高密度页理页岩油藏多相排采数学模型及动态反演

牛烺昱，程林松，王志凯，贾品，武玉程; NIU Langyu; CHENG Linsong; WANG Zhikai; JIA Pin; WU Yucheng

引 en

高密度页理页岩油藏多相排采数学模型及动态反演

牛烺昱¹
，程林松¹
，王志凯²
，贾品¹
，武玉程¹

1. 中国石油大学（北京）石油工程学院，北京 102249； 2. 中海油研究总院有限责任公司，北京 100027；

Mathematical model and interpretation analysis for multi-phase flowback in shale reservoirs with highly developed beddings

NIU Langyu¹
， CHENG Linsong¹
， WANG Zhikai²
， JIA Pin¹
， WU Yucheng¹

1. College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102249 , China； 2. CNOOC Research Institute Company Limited, Beijing 100027 , China；

作者简介:

牛烺昱（1998-），男，博士研究生，研究方向为石油与天然气工程。E-mail: niulangyu@foxmail.com。

通信作者:

贾品（1990-），男，副教授，博士，研究方向为油藏工程和渗流理论。E-mail: jiapin1990@163.com。

中图分类号:TE 34

文献标识码:A

文章编号:1673-5005(2025)05-0127-10

DOI:10.3969/j.issn.1673-5005.2025.05.012

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出版信息

参考文献 1

赵国忠,王青振,刘勇,等.松辽盆地古龙页岩油人工油藏的动态模拟及预测[J].大庆石油地质与开发,2021,40(5):170-180.ZHAO Guozhong,WANG Qingzhen,LIU Yong,et al.Dynamic simulation and prediction for artificial reservoir of Gulong shale oil in Songliao Basin[J].Petroleum Geology & Oilfield Development in Daqing,2021,40(5):170-180.

查找原文

参考文献 2

AFAGWU C,ALAFNAN S,WEIJERMARS R,et al.Multiscale and multiphysics production forecasts of shale gas reservoirs:New simulation scheme based on Gaussian pressure transients[J].Fuel,2023,336:127142.

查找原文

参考文献 3

ARPS J J.Analysis of decline curves[J].Transactions of the AIME,1999,160:228-247.

查找原文

参考文献 4

VALKO P P,LEE W J.A better way to forecast production from unconventional gas wells[R].SPE 134231,2010.

查找原文

参考文献 5

CLARK A J,LAKE L W,PATZEK T W.Production forecasting with logistic growth models[R].SPE 144790,2011.

查找原文

参考文献 6

赵康,陈民锋,王艺文,等.四川盆地SZ页岩气藏气井产量变化规律及递减预测新模型[J].中国海上油气,2024,36(3):129-136.ZHAO Kang,CHEN Minfeng,WANG Yiwen,et al.A new model for production variation patterns and decline prediction of SZ shale gas reservoir in Sichuan basin[J].China Offshore Oil and Gas,2024,36(3):129-136.

查找原文

参考文献 7

KANFAR M S,WATTENBARGER R A.Comparison of empirical decline curve methods for shale wells[R].SPE 162648,2012.

查找原文

参考文献 8

LEE S H,LOUGH M F,JENSEN C L.Hierarchical modeling of flow in naturally fractured formations with multiple length scales[J].Water Resources Research,2001,37(3):443-455.

查找原文

参考文献 9

贾品,牛烺昱,柯贤哲,等.高密度页理页岩油藏排采数值模拟及动态特征[J].中国石油大学学报(自然科学版),2023,47(4):137-144.JIA Pin,NIU Langyu,KE Xianzhe,et al.Numerical simulation and dynamic characteristics of drainage and production in high density bedding shale oil reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(4):137-144.

查找原文

参考文献 10

胡晓东,张鹏天,周福建,等.迂曲裂缝内支撑剂运移数值模拟[J].中国石油大学学报(自然科学版),2024,48(3):111-118.HU Xiaodong,ZHANG Pengtian,ZHOU Fujian,et al.Numerical simulation of proppant transport in tortuous fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(3):111-118.

查找原文

参考文献 11

王森,向杰,冯其红,等.基于深度学习加速的油藏数值模拟自动历史拟合方法[J].中国石油大学学报(自然科学版),2024,48(5):103-114.WANG Sen,XIANG Jie,FENG Qihong,et al.Deep-learning-based acceleration method for automatic history matching of reservoir numerical simulation[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):103-114.

查找原文

参考文献 12

MOINFAR A,VARAVEI A,SEPEHRNOORI K,et al.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs[J].SPE Journal,2014,19(2):289-303.

查找原文

参考文献 13

LIU Q,XUE L,SAROUT J,et al.Automatic history matching of multistage fractured shale gas reservoir constrained by microseismic data[J].Journal of Petroleum Science and Engineering,2022,213:110357.

查找原文

参考文献 14

KUCHUK F,BIRYUKOV D.Pressure-transient behavior of continuously and discretely fractured reservoirs[J].SPE Reservoir Evaluation & Engineering,2014,17(1):82-97.

查找原文

参考文献 15

姚军,王萌,樊冬艳,等.考虑层理缝岩性差异的页岩油藏压裂水平井动态分析方法[J].中国石油大学学报(自然科学版),2024,48(5):91-102.YAO Jun,WANG Meng,FAN Dongyan,et al.Dynamic analysis of fractured horizontal wells in shale reservoirs considering lithological differences of bedding fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):91-102.

查找原文

参考文献 16

ZHOU W,BANERJEE R,POE B D,et al.Semi-analytical production simulation of complex hydraulic fracture network[R].SPE 157367-MS,2012.

查找原文

参考文献 17

JIA P,CHENG L,HUANG S,et al.A semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks[J].Journal of Hydrology,2016,537:208-220.

查找原文

参考文献 18

JIA P,CHENG L,CLARKSON C R,et al.A novel method for interpreting water data during flowback and early-time production of multi-fractured horizontal wells in shale reservoirs[J].International Journal of Coal Geology,2018,200:186-198.

查找原文

参考文献 19

CLARKSON C R R,WILLIAMS-KOVACS J D D.Modeling two-phase flowback of multifractured horizontal wells completed in shale[J].SPE Journal,2013,18(4):795-812.

查找原文

参考文献 20

CLARKSON C R,QANBARI F.A semianalytical forecasting method for unconventional gas and light oil wells:a hybrid approach for addressing the limitations of existing empirical and analytical methods[R].SPE Reservoir Evaluation & Engineering,2015,18(1):94-110.

查找原文

参考文献 21

CAO C,CHENG L,JIA P,et al.A dynamic fracture model combining with Laplace transform and synchronous iteration method for transient behavior analysis of a four-zone system[J].Journal of Hydrology,2022,615:128723.

查找原文

参考文献 22

MCKEE C R,BUMB A C,KOENIG R A.Stress-dependent permeability and porosity of coal and other geologic formations[J].SPE Formation Evaluation,1988,3(1):81-91.

查找原文

参考文献 23

WATTENBARGER R A,EL-BANBI A H,VILLEGAS M E,et al.Production analysis of linear flow into fractured tight gas wells[R].SPE 39931,1998.

查找原文

参考文献 24

WANG Z,CHENG L,HAMDI H,et al.A semi-analytical model for quantifying the inter-well communication in water-bearing shale gas-condensate reservoirs[J].Geoenergy Science and Engineering,2023,228:211997.

查找原文

目录contents

摘要Abstract
关键词Keywords
1 页岩油多相排采渗流数学模型建立及半解析求解
1.1 页岩油压后缝网形态及油水赋存假设
1.2 页岩油-气-水三相排采渗流数学模型建立
1.2.1 基质流动方程。
1.2.2 开启页理缝流动方程
1.3 页岩油-气-水三相排采渗流数学模型半解析求解
1.4 油-气-水三相排采数学模型适用性评价
1.5 油-气-水三相排采动态影响因素
1.5.1 开启页理缝长度
1.5.2 开启页理缝应力敏感系数
2 页岩油压后返排动态精确反演方法
3 矿场应用
4 结论
参考文献

摘要

为准确预测高密度页理页岩油藏中的多相排采动态并反演关键渗流参数，首先建立考虑开启页理缝缝长及缝宽的动态变化的页理缝-页岩基质的油-气-水三相排采渗流数学模型，引入动态泄油面积概念（DDA）对模型进行求解；基于此模型结合特征线分析法（SLA）及自动历史拟合方法（AHM）形成排采动态反演方法；最后基于反演方法解释典型页岩油区块中的1口生产井的关键渗流参数并预测油井产能。结果表明：开启页理缝长度方向的闭合主要影响缝控基质尺寸，对峰值产量与日产气量有较大影响；同时开启页理缝缝宽方向的闭合会影响油-气两相的峰值产量及递减速度，需同时考虑两个方向的闭合机制才能较为真实地模拟页岩油压后排采过程。

Abstract

To accurately study the multiphase production dynamics in shale reservoirs with highly developed beddings, a tri-phase (oil-gas-water) production flow mathematical model considering the interaction between opened beddings and shale matrix was firstly established. A dynamic drainage area (DDA) concept was introduced to solve the model, and the dynamic changes of the length and aperture of opened beddings were accounted. Based on the model, a production dynamic interpretation method was developed in combination with the straight-line analysis (SLA) and automatic history matching (AHM) methods. In a case study, the key flow parameters of a producing well in a typical shale oil block were interpreted using the new method presented in this paper, and the well’s production capacity was predicted. The results indicate that the closure of opened beddings in the length direction mainly affects the size of the matrix controlled by the opened beddings and has a significant impact on the peak production and gas production rate. Meanwhile, the closure in the aperture direction of opened beddings affects the peak production and decline rate of the oil-gas phases. The both closure mechanisms must be considered simultaneously in order to more realistically simulate the post-fracturing production process of shale oil.

关键词

页岩油藏；多相排采；数学模型；自动历史拟合；参数反演

Keywords

shale reservoir ； multi-phase flowback ； mathematical model ； automatic history matching ； parameter interpretation

纯页岩型页岩储层中，人工裂缝在竖直方向极易沿层理缝转向^[1]，同时压后流体的二次赋存及裂缝的动态演变导致了页岩油返排动态的复杂、解释难度大。因此亟需建立针对页岩油返排阶段的数学模型，实现裂缝及储层关键参数的精确反演及油井产能的准确预测。目前页岩油返排动态解释及油井产能预测的方法主要有产量递减分析（DCA）、瞬态产量分析（RTA）及基于产能预测模型的历史拟合方法^[2]。DCA方法作为较便捷的产量分析方法，常被应用于低渗-致密-页岩储层中^[3-6]。然而此方法不能考虑流体在页岩储层中的复杂渗流机制，也无法考虑不同类型储层的边界条件^[7]。RTA方法作为另一种产量分析方法，能够考虑致密储层中的复杂渗流机制及不同边界条件。然而RTA方法需要大量精确的储层性质及井底流压数据作为输入参数，这导致该方法难以大规模应用。产能预测模型可以通过历史拟合的方法反演缝网及改造区的关键参数，并实现油井的产能预测。目前国内外部分学者提出了针对排采阶段的产能预测数值模型^[8-13]。然而数值模拟历史拟合参数反演需要耗费大量的计算资源及时间，且反演结果具有多解性。相比于数值模拟方法，半解析模型简化了部分页岩基质中的复杂机制，计算效率更高，更适用于历史拟合参数反演^[14-20]。笔者首先基于页岩油藏压后的典型缝网形态，建立针对该类油藏的返排渗流数学模型。考虑油相的挥发性及排采过程中裂缝体积的变化，基于DDA概念的半解析方法进行求解。通过水相特征线分析（SLA）初步反演缝网参数，并基于建立的模型及遗传算法（GA），形成返排动态自动拟合算法，实现缝网及改造区参数的准确反演及油井产能的精确预测。
1 页岩油多相排采渗流数学模型建立及半解析求解
1.1 页岩油压后缝网形态及油水赋存假设
页岩油多相排采正交缝网示意图^[1]如图1所示。假设：①储层为等厚储层，且忽略重力影响，人工裂缝在垂向上贯穿储层；②人工裂缝和开启的页理缝内的含水饱和度为1，基质中油-气-水三相赋存；③人工裂缝和开启的页理缝内的压力远高于原始地层压力，接近储层破裂压力；④流体从页岩基质流入开启的页理缝，再由开启的页理缝流入人工裂缝，未考虑页岩基质中的纳米限域效应。
图1 正交缝网示意图
Fig.1 Schematic diagram of orthogonal fracture networks
高密度页理页岩油藏中，垂向上整体呈现出一层页岩基质，一层页理缝的储层特性。在储层岩石脆性较大，且水平地应力差较小的情况下，水力裂缝易沿页理缝方向发生转向。同时，高压压裂液（水相）压裂造缝，将油相驱替远离裂缝，压裂液侵入开启的页理缝中，在人工压裂缝和开启的页理缝内形成高含水饱和度，高压力分区，如图2所示。本文中的物理模型中，将水力压裂后的储层划分为人工主缝，开启的页理缝和基质（该区域包含页岩基质及未开启的页理缝，采用Kazemi双重介质模型的等效参数描述）三重介质，由于页岩储层中渗透率极差较大，因此人工主缝考虑为无限导流。由于水相赋存于裂缝系统内基质油气较难动用，存在较长时间的单产水阶段。油气两相突破后，油-气-水三相同时排采。将多段压裂水平井的产量平均分配至每簇，取每簇中相邻两开启页理缝的一半缝间距为单个研究单元宽度，开启页理缝半宽为单个研究单元长度，单个研究单元中包含基质，开启页理缝，及部分水力裂缝三部分。
图2 页岩油多相排采物理模型
Fig.2 Physical model for multi-phase flow-back and production of shale oil
1.2 页岩油-气-水三相排采渗流数学模型建立
流体的流动均假设为线性流，即基质流体线性流入开启的页理缝，开启页理缝中的流体线性流入人工裂缝，开启页理缝之间为封闭边界。由于开启页理缝渗透率远大于基质渗透率，因此可以通过一维线性流方程描述各区域中各相流体的流动。以下流动方程中：下标m代表基质，n代表开启的页理缝，w代表水相，o代表油相，g代表气相，og代表溶解气。
1.2.1 基质流动方程。
基质向开启的页理缝渗流过程如图3所示。
图3 页岩基质至开启的页理缝渗流
Fig.3 Fluids flow from shale matrix to opened bedding
水相流动方程为

\frac{\partial}{\partial y} (\frac{β k_{m} k_{r, w, m}}{μ_{w, m} B_{w, m}} \frac{\partial p_{m}}{\partial y}) = \frac{\partial}{\partial t} (\frac{φ_{m} S_{w, m}}{B_{w, m}}) .

(1)

式中，β为单位转换系数，国际单位制下其数值为0.0864；k_m为基质渗透率，10^-3 μm²；k_r，w，m为基质内的水相相对渗透率；p_m为基质内的平均压力，MPa；μ_w，m为基质内的水相黏度，mPa·s；B_w，m为基质内水相的体积系数；φ_m为基质的孔隙度；S_w，m为基质内的平均含水饱和度。
气相渗流方程中应考虑渗流区压力是否降至泡点压力以下，压力降至泡点压力以下，将有气相从油相中析出。
泡点压力以上：

\frac{\partial}{\partial y} (\frac{β k_{m} k_{r, g, m}}{μ_{g, m} B_{g, m}} \frac{\partial p_{m}}{\partial y}) = \frac{\partial}{\partial t} (\frac{φ_{m} S_{g, m}}{B_{g, m}}) .

(2)

泡点压力以下：

\begin{matrix} \frac{\partial}{\partial y} [(\frac{R_{s} β k_{m} k_{r, o, m}}{μ_{o, m} B_{o, m}} + \frac{β k_{m} k_{r, g, m}}{μ_{g, m} B_{g, m}}) \frac{\partial p_{m}}{\partial y}] = \\ \frac{\partial}{\partial t} (\frac{R_{s} φ_{m} S_{o, m}}{B_{o, m}} + \frac{φ_{m} S_{g, m}}{B_{g, m}}) . \end{matrix}

(3)

式中，R_s为地层原油的溶解气油比，m³/m³；k_r，g，m和k_r，o，m分别为基质内的气相和油相相对渗透率；μ_g，m为μ_o，m分别为基质内的气相和油相黏度，mPa·s；B_o，m和B_g，m分别为基质内油相和气相的体积系数；S_g，m和S_o，m分别为基质内的平均含气率和含油饱和度。
油相流动方程为

\frac{\partial}{\partial y} (\frac{β k_{m} k_{r, o, m}}{μ_{o, m} B_{o, m}} \frac{\partial p_{m}}{\partial y}) = \frac{\partial}{\partial t} (\frac{φ_{m} S_{o, m}}{B_{o, m}}) .

(4)

控制方程的初始条件可以表示为

p_{m, t = 0} = p_{i} .

(5)

式中，p_m，_t₌₀为基质的初始压力条件，MPa；p_i为基质的初始压力，MPa。
假设封闭外边界条件：

{\frac{\partial p_{m}}{\partial y}|}_{y = y_{out}} = 0 .

(6)

式中， ${\frac{\partial p_{m}}{\partial y}|}_{y = y_{out}}$ 为基质的外边界条件。
基质与开启的页理缝通过物质平衡方法进行耦合：

q_{n, flow-in} = q_{m, flow-out}

(7)

式中，q_n，flow_-in为由流入开启页理缝的流量，m³/d；q_m，flow_-out为由基质流出的流量，m³/d。
1.2.2 开启页理缝流动方程
开启页理缝向人工裂缝的渗流过程如图4所示。
图4 开启的页理缝至人工裂缝渗流
Fig.4 Fluids flow from opened bedding to hydraulic fracture
与基质区的渗流控制方程类似，开启页理缝内的水相渗流控制方程为

\frac{\partial}{\partial x} (\frac{β k_{n} k_{r, w, n}}{μ_{w, n} B_{w, n}} \frac{\partial p_{n}}{\partial x}) + q_{w, m} = \frac{\partial}{\partial t} (\frac{φ_{n} S_{w, n}}{B_{w, n}}) .

(8)

式中，q_w，m为基质向开启页理缝的水相窜流量，m³/d。
气相（泡点压力以上）：

\frac{\partial}{\partial x} (\frac{β k_{n} k_{r, g, n}}{μ_{g, n} B_{g, n}} \frac{\partial p_{n}}{\partial x}) + q_{g, m} = \frac{\partial}{\partial t} (\frac{φ_{n} S_{g, n}}{B_{g, n}}) .

(9)

式中，q_g，m为基质向开启页理缝的气相窜流量，m³/d。
气相（泡点压力以下）：

\frac{\partial}{\partial x} [(\frac{R_{s} β k_{n} k_{r, o, n}}{μ_{o, n} B_{o, n}} + \frac{β k_{n} k_{r, g, n}}{μ_{g, n} B_{g, n}}) \frac{\partial p_{n}}{\partial x}] + q_{g, m} = \frac{\partial}{\partial t} (\frac{R_{s} φ_{n} S_{o, n}}{B_{o, n}} + \frac{φ_{n} S_{g, n}}{B_{g, n}}) .

(10)

油相：

\frac{\partial}{\partial x} (\frac{β k_{n} k_{r, o, n}}{μ_{o, n} B_{o, n}} \frac{\partial p_{n}}{\partial x}) + q_{o, m} = \frac{\partial}{\partial t} (\frac{φ_{n} S_{o, n}}{B_{o, n}}) .

(11)

式中，q_o，m为基质向开启页理缝的油相窜流量，m³/d。
开启页理缝内赋存高压的压裂液，考虑压裂后短时间闷井或者不闷井直接排采的工况，开启页理缝内部的压力可以近似等于地层的破裂压力：

p_{n, t = 0} = p_{break} .

(12)

式中，p_n，_t₌₀为开启页理缝的初始压力条件；p_break为页岩储层的破裂压力，MPa。由于人工裂缝考虑为无限导流，因此内边界条件可以表示为

{p_{n}|}_{y = y_{out}} = p_{w f} .

(13)

式中，p_wf为井底流压，MPa。
排采过程中，裂缝系统内压力变化较大，开启页理缝闭合严重。引入缝内外压差影响下裂缝在长度方向闭合的表征公式，模拟排采过程中开启页理缝闭合导致的缝控储量下降，开启页理缝的闭合过程如图5所示。
图5 开启的页理缝闭合
Fig.5 Closure of opened beddings

x_{n} = x_{nini} [1 - \frac{p_{ini} - p}{γ (p_{ini} - p_{w f})}] .

(14)

式中，γ为裂缝闭合系数^[21]，其表示裂缝闭合速率；x_n为开启页理缝半长，m；下标ini表示初始状态下的参数。
开启的页理缝一般考虑为无支撑或弱支撑裂缝，因此排采过程中其渗透率的变化可以采用指数型应力敏感进行修正^[22]为

k_{n} = k_{n i} e^{- β_{s} (p_{i} - p)} .

(15)

式中，k_ni为打开的天然裂缝初始渗透率，10^-3 μm²；β_s为应力敏感系数，表示渗透率对有效应力变化的敏感程度，数值越大表示敏感程度越高。
各分区中，考虑孔隙度的应力敏感，各分区的孔隙度应力敏感公式可以表示为

φ = φ_{i} e^{c (p - p_{i})}

(16)

式中，φ为各分区中孔隙度；φ_i为各分区中初始的孔隙度；c为各区域的压缩系数，MPa^-1。
1.3 页岩油-气-水三相排采渗流数学模型半解析求解
开启的页理缝与基质通过物质平衡方法耦合，联立该两个区域内的油-气-水三相物质平衡方程，通过分离变量求解两区域内的平均压力及各相流体的平均饱和度。当各区压力高于泡点压力时，无溶解气从油相中挥发，物质平衡方程组可以表示为

\{\begin{matrix} (V_{g, n} + A_{g, n}) \frac{\partial p_{n}}{\partial t} = H_{g, n} \frac{\partial S_{o, n}}{\partial t} + H_{g, n} \frac{\partial S_{w, n}}{\partial t} - q_{g, n - f} + q_{g, m - n}, \\ V_{g, m} \frac{\partial p_{m}}{\partial t} = H_{g, m} \frac{\partial S_{o, m}}{\partial t} + H_{g, m} \frac{\partial S_{w, m}}{\partial t} + A_{g, m} \frac{\partial y_{m y}}{\partial t} - q_{g, m - n}, \\ H_{w, n} \frac{\partial S_{w, n}}{\partial t} = - (V_{w, n} + A_{w, n}) \frac{\partial p_{n}}{\partial t} - q_{w, n - f} + q_{w, m - n}, \\ H_{w, m} \frac{\partial S_{w, n}}{\partial t} = - V_{w, m} \frac{\partial p_{m}}{\partial t} + A_{w, m} \frac{\partial y_{m y}}{\partial t} - q_{w, m - n}, \\ H_{o, n} \frac{\partial S_{o, n}}{\partial t} = - (V_{o, n} + A_{o, n}) \frac{\partial p_{n}}{\partial t} - q_{o, n - f} + q_{o, m - n}, \\ H_{o, m} \frac{\partial S_{o, m}}{\partial t} = - V_{o, m} \frac{\partial p_{m}}{\partial t} + A_{o, m} \frac{\partial y_{m y}}{\partial t} - q_{o, m - n} . \end{matrix}

(17)

其中
$\begin{matrix} V_{j, n} = \frac{x_{n} h w_{n} {\bar{S}}_{j, n} φ_{n} (c_{n} + c_{j, n})}{B_{j, n}}, \\ V_{j, m} = \frac{x_{m} h y_{m} {\bar{S}}_{j, m} φ_{m} (c_{m} + c_{j, m})}{B_{j, m}}, \\ H_{j, n} = \frac{x_{n} h w_{n} φ_{n}}{B_{j, n}}, H_{j, m} = \frac{x_{n} h y_{m} φ_{m}}{B_{j, m}}, \\ A_{j, n} = \frac{h w_{n} x_{n, i n i} φ_{n, i n i} S_{j, n, i n i}}{γ (p_{i n i} - p_{w f}) B_{j, i n i}}, \\ A_{j, m} = x_{n} h (\frac{φ_{m, i n i} S_{j, m, i n i}}{B_{j, m, i n i}} - \frac{φ_{m} {\bar{S}}_{j, m}}{B_{j, m}}) . \end{matrix}$
式中，V_j_，n为开启页理缝孔隙体积及流体体积压缩变化系数；V_j_，m为基质各相流体及孔隙体积压缩变化系数；A_j_，n为裂缝闭合导致的流体体积变化系数，考虑裂缝闭合后该部分的流体均被挤压排出开启的页理缝，流入人工裂缝；A_j_，m为基质泄油面积变化系数；H_j_，n为开启页理缝内流体饱和度变化系数；H_j_，m为开启基质内流体饱和度变化系数；q为各区域各相流体的流量，m³/s；h为储层厚度，m；w_n为开启页理缝宽度，m；y_m为基质区宽度，m； $\bar{S}$ 为分区流体的平均饱和度; 下标j表示流体的各相。
分区压力降低至泡点压力以下后，油相中溶解气挥发，气相物质平衡方程中考虑溶解气的体积变化及窜流量，物质平衡方程组变化为

\{\begin{matrix} (V_{g, n} + A_{g, n} + D_{n}) \frac{\partial p_{n}}{\partial t} = (H_{g, n} + H_{o g, n}) \frac{\partial S_{o, n}}{\partial t} + \\ H_{g, n} \frac{\partial S_{w, n}}{\partial t} - q_{g, n - f} + q_{g, m - n} - q_{o g, n - f} + q_{o g, m - n}, \\ (V_{g, m} + D_{m}) \frac{\partial p_{m}}{\partial t} = (H_{g, m} + H_{o g, m}) \frac{\partial S_{o, m}}{\partial t} + \\ H_{g, m} \frac{\partial S_{w, m}}{\partial t} + (A_{g, m} + A_{o g, m}) \frac{\partial y_{m y}}{\partial t} - q_{g, m - n} - q_{o g, m - n}, \\ H_{w, n} \frac{\partial S_{w, n}}{\partial t} = - (V_{w, n} + A_{w, n}) \frac{\partial p_{n}}{\partial t} - q_{w, n - f} + q_{w, m - n}, \\ H_{w, m} \frac{\partial S_{w, n}}{\partial t} = - V_{w, m} \frac{\partial p_{m}}{\partial t} + A_{w, m} \frac{\partial y_{m y}}{\partial t} - q_{w, m - n}, \\ H_{o, n} \frac{\partial S_{o, n}}{\partial t} = - (V_{o, n} + A_{o, n}) \frac{\partial p_{n}}{\partial t} - q_{o, n - f} + q_{o, m - n}, \\ H_{o, m} \frac{\partial S_{o, m}}{\partial t} = - V_{o, m} \frac{\partial p_{m}}{\partial t} + A_{o, m} \frac{\partial y_{m y}}{\partial t} - q_{o, m - n} . \end{matrix}

(18)

其中
$H_{o g, n} = \frac{x_{n} h w_{n} R_{s, n} φ_{n}}{B_{o, n}}, H_{o g, m} = \frac{x_{n} h y_{m} R_{s, m} φ_{m}}{B_{o, m}},$
$V_{g, n} = x_{n} h w_{n} [\frac{{\bar{S}}_{g, n} φ_{n} (c_{n} + c_{g, n})}{B_{g, n}} + \frac{R_{s, n} {\bar{S}}_{o, n} φ_{n} (c_{n} + c_{o, n})}{B_{o, n}}],$
$V_{g, m} = x_{m} h y_{m} [\frac{{\bar{S}}_{g, m} φ_{m} (c_{m} + c_{g, m})}{B_{g, m}} + \frac{R_{s, m} {\bar{S}}_{o, m} φ_{m} (c_{m} + c_{o, m})}{B_{o, m}}],$
$A_{g, n} = \frac{h w_{n} x_{n, i n i}}{γ (p_{i n i} - p_{w f})} (\frac{φ_{n, i n i} S_{g, n, i n i}}{B_{g, n, i n i}} + \frac{R_{s, n, i n i} φ_{n, i n i} S_{o, n, i n i}}{B_{o, n, i n i}}),$
$A_{o g, m} = x_{n} h (\frac{R_{s, m, i n i} φ_{m, i n i} S_{o, m, i n i}}{B_{o, m, i n i}} - \frac{R_{s, m} φ_{m} {\bar{S}}_{o, m}}{B_{o, m}}),$
$D_{n} = \frac{x_{n} h w_{n} {\bar{S}}_{o, n} φ_{n}}{B_{o, n}} \frac{\partial R_{s, n}}{\partial t}, D_{m} = \frac{x_{n} h y_{m} {\bar{S}}_{o, m} φ_{m}}{B_{0, m}} \frac{\partial R_{s, m}}{\partial t} .$
式中，H_og，n为开启页理缝中溶解气饱和度变化系数；H_og，m为基质中溶解气饱和度变化系数；V_g，n为泡点压力下的裂缝孔隙体积及流体压缩变化系数；V_g，m为泡点压力下的基质孔隙体积及流体压缩变化系数；A_g，n为开启页理缝闭合导致的孔隙体积变化系数；A_og，m为动态泄油半径导致的孔隙体积变化；D_n为开启页理缝中溶解气挥发项；D_m为基质中的溶解气挥发项。
在每个时间步内，瞬态渗流可以近似视为拟稳态渗流，结合Wattenbarger等^[23]给出的拟稳态传导系数公式，油相和水相自基质沿y_my方向流入开启的页理缝内的窜流量可以通过该区域传导系数与压差的乘积表示。
此区域内的油-气-水传导系数为

T_{j, m - n} = \frac{k_{m} k_{r, m} h}{1.842 B_{j, m} μ_{j, m} [\frac{2}{π} (\frac{y_{m y}}{x_{n}})]} .

(19)

式中，T_j_，m_-n为压力高于泡点压力时油气水由基质到开启页理缝的传导系数，m³/（d·MPa）。
基质压力低于泡点压力时溶解气相从油相中脱出，因此需要增加溶解气相的传导系数。溶解气相传导系数为

T_{o g m - n} = \frac{R_{s} k_{m} k_{r, o, m} h}{1.842 B_{o, m} μ_{o, m} [\frac{2}{π} (\frac{y_{m y}}{x_{n}})]} .

(20)

式中，T_ogm_-n为溶解气由基质到开启页理缝的传导系数，m³/（d·MPa）。
同理，开启的页理缝至人工裂缝的传导系数需要判断内部压力与泡点压力的关系，增加溶解气相传导系数。开启页理缝至人工裂缝传导系数，压力高于泡点压力时可以表示为

T_{j, n - f} = \frac{k_{n} k_{r, j, n} h}{1.842 B_{j, n} μ_{j, n} [\frac{2}{π} (\frac{y_{m x}}{w_{n}})]}

(21)

压力低于泡点压力时，

T_{o g n - f} = \frac{R_{s} k_{n} k_{r, o, n} h}{1.842 B_{o, n} μ_{o, n} [\frac{2}{π} (\frac{y_{m x}}{w_{n}})]} .

(22)

由于页岩基质极为致密，排采过程中压力及饱和度变化无法短时间内传递至基质边界，如图6所示。通过平均压力及平均饱和度描述基质内的渗流过程将造成较大的误差，因此本文中引入动态调查半径概念修正基质内的渗流过程。
图6 排采过程中基质动用过程
Fig.6 Process of matrix utilization during flowback and early-production
参考Clarkson等^[20]提出的单相动态调查半径的表征方式及Wang等^[24]提出的多相动态调查半径表征公式，基质中油-气-水三相渗流的动态调查半径可以表示为

y_{m y} = \sqrt{6 η t} .

(23)

模型的具体求解流程图7所示，通过MATLAB的非线性求解函数迭代求解。
图7 模型求解流程图
Fig.7 Flow chart of model solution
1.4 油-气-水三相排采数学模型适用性评价
在tNavigator商业数值模拟软件中建立单开启的页理缝，单页岩基质的油气水三相排采数值模型，与建立的油气水三相排采数学模型进行模型验证，针对模型的适用性进行评价。数值模型中由于基质及裂缝内均为线性流假设，为保证计算效率，x、z方向均为单一网格，y方向分布51个网格，其中表示开启的页理缝的网格宽0.01 m，其余网格宽度为0.1 m，模型长度参考单缝改造区半宽，设置为30 m，模型宽度代表开启页理缝间距的一半，设置为5.01 m，模型厚度表示压裂缝长度，设置为200 m，数值模型网格划分如图8所示。由于数值模型中无法考虑裂缝长度的变化，因此模型验证过程中，本文模型进行退化，不考虑压力变化导致的开启页理缝闭合，数值模型和本文模型井底流压均为5 MPa，基质渗透率为0.00058×10^-3 μm²，裂缝渗透率为100×10^-3 μm²，初始地层压力为35 MPa，裂缝压力为40 MPa，泡点压力为25.3 MPa。
图8 数值模型网格划分
Fig.8 Meshing of numerical model
如图9所示，本文模型与数值模型拟合程度较高，且本文模型计算速度远快于数值模拟，模型的适用性得以验证。
图9 模型验证结果
Fig.9 Model validation results
1.5 油-气-水三相排采动态影响因素
1.5.1 开启页理缝长度
本文模型中考虑了排采过程中裂缝内压力变化剧烈导致的开启页理缝长度的闭合，因此需要对开启的页理缝闭合对排采动态的影响进行分析。变缝长系数表示开启页理缝闭合速度，其数值越小表示裂缝闭合速度越快。为了更好地模拟排采过程中裂缝闭合的过程，考虑井底流压随时间变化并逐渐稳定。开启页理缝长度对排采动态的影响如图10所示。
图10 开启页理缝长度变化对油-气-水三相排采动态影响
Fig.10 Influence of fracture length on dynamic oil, gas, water three-phase drainage and production
如图10所示，油相受裂缝闭合影响较大，日产油量的峰值产量随着变缝长系数的减小而降低，变缝长系数为1的峰值产量仅为未考虑变缝长峰值产量的51%。同时，受到开启页理缝闭合的影响，基质供给区域减小，日产油量达到峰值的时间提前。随着裂缝闭合系数的减小，日产油量递减率增加；日产气量受到裂缝闭合的影响较大，未考虑裂缝闭合时，日产气量的峰值产量较高，然而产量递减较快。随着裂缝闭合系数的减小，日产气量的峰值产量下降，且受到开启页理缝闭合的影响，基质供给区域减小，基质内部的平均压力降低增快，日产气量递减率降低；水相仅赋存于开启的页理缝内，随着排采的进行，开启页理缝受缝内外压差的影响迅速闭合，裂缝内的水相被挤压排采至井筒。因此随着变缝长系数的减小，日产水量上升。
1.5.2 开启页理缝应力敏感系数
应力敏感系数值表示裂缝受应力作用下渗透率变化的程度，应力敏感系数越大，裂缝渗透率受应力影响越明显。如图11所示，裂缝应力敏感主要影响日产油量的峰值产量，随着开启页理缝应力敏感系数增加，峰值日产油量下降明显，裂缝应力敏感系数为0.5时，日产油量的峰值产量仅为不考虑裂缝应力敏感的2/3。随着应力敏感系数的增大，日产油量到达峰值产量后的递减率减小。这是由于应力敏感修正的为裂缝渗透率，随着排采的进行，开启页理缝的渗透率逐渐减小，其量级逐渐与页岩基质接近，导致开启页理缝区域的压力降落减慢，进而导致产量递减减慢。然而开启页理缝长度闭合主要影响缝控储量，在不考虑应力敏感的情况下，其对日产油量曲线形态无较大影响。因此在页岩油多相排采模型中，需要同时考虑裂缝应力敏感及裂缝长度闭合以修正排采曲线的形态与数值，仅考虑裂缝的应力敏感必然会导致产能预测偏高。日产气量的峰值产量受应力敏感的影响较大，开启页理缝应力敏感系数的增加会导致日产气量的峰值产量下降。与裂缝应力敏感对日产油量的影响类似，日产气量达到峰值产量后，产量递减率随着裂缝应力敏感系数的增加而减小。同时，裂缝应力敏感系数对日产水量的峰值产量有较大影响，裂缝应力敏感系数增加会降低日产水量的峰值产量。
图11 开启页理缝应力敏感性对油-气-水三相排采动态影响
Fig.11 Influence of stress sensitivity of open fracture on dynamic oil, gas, water three-phase drainage and production
2 页岩油压后返排动态精确反演方法
基于本文中建立的排采数学模型，结合遗传算法（GA），实现对实际页岩油生产井排采动态的自动历史拟合。首先需要确定遗传算法的优化目标函数：

f_{i, j} = {(\frac{q_{r i, j} - q_{c i, j}}{{\bar{q}}_{r, j}})}^{2}

(24)

式中，f_i_，_j为各相流体各时间步的目标函数，下标i代表时间步，j代表流体相态； ${\bar{q}}_{r ， j}$ 为真实平均日产量，m³；q_r_i_，_j为平均日产量，m³；q_c_i_，_j为排采渗流模型计算的各时间步下各相流体的产量，m³。
对单一时间步的优化目标函数进行求和加权处理，形成适用于排采阶段的全局多相优化函数，

f (x) = \underset{j}{Σ} w \overset{n}{\underset{i = 1}{Σ}} f_{i, j}

(25)

式中，w为各相总体优化目标函数的权重; f为优化目标函数，在GA算法中，需要求得f的最小值，进而达到对页岩油排采动态的自动历史拟合。
3 矿场应用
对一典型页岩油区块中的一口生产井A进行参数反演与产量预测，生产井动态如图12所示。拟合结果如图13所示，油气两相拟合效果较好。水相初期受开关井工况的影响，存在一定误差，但是排采后期拟合程度较高。反演结果：单簇人工裂缝半长为42.25 m，开启页理缝密度为0.625条/m，开启页理缝半长为5.49 m，簇间存在小部分未改造区，开启页理缝渗透率为16.71×10^-3 μm²，页岩基质渗透率为9.9×10^-7 μm²。结合反演结果，利用本文中模型计算20 a后该井的累积产油量为15138.06 m³，累积产气量为233.92×10⁴ m³。
图12 A井排采动态
Fig.12 Flow-back and production data of well A
图13 A井自动历史拟合结果
Fig.13 Automatic history matching results of well A
4 结论
（1）裂缝长度的闭合对油相排采动态曲线形态影响较小，但会较大程度地影响峰值产量。受裂缝闭合导致的缝控体积减小的影响，基质平均压力下降增速，气相排采曲线的峰值产量及产量曲线形态均发生改变。考虑开启页理缝应力敏感后，油相和气相峰值产量及排采动态曲线形态均发生改变。在页岩储层中需考虑受应力变化影响裂缝长度及裂缝渗透率才能较为真实地模拟多相排采过程。
（2）应用本文中建立的数学模型，结合GA算法，明确了优化目标函数，构建了基于GA算法的自动历史拟合函数，形成一套页岩油多相排采反演方法。该方法应用于某页岩油藏的一口生产井中取得了较好的拟合效果，并预测了该井20 a的累产油量及累产气量。
参考文献
- [1] 赵国忠,王青振,刘勇,等.松辽盆地古龙页岩油人工油藏的动态模拟及预测[J].大庆石油地质与开发,2021,40(5):170-180.ZHAO Guozhong,WANG Qingzhen,LIU Yong,et al.Dynamic simulation and prediction for artificial reservoir of Gulong shale oil in Songliao Basin[J].Petroleum Geology & Oilfield Development in Daqing,2021,40(5):170-180.
- [2] AFAGWU C,ALAFNAN S,WEIJERMARS R,et al.Multiscale and multiphysics production forecasts of shale gas reservoirs:New simulation scheme based on Gaussian pressure transients[J].Fuel,2023,336:127142.
- [3] ARPS J J.Analysis of decline curves[J].Transactions of the AIME,1999,160:228-247.
- [4] VALKO P P,LEE W J.A better way to forecast production from unconventional gas wells[R].SPE 134231,2010.
- [5] CLARK A J,LAKE L W,PATZEK T W.Production forecasting with logistic growth models[R].SPE 144790,2011.
- [6] 赵康,陈民锋,王艺文,等.四川盆地SZ页岩气藏气井产量变化规律及递减预测新模型[J].中国海上油气,2024,36(3):129-136.ZHAO Kang,CHEN Minfeng,WANG Yiwen,et al.A new model for production variation patterns and decline prediction of SZ shale gas reservoir in Sichuan basin[J].China Offshore Oil and Gas,2024,36(3):129-136.
- [7] KANFAR M S,WATTENBARGER R A.Comparison of empirical decline curve methods for shale wells[R].SPE 162648,2012.
- [8] LEE S H,LOUGH M F,JENSEN C L.Hierarchical modeling of flow in naturally fractured formations with multiple length scales[J].Water Resources Research,2001,37(3):443-455.
- [9] 贾品,牛烺昱,柯贤哲,等.高密度页理页岩油藏排采数值模拟及动态特征[J].中国石油大学学报(自然科学版),2023,47(4):137-144.JIA Pin,NIU Langyu,KE Xianzhe,et al.Numerical simulation and dynamic characteristics of drainage and production in high density bedding shale oil reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(4):137-144.
- [10] 胡晓东,张鹏天,周福建,等.迂曲裂缝内支撑剂运移数值模拟[J].中国石油大学学报(自然科学版),2024,48(3):111-118.HU Xiaodong,ZHANG Pengtian,ZHOU Fujian,et al.Numerical simulation of proppant transport in tortuous fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(3):111-118.
- [11] 王森,向杰,冯其红,等.基于深度学习加速的油藏数值模拟自动历史拟合方法[J].中国石油大学学报(自然科学版),2024,48(5):103-114.WANG Sen,XIANG Jie,FENG Qihong,et al.Deep-learning-based acceleration method for automatic history matching of reservoir numerical simulation[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):103-114.
- [12] MOINFAR A,VARAVEI A,SEPEHRNOORI K,et al.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs[J].SPE Journal,2014,19(2):289-303.
- [13] LIU Q,XUE L,SAROUT J,et al.Automatic history matching of multistage fractured shale gas reservoir constrained by microseismic data[J].Journal of Petroleum Science and Engineering,2022,213:110357.
- [14] KUCHUK F,BIRYUKOV D.Pressure-transient behavior of continuously and discretely fractured reservoirs[J].SPE Reservoir Evaluation & Engineering,2014,17(1):82-97.
- [15] 姚军,王萌,樊冬艳,等.考虑层理缝岩性差异的页岩油藏压裂水平井动态分析方法[J].中国石油大学学报(自然科学版),2024,48(5):91-102.YAO Jun,WANG Meng,FAN Dongyan,et al.Dynamic analysis of fractured horizontal wells in shale reservoirs considering lithological differences of bedding fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):91-102.
- [16] ZHOU W,BANERJEE R,POE B D,et al.Semi-analytical production simulation of complex hydraulic fracture network[R].SPE 157367-MS,2012.
- [17] JIA P,CHENG L,HUANG S,et al.A semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks[J].Journal of Hydrology,2016,537:208-220.
- [18] JIA P,CHENG L,CLARKSON C R,et al.A novel method for interpreting water data during flowback and early-time production of multi-fractured horizontal wells in shale reservoirs[J].International Journal of Coal Geology,2018,200:186-198.
- [19] CLARKSON C R R,WILLIAMS-KOVACS J D D.Modeling two-phase flowback of multifractured horizontal wells completed in shale[J].SPE Journal,2013,18(4):795-812.
- [20] CLARKSON C R,QANBARI F.A semianalytical forecasting method for unconventional gas and light oil wells:a hybrid approach for addressing the limitations of existing empirical and analytical methods[R].SPE Reservoir Evaluation & Engineering,2015,18(1):94-110.
- [21] CAO C,CHENG L,JIA P,et al.A dynamic fracture model combining with Laplace transform and synchronous iteration method for transient behavior analysis of a four-zone system[J].Journal of Hydrology,2022,615:128723.
- [22] MCKEE C R,BUMB A C,KOENIG R A.Stress-dependent permeability and porosity of coal and other geologic formations[J].SPE Formation Evaluation,1988,3(1):81-91.
- [23] WATTENBARGER R A,EL-BANBI A H,VILLEGAS M E,et al.Production analysis of linear flow into fractured tight gas wells[R].SPE 39931,1998.
- [24] WANG Z,CHENG L,HAMDI H,et al.A semi-analytical model for quantifying the inter-well communication in water-bearing shale gas-condensate reservoirs[J].Geoenergy Science and Engineering,2023,228:211997.

基本信息

中图分类号: TE 34
文献标识码: A
DOI: 10.3969/j.issn.1673-5005.2025.05.012
文章编号: 1673-5005(2025)05-0127-10

基金信息

国家自然科学基金项目（52474057）；

引用信息

牛烺昱，程林松，王志凯，等.高密度页理页岩油藏多相排采数学模型及动态反演[J].中国石油大学学报（自然科学版），2025,49（5）：127-136.

NIU Langyu, CHENG Linsong, WANG Zhikai, et al. Mathematical model and interpretation analysis for multi-phase flowback in shale reservoirs with highly developed beddings[J].Journal of China University of Petroleum(Edition of Natural Science),2025,49(5):127-136.

稿件历史

收稿日期: 2024-12-25

参考文献

[1] 赵国忠,王青振,刘勇,等.松辽盆地古龙页岩油人工油藏的动态模拟及预测[J].大庆石油地质与开发,2021,40(5):170-180.ZHAO Guozhong,WANG Qingzhen,LIU Yong,et al.Dynamic simulation and prediction for artificial reservoir of Gulong shale oil in Songliao Basin[J].Petroleum Geology & Oilfield Development in Daqing,2021,40(5):170-180.
[2] AFAGWU C,ALAFNAN S,WEIJERMARS R,et al.Multiscale and multiphysics production forecasts of shale gas reservoirs:New simulation scheme based on Gaussian pressure transients[J].Fuel,2023,336:127142.
[3] ARPS J J.Analysis of decline curves[J].Transactions of the AIME,1999,160:228-247.
[4] VALKO P P,LEE W J.A better way to forecast production from unconventional gas wells[R].SPE 134231,2010.
[5] CLARK A J,LAKE L W,PATZEK T W.Production forecasting with logistic growth models[R].SPE 144790,2011.
[6] 赵康,陈民锋,王艺文,等.四川盆地SZ页岩气藏气井产量变化规律及递减预测新模型[J].中国海上油气,2024,36(3):129-136.ZHAO Kang,CHEN Minfeng,WANG Yiwen,et al.A new model for production variation patterns and decline prediction of SZ shale gas reservoir in Sichuan basin[J].China Offshore Oil and Gas,2024,36(3):129-136.
[7] KANFAR M S,WATTENBARGER R A.Comparison of empirical decline curve methods for shale wells[R].SPE 162648,2012.
[8] LEE S H,LOUGH M F,JENSEN C L.Hierarchical modeling of flow in naturally fractured formations with multiple length scales[J].Water Resources Research,2001,37(3):443-455.
[9] 贾品,牛烺昱,柯贤哲,等.高密度页理页岩油藏排采数值模拟及动态特征[J].中国石油大学学报(自然科学版),2023,47(4):137-144.JIA Pin,NIU Langyu,KE Xianzhe,et al.Numerical simulation and dynamic characteristics of drainage and production in high density bedding shale oil reservoirs[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(4):137-144.
[10] 胡晓东,张鹏天,周福建,等.迂曲裂缝内支撑剂运移数值模拟[J].中国石油大学学报(自然科学版),2024,48(3):111-118.HU Xiaodong,ZHANG Pengtian,ZHOU Fujian,et al.Numerical simulation of proppant transport in tortuous fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(3):111-118.
[11] 王森,向杰,冯其红,等.基于深度学习加速的油藏数值模拟自动历史拟合方法[J].中国石油大学学报(自然科学版),2024,48(5):103-114.WANG Sen,XIANG Jie,FENG Qihong,et al.Deep-learning-based acceleration method for automatic history matching of reservoir numerical simulation[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):103-114.
[12] MOINFAR A,VARAVEI A,SEPEHRNOORI K,et al.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs[J].SPE Journal,2014,19(2):289-303.
[13] LIU Q,XUE L,SAROUT J,et al.Automatic history matching of multistage fractured shale gas reservoir constrained by microseismic data[J].Journal of Petroleum Science and Engineering,2022,213:110357.
[14] KUCHUK F,BIRYUKOV D.Pressure-transient behavior of continuously and discretely fractured reservoirs[J].SPE Reservoir Evaluation & Engineering,2014,17(1):82-97.
[15] 姚军,王萌,樊冬艳,等.考虑层理缝岩性差异的页岩油藏压裂水平井动态分析方法[J].中国石油大学学报(自然科学版),2024,48(5):91-102.YAO Jun,WANG Meng,FAN Dongyan,et al.Dynamic analysis of fractured horizontal wells in shale reservoirs considering lithological differences of bedding fractures[J].Journal of China University of Petroleum(Edition of Natural Science),2024,48(5):91-102.
[16] ZHOU W,BANERJEE R,POE B D,et al.Semi-analytical production simulation of complex hydraulic fracture network[R].SPE 157367-MS,2012.
[17] JIA P,CHENG L,HUANG S,et al.A semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks[J].Journal of Hydrology,2016,537:208-220.
[18] JIA P,CHENG L,CLARKSON C R,et al.A novel method for interpreting water data during flowback and early-time production of multi-fractured horizontal wells in shale reservoirs[J].International Journal of Coal Geology,2018,200:186-198.
[19] CLARKSON C R R,WILLIAMS-KOVACS J D D.Modeling two-phase flowback of multifractured horizontal wells completed in shale[J].SPE Journal,2013,18(4):795-812.
[20] CLARKSON C R,QANBARI F.A semianalytical forecasting method for unconventional gas and light oil wells:a hybrid approach for addressing the limitations of existing empirical and analytical methods[R].SPE Reservoir Evaluation & Engineering,2015,18(1):94-110.
[21] CAO C,CHENG L,JIA P,et al.A dynamic fracture model combining with Laplace transform and synchronous iteration method for transient behavior analysis of a four-zone system[J].Journal of Hydrology,2022,615:128723.
[22] MCKEE C R,BUMB A C,KOENIG R A.Stress-dependent permeability and porosity of coal and other geologic formations[J].SPE Formation Evaluation,1988,3(1):81-91.
[23] WATTENBARGER R A,EL-BANBI A H,VILLEGAS M E,et al.Production analysis of linear flow into fractured tight gas wells[R].SPE 39931,1998.
[24] WANG Z,CHENG L,HAMDI H,et al.A semi-analytical model for quantifying the inter-well communication in water-bearing shale gas-condensate reservoirs[J].Geoenergy Science and Engineering,2023,228:211997.

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高密度页理页岩油藏多相排采数学模型及动态反演

Mathematical model and interpretation analysis for multi-phase flowback in shale reservoirs with highly developed beddings

摘要

Abstract

关键词

Keywords

1 页岩油多相排采渗流数学模型建立及半解析求解

1.1 页岩油压后缝网形态及油水赋存假设

1.2 页岩油-气-水三相排采渗流数学模型建立

1.2.1 基质流动方程。

(1)

(2)

(3)

(4)

(5)

(6)

(7)

1.2.2 开启页理缝流动方程

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

1.3 页岩油-气-水三相排采渗流数学模型半解析求解

(17)

(18)

(19)

(20)

(21)

(22)

(23)

1.4 油-气-水三相排采数学模型适用性评价

1.5 油-气-水三相排采动态影响因素

1.5.1 开启页理缝长度

1.5.2 开启页理缝应力敏感系数

2 页岩油压后返排动态精确反演方法

(24)

(25)

3 矿场应用

4 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献