PRESSURE TRANSIENT MODEL OF MULTI-STAGE FRACTURED HORIZONTAL WELL WITH INDUCED FRACTURE FOR HETEROGENEOUS STIMULATED RESERVOIR VOLUME
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摘要: 为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化, 建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型, 耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解, 对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性. 基于压力导数曲线特征进行流动阶段划分和参数敏感性分析, 得到以下结果: 和常规压裂水平井井底压力导数曲线相比较, 理想模式下, 考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝 “补充”阶段、储层线性流动阶段和拟边界控制流阶段. 诱导缝条数的增加加剧了综合线性流阶段的持续时间, 降低了流体渗流阻力, 早期阶段压力曲线越低; 当诱导缝与压裂裂缝导流能力一定时, 裂缝导流能力越大, 线性流持续时间越长; 当所有压裂裂缝不在一个区域时, 沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段, 因此, 沿井筒方向两端区域渗透率越低, 早期阶段压力曲线越高; 当所有压裂裂缝在一个区域时, 渗透率变化只影响径向流阶段之后压力曲线形态, 外区渗透率越低, 早期径向流阶段之后压力曲线越高. 通过实例验证, 表明该模型和方法的实用性和准确性.Abstract: In order to simulate accurately wellbore pressure transient performance of multi-stage fractured horizontal well (MFHW) with the complex fracture network and heterogeneous in tight oil reservoirs, an unsteady seepage mathematical model of the MFHW with induced fractures in rectangular heterogeneous reservoir is established. The wellbore pressure solution is obtained by coupling the fracture model, the reservoir model and heterogeneous reservoir interface model. The wellbore pressure accuracy of the two heterogeneous reservoir models is verified by numerical solutions, boundary element method and previous model. By flow stages analysis and parameters sensitivity analysis, the following results can be obtained. Compared with the wellbore pressure derivative curve of the MFHW in homogeneous reservoir, the unique flow stages of this model in the ideal case include: the complex linear flow stage, the "supply" stage from induced fractures to fractured fractures, the linear flow stage and the pseudo boundary control flow stage. The increase of induced fracture number extends the duration of the complex linear flow stage and reduces the fluid seepage resistance. Therefore, the pressure curve of the early stage is lower. If the conductivity of induced fracture and fractured fracture is constant, the greater the conductivity is, the longer the duration of the bilinear flow regime is. When all fractured fractures are different region, the two end low permeability region along the wellbore weakens the "supply" stage. Therefore, the lower the permeability along the wellbore is, the higher the pressure curve at the early stage is. When all fractured fractures are in same area, the permeability change only affects the pressure curve shape after the radial flow stage. The lower the permeability of the outer area is, the higher the pressure curve after the early radial flow stage is. The practicability and accuracy of the model and method are demonstrated by the field example.
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图 2 非均质储层考虑诱导缝多段压裂水平井物理模型示意图
Figure 2. Physical model of fractured horizontal well with induced fracture in heterogeneous reservoir
图 4 非均质储层多段压裂水平井储层交界面和裂缝离散示意图
Figure 4. Reservoir interface and fracture dispersion of multi-stage fracturing horizontal well in heterogeneous reservoirs
图 5 非均质储层考虑诱导缝多段压裂水平井井底压力响应曲线
Figure 5. Wellbore pressure response curve of fractured horizontal well with induced fracture in heterogeneous reservoir
图 6 非均质储层多段压裂水平井物理模型
Figure 6. Saphir physical model of multi-stage fractured horizontal well in heterogeneous reservoir
图 7 非均质储层多段压裂水平井井底压力验证
Figure 7. Verification of wellbore pressure of multi stage fractured horizontal wells in heterogeneous reservoir
图 8 诱导缝条数对井底压力动态特征曲线的影响
Figure 8. Influence of induced fracture number on wellbore pressure curve
图 9 压裂裂缝条数对井底压力动态特征曲线的影响
Figure 9. Influence of hydraulic fracture number on wellbore pressure curve
图 10 不同改造区渗透对井底压力动态特征曲线的影响
Figure 10. Influence of different SRV region permeability on wellbore pressure curve
图 11 非改造区渗透率对井底压力动态特征曲线的影响
Figure 11. Influence of uSRV region permeability on wellbore pressure curve
图 12 缝间距对井底压力动态特征曲线的影响
Figure 12. Influence of fracture spacing on wellbore pressure curve
图 13 导流能力对井底压力动态特征曲线的影响
Figure 13. Influence of fracture conductivity on wellbore pressure curve
图 14 H井井底压力动态特征曲线阶段划分
Figure 14. Stage division of wellbore pressure dynamic characteristic curve of well H
表 1 模拟验证基本参数
Table 1. Basic value of validation
Parameters/unit Value reservoirs thickness/m 10 wellbore radius/m 0.1 total compressibility coefficient/MPa−1 0.001 reservoirs temperature/°C 60 initial reservoir pressure/MPa 50 volume factor 1.15 oil viscosity/(mPa·s) 1 half-length of hydraulic fracture and induced fracture/m 60/30 conductivity of hydraulic fracture and induced fracture/(mD·m) 22104/5526 horizontal well length/m 1560 hydraulic fracture and induced fracture number 3/60 permeability of region 1, region 2 and region 3/mD 0.18/0.36/0.18 
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表 2 流动阶段曲线特征及示意图
Table 2. Curve characteristics and schematic diagram of flow stage
Flowing regime Regime name and characteristic Characteristic of derivative curve Diagram regime Ⅰ bilinear flow regime: the combination of reservoir linear flow and fractures linear flow 0.25-slope straight line 
regime Ⅱ complex linear flow regime: it reflects the linear flow of fluid to the fracture and induced fracture, linear flows in the fracture and induced fracture less than 0.25-slope straight line 
regime Ⅲ "supplement" regime of induced fracture to hydraulic fractures: "cross-flowing" of
induced fracture to fracture[30]dip — regime Ⅳ reservoir linear flow regime: linear flow combination of reservoir fluid to
fractures and induced fractures0.25 ~ 0.5-slope straight line 
regime Ⅴ pseudo-boundary control flow regime: due to fracture interference, a small "circular"
non-flow boundary is formed at the intersection of the hydraulic fracture and
the induced fracturestraight line that slope is close to 1 
regime Ⅵ elliptical flow regime: ellipse flows around the fracture 0.36-slope straight line 
regime Ⅶ early radial flow stage: radial flow around the fracture[31] 0.5/M horizontal line 
regime Ⅷ late linear flow stage (Fig.6(a)) and combination of late linear flow and
outer linear flow (Fig.6(b))0.5-slope straight line (Fig.6(a)) 
regime Ⅸ boundary control flow stage unit-slope straight line —
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表 3 H井拟合结果
Table 3. Matching results of well H
Parameters Value well storage coefficient/(m3·MPa−1) 29.52 skin factor 0 half-length of hydraulic fractures/m 82 conductivity of hydraulic fractures/(mD·m) 278 half-length of induced fractures/m 32 conductivity of induced fractures/(mD·m) 103 number of heterogeneous region 6 reservoir width/m 342 width of each SRV region/m 430, 426, 501, 513, 435, 486 permeability of each SRV region/mD 2.3, 1.5, 2.6, 2.7, 2.2, 2.3
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