|
|
裂缝型多孔介质气液两相渗流的分形分叉网络模型
|
Abstract:
裂缝型多孔介质的气液两相渗流对于页岩气水平井的产量预测具有重要的理论意义，因此，为了深入理解裂缝型多孔介质的气液两相渗流机理，本文采用分形分叉网络定量表征裂缝系统拓扑结构，发展了气液两相渗流的双重介质模型，推导了裂缝型多孔介质的有效渗透率和相对渗透率，并基于有限元方法数值模拟了裂缝型多孔介质的气液两相渗流。结果表明，分形双重介质模型的预测结果与数值模拟以及实验数据吻合较好，气相和液相相对渗透率随着液相饱和度的增加分别降低和提高，孔隙率和分形维数对相对渗透率具有显著影响。
The gas-liquid two-phase permeability in fractured porous media has important theoretical significance for the production prediction of shale gas horizontal wells. Therefore, in order to further understand the gas-liquid two-phase flow mechanism through fractured porous media, the fractal bi-furcation network is used to quantitatively characterize the fracture topology. A fractal du-al-medium model for gas-liquid two-phase flow was therefore developed to derive the analytical expressions of effective permeability and relative permeability of fractured porous media. And the gas-liquid two-phase flow in fractured porous media is also simulated based on the finite element method. The predicted results by the present fractal dual-medium model are in good agreement with the numerical simulation and experimental data. The results show that the relative permeability of gas phase and liquid phase decreases and increases with the increase of liquid phase saturation, respectively. The porosity and fractal dimension indicate significant effect on the relative permeability of gas phase.
| [1] | Li, Y.M., Jiang, Y.S., Zhao, J.Z., et al. (2015) Extended Finite Element Method for Analysis of Multi-Scale Flow in Fractured Shale Gas Reservoirs. Environmental Earth Sciences, 73, 6035-6045.
https://doi.org/10.1007/s12665-015-4367-x |
| [2] | 赵金洲, 李志强, 胡永全. 考虑页岩储层微观渗流的压裂产能数值模拟[J]. 天然气工业, 2015, 35(6): 53-58. |
| [3] | Abaci, S. and Edwards, J.S. (1992) Relative Permeability Meas-urements for Two Phase Flow in Unconsolidated Sands. Mine Water and the Environment, 11, 11-26. https://doi.org/10.1007/BF02919583 |
| [4] | Andres, R.V. and Bernardo, M.R. (2020) Uncertainty Quantification and Sensitivity Analysis for Relative Permeability Models of Two-Phase Flow in Porous Media. Journal of Petroleum Sci-ence and Engineering, 192, Article ID: 107297.
https://doi.org/10.1016/j.petrol.2020.107297 |
| [5] | Snow, D.T. (1969) Anisotropic Permeability of Fractured Media. Water Resources Research, 5, 1273-1289.
https://doi.org/10.1029/WR005i006p01273 |
| [6] | 郁伯铭. 多孔介质输运性质的分形分析研究进展[J]. 力学进展, 2003, 33(3): 333-346. |
| [7] | Xu, P. (2015) A Discussion on Fractal Models for Transport Physics of Porous Media. Fractals, 23, Article ID: 1530001. https://doi.org/10.1142/S0218348X15300019 |
| [8] | Qiu, S.X., Yang, M. and Xu, P. (2020) A New Fractal Model for Porous Media Based on Low-Field Nuclear Magnetic Resonance. Journal of Hy-drology, 586, Article ID: 124890. https://doi.org/10.1016/j.jhydrol.2020.124890 |
| [9] | Luo, Y.F., Xia, B.W. and Li, H.L. (2021) Fractal Permeability Model for Dual-Porosity Media Embedded with Natural Tortuous Fractures. Fuel, 295, Article ID: 120610. https://doi.org/10.1016/j.fuel.2021.120610 |
| [10] | 徐鹏. 树状分形分叉网络的输运特性[D]: [博士学位论文]. 武汉: 华中科技大学, 2008. |
| [11] | Yu, B.M. and Cheng, P. (2002) A Fractal Permeability Model for Bi-Dispersed Porous Media. International Journal of Heat and Mass Transfer, 45, 2983-2993. https://doi.org/10.1016/S0017-9310(02)00014-5 |
| [12] | Burdine, N.T., Magnolia, P. and Dallas (1953) Relative Per-meability Calculations from Pore Size Distribution Data. Petroleum Transactions, 198, 71-78. https://doi.org/10.2118/225-G |
| [13] | Xu, P., Qiu, S.X. and Yu, B.M. (2013) Prediction of Relative Permeability in Unsaturated Porous Media with a Fractal Approach. International Journal of Heat and Mass Transfer, 64, 829-837.
https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.003 |
| [14] | Journel, A.G., Deutsch, C.V. and Desbarats, A.J. (1986) Power Averaging for Block Effective Permeability. Society of Petroleum Engineers, Los Angeles, 329-334. https://doi.org/10.2118/15128-MS |
| [15] | Kenton, A.R., Wooyong, U. and Sean, M.C. (2019) Relative Permeability for Water and Gas through Fractures in Cement. PLOS ONE, 14, e0210741. https://doi.org/10.1371/journal.pone.0210741 |
| [16] | 郭晓茜. 煤储层相对渗透率动态变化规律研究[D]: [博士学位论文]. 北京: 中国地质大学, 2016. |
