水平井水力压裂数值模拟研究
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摘要
本文首先综述了国内外水力压裂技术研究现状和水力压裂数值模拟方法的发展过程,指出了现阶段水力压裂技术存在的问题,并对各种水力压裂数值模拟方法做了简要的评述。油井水力压裂增产措施是一个复杂的过程,相应的数学模型具有高度非线性,采用解析方法无法求解。采用有限元数值模拟方法模拟现场水力压裂裂缝扩展过程,能够对裂缝起裂和扩展的机理进行分析和解释,并可以对具体地层的压裂施工过程和裂缝形态进行预测,在理论和工程应用上都有重要的意义。
采用损伤力学方法对水力压裂裂缝起裂和扩展机理进行了研究。随着压裂液的注入,一部分流体渗流进入地层,一部分存留在裂缝中,两部分流体共同作用使裂缝尖端的有效应力增大,当裂缝尖端的有效应力增大到地层介质的抗拉强度时介质中出现损伤,随着损伤的增加,裂尖处地层介质能够承受的有效应力随裂缝张开的位移增大而减小,直至完全破坏,失去抗拉能力。
根据饱和多孔介质固体骨架的平衡方程和多孔介质中流体的连续性方程,建立了储层渗流应力耦合数学模型,模型中引入了Jaumann应力速率公式描述多孔介质固体骨架的有限变形效应,并考虑了初始有效应力、初始孔隙压力、初始流体密度和初始孔隙度对耦合模型的影响。基于与微分方程等价的加权余量公式,在空间域采用有限元离散,在时间域进行隐式差分格式离散,导出了以单元节点位移和单元节点孔隙压力为未知量的储层渗流应力耦合的瞬态非线性增量有限元方程。该数学模型引入假设条件少,考虑因素全面,为储层渗流应力耦合有限元方程的一般形式。
采用大型有限元软件ABAQUS建立了水力压裂的轴对称有限元模型,对大庆油田四口水平井的压裂过程进行了数值模拟研究,其中一口水平井采用分段压裂,其余三口水平井采用限流法压裂。模型中包括射孔孔眼、套管、水泥环、油层、微环隙和横向裂缝。采用ABAQUS用户子程序UFIELD考虑了砂比变化对压裂液性能的影响。数值模拟结果输出每个压裂时刻的应力、应变、位移和孔隙压力等数据,并可以直接得到缝口压力时间历程曲线。
对于分段压裂,由于每个压裂层段射孔孔眼数较多,射孔孔眼摩阻可以忽略不计,缝口压力等于井底压力,分段压裂施工现场可以直接测量得到井底压力曲线和地面井口压力曲线,数值模拟结果得到的缝口压力曲线和压裂施工现场的井底压力曲线吻合良好,验证了数值模型的正确性。本文采用降阻比法,结合现场压裂施工曲线数据,通过修正相关系数,提出了适用于大庆油田水平井的压裂液管柱沿程摩阻计算公式。分段压裂数值模拟输出的的缝口压力和地面压力结果与相应的现场测量数据吻合良好,验证了本文提出的压裂液管柱沿程摩阻计算公式的正确性。对于限流法压裂,射孔孔眼摩阻不可忽略。提出了释放系数和孔眼直径计算公式,在此基础上得到了射孔孔眼摩阻计算公式。限流法压裂施工现场只能够测量得到地面井口压力曲线,而数值模拟的结果却只能输出缝口压力曲线。限流法压裂的数值模拟结果与现场测量数据吻合良好,验证了本文提出的释放系数和孔眼直径计算公式的正确性。
在上述模型的基础上通过改变某一参数的数值,进行了参数影响数值模拟研究,这些参数包括岩石渗透率、弹性模量、断裂能、初始有效应力、压裂液黏性系数等,并分析和解释了这些参数对模拟结果的影响。
采用三维有限元数值模拟技术对大庆油用一口水平井的分段压裂过程进行了数值模拟,计算模型包括射孔孔眼、井筒、水泥环、油层、隔层、微环隙和横向裂缝,模拟了裂缝在油层和隔层中的扩展以及在微环隙(水泥环和油层之间)中的扩展,形成了典型的T型裂缝。模拟结果和现场数据吻合良好。
考虑层状地层条件下隔层和油层的地质参数和物性参数对压裂结果(特别是裂缝高度)的影响,这些参数包括隔层地应力、隔层弹性模量、隔层抗拉强度和压裂液黏性系数。分析了这些参数对模拟结果的影响。
A comprehensive review on the state of the art in the hydraulic fracturing technology is presented. Though in the last decades, substantial effort has been devoted to develop effective hydraulic fracturing technology, there are still many problems remain. Since the hydraulic fracturing process is very complicated, there is tremendous challenge in modeling hydraulic fracturing process, and any analytic solution is impossible. In this thesis, the finite element method is adopted to model the hydraulic fracturing process. The mechanism of fracture initiation and propagation can be explained, and the fracture geometry can be predicted by numerical simulating of hydraulic fracturing with the finite element method, which is of great value in theory and application.
Damage mechanics theory is adopted to study the mechanism of fracture initiation and propagation. During the injection of fracturing fluid, part of the fracturing fluid permeates into the formation, the other remains in the fractures. The two parts of the fracturing fluid together increase the effective stress at the fracture tip. Once the effective stress at the fracture tip reachs the corresponding tensile strength, as the further increasement of damage, the value of the effective stress that the fracture tip can hold decreases as the opening displacement increases, until compete damage occurs.
From the equilibrium equations of the solid skeleton and continuity equations of fluid for saturated porous media, a mathematical model of reservoirs is constructed. In the model, Jaumann stress rate formula is introduced to address the finite deformation effect of the solid skeleton of porous media. The parameters including the in-situ stress, initial pore pressure, initial fluid density and initial porosity of a reservoir layer are also taken into account in the model. With finite element discretization in the space domain and implicit differential discretization in the time domain, an instantaneous nonlinear fluid-solid coupling incremental finite element formula is derived based on the weighted residual formula for the equivalent equations of the mathematical model. The degrees of freedom of the finite element formula include nodal displacements and nodal pore pressures. This model gains its generality due to few simplification hypothesis and comprehensive factors being taken into account.
An axisymmetric model is contructed by the FEA software ABAQUS, numerical simulation study is carried out on four oil wells in Daqing Oilfield with the model. Among the four oil wells, one is staged fractured, and the others are limited entry fractured. The model consists of perforation, wellbore, cement casing, oil layer, micro-annulus and transverse fracture. The effect of volume fraction of sand on the properties of fracturing fluid is modeled with the user subroutine UFIELD of ABAQUS. The numerical simulations yield the results including stress, strain, displacement, pore pressure, fracture geometry, and history curves of pressure at the facture mouth.
For staged fracturing, since the number of perforations is large, the perforation friction is negligible, and the pressure at the fracture mouth equals to bottomhole pressure. The pressures at bottomhole and on surface for staged fracturing can be directly measured in filed treatment. The pressure curve at the fracture mouth putputed from numerical simulation fits well with corresponding field data, which validates the model. In this paper, the drag ratio formula is adopted to calculate the pipe string friction by combining field treatment curves and correcting corresponding coefficient of drag ratio formula. From the obtained data of the pipe string friction, a formula calculating the pipe string friction by inverse seeking the parameters in the drag ratio formula is proposed. There is a good coincidence between simulated pressure at the fracture mouth and field measured bottomhole pressure, which verifies the correctness of the proposed formula of pipe string friction. For limited entry fracturing, the perforation friction is significant. A calculation formula for perforation friction based on the calculation methods of discharge coefficient and perforation diameter is derived. In limited entry fracturing, only the surface pressure can be obtained from field measured data, the surface pressure can be got from simulation results. The agreement of surface pressures from field treatment and numerical simulation validates the calculation formula of the proposed discharge coefficient and perforation diameter.
By adjusting the parameters in the aforementioned model, a parametric study is carried out to ascertain the effect of the parameters. The parameters includes the rock permeability, the elastic modulus, the fracture energy, the magnitude and direction of in-situ stress as well as the viscosity coefficient of fracturing fluid. The mechanism of parameters effect on simulation results is presented.
Furthermore three-dimensional finite element numerical simulation technology is carried out for simulating the staged fracturing process of an oil well in Daqing Oilfield with FEA software ABAQUS. The proposed numerical model includes perforation, wellbore, cement casing, oil layer, barrier layer, micro-annulus and transverse fracture. Micro-annulus fracture and transverse fracture generate simultaneously and a typical T-shaped fracture occurs at the early stage of treatment history, then the micro-annulus disappears and only the transverse fracture remains and propagates. The simulation results are in good coincidence with field measurement data.
The effect of geographic and petrophysical parameters of oil and barrier layers under the layered geographic condition on the fracture geometry (especially the fracture height), bottomhole pressure and pore pressure of the formation is studied. These parameters include the in-situ stress, elastic moduli and tensile strengths in barrier layer, and the viscosity of the fracturing fluid. The mechanism of the effect of these parameters on simulation results is analyzed.
采用损伤力学方法对水力压裂裂缝起裂和扩展机理进行了研究。随着压裂液的注入,一部分流体渗流进入地层,一部分存留在裂缝中,两部分流体共同作用使裂缝尖端的有效应力增大,当裂缝尖端的有效应力增大到地层介质的抗拉强度时介质中出现损伤,随着损伤的增加,裂尖处地层介质能够承受的有效应力随裂缝张开的位移增大而减小,直至完全破坏,失去抗拉能力。
根据饱和多孔介质固体骨架的平衡方程和多孔介质中流体的连续性方程,建立了储层渗流应力耦合数学模型,模型中引入了Jaumann应力速率公式描述多孔介质固体骨架的有限变形效应,并考虑了初始有效应力、初始孔隙压力、初始流体密度和初始孔隙度对耦合模型的影响。基于与微分方程等价的加权余量公式,在空间域采用有限元离散,在时间域进行隐式差分格式离散,导出了以单元节点位移和单元节点孔隙压力为未知量的储层渗流应力耦合的瞬态非线性增量有限元方程。该数学模型引入假设条件少,考虑因素全面,为储层渗流应力耦合有限元方程的一般形式。
采用大型有限元软件ABAQUS建立了水力压裂的轴对称有限元模型,对大庆油田四口水平井的压裂过程进行了数值模拟研究,其中一口水平井采用分段压裂,其余三口水平井采用限流法压裂。模型中包括射孔孔眼、套管、水泥环、油层、微环隙和横向裂缝。采用ABAQUS用户子程序UFIELD考虑了砂比变化对压裂液性能的影响。数值模拟结果输出每个压裂时刻的应力、应变、位移和孔隙压力等数据,并可以直接得到缝口压力时间历程曲线。
对于分段压裂,由于每个压裂层段射孔孔眼数较多,射孔孔眼摩阻可以忽略不计,缝口压力等于井底压力,分段压裂施工现场可以直接测量得到井底压力曲线和地面井口压力曲线,数值模拟结果得到的缝口压力曲线和压裂施工现场的井底压力曲线吻合良好,验证了数值模型的正确性。本文采用降阻比法,结合现场压裂施工曲线数据,通过修正相关系数,提出了适用于大庆油田水平井的压裂液管柱沿程摩阻计算公式。分段压裂数值模拟输出的的缝口压力和地面压力结果与相应的现场测量数据吻合良好,验证了本文提出的压裂液管柱沿程摩阻计算公式的正确性。对于限流法压裂,射孔孔眼摩阻不可忽略。提出了释放系数和孔眼直径计算公式,在此基础上得到了射孔孔眼摩阻计算公式。限流法压裂施工现场只能够测量得到地面井口压力曲线,而数值模拟的结果却只能输出缝口压力曲线。限流法压裂的数值模拟结果与现场测量数据吻合良好,验证了本文提出的释放系数和孔眼直径计算公式的正确性。
在上述模型的基础上通过改变某一参数的数值,进行了参数影响数值模拟研究,这些参数包括岩石渗透率、弹性模量、断裂能、初始有效应力、压裂液黏性系数等,并分析和解释了这些参数对模拟结果的影响。
采用三维有限元数值模拟技术对大庆油用一口水平井的分段压裂过程进行了数值模拟,计算模型包括射孔孔眼、井筒、水泥环、油层、隔层、微环隙和横向裂缝,模拟了裂缝在油层和隔层中的扩展以及在微环隙(水泥环和油层之间)中的扩展,形成了典型的T型裂缝。模拟结果和现场数据吻合良好。
考虑层状地层条件下隔层和油层的地质参数和物性参数对压裂结果(特别是裂缝高度)的影响,这些参数包括隔层地应力、隔层弹性模量、隔层抗拉强度和压裂液黏性系数。分析了这些参数对模拟结果的影响。
A comprehensive review on the state of the art in the hydraulic fracturing technology is presented. Though in the last decades, substantial effort has been devoted to develop effective hydraulic fracturing technology, there are still many problems remain. Since the hydraulic fracturing process is very complicated, there is tremendous challenge in modeling hydraulic fracturing process, and any analytic solution is impossible. In this thesis, the finite element method is adopted to model the hydraulic fracturing process. The mechanism of fracture initiation and propagation can be explained, and the fracture geometry can be predicted by numerical simulating of hydraulic fracturing with the finite element method, which is of great value in theory and application.
Damage mechanics theory is adopted to study the mechanism of fracture initiation and propagation. During the injection of fracturing fluid, part of the fracturing fluid permeates into the formation, the other remains in the fractures. The two parts of the fracturing fluid together increase the effective stress at the fracture tip. Once the effective stress at the fracture tip reachs the corresponding tensile strength, as the further increasement of damage, the value of the effective stress that the fracture tip can hold decreases as the opening displacement increases, until compete damage occurs.
From the equilibrium equations of the solid skeleton and continuity equations of fluid for saturated porous media, a mathematical model of reservoirs is constructed. In the model, Jaumann stress rate formula is introduced to address the finite deformation effect of the solid skeleton of porous media. The parameters including the in-situ stress, initial pore pressure, initial fluid density and initial porosity of a reservoir layer are also taken into account in the model. With finite element discretization in the space domain and implicit differential discretization in the time domain, an instantaneous nonlinear fluid-solid coupling incremental finite element formula is derived based on the weighted residual formula for the equivalent equations of the mathematical model. The degrees of freedom of the finite element formula include nodal displacements and nodal pore pressures. This model gains its generality due to few simplification hypothesis and comprehensive factors being taken into account.
An axisymmetric model is contructed by the FEA software ABAQUS, numerical simulation study is carried out on four oil wells in Daqing Oilfield with the model. Among the four oil wells, one is staged fractured, and the others are limited entry fractured. The model consists of perforation, wellbore, cement casing, oil layer, micro-annulus and transverse fracture. The effect of volume fraction of sand on the properties of fracturing fluid is modeled with the user subroutine UFIELD of ABAQUS. The numerical simulations yield the results including stress, strain, displacement, pore pressure, fracture geometry, and history curves of pressure at the facture mouth.
For staged fracturing, since the number of perforations is large, the perforation friction is negligible, and the pressure at the fracture mouth equals to bottomhole pressure. The pressures at bottomhole and on surface for staged fracturing can be directly measured in filed treatment. The pressure curve at the fracture mouth putputed from numerical simulation fits well with corresponding field data, which validates the model. In this paper, the drag ratio formula is adopted to calculate the pipe string friction by combining field treatment curves and correcting corresponding coefficient of drag ratio formula. From the obtained data of the pipe string friction, a formula calculating the pipe string friction by inverse seeking the parameters in the drag ratio formula is proposed. There is a good coincidence between simulated pressure at the fracture mouth and field measured bottomhole pressure, which verifies the correctness of the proposed formula of pipe string friction. For limited entry fracturing, the perforation friction is significant. A calculation formula for perforation friction based on the calculation methods of discharge coefficient and perforation diameter is derived. In limited entry fracturing, only the surface pressure can be obtained from field measured data, the surface pressure can be got from simulation results. The agreement of surface pressures from field treatment and numerical simulation validates the calculation formula of the proposed discharge coefficient and perforation diameter.
By adjusting the parameters in the aforementioned model, a parametric study is carried out to ascertain the effect of the parameters. The parameters includes the rock permeability, the elastic modulus, the fracture energy, the magnitude and direction of in-situ stress as well as the viscosity coefficient of fracturing fluid. The mechanism of parameters effect on simulation results is presented.
Furthermore three-dimensional finite element numerical simulation technology is carried out for simulating the staged fracturing process of an oil well in Daqing Oilfield with FEA software ABAQUS. The proposed numerical model includes perforation, wellbore, cement casing, oil layer, barrier layer, micro-annulus and transverse fracture. Micro-annulus fracture and transverse fracture generate simultaneously and a typical T-shaped fracture occurs at the early stage of treatment history, then the micro-annulus disappears and only the transverse fracture remains and propagates. The simulation results are in good coincidence with field measurement data.
The effect of geographic and petrophysical parameters of oil and barrier layers under the layered geographic condition on the fracture geometry (especially the fracture height), bottomhole pressure and pore pressure of the formation is studied. These parameters include the in-situ stress, elastic moduli and tensile strengths in barrier layer, and the viscosity of the fracturing fluid. The mechanism of the effect of these parameters on simulation results is analyzed.
引文
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