粘弹性流体在内管做行星运动的环空中流动时内管壁的受力分析
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摘要
在特殊井石油钻井中,由于钻杆自重及偏心的影响,钻杆不仅绕自身轴线自转,还绕着井眼(或套管)的轴线公转,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,在聚驱井螺杆泵采油工况下,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。因而研究粘弹性流体在内管做行星运动的环空中流动时内管壁所受的作用力,对特殊井钻井井眼轨迹控制、防止钻井卡钻以及聚驱螺杆泵采油井中分析和防治抽油杆的偏磨、杆断以及优化设计泵的工作参数具有理论指导意义。
本文针对可用变系数二阶流体模式描述其流变性的粘弹性流体,推导了粘弹性流体在内管做行星运动的环空中流动时流体作用在内管壁上的法向应力差、切向应力和扭矩的计算公式,并给出了对其进行数值求解的计算方法。计算和分析了变系数二阶流体在内管做行星运动的环空中流动时内管自转和公转速度、环空偏心度以及压力梯度对内管壁上的法向应力差、切向应力和扭矩的影响,结果表明:对于变系数二阶流体在内管做行星运动的环空中的流动,内管自转和公转速度以及环空偏心度对内管壁上的法向应力差、切向应力和扭矩的影响较大,压力梯度对内管壁上的法向应力差、切向应力和扭矩影响较小;还利用数值计算结果,对比分析了相同条件下数值计算的变系数二阶流体和幂律流体在内管做行星运动的环空中流动时内管壁上的法向应力差、切向应力和扭矩,结果表明,当变系数二阶流体弹性较小时,流体弹性对法向应力差、切向应力和扭矩没有明显影响;当变系数二阶流体弹性相对较大时,流体弹性对法向应力差影响较大,但对切向应力和扭矩影响较小。通过对Newton流体在内管做行星运动的环空中流动时内管壁法向应力差、切向应力和扭矩的数值解与解析解的对比,二者吻合较好,可以认为本文给出的粘弹性流体在内管做行星运动的环空中流动时流体作用在内管壁上的法向应力差、切向应力和扭矩的计算公式和数值计算方法是正确的。
During drilling process for special wells, the drillpipe not only rotates around its own axis but around the axis of wellbore as well, because of its own gravity and eccentricity. Therefore, the flow of drilling fluid in the annulus between the drillpipe and wellbore can be regarded as flow of viscoelastic fluid in the annulus with the inner cylinder performing a planetary motion. Likewise, in a polymer flooding production well by screw pump, the flow of the produced fluid in the annulus between pumping rod and oil tube can also be regarded as the same flow pattern. Research on the forces exerted on the inner cylinder by viscoelastic fluid flowing in annulus with the inner cylinder performing a planetary motion is of great theoretical significance for special well trajectory control of drilling and preventing drillpipe sticking, as well as for analyzing and controlling eccentric wear and breakage of pump rod, optimizing and designing the parameters of pump in screw pump production wells by polymer flooding.
In this paper, the rheological properties of the viscoelastic fluid are described by the model of second order fluid with variable coefficients. The calculation formulae of normal stress difference, tangential stress and moment, exerted on the inner cylinder by the second order fluid with variable coefficients flowing in the annulus with the inner cylinder performing a planetary motion, are derived; and corresponding calculation methods of numerical solution of are given. The effects of rotation and revolution velocities of the inner cylinder, eccentricity and pressure gradient on normal stress difference, tangential stress and moment acted on the inner cylinder when second order fluid with variable coefficients flows in annulus with the inner cylinder executing a planetary motion are calculated and analyzed. The results indicate that as to the flow of second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion, the influences of rotation and revolution velocities and eccentricity on normal stress difference, tangential stress and moment acted on the inner cylinder are obvious; the influence of pressure gradient on normal stress difference, tangential stress and moment is weak; using the results of numerical calculation, normal stress difference, tangential stress and moment exerted on the inner cylinder as to the second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion are compared with those as to the power law fluid under the same conditions, and the results of which show that if the elasticity of second order fluid with variable coefficients is small, the influence of elasticity of the fluid on normal stress difference, tangential stress and moment is weak; if the elasticity of second order fluid with variable coefficients is large, the influence of elasticity of the fluid on normal stress difference is obvious while on tangential stress and moment is weak. The comparison between the analytical solutions and the numerical solutions of normal stress difference, tangential stress and moment exerted on the inner cylinder as to the flow of Newtonian fluid in annulus with the inner cylinder performing a planetary motion, shows that they match perfectly. This indicates that the calculation formulae and numerical calculation methods of normal stress difference, tangential stress and moment exerted on the inner cylinder by the viscoelastic fluid given in this paper are correct.
本文针对可用变系数二阶流体模式描述其流变性的粘弹性流体,推导了粘弹性流体在内管做行星运动的环空中流动时流体作用在内管壁上的法向应力差、切向应力和扭矩的计算公式,并给出了对其进行数值求解的计算方法。计算和分析了变系数二阶流体在内管做行星运动的环空中流动时内管自转和公转速度、环空偏心度以及压力梯度对内管壁上的法向应力差、切向应力和扭矩的影响,结果表明:对于变系数二阶流体在内管做行星运动的环空中的流动,内管自转和公转速度以及环空偏心度对内管壁上的法向应力差、切向应力和扭矩的影响较大,压力梯度对内管壁上的法向应力差、切向应力和扭矩影响较小;还利用数值计算结果,对比分析了相同条件下数值计算的变系数二阶流体和幂律流体在内管做行星运动的环空中流动时内管壁上的法向应力差、切向应力和扭矩,结果表明,当变系数二阶流体弹性较小时,流体弹性对法向应力差、切向应力和扭矩没有明显影响;当变系数二阶流体弹性相对较大时,流体弹性对法向应力差影响较大,但对切向应力和扭矩影响较小。通过对Newton流体在内管做行星运动的环空中流动时内管壁法向应力差、切向应力和扭矩的数值解与解析解的对比,二者吻合较好,可以认为本文给出的粘弹性流体在内管做行星运动的环空中流动时流体作用在内管壁上的法向应力差、切向应力和扭矩的计算公式和数值计算方法是正确的。
During drilling process for special wells, the drillpipe not only rotates around its own axis but around the axis of wellbore as well, because of its own gravity and eccentricity. Therefore, the flow of drilling fluid in the annulus between the drillpipe and wellbore can be regarded as flow of viscoelastic fluid in the annulus with the inner cylinder performing a planetary motion. Likewise, in a polymer flooding production well by screw pump, the flow of the produced fluid in the annulus between pumping rod and oil tube can also be regarded as the same flow pattern. Research on the forces exerted on the inner cylinder by viscoelastic fluid flowing in annulus with the inner cylinder performing a planetary motion is of great theoretical significance for special well trajectory control of drilling and preventing drillpipe sticking, as well as for analyzing and controlling eccentric wear and breakage of pump rod, optimizing and designing the parameters of pump in screw pump production wells by polymer flooding.
In this paper, the rheological properties of the viscoelastic fluid are described by the model of second order fluid with variable coefficients. The calculation formulae of normal stress difference, tangential stress and moment, exerted on the inner cylinder by the second order fluid with variable coefficients flowing in the annulus with the inner cylinder performing a planetary motion, are derived; and corresponding calculation methods of numerical solution of are given. The effects of rotation and revolution velocities of the inner cylinder, eccentricity and pressure gradient on normal stress difference, tangential stress and moment acted on the inner cylinder when second order fluid with variable coefficients flows in annulus with the inner cylinder executing a planetary motion are calculated and analyzed. The results indicate that as to the flow of second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion, the influences of rotation and revolution velocities and eccentricity on normal stress difference, tangential stress and moment acted on the inner cylinder are obvious; the influence of pressure gradient on normal stress difference, tangential stress and moment is weak; using the results of numerical calculation, normal stress difference, tangential stress and moment exerted on the inner cylinder as to the second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion are compared with those as to the power law fluid under the same conditions, and the results of which show that if the elasticity of second order fluid with variable coefficients is small, the influence of elasticity of the fluid on normal stress difference, tangential stress and moment is weak; if the elasticity of second order fluid with variable coefficients is large, the influence of elasticity of the fluid on normal stress difference is obvious while on tangential stress and moment is weak. The comparison between the analytical solutions and the numerical solutions of normal stress difference, tangential stress and moment exerted on the inner cylinder as to the flow of Newtonian fluid in annulus with the inner cylinder performing a planetary motion, shows that they match perfectly. This indicates that the calculation formulae and numerical calculation methods of normal stress difference, tangential stress and moment exerted on the inner cylinder by the viscoelastic fluid given in this paper are correct.
引文
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