rate, including zero and high shear viscosities, and first normal stress difference. The lack of correlation is attributed to the large variation of velocity, shear rate and viscosity across the gap. We developed a model for dynamic settling based on Stokes law and local flow and viscosity parameters, which were obtained by numerically solving the flow equations. The model prediction of the dynamic settling velocity is from 0.3 to 1.4 times that of the measured velocities. According to the model, the dynamic settling velocity is strongly correlated with the average reciprocal viscosity across the slot gap. It was found that the static settling velocity is several times larger than the dynamic settling velocity for most samples and the correlation between the two velocities is poor. Thus, popular sand settling tests conducted in a column may not reflect the dynamic sand carrying capability. The large differences between dynamic and static settling behavior are contributed to particle clustering that particularly dominate the static settling process.
The dynamic settling velocity and rheological results may serve as a data set for sand settling model development. The model proposed in this study provides a better method to assess the proppant transport capacity of hydraulic fracturing fluids than common practice of using single shear rate viscosity.
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