粘弹性流体在内管做轴向往复运动的偏心环空中的非定常流
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摘要
聚合物驱油在大庆油田工业化应用以来,得到了较好的驱油效果。与此同时,聚驱抽油机井与水驱抽油机井相比有诸如示功图肥大、泵效下降、抽油杆偏磨、检泵周期缩短等问题。这些问题的发生与产出液的粘弹性特征不无关系,而做轴向往复运动的抽油杆在油管中往往处于偏心的位置工作,这更加重了以上问题的产生。显然,研究聚驱井产出液在抽油杆做轴向往复运动的井筒中的流动规律,对于聚驱井抽油机工作参数的优选,防止抽油杆偏磨具有重要的工程实际意义。
本文采用变系数二阶流体本构方程来描述聚驱井产出液的粘弹性流变性,研究了变系数二阶流体在内管做轴向往复运动的偏心环空中的非定常流。
分别建立了直角坐标系和双极坐标系下变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的基本方程;建立了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流时内管壁上的压力分布公式。
利用双层的Crank-Nicholson 隐式差分格式对变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的基本方程进行了离散,利用Matlab 的左除操作对由运动方程形成的稀疏线性方程组进行了数值求解,从而得到了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的数值解。
通过对运动方程的数值求解,获得了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的速度分布、瞬时流量分布、平均流量和内管壁压力分布;分析了内外管偏心度、内管冲程及冲次对速度分布、瞬时流量分布、平均流量和内管壁压力分布的影响;还利用数值计算结果,对比分析了相同条件下数值计算出的变系数二阶流体和幂律流体在内管做轴向往复运动的偏心环空中非定常流的速度分布、瞬时流量分布、平均流量和内管壁压力分布。
对比分析结果显示,变系数二阶流体和幂律流体在速度分布和瞬时流量分布上都有较大的差异;而相同条件下用变系数二阶流体模型计算的平均流量比用幂律流体模型计算的平均流量小;同时由于变系数二阶流体模型中的第二法向应力差系数使得上冲程存在一个使内管居中的效应,下冲程存在一个使内管偏心的效应,而对于幂律流体和Weissenberg 流体则无此效应。通过两种不同质量百分比浓度的HPAM 水溶液在内管做轴向往复运动的偏心环空中的非定常流实验,把忽略弹性项后数值计算的平均流量与实验实测的平均流量进行了比较,二者吻合较好。可以认为,本文建立的基本方程和数值计算方法是正确的。
Since the industrial application of polymer flooding in the Daqing Oil Field, a preferable driving effect has been achieved. At the same time, there exist a lot of problems in the rod-pumped wells of polymer flooding compared with water flooding, such as greater ergogram, lower pumping efficiency, eccentric wear of the sucker rod, shorter period of pump checking, etc. The occurrence of these problems is greatly related with the viscoelastic property of the produced fluid. And the sucker rod reciprocating axially is always in a condition of eccentric, which will even aggravate the mentioned problems. The flow law in the eccentric annuli with inner cylinder reciprocating axially of the produced fluid in the polymer flooding wells is studied in this paper.
It’s obviously that the study has a significant engineering meaning in the optimizing of the parameters of the pumping unit and in the prevention of the eccentric wear of the sucker rod. The second order fluid with variable coefficients is used to describe the rheological property of the produced fluid in the polymer flooding wells, and the unsteady flow of such a fluid in the eccentric annuli with inner cylinder reciprocating axially is studied in this paper.
The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially in rectangular and bipolar coordinate are established respectively in this paper, and the formula of normal stress on the inner cylinder is given.
The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are dispersed with the doublelayer Crank-Nicholson latent difference scheme. By the using of the left divide of Matlab, the sparse system of linear equations is numerically calculated, and the numerical solution of the unsteady flow of second order fluid in the eccentric annuli with inner cylinder reciprocating axially is obtained.
By the numerical calculation of the equations of motion, the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are obtained; and the influences of eccentricity, stroke and frequency of the inner cylinder on the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder are analyzed; the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with the inner cylinder reciprocating axially are compared with that of the power-law fluid under the same flowing condition. The results show that, the velocity and instantaneous flow rate distribution of second order fluid with variable coefficients differ greatly from the ones of the power-law fluid; the average flow of second order fluid with variable coefficients is smaller than that of the power-law fluid under the same condition; and as the existence of the second normal
stress coefficient in the model of second order fluid with variable coefficients, there is a concentric effect in the upstroke and a eccentric effect in the down stroke, but there is no such a effect for the power-law fluid or for the Weissenberg fluid. The unsteady flow experiments of the HPAM aqueous solution of two kinds of different mass concentration in the eccentric annuli with inner cylinder reciprocating axially are carried out. The calculated flow rate neglected the elastic item is compared with the experimental flow rate, and the results show that they are coinsistent well. It can be considered that the basic equations and numerical method presented in this paper are correct.
本文采用变系数二阶流体本构方程来描述聚驱井产出液的粘弹性流变性,研究了变系数二阶流体在内管做轴向往复运动的偏心环空中的非定常流。
分别建立了直角坐标系和双极坐标系下变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的基本方程;建立了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流时内管壁上的压力分布公式。
利用双层的Crank-Nicholson 隐式差分格式对变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的基本方程进行了离散,利用Matlab 的左除操作对由运动方程形成的稀疏线性方程组进行了数值求解,从而得到了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的数值解。
通过对运动方程的数值求解,获得了变系数二阶流体在内管做轴向往复运动的偏心环空中非定常流的速度分布、瞬时流量分布、平均流量和内管壁压力分布;分析了内外管偏心度、内管冲程及冲次对速度分布、瞬时流量分布、平均流量和内管壁压力分布的影响;还利用数值计算结果,对比分析了相同条件下数值计算出的变系数二阶流体和幂律流体在内管做轴向往复运动的偏心环空中非定常流的速度分布、瞬时流量分布、平均流量和内管壁压力分布。
对比分析结果显示,变系数二阶流体和幂律流体在速度分布和瞬时流量分布上都有较大的差异;而相同条件下用变系数二阶流体模型计算的平均流量比用幂律流体模型计算的平均流量小;同时由于变系数二阶流体模型中的第二法向应力差系数使得上冲程存在一个使内管居中的效应,下冲程存在一个使内管偏心的效应,而对于幂律流体和Weissenberg 流体则无此效应。通过两种不同质量百分比浓度的HPAM 水溶液在内管做轴向往复运动的偏心环空中的非定常流实验,把忽略弹性项后数值计算的平均流量与实验实测的平均流量进行了比较,二者吻合较好。可以认为,本文建立的基本方程和数值计算方法是正确的。
Since the industrial application of polymer flooding in the Daqing Oil Field, a preferable driving effect has been achieved. At the same time, there exist a lot of problems in the rod-pumped wells of polymer flooding compared with water flooding, such as greater ergogram, lower pumping efficiency, eccentric wear of the sucker rod, shorter period of pump checking, etc. The occurrence of these problems is greatly related with the viscoelastic property of the produced fluid. And the sucker rod reciprocating axially is always in a condition of eccentric, which will even aggravate the mentioned problems. The flow law in the eccentric annuli with inner cylinder reciprocating axially of the produced fluid in the polymer flooding wells is studied in this paper.
It’s obviously that the study has a significant engineering meaning in the optimizing of the parameters of the pumping unit and in the prevention of the eccentric wear of the sucker rod. The second order fluid with variable coefficients is used to describe the rheological property of the produced fluid in the polymer flooding wells, and the unsteady flow of such a fluid in the eccentric annuli with inner cylinder reciprocating axially is studied in this paper.
The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially in rectangular and bipolar coordinate are established respectively in this paper, and the formula of normal stress on the inner cylinder is given.
The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are dispersed with the doublelayer Crank-Nicholson latent difference scheme. By the using of the left divide of Matlab, the sparse system of linear equations is numerically calculated, and the numerical solution of the unsteady flow of second order fluid in the eccentric annuli with inner cylinder reciprocating axially is obtained.
By the numerical calculation of the equations of motion, the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are obtained; and the influences of eccentricity, stroke and frequency of the inner cylinder on the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder are analyzed; the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with the inner cylinder reciprocating axially are compared with that of the power-law fluid under the same flowing condition. The results show that, the velocity and instantaneous flow rate distribution of second order fluid with variable coefficients differ greatly from the ones of the power-law fluid; the average flow of second order fluid with variable coefficients is smaller than that of the power-law fluid under the same condition; and as the existence of the second normal
stress coefficient in the model of second order fluid with variable coefficients, there is a concentric effect in the upstroke and a eccentric effect in the down stroke, but there is no such a effect for the power-law fluid or for the Weissenberg fluid. The unsteady flow experiments of the HPAM aqueous solution of two kinds of different mass concentration in the eccentric annuli with inner cylinder reciprocating axially are carried out. The calculated flow rate neglected the elastic item is compared with the experimental flow rate, and the results show that they are coinsistent well. It can be considered that the basic equations and numerical method presented in this paper are correct.
引文
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