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基于页岩油水两相渗流特性的油井产能模拟研究

孙鑫, 刘礼军, 侯树刚, 戴彩丽, 杜焕福, 王春伟

孙鑫,刘礼军,侯树刚,等. 基于页岩油水两相渗流特性的油井产能模拟研究[J]. 石油钻探技术,2023, 51(5):167-172. DOI: 10.11911/syztjs.2023084
引用本文: 孙鑫,刘礼军,侯树刚,等. 基于页岩油水两相渗流特性的油井产能模拟研究[J]. 石油钻探技术,2023, 51(5):167-172. DOI: 10.11911/syztjs.2023084
SUN Xin, LIU Lijun, HOU Shugang, et al. Numerical simulation of shale oil well productivity based on shale oil-water two-phase flow characteristics [J]. Petroleum Drilling Techniques,2023, 51(5):167-172. DOI: 10.11911/syztjs.2023084
Citation: SUN Xin, LIU Lijun, HOU Shugang, et al. Numerical simulation of shale oil well productivity based on shale oil-water two-phase flow characteristics [J]. Petroleum Drilling Techniques,2023, 51(5):167-172. DOI: 10.11911/syztjs.2023084

基于页岩油水两相渗流特性的油井产能模拟研究

基金项目: 四川省自然科学基金项目“基于流固耦合数值模拟的陆相页岩凝析气藏合理开发方式探索”(编号:2022NSFSC1077)、青岛市博士后项目“东营凹陷页岩油测录井产能预测方法研究”(编号:QDBSH20220201023)、中石化经纬有限公司博士后研究项目“东营凹陷页岩油测录井产能预测方法研究”(编号:JWBH2203)联合资助
详细信息
    作者简介:

    孙鑫(1993—),男,山东昌邑人,2016年毕业于中国石油大学(华东)石油工程专业,2021年获中国石油大学(华东)油气田开发工程专业博士学位,博士后,主要从事非常规储层评价与产能预测技术研究工作。E-mail:upcsunxin@163.com

    通讯作者:

    刘礼军,liulijun@cdut.edu.cn

  • 中图分类号: TE32+8

Numerical Simulation of Shale Oil Well Productivity Based on Shale Oil-Water Two-Phase Flow Characteristics

  • 摘要:

    页岩孔隙结构及固液相互作用复杂,其微观渗流特性加大了页岩油产能预测的难度。为准确评价体积压裂后多尺度孔隙结构发育的页岩油藏产能,基于页岩储层油水两相相渗计算方法和嵌入式离散裂缝模型,考虑页岩真实孔隙结构作用下的微观油水两相渗流特性,形成了考虑页岩体积压裂页岩油藏产能的数值模拟方法。基于页岩储层孔径分布计算油水相渗曲线,结合页岩油藏压裂/生产流程,开展了页岩油藏压裂液空间分布以及油井产能评价模拟分析。结果表明,不同孔径分布下的页岩油水两相相渗曲线存在差异,压裂液主要分布在压裂裂缝、与其相连的天然裂缝以及其周边基质中,在闷井过程中裂缝内压裂液逐渐渗吸进入基质并置换基质中原油,经体积压裂可实现改造区域的整体动用。研究结果可以从微观油水两相渗流特性与宏观产能评价角度为页岩油藏高效开发提供技术支撑。

    Abstract:

    The pore structure of shale is complex, and solid-liquid interaction occurs. In addition, its microscopic flow characteristics increase the difficulty of shale oil productivity prediction. In order to accurately evaluate the productivity of shale oil reservoirs with multi-scale pore structures after volume fracturing, the microscopic multi-phase flow characteristics under the action of real pore structure of shale were considered based on the oil-water two-phase relative permeability calculation method and embedded discrete fracture model (EDFM) of shale reservoirs. As a result, a numerical simulation method for shale oil reservoir productivity considering shale volume fracturing was developed. The oil-water two-phase relative permeability curve was calculated based on the pore size distribution of shale reservoirs, and combined with the fracturing/production process of shale reservoirs, the spatial distribution of fracturing fluid in shale oil reservoirs and the productivity evaluation of oil well were simulated and analyzed. The results show that there are differences in the oil-water two-phase relative permeability curves of shale under different pore size distributions. Fracturing fluids are mainly distributed in fracturing fractures, natural fractures connected with them, and the surrounding matrix. During the process of shut-in, the fracturing fluid in the fracture is gradually imbibed into the matrix, displacing the crude oil in the matrix and realizing the whole utilization of the stimulated area by volume fracturing. The research results can provide technical support for the efficient development of shale oil reservoirs from the perspective of microscopic oil-water two-phase flow characteristics and macroscopic productivity evaluation.

  • 我国油气对外依存度持续上升,常规油气田进入开发后期,页岩油气等非常规油气资源的重要性日益显著[1-2]。2022年,中国石油的页岩油产量突破300×104 t,页岩油作为油气资源的后起之秀,其规模化开发正加速推进[3]。作为实现页岩油藏规模效益开发的关键技术,水平井和体积压裂技术受页岩复杂孔隙结构和固液相互作用影响[4-5],目前在页岩油渗流机理、压裂液返排规律及产能预测等方面仍面临诸多问题与挑战。

    页岩油藏压裂过程中,高压泵注的压裂液使主裂缝和次生裂缝延伸,形成复杂人工裂缝网络;同时,压裂液会通过渗吸作用进入并滞留在基质中,返排过程中少量排出,影响页岩油后续产能[6-8]。实践表明,不同页岩油藏储层的压裂液返排率与产能差异较大,其返排特征主要受页岩储层中油水两相渗流特性影响,由页岩孔隙结构特征控制。页岩油储层孔隙结构通常具有纳米级孔隙发育、孔径分布范围广的特点,前人基于页岩孔隙内流体流动规律、孔径分布等提出了多种两相相对渗透率计算方法。Wang Jinxun等人[9]将多孔介质概念化为不同尺寸管道串并联的毛细管模型,考虑孔隙尺寸分布及孔隙形状,推导了储层相渗的经典计算方法。Li Ran等人[10]综合考虑单孔内两相流动特征和孔隙分形结构,建立了页岩两相相渗计算方法,并分析了孔隙尺寸和结构对相渗特征的影响。Su Yuliang等人[11]考虑页岩有机和无机孔隙内油水赋存特征,建立了页岩油水两相相渗计算方法。数值模拟是常用的油藏产能评价手段,但体积压裂后的页岩油藏多尺度孔隙和裂缝储渗空间发育[12-13],传统双重介质模型、局部网格加密等模拟方法具有计算量大、难以处理复杂结构裂缝等局限,同时,页岩油流动受多种机理影响[14-17],数值模拟难度大。

    嵌入式离散裂缝模型是将复杂裂缝几何形态直接嵌入正交背景网格中,简化了裂缝的几何剖分过程,极大地降低了计算量和复杂度[18]。国内外学者综合页岩油渗流机理和嵌入式离散裂缝模型,开展了页岩油井产能模拟分析[19-20],但目前尚未实现微观页岩油水相渗计算与宏观页岩油井产能的耦合。因此,笔者结合页岩油藏相渗计算方法、嵌入式离散裂缝模型和油水两相渗流数学模型,提出了考虑页岩孔隙结构作用下油水两相渗流特性的页岩油井产能数值模拟方法,分析了体积压裂后页岩油藏压裂液空间分布特征和油井产能,实现了页岩微观油水两相渗流特性与宏观油井产能的一体化评价。

    基于毛细管相渗计算模型,结合实际页岩孔隙形状和孔径分布,建立页岩油藏油水两相相渗计算方程。考虑页岩储层中复杂的孔隙形状,采用三角形毛细管模型表征页岩油藏储层。根据三角形毛细管中油水分布状态,单个毛细管中的油水两相流动规律可表示为:

    Qo=πr4eff8μoLΔp (1)
    Qw=(14Gπ)r4dζμwLΔp (2)

    式中:QoQw分别为毛细管中油相和水相的流量,m3/s;μoμw分别为油相和水相黏度,Pa·s;L为毛细管长度,m;Δp为施加在毛细管上的压差,Pa;ζ为水与孔隙壁面相互作用的无因次阻力系数(用于表征孔隙表面性质对流体流动的影响);reff为毛细管有效油相半径,m;G为三角形毛细管的形状因子;rd为油水稳定状态下的界面曲率半径,m。

    reff=21GP2(14Gπ)r2dπ+1rin (3)
    rd=P0.5G+πG (4)

    式中:P为三角形毛细管截面周长,m;rin为毛细管内切圆半径,m。

    结合单个毛细管中油水流动规律和页岩孔径分布,可得页岩储层油水相对渗透率计算公式:

    Kro,m=5πmk=1fkr4eff,k6nk=1fkr2in,kAk (5)
    Krw,m=20mk=1fk(14Gπ)r4d,k3βnk=1fkr2in,kAk+nk=m+1fkr2in,kAknk=1fkr2in,kAk (6)
    Sw,m=mk=1fk(14Gπ)r2d,k+14Gnk=m+1fkr2in,knk=1fkAk (7)

    式中:n为不同尺寸孔隙总数,其中,1~m为中心含水的孔隙尺寸数量,m+1~n为边缘含水的孔隙尺寸数量;Ak为第k个尺寸的毛细管截面积,m2f k为第k个尺寸的毛细管所占比例。

    因此,已知页岩储层的孔径分布后,便可根据式(5)—式(7)计算出页岩油水相对渗透率

    考虑页岩油藏中的油水两相渗流过程,其基质和裂缝中油水两相流体质量守恒关系可统一表达为连续性方程。

    \frac{\partial }{{\partial t}}\left( {\phi {\rho _\beta }{S_\beta }} \right) = - \nabla \cdot \left( {{\rho _\beta }{{\boldsymbol{v}}_\beta }} \right) + {q_\beta } (8)

    式中:β为o或w,代表油相或水相;ϕ为孔隙度;ρββ相流体的密度,kg/m3Sββ相流体饱和度;qββ相流体的源汇项,kg/(m3·s);vββ相流体的渗流速度,m/s。

    考虑页岩中流体流动的最小启动压力梯度效应,用非线性渗流模型描述基质中油水两相流动[21]。裂缝中通常不存在启动压力梯度效应,因此采用常规达西定律描述裂缝内的油水两相流动过程:

    {{\boldsymbol{v}}_\beta } = - \frac{{K{K_{{\text{r}}\beta }}}}{{{\mu _\beta }}}\nabla {\psi _\beta }\left( {1 - \frac{{\text{1}}}{{a + b\left| {\nabla {\psi _\beta }} \right|}}} \right) (9)
    \psi_\beta=p_\beta-\rho_\beta \mathrm{g} h (10)

    式中:K为绝对渗透率,m2Krββ相流体的相对渗透率;b为拟启动压力梯度的倒数,(Pa/m)−1a为非线性渗流凹形曲线段的影响因子;ψββ相流体的流动势,Pa;pββ相流体压力,Pa;h为深度,m。

    为了高效求解页岩油藏油水两相流体流动,基于嵌入式离散裂缝模型对体积压裂后页岩油藏中复杂裂缝进行几何离散和网格剖分(见图1)。对于给定的体积压裂页岩油藏模型,采用结构化网格对基质区域进行剖分,将水力压裂缝和天然裂缝网络嵌入至剖分后的结构化网格中,利用结构化网格边界切割裂缝网络,形成离散裂缝网格单元,综合形成页岩油藏数值模拟的网格单元系统。

    图  1  嵌入式离散裂缝模型示意
    Figure  1.  Embedded discrete fracture model

    基于网格单元系统,采用有限体积法对油水两相渗流模型进行数值离散,并推导得到离散方程的残差形式:

    \begin{split} R_{\beta ,i}^{t + 1} = &\sum\limits_{j \in {\eta _i}} {\left[ {\left( {{\rho _\beta }{\lambda _\beta }} \right)_{ij + \frac{1}{2}}^{t + 1}T_{ij}^{t + 1}\left( {\psi _{\beta j}^{t + 1} - \psi _{\beta i}^{t + 1}} \right)\left( {1 - \gamma _{ij}^{t + 1}} \right)} \right]} + \\ &\left( {V{q_\beta }} \right)_i^{t + 1} - \frac{{\left( {V\phi {\rho _\beta }{S_\beta }} \right)_i^{t + 1} - \left( {V\phi {\rho _\beta }{S_\beta }} \right)_i^t}}{{\Delta t}} \end{split} (11)

    式中:ij+\dfrac{1}{2}表示单元ij界面上的加权平均;Rβ,i为单元iβ相连续性方程的残差,kg/s;ηi为单元i的邻近单元集合;t+1为当前时间步;t为上一时间步;Δt为当前时间步长,s;V为单元体积,m3λ为流度,定义为λ= Kr /μ,(Pa·s)−1Tij为单元ij间的传导率,可分为基质和裂缝不同介质单元组合间的传导率[22-23]γij为启动压力梯度引起的附加阻力系数。

    {\gamma _{ij}} = \frac{1}{{a + \dfrac{{b\left| {\psi _{\beta j}^{t + 1} - \psi _{\beta i}^{t + 1}} \right|}}{{{d_{ij}}}}}} (12)

    式中:dij为单元ij间的距离,m。

    采用牛顿-拉夫森方法求解离散的残差方程。

    \sum\limits_c {\frac{{\partial R_{\beta ,i}^{t + 1}\left( {{\boldsymbol{x}}_k^{t + 1}} \right)}}{{\partial {x_c}}}} \delta {x_{c,k + 1}} = - R_{\beta ,i}^{t + 1}\left( {{\boldsymbol{x}}_k^{t + 1}} \right) (13)
    {\boldsymbol{x}}_{k + 1}^{t + 1} = {\boldsymbol{x}}_k^{t + 1} + {\mathbf{\delta }}{{\boldsymbol{x}}_{k + 1}} (14)

    式中:k为迭代层次;c为主变量向量元素;x为主变量向量,选取油相压力和含水饱和度为主变量。

    在每个时间步中,采用上述求解格式进行迭代计算,并更新主变量至残差向量的范数小于设定的允许误差,进入下一个时间步进行计算。

    选取单峰型孔径分布和双峰型孔径分布2种典型孔径分布页岩(见图2),在孔隙形状参数相同的基础上,采用页岩油藏相渗计算方法计算油水相对渗透率,结果见图3。由图3可知,相比于单峰型孔径分布,双峰型孔径分布的孔隙尺寸更大,油相的流动能力更强。因此,双峰型孔径分布的页岩储层油相相对渗透率更大,水相相对渗透率更小。

    图  2  两种典型页岩孔径分布概率曲线
    Figure  2.  Two typical probability curves for shale pore size distribution
    图  3  两种孔径分布计算的油水两相相渗曲线
    Figure  3.  Oil-water two-phase relative permeability curves calculated with two pore size distributions

    为分析压裂过程中压裂液的分布特征,基于胜利油田某页岩油井地质及压裂设计资料,结合嵌入式离散裂缝模型,建立体积压裂页岩油藏模型(见图4)。该页岩油藏基质孔隙度7.0%,渗透率0.5 μD;水力裂缝开度为4 mm,渗透率为5 D;天然裂缝开度为0.3 mm,渗透率0.1 D;初始油藏压力40 MPa,初始含水饱和度为0.05,油相和水相的黏度分别为0.40和0.25 mPa∙s,压裂液注入量为1.0×104 m3,压裂后闷井时间为30 d,油水相对渗透率曲线采用图3中单峰型孔径分布的计算结果。注入压裂液后的页岩油藏基质、裂缝中的压力和含水饱和度分布模拟结果如图5所示,压裂结束闷井30 d后的基质、裂缝中的压力和含水饱和度分布则如图6所示。

    图  4  体积压裂页岩油藏模型
    Figure  4.  Shale oil reservoir model by volume fracturing
    图  5  压裂结束时页岩油藏压力和含水饱和度分布模拟结果
    Figure  5.  Simulation results of pressure and water saturation distribution in shale oil reservoir after fracturing
    图  6  闷井30 d后页岩油藏压力和含水饱和度分布模拟结果
    Figure  6.  Simulation results of pressure and water saturation distribution in shale oil reservoir after 30 days of shut-in

    图5图6可以看出,压裂液主要进入压裂缝及其周边天然裂缝和基质中,引起近水力裂缝周边区域压力升高,该区域裂缝内含水饱和度显著上升,近水力裂缝基质内含水饱和度有所提升。进入闷井阶段后,裂缝和基质中的压力逐渐向周围区域耗散,近水力裂缝高压区域内的压力逐渐降低。同时,裂缝内的压裂液在毛细管力作用下渗吸进入基质,裂缝内含水饱和度降低,对基质中的原油产生一定的渗吸置换作用。

    在压裂液注入和闷井的模拟结果基础上,开展页岩油藏压后产能数值模拟,对页岩油藏衰竭开发动用范围和产油量进行评价。衰竭开发1 000 d后的储层基质和裂缝中的压力和含油饱和度分布如图7所示。经体积压裂后的页岩油藏裂缝网络发育,衰竭开发过程中油藏动用程度高,天然裂缝发育范围内基本可以动用开发。此外,衰竭开发后裂缝内含水量低,但基质内的含水饱和度分布与生产前差异不大,其原因在于压裂液在毛管力作用下滞留在基质中,生产压差难以克服毛管阻力,这也解释了实际页岩储层压裂后压裂液返排率低的现象。页岩油藏生产1 000 d的日产油量和累计产油量曲线如图8所示。体积压裂页岩油藏衰竭开发产量递减速度快,经1 000 d开发后油井累计产油量可达61 145 m3。此外,开发过程中累计产水量为3 335 m3,忽略地层水产出,计算得出压裂液反排率为33%,与现场实际基本符合。由此可见,受页岩油水两相渗流特性及毛管力作用影响,页岩储层压裂后压裂液返排率较低,但体积压裂后的页岩油藏动用程度较好。

    图  7  生产1 000 d后页岩油藏压力和含水饱和度分布模拟结果
    Figure  7.  Simulation results of pressure and water saturation distribution in shale oil reservoir after 1000 days of production
    图  8  生产 1 000 d后页岩油藏日产油量和累积产油量曲线
    Figure  8.  Daily oil production and cumulative oil production curves of shale oil reservoir after 1000 days of production

    1)考虑页岩孔隙结构作用下油水两相渗流特性,压裂页岩油藏产能数值模拟方法可实现页岩油藏油水相对渗透率、压裂液分布和返排以及油井产能的全流程评价。

    2)基于页岩储层孔径分布以及孔隙结构参数,采用毛细管模型可得到页岩油藏油水相对渗透率,不同页岩孔径分布下油水相对渗透率存在较大差异。

    3)压裂液主要分布于压裂缝及其周边的天然裂缝和基质中,闷井阶段进入周边基质,基质毛管阻力作用导致压裂液返排率较低,但体积压裂后的页岩油藏动用范围和程度较好。

  • 图  1   嵌入式离散裂缝模型示意

    Figure  1.   Embedded discrete fracture model

    图  2   两种典型页岩孔径分布概率曲线

    Figure  2.   Two typical probability curves for shale pore size distribution

    图  3   两种孔径分布计算的油水两相相渗曲线

    Figure  3.   Oil-water two-phase relative permeability curves calculated with two pore size distributions

    图  4   体积压裂页岩油藏模型

    Figure  4.   Shale oil reservoir model by volume fracturing

    图  5   压裂结束时页岩油藏压力和含水饱和度分布模拟结果

    Figure  5.   Simulation results of pressure and water saturation distribution in shale oil reservoir after fracturing

    图  6   闷井30 d后页岩油藏压力和含水饱和度分布模拟结果

    Figure  6.   Simulation results of pressure and water saturation distribution in shale oil reservoir after 30 days of shut-in

    图  7   生产1 000 d后页岩油藏压力和含水饱和度分布模拟结果

    Figure  7.   Simulation results of pressure and water saturation distribution in shale oil reservoir after 1000 days of production

    图  8   生产 1 000 d后页岩油藏日产油量和累积产油量曲线

    Figure  8.   Daily oil production and cumulative oil production curves of shale oil reservoir after 1000 days of production

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  • 期刊类型引用(1)

    1. 曲鸿雁,胡佳伟,周福建,史纪龙,刘成. 深层裂缝性致密砂岩气藏基质–裂缝气体流动机理. 石油钻探技术. 2024(02): 153-164 . 本站查看

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出版历程
  • 收稿日期:  2023-05-16
  • 修回日期:  2023-07-31
  • 录用日期:  2023-08-29
  • 网络出版日期:  2023-09-02
  • 刊出日期:  2023-10-30

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