幂律流体在内管带等距圆环体且旋转的变截面环空中的流动
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摘要
在抽油杆上加装扶正器是解决水驱螺杆泵采油井生产过程中出现的杆管偏磨的一项重要手段。水驱螺杆泵采油井采出液在带扶正器的抽油杆与油管构成的环空中的流动可视为流体在内管带等距圆环体且旋转的变载面环空中的流动。开展流体在内管带等距圆环体且旋转的变截面环空中流动的研究,可以为抽油杆加装扶正器后水驱螺杆泵采油井工作参数的优化提供理论依据,具有工程实际意义。
本文采用幂律流体模式来描述水驱螺杆泵采油井中采出液的流变性；建立了杜坐标系下幂律流体在内管带等距圆环体且旋转的变截面环空中流动的控制方程及压降计算公式；给出了相应的数值计算方法；并以HPAM水溶液为例,对其在内管带等距圆环体且旋转的变截面环空中流动的控制方程及压降计算公式进行了数值计算；分析了HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动时圆环体几何结构参数及流动参数对流函数分布,速度分布及压降的影响。
从柱坐标系下流体在内管带等距圆环体且旋转的变截面环空中流动的运动方程出发,引入Hanks流动稳定性理论,推导了判断幂律流体在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的数学表达式,并对HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的分布进行了数值计算和分析。
通过质量百分比浓度分别为0.050%、0.100%和0.125%的HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动的室内实验和上述控制方程、压降及稳定性参数H计算公式及相应的数值计算方法,将计算压降与实测压降进行了对比,并确定了稳定性参数H的临界最大值。结果表明：计算压降与实测压降的最大平均相对百分比误差为4.89%,可以认为本文建立的柱坐标系下幂律流体在内管带等距圆环体且旋转的变截面环空中流动的控制方程、压降计算公式及给出的相应数值计算方法是正确的；幂律流体在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的临界最大值为398.2。
In order to solving eccentric wearing in the production of the screw pump well, centering guides be installed on suker rod. The flow of produced liquid in annulus consisted of sucker rod having centering guides and oil pipe can be regarded as the flow of fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid. So research on the flow of fluid in variable cross-section annlus with the rotating inner cylinder having uniform distance annulus solid is of certain theoretical instruction and engineering significance for optimizing and designing the parameters of pump in screw pump production well.
In this paper, the rheological properties of the produced liquid in screw pump production well are described by the model of power-law fluid. The governing equations and pressure drop equation of the flow of power-law fluid in variabel cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system are established, and the relative numerical calculation method were given in this paper. Taking HPAM aqueous solution for examples, the govering equations and the computational formula of pressure drop of the flow are numerically calculated. The influences of the geometry parameters of annulus solid and flow parameters on the distribution of stream function, the distribution of velocity and the pressure drop were analyzed.
Based on the equations of motion of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system, the Hanks's theory of the flow stability is introduced, then the mathematical expression of the stability parameter H of the flow of the power-law fluid in variable cross-section with the rotating inner cylinder having uniform distance annulus solid was deduced, the stability parameter H of the HPAM aqueous solution in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is numerically calculated and analyzed.
Through the experiments of the flow of HPAM aqueous solution, the mass percentage concentration of which is 0.050%,0.100% and 0.125% respectively, in variable cross-cection annulus with the rotating inner cylinder having uniform distance annulus solid, based on the governing equation, computational formula of pressure drop, the formula of stability parameter H and the corresponding numerical methods established and presented, the pressure drop numerically calculated are compared with those experimentally measured, and the critical maximum value of the stability parameter H of the flow is determined. The results show that the maximum average relative errors between the pressure drop numerically calculated and those experimentally measured is 4.89%, so that the governing equation, the computational formula of pressure drop and the corresponding numerical methods established and presented in this paper can be testified to be correct, and the critical maximum value of the stability parameter H of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is 398.2.
本文采用幂律流体模式来描述水驱螺杆泵采油井中采出液的流变性；建立了杜坐标系下幂律流体在内管带等距圆环体且旋转的变截面环空中流动的控制方程及压降计算公式；给出了相应的数值计算方法；并以HPAM水溶液为例,对其在内管带等距圆环体且旋转的变截面环空中流动的控制方程及压降计算公式进行了数值计算；分析了HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动时圆环体几何结构参数及流动参数对流函数分布,速度分布及压降的影响。
从柱坐标系下流体在内管带等距圆环体且旋转的变截面环空中流动的运动方程出发,引入Hanks流动稳定性理论,推导了判断幂律流体在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的数学表达式,并对HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的分布进行了数值计算和分析。
通过质量百分比浓度分别为0.050%、0.100%和0.125%的HPAM水溶液在内管带等距圆环体且旋转的变截面环空中流动的室内实验和上述控制方程、压降及稳定性参数H计算公式及相应的数值计算方法,将计算压降与实测压降进行了对比,并确定了稳定性参数H的临界最大值。结果表明：计算压降与实测压降的最大平均相对百分比误差为4.89%,可以认为本文建立的柱坐标系下幂律流体在内管带等距圆环体且旋转的变截面环空中流动的控制方程、压降计算公式及给出的相应数值计算方法是正确的；幂律流体在内管带等距圆环体且旋转的变截面环空中流动的稳定性参数H的临界最大值为398.2。
In order to solving eccentric wearing in the production of the screw pump well, centering guides be installed on suker rod. The flow of produced liquid in annulus consisted of sucker rod having centering guides and oil pipe can be regarded as the flow of fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid. So research on the flow of fluid in variable cross-section annlus with the rotating inner cylinder having uniform distance annulus solid is of certain theoretical instruction and engineering significance for optimizing and designing the parameters of pump in screw pump production well.
In this paper, the rheological properties of the produced liquid in screw pump production well are described by the model of power-law fluid. The governing equations and pressure drop equation of the flow of power-law fluid in variabel cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system are established, and the relative numerical calculation method were given in this paper. Taking HPAM aqueous solution for examples, the govering equations and the computational formula of pressure drop of the flow are numerically calculated. The influences of the geometry parameters of annulus solid and flow parameters on the distribution of stream function, the distribution of velocity and the pressure drop were analyzed.
Based on the equations of motion of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid under the cylindrical coordinate system, the Hanks's theory of the flow stability is introduced, then the mathematical expression of the stability parameter H of the flow of the power-law fluid in variable cross-section with the rotating inner cylinder having uniform distance annulus solid was deduced, the stability parameter H of the HPAM aqueous solution in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is numerically calculated and analyzed.
Through the experiments of the flow of HPAM aqueous solution, the mass percentage concentration of which is 0.050%,0.100% and 0.125% respectively, in variable cross-cection annulus with the rotating inner cylinder having uniform distance annulus solid, based on the governing equation, computational formula of pressure drop, the formula of stability parameter H and the corresponding numerical methods established and presented, the pressure drop numerically calculated are compared with those experimentally measured, and the critical maximum value of the stability parameter H of the flow is determined. The results show that the maximum average relative errors between the pressure drop numerically calculated and those experimentally measured is 4.89%, so that the governing equation, the computational formula of pressure drop and the corresponding numerical methods established and presented in this paper can be testified to be correct, and the critical maximum value of the stability parameter H of the flow of the power-law fluid in variable cross-section annulus with the rotating inner cylinder having uniform distance annulus solid is 398.2.
引文
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