Effects of the Inner Pipe Rotation and Rheological Parameters on the Axial and Tangential Velocity Profiles and Pressure Drop of Yield Power-Law Fluid in Eccentric Annulus
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Abstract:
Drilling fluid mostly behaves as non-Newtonian fluid and it can be modelled by the Herschel-Bulkley model, which is also called yield power-law (YPL). This model provides accurate results for a wide range of shear rate. In the present paper, a numerical study of the Herschel-Bulkley fluid through the eccentric annulus (E=0.5) was performed for the laminar flow regime using finite volume method (FVM). Effect of the inner pipe rotation and rheology parameters (yield stress τ0, consistency index K and behavior index n) on the axial and tangential velocity profiles and pressure drop gradient were studied. Results showed that increasing the inner pipe rotation from 100 to 400 rpm induces an increase of 120 % of the maximum axial velocity. Low value of the behavior index (n=0.2) causes the appearance of the secondary flow in the wide region of the annulus. The variation of the inner pipe rotation and rheological parameters of the Herschel-Bulkley fluid have a negligible effect on the tangential velocity profile in the wide region of the eccentric annulus. Furthermore, It was observed that the increase of the inner pipe rotation from 0 rpm to 400 rpm causes a decrease of 10% of pressure drop gradient of yield power-law fluid for all eccentric annulus (E=0.2, E=0.4, E=0.6 and E=0.8).
摘要:Herschel-Bulkley模型（即屈服幂率模型）可用于研究非牛顿流体的流动特性，并能在大范围剪切速率条件下得到准确的预测结果。为此，采用有限体积方法（FVM），研究了内部管柱旋转及流变参数（屈服应力τ0、稠度系数K和流性指数n）对偏心环空（E=0.5）中Herschel-Bulkley流体层流区域的轴向、切向速度剖面与压降梯度的影响。研究结果表明，内部管柱转速从100 r/min增加至400 r/min时，会引起最大轴向速度增加，增幅为120%；较低的流性指数（n=0.2）会引起偏心环空宽区域出现二次流；内部管柱转速及流变参数的变化对偏心环空宽区域切向速度剖面有不良影响；内部管柱转速从0增加至400 r/min时，会引起不同偏心环空（E=0.2, 0.4, 0.6和0.8）内幂率流体压降梯度降低，降低幅度为10%。
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Figure 4. Axial and tangential velocity profiles for various inner pipe rotations (τ0=32 Pa, K=16 Pa·s n, n=0.32)
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Figure 5. Axial and tangential velocity profiles for various yield stresses (ω = 131.84 r/min, K=16 Pa·s n, n=0.43)
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Figure 6. Axial and tangential velocity profiles for various consistency indexes (ω = 131.84 r/min, τ0=32 Pa, n=0.43)
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Figure 7. Axial and tangential velocity profiles for various behavior indexes (ω = 131.84 r/min, τ0=32 Pa, K=16 Pa·s n)
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Figure 8. Effect of the pipe rotation on pressure drop gradient for different eccentricities (Re = 12.05, τ0 = 32 Pa, K = 16 Pa·s n, n = 0.43)
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Figure 9. Effect of the yield stress on pressure drop gradient for different eccentricities (Re = 12.05~14.10, ω = 200 r/min, K = 16 Pa·s n, n = 0.43).
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Figure 10. Effect of the flow consistency index on pressure drop gradient for different eccentricities (Re = 12.05~30.66, ω = 200 r/min, τ0 = 32 Pa, n = 0.43).
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