基于岩土介质三维孔隙结构的两相流模型

张鹏伟; 胡黎明; MeegodaJay N; CeliaMichael A

doi:10.11779/CJGE202001004

基于岩土介质三维孔隙结构的两相流模型 English Version

张鹏伟^{1, 2, 4,},
胡黎明^1, ,,
MeegodaJay N³,
CeliaMichael A⁴

1.
清华大学水沙科学与水利水电工程国家重点实验室,北京100084
2.
北京交通大学,北京100044
3.
新泽西理工学院,美国07102
4.
普林斯顿大学,美国08544

基金项目:

清华大学自主科研计划项目 THZ-2016-02

中央高校基本科研业务费专项资金项目 2019RC054

详细信息

作者简介:
张鹏伟（1990— ）,男,工学博士,主要从事岩土介质孔隙尺度多相流、多组分运移数值计算,以及油气藏、水合物三维、四维地质力学计算等方面的研究工作。E-mail：zpw12@tsinghua.org.cn

通讯作者:
胡黎明, E-mail：gehu@tsinghua.edu.cn

中图分类号: TU43
计量
- 文章访问数: 0285
- HTML全文浏览量: 0
- PDF下载量: 0273
出版历程
- 收稿日期: 2019-04-19
- 网络出版日期: 2022-12-07
- 刊出日期: 2019-12-31

Two-phase flow model based on 3D pore structure of geomaterials

1.
State Key Laboratory of Hydro-science and Engineering, Tsinghua University, Beijing 100084, China
2.
Beijing JiaoTong University, Beijing 100044, China
3.
New Jersey Institute of Technology, Newark 07102, USA
4.
Princeton University, Princeton 08544, USA

摘要

摘要: 地下储层中岩土介质一般具有较低的孔隙连通性,宏观流动模拟一般忽略微观尺度的孔隙连通性,通过渗透率、弯曲度等参数反映储层的整体特性。但岩土介质的多孔性及孔隙间复杂的连通性,使得宏观描述流体在岩土介质中流动不能反映其内在流动特征。孔隙结构模型的建立可以反映岩土介质中孔隙的几何形态及空间连通性,为解释流体在复杂多孔介质中的流动特性提供有效手段。通过考虑岩土介质孔隙尺寸分布、孔隙孔喉空间相关性、孔隙连通性等特征参数,建立了反映不同岩土介质连通性、各向异性特征的等效孔隙网络模型。等效孔隙网络模型通过水力特征参数等效的方式反映岩土介质三维微观孔隙结构,通过渗透率计算验证了模型的有效性。此外,基于建立的孔隙结构模型,开发了孔隙尺度动态两相流计算模型,模型可以反映孔隙内弯液面的动态运动过程,直观反映多孔介质中的优势渗流,可以为不同孔隙尺度岩土介质提供表观渗透率、击穿曲线、相对渗透率曲线等宏观计算参数。将孔隙尺度两相流模型应用于页岩气开采中水力阻滞特性研究,结果表明：页岩基质的残余饱和度约为30%,随着平均配位数的增加,残余饱和度显著降低。
- 两相流 /
- 等效孔隙网络模型 /
- 相对渗透率 /
- 页岩气 /
- 优势渗流
Abstract: Geomaterials normally have low pore-connectivity in underground reservoir, and the macro-scale flow simulation normally ignores the micro pore connectivity and uses macro parameters such as permeability and tortuosity to reflect the conductivity of underground reservoir. However, due to the complex pore structure and pore connectivity of geomaterials, the macro-scale method cannot reflect the micro flow mechanisms. The pore-structure model provides an effective way to reflect the micro-flow mechanisms for complex porous media since the pore geometry and pore connectivity can be included in the model itself. In this work, an equivalent pore-network model (EPNM) is established considering pore-size distribution, spatial correlation and pore-connectivity. EPNM aims at reflecting 3D pore structure of geomaterials by the equivalent hydraulic parameters, and the effectiveness is verified by permeability tests. Furthermore, a dynamic two-phase flow model is developed based on EPNM, and simulate the dynamic invasion of each phase, reflect the preferential flow in porous media, and it can provide apparent permeability, relative permeability curve, breakthrough curve for macro-scale simulation. Finally, the dynamic two-phase flow model is applied to the wetting phase trap during shale gas exploitation. The results show that the residual saturation in shale matrix is around 30%, and this residual saturation decreases significantly with the increase of the average pore coordination number.
- two-phase flow /
- equivalent pore-network model /
- relative permeability /
- shale gas /
- preferential flow

HTML全文

图 1 等效孔隙网络模型构建流程图

Figure 1. Flow chart of establishing EPNM

下载: 全尺寸图片幻灯片

图 2 孔隙连通代表性单元

Figure 2. Representative element of pore connectivity

下载: 全尺寸图片幻灯片

图 3 三维孔隙网络模型

Figure 3. 3D pore-network model

下载: 全尺寸图片幻灯片

图 4 孔隙网络模型稳定性验证结果

Figure 4. Stability analysis of pore-network model

下载: 全尺寸图片幻灯片

图 5 砂土介质孔隙网络模型（高连通性各向同性）

Figure 5. Pore-network model for sand (high connectivity isotropy)

下载: 全尺寸图片幻灯片

图 6 Berea砂岩等效孔隙网络模型（低连通性各向同性）

Figure 6. Equivalent pore-network model for Berea sandstone (low connectivity isotropy)

下载: 全尺寸图片幻灯片

图 7 Fontainebleau砂岩等效孔隙网络模型（低连通性各向同性）

Figure 7. Equivalent pore-network model for Fontainebleau sandstone (low connectivity isotropy)

下载: 全尺寸图片幻灯片

图 8 页岩等效孔隙网络模型（低连通性各向异性）

Figure 8. Equivalent pore-network model for shale (low connectivity anisotropy)

下载: 全尺寸图片幻灯片

图 9 弯液面动态入侵过程

Figure 9. Dynamic invasion process of meniscus

下载: 全尺寸图片幻灯片

图 10 页岩基质两相流动物理模型

Figure 10. Physical model for two-phase flow in shale matrix

下载: 全尺寸图片幻灯片

图 11 孔隙连通性与饱和度变化关系

Figure 11. Variation of saturation with pore connectivity

下载: 全尺寸图片幻灯片

图 12 相对渗透率关系曲线

Figure 12. Relative permeability curves

下载: 全尺寸图片幻灯片

图 13 两相流空间展布(平均配位数=3)

Figure 13. Spatial distribution of two-phase flow (N_ave=3)

下载: 全尺寸图片幻灯片

图 14 两相流空间展布(平均配位数=4)

Figure 14. Spatial distribution of two-phase flow (N_ave=4)

下载: 全尺寸图片幻灯片

表 1 不同岩土介质孔隙连通性

Table 1 Pore connectivity of different geomaterials

土壤类别	孔隙平均配位数
砂土	6.5~12
砂岩	3.5~4.5
页岩	≤3.5

下载: 导出CSV

表 2 不同孔隙度砂土介质固有渗透率

Table 2 Intrinsic permeability for sand soil with different porosities

孔隙度 Φ	固有渗透率k/(10^-10 m²)
0.300	4.72
0.325	4.75
0.350	4.97
0.375	5.48
0.400	6.20

下载: 导出CSV

表 3 砂岩等效孔隙网络模型基本参数

Table 3 Parameters of equivalent pore-network model for sandstone

砂岩类别	模型尺寸	孔隙度	最大孔隙尺寸/μm	最小孔隙尺寸/μm	平均孔隙尺寸/μm	平均配位数	计算值渗透率/(10^-15 m²)	试验值渗透率/(10^-15 m²)
Berea砂岩	15 m×15 m×15 m	0.20	235.1	0.01	40	3.0	403	350
Fontainebleau砂岩	15 m×15 m×15 m	0.05	0.871	0.01	0.13	2.5	0.00152	0.00120

下载: 导出CSV

表 4 典型页岩基本岩石物理参数

Table 4 Physical parameters of typical shale

基本参数	最大孔隙尺寸/nm	最小孔隙尺寸/nm	平均孔隙尺寸/nm	孔隙度	平均配位数	X方向折减因子	Y方向折减因子	Z方向折减因子
取值	500	50	300	0.07	3	0.30	0.35	0.45

下载: 导出CSV

参考文献(26)

[1]	FATT I. The network model of porous media: I capillary pressure characteristics[J]. Trans. AIME, 1956, 207: 144. doi: 10.2118/574-G
[2]	NICHOLSON D, PETROPOULOS J H. Capillary models for porous media: Ⅲ two-phase flow in three-dimensional network with Gaussian radius distribution[J]. Journal of Physics D: Applied Physics, 1971, 4(2): 181-189. doi: 10.1088/0022-3727/4/2/302
[3]	DULLIEN F A. Porous Media-fluid Transport and Pore Structure[M]. New York: Academic Press, 1979.
[4]	REEVES P C, CELIA M A. A function relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model[J]. Water Resources Research, 1996, 32(8): 2345-2358. doi: 10.1029/96WR01105
[5]	ACHARYA R C, SJOERD E A T M, LEIJNSE A. Porosity-permeability properties generated with a new 2-parameter 3D hydraulic pore-network model for consolidated and unconsolidated porous media[J]. Advances in Water Resources, 2004, 27: 707-723. doi: 10.1016/j.advwatres.2004.05.002
[6]	RAOOF A, HASSANIZADEH S M. A New method for generating pore-network models of porous media[J]. Transport in Porous Media, 2009, 81(3): 391-407.
[7]	GAO S Y, MEEGODA J N, HU L M. Two methods for pore network of porous media[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 36: 1954-1970. doi: 10.1002/nag.1134
[8]	王晨晨, 姚军, 杨永飞, 等. 基于规则网络的碳酸盐岩多尺度网络模型构建方法研究[J]. 计算力学学报, 2013, 30(2): 0231-0235. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201302011.htm WANG Chen-chen, YAO Jun, YANG Yong-fei, et al. The construction of carbonate multiscale network model based on regular network[J]. Chinese Journal of Computational Mechanics, 2013, 30(2): 0231-0235. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201302011.htm
[9]	ARNS J Y, ROBINS V, SHEPPARD A P, et al. Effect of network topology on relative permeability[J]. Transport in Porous Media, 2004, 55: 21-46. doi: 10.1023/B:TIPM.0000007252.68488.43
[10]	BLUNT M J, JACKSON M D, PIRI M, et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow[J]. Advances in Water Resources, 2002, 25: 1069-1089. doi: 10.1016/S0309-1708(02)00049-0
[11]	JOEKAR-NIASAR V, HASSANIZADEH S M, LEIJNSE A. Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modeling[J]. Transport in Porous Media, 2008, 74: 201-219. doi: 10.1007/s11242-007-9191-7
[12]	KOPLIK J, LASSETER T J. One and two-phase flow in network models of porous media[J]. Chemical Engineering Communications, 1984, 26: 285-295. doi: 10.1080/00986448408940216
[13]	JOEKAR-NIASAR V, HASSANIZADEH S M, DAHLE H K. Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling[J]. Journal of Fluid Mechanics, 2010, 655: 38-71. doi: 10.1017/S0022112010000704
[14]	GAO S Y, MEEGODA J N, HU L M. A dynamic two-phase flow model for air sparging[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37: 1801-1821. doi: 10.1002/nag.2109
[15]	HUANG X W, BANDILLA K W, CELIA M A. Multi-physics pore-network modeling of two-phase shale matrix flows[J]. Transport in Porous Media, 2016, 111: 123-141. doi: 10.1007/s11242-015-0584-8
[16]	MAHMOODLU M G, RAOOF A, SWEIJEN T, et al. Effects of sand compaction and mixing on pore structure and the unsaturated soil hydraulic properties[J]. Vadose Zone Journal, 2016, 15(8): 1-11. doi: 10.2136/vzj2015.12.0157
[17]	HAUGHEY D P, BEVERIDGE G G. Local voidage variation in arandomly packed bed of equal-sized spheres[J]. Chemical Engineering Science, 1966, 21(10): 905-915. doi: 10.1016/0009-2509(66)85084-4
[18]	ØREN P E, BAKKE S. Process based reconstruction of sandstones and prediction of transport properties[J]. Transport in Porous Media, 2002, 46: 311-343. doi: 10.1023/A:1015031122338
[19]	VALVATNE P H, PIRI M, LOPEZ X, et al. Predictive pore-scale modeling of single phase and multiphase flow[J]. Transport in Porous Media, 2005, 58: 23-41. doi: 10.1007/s11242-004-5468-2
[20]	MADONNA C, QUINTAL B, FREHNER M, et al. Synchrotron-based X-ray tomography microscopy for rock physics investigations[J]. Geophysics, 2013, 78(1): 53-64. doi: 10.1190/geo2012-0113.1
[21]	SHARQAWY M H. Construction of pore network models for Berea and Fontainebleau sandstones using non-linear programing and optimization techniques[J]. Advances in Water Resources, 2016, 98: 198-210. doi: 10.1016/j.advwatres.2016.10.023
[22]	SOEDER D J. Porosity and permeability of Eastern Devonian gas shale[J]. SPE Formation Evaluation, 1988, 3: 116-124. doi: 10.2118/15213-PA
[23]	CURTIS M E, SONDERGELD C H, AMBROSE R J, et al. Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging[J]. AAPG Bulletin, 2012, 96(4): 665-677. doi: 10.1306/08151110188
[24]	CHALMERS G R, BUSTIN R M, POWER I M. Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units[J]. AAPG Bulletin, 2012, 96(6): 1099-1108. doi: 10.1306/10171111052
[25]	郭为, 熊伟, 高树生, 等. 页岩气等温吸附/解吸特征[J]. 中南大学学报(自然科学版), 2013,44(7): 2836-2840. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201307029.htm GUO Wei, XIONG Wei, GAO Shu-sheng, et al. Isothermal adsorption/desorption characteristics of shale gas[J]. Journal of Central South University (Science and Technology), 2013, 44(7): 2836-2840. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201307029.htm
[26]	ROYCHAUDHURI B, TSOTSIS T, JESSEN K. An experimental investigation of spontaneous imbibition in gas shales[J]. Journal of Petroleum Science and Engineering, 2013, 111: 87-97. doi: 10.1016/j.petrol.2013.10.002

施引文献(5)

期刊类型引用(3)

1.	黎春林. 考虑主应力偏转的隧道松动土压力计算方法. 河海大学学报(自然科学版). 2025(02): 107-114 . 百度学术
2.	赵凯，谢良甫，钱建固，晋智毅，马莉. 浅埋黄土盾构隧道松动土压力求解与影响因素研究. 现代隧道技术. 2024(S1): 454-465 . 百度学术
3.	陈星欣，何明高，施文城，郭力群. 土岩复合地层盾构地中对接法刀盘拆卸不完全拱压力计算. 岩土工程学报. 2024(12): 2652-2660 . 本站查看