粘弹性流体在内管做行星运动的环空中流动的数值计算
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摘要
在特殊工艺井的钻井过程中,钻杆不仅绕自身轴线自转,还绕着井眼(或套管)的轴线公转,特殊钻井液在钻杆与井眼(或套管)所形成的偏心环空中的流动可视为粘弹性流体在内管做行星运动的环空中的流动。同样,在聚驱螺杆泵采油工况下,抽油杆不仅绕自身轴线自转,还绕油管的轴线公转,采出液在抽油杆和油管所形成的偏心环空中的流动也可视为粘弹性流体在内管做行星运动的环空中的流动。因此研究粘弹性流体在内管做行星运动的环空中的流动规律,对分析特殊工艺井钻井液在井筒中的携屑能力以及优化聚驱螺杆泵采油井生产参数具有重要的指导意义。
本文用变系数二阶流体模型描述粘弹性流体的流变性,对粘弹性流体在内管做行星运动的环空中流动的速度分布、流量和压力梯度做了数值计算。
本文在运动双极坐标系下变系数二阶流体在内管做行星运动的环空中流动的控制方程的基础上,给出了变系数二阶流体在内管做行星运动的环空中流动的流量公式和压力梯度方程组及其相应数值计算方法;以可视为变系数二阶流体的HPAM水溶液为例,在采用有限差分法对上述控制方程进行数值求解,得到轴向速度分布的基础上,对该流动的流量进行了数值计算;根据上述压力梯度方程组,对该流动的压力梯度进行了数值计算;分析了环空内管公转速度、自转速度、环空偏心度、压力梯度、惯性力及溶液的弹性对该流动的切向速度分布、径向速度分布、轴向速度分布及流量的影响;分析了环空内管公转速度、自转速度、环空偏心度、惯性力及溶液的弹性对该流动的压力梯度的影响。
把利用本文给出的变系数二阶流体在内管做行星运动的环空中流动的速度分布的数值计算方法算得的可视为Newton流体的水在内管做行星运动的环空中流动的切向速度分布、径向速度分布、轴向速度分布与利用解析解算得的切向速度分布、径向速度分布、轴向速度分布进行了对比,结果吻合较好;通过可视为变系数二阶流体的HPAM水溶液在内管做行星运动的环空中流动的室内实验,分别把算得的流量、压力梯度和实验测得的流量、压力梯度进行了对比,它们之间的平均相对百分比误差均在5%以内。可以认为本文给出的变系数二阶流体在内管做行星运动的环空中流动的速度分布、流量和压力梯度的数值计算方法是正确的。
During the exceptional well drilling process, the drill pipe rotates not only around its own axis but also around the axis of wellbore (casing tube), the flow of particular drilling fluid in eccentric annulus between the drill pipe and wellbore(casing tube) could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. Under the behavior of production by polymer flooding screw pump, the pump rod rotates not only around its own axis but also around the axis of the oil tube, the flow of production liquid in eccentric annulus formed by the pump rod and the oil tube could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. So researching on the flow rules of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion has important guidance significance for analyzing the carrying debris capacity in bore hole of particular drilling fluid and optimizing production parameters of polymer flooding screw pump production wells.
In this paper, the second order fluid with variable coefficients model was used to describe rheological property for the viscoelastic fluid, and the velocity distribution, the flow rate and the pressure gradient for the flow of it in annulus with the inner cylinder executing a planetary motion were numerically calculated.
With the governing equations for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate formula and the pressure gradient equation group for the flow and the relative numerical calculation method were given in this paper.Using HPAM aqueous solution which can be regarded as a second order fluid with variable coefficients, the flow rate for this flow was numerically calculated on the basis of the results of axial velocity distribution by solving numerically the governing equations menthioned above. The pressure gradient for this flow was numerically calculated on the basis of the pressure gradient equation group mentioned above. The influences on the tangential velocity distribution, the radial velocity distribution, the axial velocity distribution and the flow rate by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity and the pressure gradient in annulus, the inertia force and the elasticity of solution were analyzed. The influences on the pressure gradient by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity in annulus, the inertia force and the elasticity of solution were analyzed.
The tangential velocity distribution, the radial velocity distribution, the axial velocity distribution for the flow of water, which can be regarded as a Newtonian fluid, calculated by the numerical method for the velocity distribution for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion given in this paper were compared with those calculated by the analytic solutions, they coincide well. Through the experiments on the flow of HPAM solution which can be regarded as a second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate values and the pressure gradient values calculated numerically were compared with those measured in the experiments, the even relative percent errors between them were both smaller than 5%, it shows that the numerical calculation methods for the velocity distribution, the flow rate and the pressure gradient for the flow of the second order fluid with variable coefficients in annuls with the inner cylinder executing a planetary motion are correct.
本文用变系数二阶流体模型描述粘弹性流体的流变性,对粘弹性流体在内管做行星运动的环空中流动的速度分布、流量和压力梯度做了数值计算。
本文在运动双极坐标系下变系数二阶流体在内管做行星运动的环空中流动的控制方程的基础上,给出了变系数二阶流体在内管做行星运动的环空中流动的流量公式和压力梯度方程组及其相应数值计算方法;以可视为变系数二阶流体的HPAM水溶液为例,在采用有限差分法对上述控制方程进行数值求解,得到轴向速度分布的基础上,对该流动的流量进行了数值计算;根据上述压力梯度方程组,对该流动的压力梯度进行了数值计算;分析了环空内管公转速度、自转速度、环空偏心度、压力梯度、惯性力及溶液的弹性对该流动的切向速度分布、径向速度分布、轴向速度分布及流量的影响;分析了环空内管公转速度、自转速度、环空偏心度、惯性力及溶液的弹性对该流动的压力梯度的影响。
把利用本文给出的变系数二阶流体在内管做行星运动的环空中流动的速度分布的数值计算方法算得的可视为Newton流体的水在内管做行星运动的环空中流动的切向速度分布、径向速度分布、轴向速度分布与利用解析解算得的切向速度分布、径向速度分布、轴向速度分布进行了对比,结果吻合较好;通过可视为变系数二阶流体的HPAM水溶液在内管做行星运动的环空中流动的室内实验,分别把算得的流量、压力梯度和实验测得的流量、压力梯度进行了对比,它们之间的平均相对百分比误差均在5%以内。可以认为本文给出的变系数二阶流体在内管做行星运动的环空中流动的速度分布、流量和压力梯度的数值计算方法是正确的。
During the exceptional well drilling process, the drill pipe rotates not only around its own axis but also around the axis of wellbore (casing tube), the flow of particular drilling fluid in eccentric annulus between the drill pipe and wellbore(casing tube) could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. Under the behavior of production by polymer flooding screw pump, the pump rod rotates not only around its own axis but also around the axis of the oil tube, the flow of production liquid in eccentric annulus formed by the pump rod and the oil tube could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. So researching on the flow rules of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion has important guidance significance for analyzing the carrying debris capacity in bore hole of particular drilling fluid and optimizing production parameters of polymer flooding screw pump production wells.
In this paper, the second order fluid with variable coefficients model was used to describe rheological property for the viscoelastic fluid, and the velocity distribution, the flow rate and the pressure gradient for the flow of it in annulus with the inner cylinder executing a planetary motion were numerically calculated.
With the governing equations for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate formula and the pressure gradient equation group for the flow and the relative numerical calculation method were given in this paper.Using HPAM aqueous solution which can be regarded as a second order fluid with variable coefficients, the flow rate for this flow was numerically calculated on the basis of the results of axial velocity distribution by solving numerically the governing equations menthioned above. The pressure gradient for this flow was numerically calculated on the basis of the pressure gradient equation group mentioned above. The influences on the tangential velocity distribution, the radial velocity distribution, the axial velocity distribution and the flow rate by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity and the pressure gradient in annulus, the inertia force and the elasticity of solution were analyzed. The influences on the pressure gradient by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity in annulus, the inertia force and the elasticity of solution were analyzed.
The tangential velocity distribution, the radial velocity distribution, the axial velocity distribution for the flow of water, which can be regarded as a Newtonian fluid, calculated by the numerical method for the velocity distribution for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion given in this paper were compared with those calculated by the analytic solutions, they coincide well. Through the experiments on the flow of HPAM solution which can be regarded as a second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate values and the pressure gradient values calculated numerically were compared with those measured in the experiments, the even relative percent errors between them were both smaller than 5%, it shows that the numerical calculation methods for the velocity distribution, the flow rate and the pressure gradient for the flow of the second order fluid with variable coefficients in annuls with the inner cylinder executing a planetary motion are correct.
引文
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