Multiscale Simulation and Analysis for Gas Flow in Deep-Seated Micronano Pore
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摘要: 页岩气是未来中国能源结构中的重要组成部分，但中国页岩气埋藏深度大，不能直接照搬美国对浅层页岩气的开采经验，需要对其输运机理有更清晰的认识.介绍了跨尺度混合模拟算法，分析了基于孔隙尺度模拟来研究场尺度的气井衰减曲线分析等问题，揭示了高努森数效应与非理想气体效应之间的耦合机理；介绍了考虑多孔介质弹性形变对渗流影响时计算表观渗透率的特征压力模型，为页岩气勘探开发提供了相关理论支持.Abstract: Shale gas will become an important energy source in China in the near future. However, most shale gas in China is deeply buried, so the experience of shallow-seated shale gas exploitation in US can not be directly employed. A better understanding of shale gas transport mechanism can surely facilitate the precise prediction of production and the exploitation optimization of deep-seated shale gas. In this paper, we establish a multiscale simulation method named pore-field iteration. Field-scale problems such as inflow performance relationship and decline curve analysis are solved based on pore-scale simulation directly. In addition, the coupling between the high Knudsen number effect in micro flow and the non-ideal gas effect caused by the high pressure and temperature underground is investigated from a theoretical perspective. Finally, we incorporate the influence of the elastic structural deformation in our modeling and propose the characteristic pressure model to calculate apparent permeability, which supports shale gas exploitation by providing theoretical analysis.
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Key words:
- shale gas /
- non-ideal gas effect /
- fluid-solid interaction /
- petroleum geology
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图 1 中国页岩气在2012年至2015年的产量
据国家能源局(2012)；中国地质调查局(2015)；李杏茹等(2016)
Fig. 1. The shale gas production in China from 2012 to 2015
图 3 页岩在宏观尺度下的各向异性
a.Barnett页岩中岩心样品的分层结构，深色层的有机质含量和孔隙度都大大高于浅色层(Bhandari and Flemings, 2015)；b.Eagle Ford页岩中的微裂缝有着明显的方向性(Sone and Zoback, 2013)
Fig. 3. The anisotropy of shale in macroscale
图 4 Wilcox页岩的扫描电镜图片
据Kwon et al.(2004).有机质孔隙具有很大的长宽比，结构在孔隙尺度下呈现出明显的各向异性
Fig. 4. SEM images of Wilcox shale
图 5 牛蹄塘页岩的扫描电镜图片
a.拍摄方向平行于地层；b.拍摄方向垂直于地层；在平行和垂直方向页岩结构的差异很大；据Wan et al.(2015)
Fig. 5. SEM images of Niutitang shale
图 7 龙马溪页岩中孔隙的非均匀分布
Fig. 7. The heterogeneous distribution of pore of Longmaxi shale
图 8 甲烷在373 K下的非理想气体效应
a.状态方程；b.动力粘性系数；数据来自NIST数据库(Younglove and Ely, 1987; Setzmann and Wagner, 1991)
Fig. 8. The real gas effect of methane in 373 K
图 9 甲烷在373 K下，实际的努森数与基于理想气体模型预测的偏差
Fig. 9. Deviation between real and predicted Kn based on ideal gas model
图 10 基于随机生长方法重构的各向异性与非均质性结构示例
a.各向异性；b.非均质性；上面两图为截面图，其中红色为固体，蓝色为孔隙；下面两图为三维图
Fig. 10. Example of the anisotropic and heterogeneity structures based on QSGS method
图 11 体心立方结构(孔隙度为0.582，边长为320 nm)
Fig. 11. The BCC structure with porosity 0.582 and length 320 nm
图 12 体心立方结构的本征渗透率模拟结果
a.模型稳定性；b.模拟精度
Fig. 12. Simulation results about intrinsic permeability of BCC structure
图 13 格子玻尔兹曼模拟结果与Beskok等的模型对比
a.用平均速度归一化后的速度剖面；b.用本征渗透率归一化后的表观渗透率；据Beskok and Karniadakis(1999)
Fig. 13. Comparison between LBM simulation and Beskok model
图 14 孔-场跨尺度混合模拟算法示意
Fig. 14. Schematic of the pore-field-iteration (PFI) simulation method
图 15 不同入口压力下稳态无滑移理想气体流动的压力分布
Fig. 15. Pressure distributions of steady state flow with different inlet pressure
图 16 气体在多孔介质中的稳态流动过程
气体在进出口压力差的驱动下，有着恒定的质量流率Qm
Fig. 16. Schematic for steady state gas flow in porous media
图 17 甲烷在不同温度T和入口压力p1下，非理想气体效应对流动的影响
在蓝色区域非理想气体效应促进流动，在红色区域非理想气体效应抑制流动，出口压力固定为1 MPa
Fig. 17. The impact of real gas effect on methane flow under different T, p1 condition
图 18 甲烷在直通道内的流动模拟(a)和理论分析(b)
a.模拟得到的质量流率；b.理论分析得到的无量纲数；当入口压力为37.9 MPa时，高努森数效应和非理想气体效应对流动的影响相互抵消
Fig. 18. Simulation (a) and theoretical analysis (b) of CH4 flow in straight channel
图 19 二氧化碳在直通道内的流动模拟(a)和理论分析(b)
a.模拟得到的质量流率；b.理论分析得到的无量纲数；当入口压力为8.3 MPa时，高努森数效应和非理想气体对流动有着相同程度的促进作用
Fig. 19. Simulation (a) and theoretical analysis (b) of CO2 flow in straight channel
图 20 拟稳态流动模拟中基于QSGS法重构的微孔结构
Fig. 20. Micro-pore structure reconstructed based on QSGS in quasi-steady state flow simulation
图 21 气井流入动态曲线
a.高努森数效应和非理想气体效应对流入动态的影响；b.无滑移理想气体的流入动态曲线归一化后与理论模型的对比
Fig. 21. IPR curves with high Kn effect and/or real gas effect (a) and comparison of the simulation to theoretical result (b)
图 22 衰减曲线分析
井底压力(a)和质量流率(b)随时间的变化
Fig. 22. Decline curves of (a) bottom hole pressure and (b) gas production for pseudo-steady state flow in channel
图 23 高努森数实际气体的衰减曲线与Arps经验关系式的对比
Fig. 23. Comparison of the high Kn real gas flow simulation to Arps hyperbolic relation for the production decline curve
图 24 气体在多孔介质中的稳态流动过程
质量流率恒定为Qm，多孔介质两端分别为入口压力p1和出口压力p2，周围为恒定的围压pc
Fig. 24. Scheme of the system considered in the model
图 25 可变形通道内的流动模拟的示意
Fig. 25. Scheme to illustrate the flow simulation in a elastic-deformable channel
图 26 基于二氧化碳在不同应力敏感性的通道内的流动模拟结果
a.Klinkenberg图；b.修正形变后的渗透率随努森数的变化；根据特征压力模型计算得到的表观渗透率；星形和圆形分别为简化前和简化后的特征压力模型；图b中的虚线为线性趋势线，红点为K0, ref的理论值
Fig. 26. Simulation results of different stress sensitivities for CO2 flow
图 27 基于不同气体在相同应力敏感性的通道内的流动模拟结果
a.Klinkenberg图；b.修正形变后的渗透率随努森数的变化；根据特征压力模型计算得到的表观渗透率.其中星形和圆形分别为简化前和简化后的特征压力模型.图b中的虚线为线性趋势线，红点为K0, ref的理论值
Fig. 27. Simulation results for different kinds of gas flows in the same channel
图 28 用不同模型计算得到的表观渗透率
a.煤；b.页岩；图据Klinkenberg(1941)
Fig. 28. Apparent permeability predicted by different models
表 1 4种不同类型的高努森数效应和非理想气体效应的耦合
Table 1. Four kinds of couplings of high Kn effect and real gas effect
非理想气体效应抑制流动 非理想气体效应促进流动 非理想气体效应占主导 γ∈(-∞, -1) γ∈(1, +∞) 高努森数效应占主导 γ∈(-1, 0) γ∈(0, 1) 
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表 2 直通道内气体流动模拟的物理条件
Table 2. Physics conditions of gas flow simulation in straight channel
模拟条件 气体种类 通道高度l(nm) 通道长度L(m) 出口压力p2(MPa) 入口压力p1(MPa) 温度T(K) 实例1 甲烷 10 10 10 14, 18, 22, …, 50 373 实例2 二氧化碳 50 10 1 2, 3, 4, …, 10 323
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表 3 气井流入动态中的物理条件
Table 3. Physical conditions of the gas well inflow
温度
T(K)储层压力
pr(MPa)井底压力
pw(MPa)气场长度
L(m)373 40 5, 10, 20, 30 15
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表 4 衰减曲线分析中的物理条件
Table 4. The physical condition of the attenuation curve analysis
温度
T(K)储层压力
pr(MPa)井底压力
pw(MPa)气场长度
L(m)373 40, 35, 30, 25, 20 30, 25, 20, 15, 10 15
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表 5 可变形直通道内流动模拟的物理条件
Table 5. Physics conditions for flow simulation in the elastic-deformable channel
气体类型 通道的应力敏感性α
(MPa-1)通道参考高度
lref(nm)通道长度
L(m)入口压力
p1(MPa)出口压力
p2(MPa)温度
T(K)甲烷、二氧化碳、乙烷 0, 0.025, 0.05, 0.1 100 0.05 0.5~10.0 0.1 318
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表 6 岩心样本测量的实验条件
Table 6. Parameters for the experimental conditions of the core samples
实验条件 岩心类型 气体种类 岩心长度
L(m)岩心横截面积
S(m2)围压
pc(MPa)出口压力
p1(MPa)温度
T(K)岩心1 煤 甲烷 0.033 3 0.001 155 15 0.15 298 岩心2 页岩 二氧化碳 0.013 0 0.001 155 40 0.10 318
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表 7 气体渗透率计算模型
Table 7. Models for the gas permeability prediction
模型名称 理想气体模型 粘性近似模型 粘性及压缩因子近似模型 特征压力模型 代表文献 Klinkenberg(1941) Gensterblum et al.(2014) Rushing et al.(2004) 本工作 表观渗透
率表达式$K(\mathit{\bar p}) = \frac{{2{\mu ^{{\rm{id}}}}L{Q_m}}}{{p_1^2 - p_2^2}}{R_g}T$ $K(\mathit{\bar p}) = \frac{{2\mu {\rm{(}}\mathit{\bar p}{\rm{)}}L{Q_m}}}{{p_1^2 - p_2^2}}{R_g}T$ $K(\mathit{\bar p}) = \frac{{2\mu {\rm{(}}\mathit{\bar p}{\rm{)}}L{Q_m}}}{{p_1^2 - p_2^2}}Z(\mathit{\bar p}, \mathit{T}){R_g}T$ $K(\mathit{p}_{{\rm{char}}}^{{\rm{smp}}}) = \frac{{{Q_m}Lv(\mathit{p}_{{\rm{char}}}^{{\rm{smp}}})}}{{{p_1} - {p_2}}}$
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