水力压裂垂直裂缝形态及缝高控制数值模拟研究
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摘要
水力压裂是油田增产的最主要技术措施之一。地层条件不同,水力压裂形成的裂缝可能是水平缝,也可能是垂直缝。对于垂直裂缝,其三维形态,尤其是裂缝的高度以及在地层中的穿层情况,直接影响压裂效果,是工程师非常关心的问题。本文以大型有限元软件ABAQUS为平台,模拟了地层中的水力压裂过程,重点研究了多种影响裂缝形态和缝高控制的因素,对水力压裂设计和工程实践有指导意义。
本文从介绍水力压裂的概念以及水力压裂的作用出发,综述了国内外水力压裂技术的发展和应用的历程,回顾了模拟水力压裂的各种模型,介绍了相关的岩石力学理论和水力压裂涉及到的多种问题(近井筒效应,支撑剂的选择,页岩气体积压裂等)。通过说明垂直裂缝缝高控制的重要性和前人对缝高控制的研究,解释了本文的研究内容和意义。
油藏通常都是多孔介质,可以看成是由固体骨架和骨架之间的孔隙组成的结构,采用Terzaghi有效应力原理实现多孔介质变形和渗流之间的耦合。总结了岩石固体骨架变形和孔隙流体渗流流动的基本方程组和边界条件,以及相应的瞬态有限元求解列式,该列式是本文模拟的数学基础。采用带有孔隙压力的cohesive单元模拟裂缝的行为,介绍了裂缝的起裂准则和扩展准则,引入无量纲的损伤因子表征裂缝起裂之后单元的损伤情况(单元刚度的退化)。流体在裂缝中的流动是线性的,切向流动的速率与缝内压力梯度成正比,法向流动的速率与裂缝中心和裂缝上下表面的压差成正比。阐述了线弹性模型和粘弹性模型的基本理论以及一种典型的粘弹性模型——标准线性固体的本构关系。说明了处理支撑剂浓度的方法,将支撑剂浓度分布对压裂的影响表征为压裂液粘性的变化。
建立二维平面应变模型,模拟水力压裂过程中裂缝的垂向扩展过程。二维模型,有计算成本低,耗时少等优点。通过模拟大庆油田一口油井现场的实际压裂过程,得到井底压力,引用计算摩阻的经验公式,推算出井口压力,它与现场实测的井口压力演化吻合良好,验证了二维模型的可行性和合理性。采用该模型模拟了三层地层(一个产层夹在上下隔层中间)的地质参数对裂缝高度的影响,结果表明,高地应力、低弹性模量和高抗拉强度的隔层会使得裂缝高度减小,能很好的限制裂缝穿层。
建立全三维模型,研究水力压裂过程中裂缝的三维形态和多种参数对裂缝形态和缝高控制的影响,包括：
(1)多层地层中的水力压裂。首先通过模拟一口现场油井的压裂过程,对比模拟得到的井底缝口压力曲线和现场实测的曲线,验证了三维模型的可靠性。然后对多产层和隔层交替出现的油藏中的水力压裂过程进行模拟。结果表明,较高的隔层地应力和抗拉强度以及较小的弹性模量会使得裂缝高度减小,长度增大,原因是地层的地应力与抗拉强度对裂缝张开起到阻碍作用；而弹性模量越大则缝宽越小,裂缝对流体流动的抵制作用增强,流体压力增大,裂缝高度就越大。由于产层和隔层的交替出现,裂缝的横截面形态呈现波浪形。
(2)岩石孔隙度和泥质含量对水力压裂的影响。根据线弹性体波速与弹性参数的关系,以及前人基于实验和测井数据拟合的波速与孔隙度和泥质含量的经验公式,给出了孔隙度和泥质含量与岩石弹性模量、泊松比、抗拉强度和渗透率之间的关系。模拟结果表明,地层的孔隙度和泥质含量越高,裂缝高度越小,这是因为孔隙度越大则地层渗透率越大,压裂液滤失的更多,而泥质含量越大则岩石弹性模量越小、抗拉强度越大,地层越难以被破坏,这些因素导致裂缝高度被限制住。
(3)渗透率各项异性对水力压裂的影响。模拟了正交各向异性渗透率张量的三个分量对裂缝形态和井底压力的影响,结果表明,沿着裂缝宽度方向的渗透率分量越大,则裂缝长度和高度以及井底压力越小,而沿着裂缝长度和高度方向的渗透率分量对裂缝形态及井底压力的影响不大。这是因为,裂缝内的流体滤失是沿着裂缝壁面的法线方向的,它主要受沿着裂缝宽度方向的渗透率分量影响,该渗透率分量越大则滤失越大,另外两个方向的渗透率分量对流体滤失的影响很小。
(4)粘弹性本构关系的地层中水力压裂过程的模拟。采用标准线性固体模型表征地层的应力应变关系,模拟结果表明,粘性系数与标准线性固体中的开尔文体的剪切模量越小,裂缝高度就越小,这是因为粘性系数或开尔文体的剪切模量减小,会导致材料的松弛模量降低,应力松弛,井底缝口压力下降,所以裂缝的高度变小。粘弹性模型模拟的裂缝高度比相应的线弹性模型模拟出的结果小
(5)支撑剂沉降对水力压裂的影响。推导了支撑剂沉降模型并用于水力压裂的模拟,结果表明,由于支撑剂沉降,裂缝的横截面不是上下对称的,裂缝下半部比上半部宽。支撑剂沉降模型模拟的裂缝横截面积比均匀分布模型大,原因是均匀分布模型没有考虑裂缝中的流体滤失引起的支撑剂浓度升高——携砂液粘性增加——滤失减小这一过程,通过模拟现场一口油井的压裂过程可以看出支撑剂沉降模型得到的井底压力变化曲线比支撑剂均匀分布模型得到的曲线更接近现场实测结果。
(6)层间剪切对水力压裂的影响。模拟了产层和隔层之间的界面剪切强度对裂缝形态的影响,结果表明,当界面剪切强度小于一个零界值的时候,裂缝延伸至界面时会引起界面剪切破坏,出现明显的层间滑移,裂缝尖端变钝,缝高被限制住,缝长大大增加；反之,当界面剪切强度较大时,界面不会被破坏,没有层间滑移现象,裂缝能够穿入隔层。
本文的研究揭示了影响裂缝高度的关键因素及规律,对于水力压裂设计和工程实践有很好的参考价值。
Hydraulic fracturing is one of the primary technologies used for reservoir production enhancement. For different formation conditions, the hydraulic fracture shape may be horizontal or vertical. For vertical fracture, engineers pay close attention to the three dimensional fracture configurations, especially to the fracture height and the crossing layer situation. In this dissertation, the finite element software ABAQUS is used as a platform to simulate the hydraulic fracturing processes. The key point is to study the effect of various parameters on fracture configuration and fracture height control. The results are valuable for hydraulic treatment design and practice.
First, the concept and function of hydraulic fracturing is introduced. The processes of hydraulic fracturing technology development and application at home and abroad are briefly reviewed. Different hydraulic fracturing models are summarized. Hydraulic fracturing related rock mechanics and other concerned problems (near wellbore effect, proppant choosing, volume fracturing in shale-gas reservoirs and so on) are expounded. Through the explanation of the importance of the fracture height control and the current results from other researchers, the contents and significance of this dissertation are presented.
Usually the reservoir is a kind of porous media, and it is regarded as a structure constructed by solid framework and pore. The Terzaghi effective stress principle is adopted to couple the solid deformation and seepage flow. The basic equations and boundary conditions as well as the corresponding incremental finite element solution formulae are summarized. The formulae are the math foundation of this dissertation. Cohesive elements with pore pressure freedom are used to simulate the fracture behavior. The fracture initiation and propagation laws are explained. The dimensionless scalar-damage factor is introduced to characterize the damage situation of the elements (the stiffness of the damaged elements may decrease). The fluid flow in the fracture is assumed to be linear. The tangential flow rate is proportional to the pressure gradient in the fracture, and the normal flow rate is proportional to the pressure difference between the fracture center and the fracture top/bottom surface. The basic theories of linear elastic and viscolinear elastic are stated, and the constitutive relation of a typical viscoelastic model-standard linear model is introduced. The ways of dealing with proppant concentration are presented, and the influence of proppant concentration distribution on hydraulic fracturing is represented by the fracturing fluid viscocity vatiation.
Two-dimensional plane strain model is established to simulate the vertical growth of hydraulic fracture. The advantages of two dimensional model are the small computational overburden and save of time. A hydraulic fracturing process of a well in Daqing Oilfield is simulated. Combing the obtained bottomhole pressure and the frictions based on the empirical formulae, the surface pressure can be derived. The surface pressure curve from the simulation is consistent with field-measured data, and thus the feasibility of the two-dimensional model is approved. For the three layered formation (one pay layer sandwiched between two barrier layers), the effect of lithological parameters on fracture height is investigated. The results indicate that larger in-situ stress, smaller elastic modulus and larger tensile strength in barrier layers could make the fracture height smaller, and the crossing layer status is restricted.
Fully three-dimensional model is established to study various factors which may influence the three-dimensional fracture configuration and fracture height. Main results are summarized below.
(1) Hydraulic fracturing process in multi-layered reservoir. A typical hydraulic fracturing process of a well in Oilfield is simulated. The bottomhole pressure curve obtained from the simulation is compared with field-measured data, and the three-dimensional model is validated. Then hydraulic fracturing processes in multi-layered reservoir are simulated. The results show that larger in-situ stress and tensile strength, as well as smaller elastic modulus in barrier layers could make the fracture to be lower and longer. The reason is that in-situ stress and tensile strength hinder the fracture from opening; larger elastic modulus will make the fracture to be narrower, which has larger resistance to fluid flow, leading to the enlarged bottomhole pressure and fracture height. Since the pay layers and the barrier layers are interlinked by turns, the fracture cross-section is wave-shape.
(2) Effect of rock porosity and clay content on hydraulic fracturing. According to the relation between linear elastic wave velocity and elastic parameters, as well as several empirical formulae based on the laboratory test and well logging data, porosity and clay content are connected to elastic modulus, Poisson's ratio, tensile strength and permeability. Numerical results indicate that larger porosity and clay content could confine the fracture height. Larger porosity will make the permeability increase, and more fracturing fluid may leak off into the reservoir. Larger clay content will make the elastic modulus decrease and tensile strength enlarge, and therefore the formation will become harder to be damaged. All these factors will lead the fracture height smaller.
(3) Effect of orthotropic permeability on hydraulic fracturing. The influence of orthotropic permeability components on fracture configuration and bottomhole pressure is discussed. The conclusion is that as the permeability component along the fracture width direction increase, the fracture length, fracture height and bottomhole pressure may decrease. The influence of the permeability components along the fracture length and height directions on hydraulic fracturing is not evident. This may be interpreted with the direction of fluid leaking off. The fluid leaking off is mainly governed by the permeability component along the fracture width direction. The other two permeability components have little influence on fluid leaking off.
(4) Simulation of hydraulic fracture propagating in the formation with viscoelastic property. Standard linear solid model is used to characterize the constitutive relation of formation. Numerical results indicate that as the viscosity and the shear modulus of Kelvin body in the standard linear solid decrease, the fracture height decreases. When any of the two parameters decreases, the relaxation modulus decreases, leading to stress relaxation and bottomhole pressure drop. As a result, the fracture height will be reduced. The fracture height predicted by viscoelastic model is smaller than that predicted by the corresponding linear elastic model.
(5) Effect of proppant setting on hydraulic fracturing. The proppant setting model is proposed and its application in hydraulic fracturing modeling is discussed. The results demonstrate that duo to proppant settling, the fracture cross-section shape should be asymmetric, i.e. the lower half part of the fracture cross-section is wider than the upper half part. Compared to the proppant uniform distribution model, the fracture cross-section area obtained from the proppant settling model is larger. This is caused by neglecting the influence of fluid leaking off on proppant concentration in uniform distribution model. The influence of fluid leaking off is the increase of proppant concentration, and then the viscosity of fluid will be larger. As a result, the fluid leaking off is restrained. A hydraulic fracturing process of a well in Oilfield is simulated, and the bottomhole pressure curve obtained from the proppant settling model is closer to the field-measured data than that obtained from uniform distribution model.
(6) Effect of interface shear failure on hydraulic fracturing. The influence of shear strength of interface between barrier layer and pay layer on fracture configuration is investigated. The results demonstrate that when the shear strength of interface is lower than a critical value, the interface will be damaged so that serious slippage along the interface will occur and the facture tip becomes blunted. The fracture height is confined and the fracture length will increase. On the contrary, when the shear strength of interface is large enough, the interface will not be damaged and there is no slippage along the interface. The fracture vertical growth cannot be stopped and it may penetrate into barrier layer.
The present dissertation explores the key factors influencing fracture height. The obtained results are valuable for design and engineering practice of hydraulic fracturing.
本文从介绍水力压裂的概念以及水力压裂的作用出发,综述了国内外水力压裂技术的发展和应用的历程,回顾了模拟水力压裂的各种模型,介绍了相关的岩石力学理论和水力压裂涉及到的多种问题(近井筒效应,支撑剂的选择,页岩气体积压裂等)。通过说明垂直裂缝缝高控制的重要性和前人对缝高控制的研究,解释了本文的研究内容和意义。
油藏通常都是多孔介质,可以看成是由固体骨架和骨架之间的孔隙组成的结构,采用Terzaghi有效应力原理实现多孔介质变形和渗流之间的耦合。总结了岩石固体骨架变形和孔隙流体渗流流动的基本方程组和边界条件,以及相应的瞬态有限元求解列式,该列式是本文模拟的数学基础。采用带有孔隙压力的cohesive单元模拟裂缝的行为,介绍了裂缝的起裂准则和扩展准则,引入无量纲的损伤因子表征裂缝起裂之后单元的损伤情况(单元刚度的退化)。流体在裂缝中的流动是线性的,切向流动的速率与缝内压力梯度成正比,法向流动的速率与裂缝中心和裂缝上下表面的压差成正比。阐述了线弹性模型和粘弹性模型的基本理论以及一种典型的粘弹性模型——标准线性固体的本构关系。说明了处理支撑剂浓度的方法,将支撑剂浓度分布对压裂的影响表征为压裂液粘性的变化。
建立二维平面应变模型,模拟水力压裂过程中裂缝的垂向扩展过程。二维模型,有计算成本低,耗时少等优点。通过模拟大庆油田一口油井现场的实际压裂过程,得到井底压力,引用计算摩阻的经验公式,推算出井口压力,它与现场实测的井口压力演化吻合良好,验证了二维模型的可行性和合理性。采用该模型模拟了三层地层(一个产层夹在上下隔层中间)的地质参数对裂缝高度的影响,结果表明,高地应力、低弹性模量和高抗拉强度的隔层会使得裂缝高度减小,能很好的限制裂缝穿层。
建立全三维模型,研究水力压裂过程中裂缝的三维形态和多种参数对裂缝形态和缝高控制的影响,包括：
(1)多层地层中的水力压裂。首先通过模拟一口现场油井的压裂过程,对比模拟得到的井底缝口压力曲线和现场实测的曲线,验证了三维模型的可靠性。然后对多产层和隔层交替出现的油藏中的水力压裂过程进行模拟。结果表明,较高的隔层地应力和抗拉强度以及较小的弹性模量会使得裂缝高度减小,长度增大,原因是地层的地应力与抗拉强度对裂缝张开起到阻碍作用；而弹性模量越大则缝宽越小,裂缝对流体流动的抵制作用增强,流体压力增大,裂缝高度就越大。由于产层和隔层的交替出现,裂缝的横截面形态呈现波浪形。
(2)岩石孔隙度和泥质含量对水力压裂的影响。根据线弹性体波速与弹性参数的关系,以及前人基于实验和测井数据拟合的波速与孔隙度和泥质含量的经验公式,给出了孔隙度和泥质含量与岩石弹性模量、泊松比、抗拉强度和渗透率之间的关系。模拟结果表明,地层的孔隙度和泥质含量越高,裂缝高度越小,这是因为孔隙度越大则地层渗透率越大,压裂液滤失的更多,而泥质含量越大则岩石弹性模量越小、抗拉强度越大,地层越难以被破坏,这些因素导致裂缝高度被限制住。
(3)渗透率各项异性对水力压裂的影响。模拟了正交各向异性渗透率张量的三个分量对裂缝形态和井底压力的影响,结果表明,沿着裂缝宽度方向的渗透率分量越大,则裂缝长度和高度以及井底压力越小,而沿着裂缝长度和高度方向的渗透率分量对裂缝形态及井底压力的影响不大。这是因为,裂缝内的流体滤失是沿着裂缝壁面的法线方向的,它主要受沿着裂缝宽度方向的渗透率分量影响,该渗透率分量越大则滤失越大,另外两个方向的渗透率分量对流体滤失的影响很小。
(4)粘弹性本构关系的地层中水力压裂过程的模拟。采用标准线性固体模型表征地层的应力应变关系,模拟结果表明,粘性系数与标准线性固体中的开尔文体的剪切模量越小,裂缝高度就越小,这是因为粘性系数或开尔文体的剪切模量减小,会导致材料的松弛模量降低,应力松弛,井底缝口压力下降,所以裂缝的高度变小。粘弹性模型模拟的裂缝高度比相应的线弹性模型模拟出的结果小
(5)支撑剂沉降对水力压裂的影响。推导了支撑剂沉降模型并用于水力压裂的模拟,结果表明,由于支撑剂沉降,裂缝的横截面不是上下对称的,裂缝下半部比上半部宽。支撑剂沉降模型模拟的裂缝横截面积比均匀分布模型大,原因是均匀分布模型没有考虑裂缝中的流体滤失引起的支撑剂浓度升高——携砂液粘性增加——滤失减小这一过程,通过模拟现场一口油井的压裂过程可以看出支撑剂沉降模型得到的井底压力变化曲线比支撑剂均匀分布模型得到的曲线更接近现场实测结果。
(6)层间剪切对水力压裂的影响。模拟了产层和隔层之间的界面剪切强度对裂缝形态的影响,结果表明,当界面剪切强度小于一个零界值的时候,裂缝延伸至界面时会引起界面剪切破坏,出现明显的层间滑移,裂缝尖端变钝,缝高被限制住,缝长大大增加；反之,当界面剪切强度较大时,界面不会被破坏,没有层间滑移现象,裂缝能够穿入隔层。
本文的研究揭示了影响裂缝高度的关键因素及规律,对于水力压裂设计和工程实践有很好的参考价值。
Hydraulic fracturing is one of the primary technologies used for reservoir production enhancement. For different formation conditions, the hydraulic fracture shape may be horizontal or vertical. For vertical fracture, engineers pay close attention to the three dimensional fracture configurations, especially to the fracture height and the crossing layer situation. In this dissertation, the finite element software ABAQUS is used as a platform to simulate the hydraulic fracturing processes. The key point is to study the effect of various parameters on fracture configuration and fracture height control. The results are valuable for hydraulic treatment design and practice.
First, the concept and function of hydraulic fracturing is introduced. The processes of hydraulic fracturing technology development and application at home and abroad are briefly reviewed. Different hydraulic fracturing models are summarized. Hydraulic fracturing related rock mechanics and other concerned problems (near wellbore effect, proppant choosing, volume fracturing in shale-gas reservoirs and so on) are expounded. Through the explanation of the importance of the fracture height control and the current results from other researchers, the contents and significance of this dissertation are presented.
Usually the reservoir is a kind of porous media, and it is regarded as a structure constructed by solid framework and pore. The Terzaghi effective stress principle is adopted to couple the solid deformation and seepage flow. The basic equations and boundary conditions as well as the corresponding incremental finite element solution formulae are summarized. The formulae are the math foundation of this dissertation. Cohesive elements with pore pressure freedom are used to simulate the fracture behavior. The fracture initiation and propagation laws are explained. The dimensionless scalar-damage factor is introduced to characterize the damage situation of the elements (the stiffness of the damaged elements may decrease). The fluid flow in the fracture is assumed to be linear. The tangential flow rate is proportional to the pressure gradient in the fracture, and the normal flow rate is proportional to the pressure difference between the fracture center and the fracture top/bottom surface. The basic theories of linear elastic and viscolinear elastic are stated, and the constitutive relation of a typical viscoelastic model-standard linear model is introduced. The ways of dealing with proppant concentration are presented, and the influence of proppant concentration distribution on hydraulic fracturing is represented by the fracturing fluid viscocity vatiation.
Two-dimensional plane strain model is established to simulate the vertical growth of hydraulic fracture. The advantages of two dimensional model are the small computational overburden and save of time. A hydraulic fracturing process of a well in Daqing Oilfield is simulated. Combing the obtained bottomhole pressure and the frictions based on the empirical formulae, the surface pressure can be derived. The surface pressure curve from the simulation is consistent with field-measured data, and thus the feasibility of the two-dimensional model is approved. For the three layered formation (one pay layer sandwiched between two barrier layers), the effect of lithological parameters on fracture height is investigated. The results indicate that larger in-situ stress, smaller elastic modulus and larger tensile strength in barrier layers could make the fracture height smaller, and the crossing layer status is restricted.
Fully three-dimensional model is established to study various factors which may influence the three-dimensional fracture configuration and fracture height. Main results are summarized below.
(1) Hydraulic fracturing process in multi-layered reservoir. A typical hydraulic fracturing process of a well in Oilfield is simulated. The bottomhole pressure curve obtained from the simulation is compared with field-measured data, and the three-dimensional model is validated. Then hydraulic fracturing processes in multi-layered reservoir are simulated. The results show that larger in-situ stress and tensile strength, as well as smaller elastic modulus in barrier layers could make the fracture to be lower and longer. The reason is that in-situ stress and tensile strength hinder the fracture from opening; larger elastic modulus will make the fracture to be narrower, which has larger resistance to fluid flow, leading to the enlarged bottomhole pressure and fracture height. Since the pay layers and the barrier layers are interlinked by turns, the fracture cross-section is wave-shape.
(2) Effect of rock porosity and clay content on hydraulic fracturing. According to the relation between linear elastic wave velocity and elastic parameters, as well as several empirical formulae based on the laboratory test and well logging data, porosity and clay content are connected to elastic modulus, Poisson's ratio, tensile strength and permeability. Numerical results indicate that larger porosity and clay content could confine the fracture height. Larger porosity will make the permeability increase, and more fracturing fluid may leak off into the reservoir. Larger clay content will make the elastic modulus decrease and tensile strength enlarge, and therefore the formation will become harder to be damaged. All these factors will lead the fracture height smaller.
(3) Effect of orthotropic permeability on hydraulic fracturing. The influence of orthotropic permeability components on fracture configuration and bottomhole pressure is discussed. The conclusion is that as the permeability component along the fracture width direction increase, the fracture length, fracture height and bottomhole pressure may decrease. The influence of the permeability components along the fracture length and height directions on hydraulic fracturing is not evident. This may be interpreted with the direction of fluid leaking off. The fluid leaking off is mainly governed by the permeability component along the fracture width direction. The other two permeability components have little influence on fluid leaking off.
(4) Simulation of hydraulic fracture propagating in the formation with viscoelastic property. Standard linear solid model is used to characterize the constitutive relation of formation. Numerical results indicate that as the viscosity and the shear modulus of Kelvin body in the standard linear solid decrease, the fracture height decreases. When any of the two parameters decreases, the relaxation modulus decreases, leading to stress relaxation and bottomhole pressure drop. As a result, the fracture height will be reduced. The fracture height predicted by viscoelastic model is smaller than that predicted by the corresponding linear elastic model.
(5) Effect of proppant setting on hydraulic fracturing. The proppant setting model is proposed and its application in hydraulic fracturing modeling is discussed. The results demonstrate that duo to proppant settling, the fracture cross-section shape should be asymmetric, i.e. the lower half part of the fracture cross-section is wider than the upper half part. Compared to the proppant uniform distribution model, the fracture cross-section area obtained from the proppant settling model is larger. This is caused by neglecting the influence of fluid leaking off on proppant concentration in uniform distribution model. The influence of fluid leaking off is the increase of proppant concentration, and then the viscosity of fluid will be larger. As a result, the fluid leaking off is restrained. A hydraulic fracturing process of a well in Oilfield is simulated, and the bottomhole pressure curve obtained from the proppant settling model is closer to the field-measured data than that obtained from uniform distribution model.
(6) Effect of interface shear failure on hydraulic fracturing. The influence of shear strength of interface between barrier layer and pay layer on fracture configuration is investigated. The results demonstrate that when the shear strength of interface is lower than a critical value, the interface will be damaged so that serious slippage along the interface will occur and the facture tip becomes blunted. The fracture height is confined and the fracture length will increase. On the contrary, when the shear strength of interface is large enough, the interface will not be damaged and there is no slippage along the interface. The fracture vertical growth cannot be stopped and it may penetrate into barrier layer.
The present dissertation explores the key factors influencing fracture height. The obtained results are valuable for design and engineering practice of hydraulic fracturing.
引文
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