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Turbulent Flow of Polymer Fluids Over the Sand Bed in Horizontal Concentric Annulus

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Abstract

Turbulent flow of non-Newtonian fluids over stationary sand bed deposits are commonly encountered during the wellbore clean-out operations conducted to remove the cuttings (solids deposited as a result of drilling or post-fracking operations) from the horizontal wellbore. We have investigated the impact of the presence of a stationary sand bed deposit on the characteristics of the flow in a horizontal concentric annulus using Particle Image Velocimetry (PIV)technique. Velocity profiles, Reynolds stresses, and axial turbulence intensities are measured in the lower and upper half of the annulus to assess the impact of the sand bed on the flow. Results show that the presence of the sand bed causes the reduction of the volumetric flow rate in the lower part of the annulus with an associated decrease in the local fluid velocity and the flow turbulence. In the upper part of the annulus, however, increased level of turbulence and flat velocity profiles were observed.

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Acknowledgments

This research is financially supported by the funds available from Natural Sciences and Engineering Research Council of Canada (NSERC RGPIN-2016-04647 KURU and NSERC RGPIN 238623 KURU).The authors wish to thank Camara United for providing us the polymer used in this study (Alcomer 110RD).

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  1. University of Alberta, Edmonton, AB, Canada

    Majid Bizhani & Ergun Kuru

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  1. Majid Bizhani
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Correspondence to Ergun Kuru.

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This research is financially supported by the funds available from Natural Sciences and Engineering Research Council of Canada (NSERC RGPIN-2016-04647 KURU and NSERC RGPIN 238623 KURU).

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Appendix A: Models for Calculations of Hydraulic Diameter and Annular Area Open for Flow with the Presence of the Cuttings Bed Deposit

Appendix A: Models for Calculations of Hydraulic Diameter and Annular Area Open for Flow with the Presence of the Cuttings Bed Deposit

The hydraulic diameter and annular cross-section available to fluid in the presence of sand bed is defined following the work of Duan, Miska [40]. For the case of the concentric annulus, assuming a bed of cutting with a height of h, following relations hold (Fig. 24):

$$\begin{array}{@{}rcl@{}} S_{o}&=&2R {arccos}\left( \frac{h-R}{R} \right) \end{array} $$
(A-1)
$$\begin{array}{@{}rcl@{}} S_{i}&=&2\pi r, \end{array} $$
(A-2)
$$\begin{array}{@{}rcl@{}} S_{b}&=&2\sqrt {R^{2}-\left( R-h \right)^{2}} , \end{array} $$
(A-3)
$$\begin{array}{@{}rcl@{}} A_{f}&=&R^{2} {arccos}\left( \frac{h-R}{R} \right)+\left( R-h \right)\sqrt {R^{2}-\left( R-h \right)^{2}} -\pi r^{2}, \end{array} $$
(A-4)
$$\begin{array}{@{}rcl@{}} D_{h}&=&\frac{{4A}_{f}}{S_{o}+S_{i}+S_{b}}, \end{array} $$
(A-5)
Fig. 24
figure 24

Schematic of the bed and the annulus cross section [41]

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Bizhani, M., Kuru, E. Turbulent Flow of Polymer Fluids Over the Sand Bed in Horizontal Concentric Annulus. Flow Turbulence Combust 102, 589–612 (2019). https://doi.org/10.1007/s10494-018-9984-5

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