水力压裂水平裂缝扩展的数值模拟研究
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摘要
水力压裂是当前油气开采工程中最重要的增产技术之一。从水力裂缝的几何形态上区分,水力压裂作业可能形成垂直裂缝或水平裂缝。而水平裂缝是石油工程在较浅地层中进行水力压裂作业时常见的裂缝形态,但是相对垂直裂缝所作的研究工作较少,由于缺乏水平裂缝压裂理论方面的研究,实际工程在压裂水平裂缝时受到很大困扰。本文则针对这一问题采用有限元方法对水力压裂水平缝问题进行了系统的研究,分析了水平裂缝出现的条件,并以ABAQUS软件为平台,采用有限元方法对水平裂缝扩展问题进行了模拟,得到了相应的结论,可作为水平裂缝压裂及控制技术的理论依据。
本文首先从工程和力学的角度介绍了水力压裂技术,回顾了水力压裂问题的控制方程以及传统的解法,介绍了水力压裂数学模型的发展历史和最新的研究进展。再从有限元方法的角度分析了水力压裂问题,推导了水力压裂这一非线性大变形、流固耦合问题的控制方程,给出了可直接用于编制程序的离散形式的系统控制方程组,讨论了相应的求解方法。
本文推导了无射孔和单射孔(或忽略射孔间影响)情况下井筒壁应力分布的解析解,利用数值方法计算了螺旋射孔下的井壁应力和地层破裂压力。通过ABAQUS软件和用户子程序,模拟了水力压裂水平裂缝起裂和扩展的过程,采用应力渗流耦合单元描述岩石行为,采用cohesive单元描述裂缝行为,将典型油井模拟结果与现场实测数据进行了比较,对计算模型和子程序进行了验证,在此基础上研究了各参数对水平裂缝扩展的影响,给出了水平裂缝扩展的控制因素。通过用户子程序实现了垂直井水平缝分层压裂过程的模拟,再现了前期压裂裂缝闭合在支撑剂上对后续裂缝的影响,选取了典型分层压裂油井并将模拟结果与实测结果进行了对比。以所选油井建立的模型为基础,对不同裂缝间距条件下水平裂缝的分层压裂的扩展过程进行了模拟,从裂缝几何形态、压力和压后产能的角度分析了多水平压裂裂缝间的干扰规律。本文还对对螺旋射孔条件下水平裂缝的空间形态进行了计算,给出了不同射孔方案下水平多裂缝的空间形态和压裂时的压力变化。最后还进行了螺旋射孔条件下水力压裂的物理模拟实验,用于与数值模拟结果进行对比和验证。
通过计算分析得到了以下结论。主要有:
1.得到了裸眼井和射孔井井壁应力的解析表达式,推导了水平裂缝的出现条件,可作为工程中裂缝形态判别的初步依据。对螺旋射孔条件,采用有限元方法计算了破裂压力,得到了螺旋射孔参数与地层破裂压力的关系,给出了相应的射孔参数的优选方案。
2.模拟了一口典型的水平缝压裂油井裂缝扩展的整个过程,在模拟结果与现场实测结果符合良好的基础上改变不同参数,得到了这些参数对水平裂缝扩展的影响规律,为实际的水平裂缝水力压裂的设计和施工提供了参考。
3.对某薄差层压裂油井的分层压裂过程进行了模拟,通过自编程序实现了前期裂缝闭合在支撑剂上对后续压裂的影响,模拟数据与现场实测结果符合良好,在此基础上从裂缝形态、压力和压后产能的角度,给出薄差储层开采过程中水平多裂缝之间的干扰规律,界定了薄差储层的有效开采间距。
4.对不同射孔形式下水平裂缝的扩展过程进行了物理和数值模拟研究,得到了不同射孔条件下水平裂缝扩展的压力和空间形态规律,给出了水平裂缝压裂时射孔参数的优选方案。
本论文系统的研究了水平裂缝压裂问题,提出的模型能确切地表征水平裂缝水力压裂工艺过程的机理,得到的结论为相应的控制技术提出了具体的建议和参考。
Hydraulic fracturing is one of the most important technologies for increasing production in oil and gas industries. Horizontal fracture or vertical fracture may develop. Horizontal fracture is the most common fracture configuration during hydraulic fracture treatments in reservoirs at shallow depth. Most studies of vertical well are focused on the vertical fractures. However studies on horizontal fracture are seldom found in the literature. Horizontal fracture is studied by the Finite Element Method in this thesis. The presence conditions of horizontal fractures are conducted theoretically. The propagation process of horizontal fractures are simulated by the Finite Element Method using the commercial FEM code ABAQUS and some important conclusions are obtained. The implement of horizontal fracture and corresponding control technique can refer to these conclusions.
First in this thesis, the hydraulic fracturing technology is introduced in the view of engineering and mechanics. The control equations of this physic process and traditional solution are presented. The history of the theory models for hydraulic fracturing and the present research development are briefly reviewed. Then the hydraulic fracturing is analyzed using Finite Element Method and the control equations of the nonlinear fliud-solid coupling problem are derived. The discrete form of the equations that can be used in programming is brought out and the corresponding solution strategy is discussed.
The analytical solution of the stress distribution on wall of non-perforated and single perforated well is conducted. For the complex situation of helical perforated well, the formation fracture initiation pressure is studied by the numerical method. The hydraulic fracturing process of the horizontal fracture is simulated by the commercial FEM code ABAQUS and user self-developed subroutines. The fluid-solid coupling elements are used to describe the mechanical behavior of rock while cohesive elements are employed to simulate the process of fracture initiation and propagation in the formation. The results obtained from numerical simulation are compared with the field measurement data for a fractured oil well with horizontal fracture. Based on the simulation of the selected oil well, the influences of different parameters on horizontal fracture propagation are analyzed. The layer by layer fracturing process of an oil well is simulated either. The simulation of preceding fractures closes on the proppant is implemented by the user self-developed subroutines. The results obtained from the numerical simulation are compared with the field measurement data. Based on the simulation of the layer by ayer fracturing process of a selected oil well, the fracturing processes under different fracture spacings are simulated. The interference among horizontal multi-fractures are studied from the fracture geometry, pressure and the post-fracture flow rate. The propagations of horizontal fractures under helical perforated conditions are studied by numerical and experimental methods. Fracture geometry and treatment pressure are obtained.
Several conclusions are drawn from the simulation results.
1. The analytical solution of the stress distribution on wall of non-perforated and perforated well is conducted. The occurrence conditions of horizontal fractures are given. The conclusions can be used in engineering to predict the fracture geometry mode. For the conditions of helical perforation that analytical solution can not be obtained, the formation fracture initiation pressure is calculated by the numerical method FEA. The influences of helical perforation parameters on fracture initiation pressure are analyzed and the optimization method is given.
2. The hydraulic fracturing process of an oil well in a reservoir is simulated. Based on the consistency between numerical simulation and field measurement data, the influences of different parameters on horizontal fracture propagation are analyzed. The design and implement of horizontal fracture can refer to these conclusions.
3. The layer by layer fracturing process of poor and thin formations is studied. Using the user self-developed subroutines, the preceding hydraulic fractures supported by the proppant is modeled and the change of original in-situ stress and pore pressure by the preceding fractures are considered. The results obtained from numerical simulation is consistent well with field measurement results, based on which the interference among horizontal multi-fractures are studied from the fracture geometry, pressure and the post-fracture flow rate. The influences of different fracture spacings on horizontal multi-fractures interference are obtained. The concept of effective fracturing spacing is proposed.
4. The horizontal fractures geometry and propagation pressure under different helical perforation parameters are obtained by numerical and physical methods. The optimization for parameters of helical perforation is given. This thesis presents a comprehensive study on the hydraulic fracturing of horizontal fractures. And the conclusions supply the mechanism of hydraulic fracture of horizontal fractures.
本文首先从工程和力学的角度介绍了水力压裂技术,回顾了水力压裂问题的控制方程以及传统的解法,介绍了水力压裂数学模型的发展历史和最新的研究进展。再从有限元方法的角度分析了水力压裂问题,推导了水力压裂这一非线性大变形、流固耦合问题的控制方程,给出了可直接用于编制程序的离散形式的系统控制方程组,讨论了相应的求解方法。
本文推导了无射孔和单射孔(或忽略射孔间影响)情况下井筒壁应力分布的解析解,利用数值方法计算了螺旋射孔下的井壁应力和地层破裂压力。通过ABAQUS软件和用户子程序,模拟了水力压裂水平裂缝起裂和扩展的过程,采用应力渗流耦合单元描述岩石行为,采用cohesive单元描述裂缝行为,将典型油井模拟结果与现场实测数据进行了比较,对计算模型和子程序进行了验证,在此基础上研究了各参数对水平裂缝扩展的影响,给出了水平裂缝扩展的控制因素。通过用户子程序实现了垂直井水平缝分层压裂过程的模拟,再现了前期压裂裂缝闭合在支撑剂上对后续裂缝的影响,选取了典型分层压裂油井并将模拟结果与实测结果进行了对比。以所选油井建立的模型为基础,对不同裂缝间距条件下水平裂缝的分层压裂的扩展过程进行了模拟,从裂缝几何形态、压力和压后产能的角度分析了多水平压裂裂缝间的干扰规律。本文还对对螺旋射孔条件下水平裂缝的空间形态进行了计算,给出了不同射孔方案下水平多裂缝的空间形态和压裂时的压力变化。最后还进行了螺旋射孔条件下水力压裂的物理模拟实验,用于与数值模拟结果进行对比和验证。
通过计算分析得到了以下结论。主要有:
1.得到了裸眼井和射孔井井壁应力的解析表达式,推导了水平裂缝的出现条件,可作为工程中裂缝形态判别的初步依据。对螺旋射孔条件,采用有限元方法计算了破裂压力,得到了螺旋射孔参数与地层破裂压力的关系,给出了相应的射孔参数的优选方案。
2.模拟了一口典型的水平缝压裂油井裂缝扩展的整个过程,在模拟结果与现场实测结果符合良好的基础上改变不同参数,得到了这些参数对水平裂缝扩展的影响规律,为实际的水平裂缝水力压裂的设计和施工提供了参考。
3.对某薄差层压裂油井的分层压裂过程进行了模拟,通过自编程序实现了前期裂缝闭合在支撑剂上对后续压裂的影响,模拟数据与现场实测结果符合良好,在此基础上从裂缝形态、压力和压后产能的角度,给出薄差储层开采过程中水平多裂缝之间的干扰规律,界定了薄差储层的有效开采间距。
4.对不同射孔形式下水平裂缝的扩展过程进行了物理和数值模拟研究,得到了不同射孔条件下水平裂缝扩展的压力和空间形态规律,给出了水平裂缝压裂时射孔参数的优选方案。
本论文系统的研究了水平裂缝压裂问题,提出的模型能确切地表征水平裂缝水力压裂工艺过程的机理,得到的结论为相应的控制技术提出了具体的建议和参考。
Hydraulic fracturing is one of the most important technologies for increasing production in oil and gas industries. Horizontal fracture or vertical fracture may develop. Horizontal fracture is the most common fracture configuration during hydraulic fracture treatments in reservoirs at shallow depth. Most studies of vertical well are focused on the vertical fractures. However studies on horizontal fracture are seldom found in the literature. Horizontal fracture is studied by the Finite Element Method in this thesis. The presence conditions of horizontal fractures are conducted theoretically. The propagation process of horizontal fractures are simulated by the Finite Element Method using the commercial FEM code ABAQUS and some important conclusions are obtained. The implement of horizontal fracture and corresponding control technique can refer to these conclusions.
First in this thesis, the hydraulic fracturing technology is introduced in the view of engineering and mechanics. The control equations of this physic process and traditional solution are presented. The history of the theory models for hydraulic fracturing and the present research development are briefly reviewed. Then the hydraulic fracturing is analyzed using Finite Element Method and the control equations of the nonlinear fliud-solid coupling problem are derived. The discrete form of the equations that can be used in programming is brought out and the corresponding solution strategy is discussed.
The analytical solution of the stress distribution on wall of non-perforated and single perforated well is conducted. For the complex situation of helical perforated well, the formation fracture initiation pressure is studied by the numerical method. The hydraulic fracturing process of the horizontal fracture is simulated by the commercial FEM code ABAQUS and user self-developed subroutines. The fluid-solid coupling elements are used to describe the mechanical behavior of rock while cohesive elements are employed to simulate the process of fracture initiation and propagation in the formation. The results obtained from numerical simulation are compared with the field measurement data for a fractured oil well with horizontal fracture. Based on the simulation of the selected oil well, the influences of different parameters on horizontal fracture propagation are analyzed. The layer by layer fracturing process of an oil well is simulated either. The simulation of preceding fractures closes on the proppant is implemented by the user self-developed subroutines. The results obtained from the numerical simulation are compared with the field measurement data. Based on the simulation of the layer by ayer fracturing process of a selected oil well, the fracturing processes under different fracture spacings are simulated. The interference among horizontal multi-fractures are studied from the fracture geometry, pressure and the post-fracture flow rate. The propagations of horizontal fractures under helical perforated conditions are studied by numerical and experimental methods. Fracture geometry and treatment pressure are obtained.
Several conclusions are drawn from the simulation results.
1. The analytical solution of the stress distribution on wall of non-perforated and perforated well is conducted. The occurrence conditions of horizontal fractures are given. The conclusions can be used in engineering to predict the fracture geometry mode. For the conditions of helical perforation that analytical solution can not be obtained, the formation fracture initiation pressure is calculated by the numerical method FEA. The influences of helical perforation parameters on fracture initiation pressure are analyzed and the optimization method is given.
2. The hydraulic fracturing process of an oil well in a reservoir is simulated. Based on the consistency between numerical simulation and field measurement data, the influences of different parameters on horizontal fracture propagation are analyzed. The design and implement of horizontal fracture can refer to these conclusions.
3. The layer by layer fracturing process of poor and thin formations is studied. Using the user self-developed subroutines, the preceding hydraulic fractures supported by the proppant is modeled and the change of original in-situ stress and pore pressure by the preceding fractures are considered. The results obtained from numerical simulation is consistent well with field measurement results, based on which the interference among horizontal multi-fractures are studied from the fracture geometry, pressure and the post-fracture flow rate. The influences of different fracture spacings on horizontal multi-fractures interference are obtained. The concept of effective fracturing spacing is proposed.
4. The horizontal fractures geometry and propagation pressure under different helical perforation parameters are obtained by numerical and physical methods. The optimization for parameters of helical perforation is given. This thesis presents a comprehensive study on the hydraulic fracturing of horizontal fractures. And the conclusions supply the mechanism of hydraulic fracture of horizontal fractures.
引文
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[91]王兴文,任山,宋燕高.多层分层压裂的产层间距问题探讨[J].天然气工业, 2009, 29(2):92~94
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