聚合物驱抽油机井抽油杆柱的力学行为研究
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摘要
聚合物驱油成为一种日趋成熟的提高原油采收率的方法,但抽油杆柱偏磨严重,造成检泵周期缩短,综合经济效益降低。有效的解决抽油杆柱的偏磨,是保证原油生产和提高油田开发经济效益的当务之急。因此,研究抽油杆在抽汲井液过程中的力学行为,以分析造成杆管偏磨的成因及影响因素是十分必要的。目前国内外学者研究杆柱的力学行为是建立在波动方程和静力学理论基础上的,与抽油杆的实际工况相差甚远,采油工程界迫切需要新的研究方法和技术,准确描述抽油杆柱在有限空间内含聚井液中运动的力学行为和影响因素,提出防治杆管偏磨措施,以保证有杆抽油系统的安全、正常生产,对完善有杆抽油系统故障诊断技术,丰富有杆抽油系统故障诊断的理论,促进相关学科发展具有一定的理论意义。
研究抽油机井抽油杆柱的力学行为的核心问题之一是确定井筒中抽油杆柱在各种载荷作用下的复杂变形状态,它涉及到对采油工程、固体力学、流体力学、计算力学和聚合物流变学等学科的深刻理解和应用,本文通过力学分析,建立了抽油杆柱的力学模型。运用动量定理和动力学原理建立了抽油杆柱在有限变形范围内的Kirchhoff平衡方程和瞬态动力学平衡方程。根据抽油杆柱的结构参数和运动条件推导了接触界面不可侵彻度量方程,并根据变分原理和更新的Lagrange格式推导了平衡方程的弱形式。采用增广Lagrange乘子法建立抽油杆柱与油管界面动量方程。采用有限元方法,运用Newton-Raphson法、载荷增量法、增广Lagrange乘子法,Newmark法联合求解,计算有杆抽油系统井下设备在多重耦合情况下的受力和变形状态。
抽油机井见聚后,采出液属于粘弹性非牛顿流体,井液粘度的增大,影响了杆液摩擦阻力以及柱塞与泵筒的摩擦阻力。井液的弹性,使其在杆管环空流动过程中,在抽油杆法向方向产生一个作用力,加剧了抽油杆柱的失稳。本文运用非牛顿流体力学理论建立了聚合物采出液流体控制方程,根据有限元理论,采用控制体积法对控制方程进行离散,获得其有限元格式;采用SIMPLE算法对方程进行求解,确定了杆管环空内聚合物采出液流动时速度分布;并根据流体力学理论,运用Rouse-Zimn模型本构方程确定了聚合物采出液的松弛时间。在室内研究聚合物溶液零剪切速率实验为基础上,结合聚合物溶液注入前后流体特性的变化规律,对零剪切速率公式进行修正,得到了聚合物驱采出液零剪切速率计算公式;依此结合上随体MAXWELL模型推导的法向力计算公式,获得法向力随抽油杆速度、聚合物浓度的变化规律,为准确计算聚合物驱抽油杆柱的变形状态奠定了基础。
为了检验抽油杆柱分析方法的准确性和实用性,进行了现场测试。在生产井的抽油杆柱上安装拉压传感器,测量出抽油杆柱的轴向力随时间的变化曲线。将试验结果与计算结果相对比,轴向力平均误差为5.07%。同时计算了由于断脱而作业的生产井,计算结果与生产井抽油杆柱的断脱和磨损位置基本一致。充分证明了诊断方法的正确性。
通过计算,分析了抽油杆柱纵向振动的主要影响因素。并且发现抽油杆柱纵向振动可引起抽油杆柱动力失稳,进而引发横向振动,因此,采用在抽油杆体上安装减震器,减小抽油杆柱的纵向振动幅值,减弱其横向的动力失稳,可达到减缓抽油杆柱偏磨的目的。
聚合物驱井法向力影响抽油杆柱的变形状态,当聚合物浓度大于300mg/L时,其产生的法向力可改变抽油杆柱的变形状态,加剧抽油杆柱的偏磨,当浓度小于300mg/L时,其法向力对抽油杆柱的侧向屈曲影响较小,对偏磨的影响可忽略。针对目前常用扶正器方式防止抽油杆柱的偏磨问题,提出了扶正器合理安装方式。
本文所提出的抽油杆柱的分析方法对杆柱的偏磨问题具有较强的针对性,其分析结果和所提出的改进措施将为防止抽油杆柱的偏磨,以保证有杆抽油系统正常生产、延长生产周期、提高原油产量和降低生产成本有所启迪,对提高油田开发的技术水平和经济效益具有一定的现实意义和实用价值。
Polymer flooding is a mature technology to improve oil recovery. However, the fact that serious eccentric wear on sucker rod string reduces the pumping inspection period and overall economic efficiency. It is urgent to solve the problems of eccentric wear on sucker rod so that to guarantee the crude oil production and to improve the oilfield exploitation’s benefit. So, it is necessary to research the mechanical behaviors of sucker rod in the pumping fluid process in order to analyze the reasons and influential factors resulting in sucker rod’s eccentric wear. The current research studied by domestic and overseas scholars on mechanical behavior of sucker rod is based on the wave equation and static theory, which is far away from the sucker rod’s real working situation. New methods and technologies are urgently studied to accurately describe sucker rod’s mechanical movement behavior and influential factors in the limited space full of polymer fluid. Effective measures need to be put forward to prevent eccentric wear, and finally accomplish the goals of pumping system’s safe and proper production, which will play significant roles in perfecting pumping system’s error diagnose technologies and enriching its theories, and accordingly promoting relevant discipline’s development.
The key problem of sucker rod’s mechanical behavior is to confirm its deformation condition under different loads in the wellbores. Therefore, studies are related to other relevant disciplines, such as production engineering, solid mechanics, fluid mechanics, computing mechanics and polymer rheology. This paper sets up sucker rod’s mechanical model through mechanical analysis; and also establishes the sucker rod’s Kirchhoff equation and transient dynamic equation in the limited deformation range through using momentum theorem and dynamics principle. Impenetrable equation on contact interface is deduced according to sucker rod’s structure parameters and movement conditions. Meanwhile, the weak form of balanced equation is derived from variational principle and updated Lagrangian function. Using augmented Lagrange multiplier sets up the momentum equation between sucker rod and tubing interface. Sucker rod’s force and deformation state under multiple coupling are calculated through combing FEM (finite element method) with other several methods, such as Newton-Raphson method, load increment method, augmented Lagrange multiplier method and Newmark method.
Produced fluid in the polymer flooding pumping wells is viscoelastic non-Newton fluid. Increasing viscosity of produced fluid has great influence on the frictional resistance between sucker rod and polymer fluid, as well as that between plunger and pump wall. Polymer fluid’s elasticity creates an acting force upon sucker rod along the normal direction flowing through annular, which leads to sucker rod’s instability. This paper presents polymer-produced fluid’s flow controlling equation through using non-Newton fluid theory. Basing on finite element theory, controlling equation is dispersed through controlling volume method, and acquiring polymer fluid’s finite element form. Using SIMPLE algorithm solves the equation, polymer fluid’s flowing velocity distribution through annular can be determined. Meanwhile, basing on fluid mechanics, polymer produced fluid’s relaxing time can be confirmed by using Rouse-Zimn model. On the ground of past laboratory tests on polymer fluid’s zero shear rate and combining with produced fluid’s mutative law before and after injecting polymer fluid, the zero shear rate formula has been modified and then polymer produced fluid’s zero shear rate calculating equation has been successfully acquired. Combined with the normal force formula deduced from the MAXWELL model, normal force’s mutative law can be obtained along with sucker rod’s movement velocity and polymer’s density, which will build up a stable foundation for accurately calculating sucker rod’s deformation state in the polymer wells.
In order to verify the veracity and practicability of analysis approach on sucker rod, a tension and pressure sensor was fixed on the sucker rod to measure the variation curve of sucker rod’s longitudinal force with time. By comparing testing results with calculating results, the longitudinal force’s average error is 5.07%. Meanwhile, the producing wells whose sucker rods were broken were also calculated. The comparison results show that the calculating result is consistent with real sucker rod broken and wear location, which fully proves the validity of the diagnostic method.
The main influential factors on the longitudinal vibration of sucker rod were analyzed. This longitudinal vibration makes for sucker rod’s dynamic instability, which further cause sucker rod vibrating along transverse direction. As a result, fixing absorber on the sucker rod can greatly reduce sucker rod’s longitudinal vibrating amplitude; lower transverse dynamic instability; and hence realize the goal of preventing sucker rod’s eccentric wear.
The axial force can influence the sucker rod’s deformation state in the polymer wells. When polymer’s concentration is more than 300mg/L, axial force can change sucker rod’s deformation state and worsen its eccentric wear. On the contrary, when polymer’s concentration is less than 300mg/L, axial force has little influence on sucker rod so that the result can be ignored. Aiming at adopting centralizers to prevent sucker rod’s eccentric wear problem, centralizers’reasonable fixing measure need to be put forward.
The analysis approach put forward in this paper has strong pertinence to sucker rod’s eccentric wear problem. The analysis results and improved measures will play important roles in preventing sucker rod’s eccentric wear, so that to guarantee pumping system’s safe production; prolong its working cycle; enhance crude oil production and reduce operating costs. All of these works will certainly improve the oilfield exploitation level and increase overall economic benefit.
研究抽油机井抽油杆柱的力学行为的核心问题之一是确定井筒中抽油杆柱在各种载荷作用下的复杂变形状态,它涉及到对采油工程、固体力学、流体力学、计算力学和聚合物流变学等学科的深刻理解和应用,本文通过力学分析,建立了抽油杆柱的力学模型。运用动量定理和动力学原理建立了抽油杆柱在有限变形范围内的Kirchhoff平衡方程和瞬态动力学平衡方程。根据抽油杆柱的结构参数和运动条件推导了接触界面不可侵彻度量方程,并根据变分原理和更新的Lagrange格式推导了平衡方程的弱形式。采用增广Lagrange乘子法建立抽油杆柱与油管界面动量方程。采用有限元方法,运用Newton-Raphson法、载荷增量法、增广Lagrange乘子法,Newmark法联合求解,计算有杆抽油系统井下设备在多重耦合情况下的受力和变形状态。
抽油机井见聚后,采出液属于粘弹性非牛顿流体,井液粘度的增大,影响了杆液摩擦阻力以及柱塞与泵筒的摩擦阻力。井液的弹性,使其在杆管环空流动过程中,在抽油杆法向方向产生一个作用力,加剧了抽油杆柱的失稳。本文运用非牛顿流体力学理论建立了聚合物采出液流体控制方程,根据有限元理论,采用控制体积法对控制方程进行离散,获得其有限元格式;采用SIMPLE算法对方程进行求解,确定了杆管环空内聚合物采出液流动时速度分布;并根据流体力学理论,运用Rouse-Zimn模型本构方程确定了聚合物采出液的松弛时间。在室内研究聚合物溶液零剪切速率实验为基础上,结合聚合物溶液注入前后流体特性的变化规律,对零剪切速率公式进行修正,得到了聚合物驱采出液零剪切速率计算公式;依此结合上随体MAXWELL模型推导的法向力计算公式,获得法向力随抽油杆速度、聚合物浓度的变化规律,为准确计算聚合物驱抽油杆柱的变形状态奠定了基础。
为了检验抽油杆柱分析方法的准确性和实用性,进行了现场测试。在生产井的抽油杆柱上安装拉压传感器,测量出抽油杆柱的轴向力随时间的变化曲线。将试验结果与计算结果相对比,轴向力平均误差为5.07%。同时计算了由于断脱而作业的生产井,计算结果与生产井抽油杆柱的断脱和磨损位置基本一致。充分证明了诊断方法的正确性。
通过计算,分析了抽油杆柱纵向振动的主要影响因素。并且发现抽油杆柱纵向振动可引起抽油杆柱动力失稳,进而引发横向振动,因此,采用在抽油杆体上安装减震器,减小抽油杆柱的纵向振动幅值,减弱其横向的动力失稳,可达到减缓抽油杆柱偏磨的目的。
聚合物驱井法向力影响抽油杆柱的变形状态,当聚合物浓度大于300mg/L时,其产生的法向力可改变抽油杆柱的变形状态,加剧抽油杆柱的偏磨,当浓度小于300mg/L时,其法向力对抽油杆柱的侧向屈曲影响较小,对偏磨的影响可忽略。针对目前常用扶正器方式防止抽油杆柱的偏磨问题,提出了扶正器合理安装方式。
本文所提出的抽油杆柱的分析方法对杆柱的偏磨问题具有较强的针对性,其分析结果和所提出的改进措施将为防止抽油杆柱的偏磨,以保证有杆抽油系统正常生产、延长生产周期、提高原油产量和降低生产成本有所启迪,对提高油田开发的技术水平和经济效益具有一定的现实意义和实用价值。
Polymer flooding is a mature technology to improve oil recovery. However, the fact that serious eccentric wear on sucker rod string reduces the pumping inspection period and overall economic efficiency. It is urgent to solve the problems of eccentric wear on sucker rod so that to guarantee the crude oil production and to improve the oilfield exploitation’s benefit. So, it is necessary to research the mechanical behaviors of sucker rod in the pumping fluid process in order to analyze the reasons and influential factors resulting in sucker rod’s eccentric wear. The current research studied by domestic and overseas scholars on mechanical behavior of sucker rod is based on the wave equation and static theory, which is far away from the sucker rod’s real working situation. New methods and technologies are urgently studied to accurately describe sucker rod’s mechanical movement behavior and influential factors in the limited space full of polymer fluid. Effective measures need to be put forward to prevent eccentric wear, and finally accomplish the goals of pumping system’s safe and proper production, which will play significant roles in perfecting pumping system’s error diagnose technologies and enriching its theories, and accordingly promoting relevant discipline’s development.
The key problem of sucker rod’s mechanical behavior is to confirm its deformation condition under different loads in the wellbores. Therefore, studies are related to other relevant disciplines, such as production engineering, solid mechanics, fluid mechanics, computing mechanics and polymer rheology. This paper sets up sucker rod’s mechanical model through mechanical analysis; and also establishes the sucker rod’s Kirchhoff equation and transient dynamic equation in the limited deformation range through using momentum theorem and dynamics principle. Impenetrable equation on contact interface is deduced according to sucker rod’s structure parameters and movement conditions. Meanwhile, the weak form of balanced equation is derived from variational principle and updated Lagrangian function. Using augmented Lagrange multiplier sets up the momentum equation between sucker rod and tubing interface. Sucker rod’s force and deformation state under multiple coupling are calculated through combing FEM (finite element method) with other several methods, such as Newton-Raphson method, load increment method, augmented Lagrange multiplier method and Newmark method.
Produced fluid in the polymer flooding pumping wells is viscoelastic non-Newton fluid. Increasing viscosity of produced fluid has great influence on the frictional resistance between sucker rod and polymer fluid, as well as that between plunger and pump wall. Polymer fluid’s elasticity creates an acting force upon sucker rod along the normal direction flowing through annular, which leads to sucker rod’s instability. This paper presents polymer-produced fluid’s flow controlling equation through using non-Newton fluid theory. Basing on finite element theory, controlling equation is dispersed through controlling volume method, and acquiring polymer fluid’s finite element form. Using SIMPLE algorithm solves the equation, polymer fluid’s flowing velocity distribution through annular can be determined. Meanwhile, basing on fluid mechanics, polymer produced fluid’s relaxing time can be confirmed by using Rouse-Zimn model. On the ground of past laboratory tests on polymer fluid’s zero shear rate and combining with produced fluid’s mutative law before and after injecting polymer fluid, the zero shear rate formula has been modified and then polymer produced fluid’s zero shear rate calculating equation has been successfully acquired. Combined with the normal force formula deduced from the MAXWELL model, normal force’s mutative law can be obtained along with sucker rod’s movement velocity and polymer’s density, which will build up a stable foundation for accurately calculating sucker rod’s deformation state in the polymer wells.
In order to verify the veracity and practicability of analysis approach on sucker rod, a tension and pressure sensor was fixed on the sucker rod to measure the variation curve of sucker rod’s longitudinal force with time. By comparing testing results with calculating results, the longitudinal force’s average error is 5.07%. Meanwhile, the producing wells whose sucker rods were broken were also calculated. The comparison results show that the calculating result is consistent with real sucker rod broken and wear location, which fully proves the validity of the diagnostic method.
The main influential factors on the longitudinal vibration of sucker rod were analyzed. This longitudinal vibration makes for sucker rod’s dynamic instability, which further cause sucker rod vibrating along transverse direction. As a result, fixing absorber on the sucker rod can greatly reduce sucker rod’s longitudinal vibrating amplitude; lower transverse dynamic instability; and hence realize the goal of preventing sucker rod’s eccentric wear.
The axial force can influence the sucker rod’s deformation state in the polymer wells. When polymer’s concentration is more than 300mg/L, axial force can change sucker rod’s deformation state and worsen its eccentric wear. On the contrary, when polymer’s concentration is less than 300mg/L, axial force has little influence on sucker rod so that the result can be ignored. Aiming at adopting centralizers to prevent sucker rod’s eccentric wear problem, centralizers’reasonable fixing measure need to be put forward.
The analysis approach put forward in this paper has strong pertinence to sucker rod’s eccentric wear problem. The analysis results and improved measures will play important roles in preventing sucker rod’s eccentric wear, so that to guarantee pumping system’s safe production; prolong its working cycle; enhance crude oil production and reduce operating costs. All of these works will certainly improve the oilfield exploitation level and increase overall economic benefit.
引文
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