Mechanisms and equation improvement for gas seepage in coal seams around boreholes subjected to high-pressure CO₂ foam fracturing

Authors

PANG Mingkun, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, ChinaFollow
ZHANG Tianyu, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
PAN Hongyu, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
SONG Xianfeng, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
WU Shan, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
ZHANG Tianjun, College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China; Key Laboratory of Western Mine Exploitation and Hazard Prevention, Ministry of Education, Xi’an 710054, China

Abstract

Objective The special low-porosity, low-permeability structures of high-gas-content coal seams restrict efficient gas drainage. To address this issue, this study accurately determined the seepage parameters of annularly fractured coals around boreholes subjected to CO₂ foam fracturing to enhance both the design accuracy of boreholes for gas pre-drainage from coal seams and gas drainage efficiency. Methods Using an independently developed apparatus for gas seepage experiments on fractured coals around boreholes, this study investigated the coals with pores and fractures distributed in an annular pattern around boreholes from the perspective of varying initial pore structures. Specifically, this study analyzed the evolutionary characteristics of the permeability of fractured coals around boreholes by testing the permeability of coal specimens with varying initial pore structures. Based on the improved Ergun equation, this study derived the fundamental equation for gas seepage in fractured coal media and verified its rationality. Results The results indicate that the annularly fractured coals around boreholes experienced three stages of rupture and deformations during their compaction. When the stress ranged from 1.2 kPa to 1.3 kPa, corresponding to the late deformation stage of particles, the quantity of fractured particles significantly decreased. The reason is that fine-grained particles produced before the late stage of particle deformation filled most of the pores. Under external loading, the coal particles underwent further compression and deformation. As a result, the particles were subjected to mutual compression, forming a dense whole. As the seepage velocity continuously increased, the flow was primarily governed by inertial force. By setting parameters in the quadratic term coefficient in the Ergun equation at a variable associated with the flow state, it can be found that the relationship between the a/b ratio of the Ergun equation and seepage velocity v roughly followed a negative exponential relationship. The improved Ergun equation overcame the limitations of the conventional seepage equation, enabling the effective prediction of the negative pressure loss during seepage in porous media under varying porosities, particle diameters, and flow velocities. Conclusions For gas pre-drainage from coal seams, the permeability of annularly fractured coal around boreholes for gas pre-drainage can be calculated using the improved gas seepage equation for fractured coals. Accordingly, the effective fracturing radius can be determined accurately. This study provides an important theoretical basis for optimizing the arrangement of gas drainage boreholes. Meanwhile, it offers a novel approach to green, efficient gas drainage from widely distributed high-gas-content, low-permeability coal seams in China.

Keywords

energy security, CO2 foam fracturing, fracture propagation, seepage theory, seepage equation, permeability

DOI

10.12363/issn.1001-1986.25.01.0054

Recommended Citation

PANG Mingkun, ZHANG Tianyu, PAN Hongyu, et al. (2025) "Mechanisms and equation improvement for gas seepage in coal seams around boreholes subjected to high-pressure CO₂ foam fracturing," Coal Geology & Exploration: Vol. 53: Iss. 5, Article 4.
DOI: 10.12363/issn.1001-1986.25.01.0054
Available at: https://cge.researchcommons.org/journal/vol53/iss5/4

Reference

[1] 李树刚，张静非，尚建选，等. 双碳目标下煤气同采技术体系构想及内涵[J]. 煤炭学报，2022，47(4)：1416−1429.

LI Shugang，ZHANG Jingfei，SHANG Jianxuan，et al. Conception and connotation of coal and gas co–extraction technology system under the goal of carbon peak and carbon neutrality[J]. Journal of China Coal Society，2022，47(4)：1416−1429.

[2] 唐跃刚，王绍清，王晓帅，等. 洁净煤地质内涵、现状与未来发展方向[J]. 煤田地质与勘探，2025，53(1)：36−63.

TANG Yuegang，WANG Shaoqing，WANG Xiaoshuai，et al. Connotation，research status，and development directions of clean coal geology in China[J]. Coal Geology & Exploration，2025，53(1)：36−63.

[3] YAN Min，ZHOU Ming，LI Shugang，et al. Numerical investigation on the influence of micropore structure characteristics on gas seepage in coal with lattice Boltzmann method[J]. Energy，2021，230：120773.

[4] 王呈云. 高瓦斯低透气性煤层水力压裂增透技术应用研究[J]. 能源技术与管理，2024，49(3)：47–49

[5] 王义均，黄光利. 高瓦斯矿井低含量煤层工作面瓦斯预抽必要性论证[J]. 煤炭技术，2021，40(2)：103−106.

WANG Yijun，HUANG Guangli. Necessity demonstration of gas pre–drainage from low content coal seam working face in high gas mine[J]. Coal Technology，2021，40(2)：103−106.

[6] GUO Haijun，TANG Hanlu，WU Yuchen，et al. Gas seepage in underground coal seams：Application of the equivalent scale of coal matrix–fracture structures in coal permeability measurements[J]. Fuel，2021，288：119641.

[7] 庞明坤，潘红宇，朱诗鹏，等. 抽采钻孔孔周煤体瓦斯pre–Darcy/Darcy/non–Darcy渗流型态判定[J]. 煤炭学报，2024，49(增刊2)：1025−1032.

PANG Mingkun，PAN Hongyu，ZHU Shipeng，et al. Determination of pre–Darcy/Darcy/non–Darcy seepage patterns in coal around extraction boreholes[J]. Journal of China Coal Society，2024，49(Sup.2)：1025−1032.

[8] 陈冬冬. 彬长矿区中硬煤层长钻孔分段水力压裂瓦斯抽采技术[J]. 煤炭工程，2023，55(7)：72−77.

CHEN Dongdong. Gas extraction technology with long borehole segmented hydraulic fracturing in medium-hard coal seam of Binchang mining area[J]. Coal Engineering，2023，55(7)：72−77.

[9] 庞明坤. 瓦斯抽采钻孔孔周煤体“双孔–双渗”结构特征及分区渗透机制研究[D]. 西安：西安科技大学，2022.

PANG Mingkun. Study on the structural characteristics of“dual porosity–dual permeability”and the mechanism of zoning–permeability of coal around gas extraction boreholes[D]. Xi’an：Xi’an University of Science and Technology，2022.

[10] 张天军，孟钰凯，庞明坤，等. 有效应力对孔周破裂煤体渗透率演化规律的影响[J]. 煤炭科学技术，2023，51(增刊1)：122−131.

ZHANG Tianjun，MENG Yukai，PANG Mingkun，et al. Effect of effective stress on the evolution of permeability patterns in perforated fractured coal bodies[J]. Coal Science and Technology，2023，51(Sup.1)：122−131.

[11] NAN Yalin，ZHAO Zaikun，JIN Xin，et al. Permeability coefficient of unsaturated loess and its gaseous and liquid water migration modeling[J]. Advances in Civil Engineering，2021，2021(1)：6689603.

[12] HOU Bing，ZHANG Ruxin，CHEN Mian，et al. Investigation on acid fracturing treatment in limestone formation based on true tri–axial experiment[J]. Fuel，2019，235：473−484.

[13] 胡千庭，李晓旭，陈强，等. 酸性压裂液防治低渗煤层水锁损害实验研究[J]. 煤炭学报，2022，47(12)：4466−4481.

HU Qianting，LI Xiaoxu，CHEN Qiang，et al. Mitigating water blockage in low–permeability coal seam by acid–based fracturing fluid[J]. Journal of China Coal Society，2022，47(12)：4466−4481.

[14] 吕其超，张星，周同科，等. SiO₂纳米颗粒强化的CO₂泡沫压裂液体系[J]. 中国石油大学学报(自然科学版)，2020，44(3)：114−123.

LYU Qichao，ZHANG Xing，ZHOU Tongke，et al. CO₂ foam fracturing fluid system enhanced by SiO₂ nanoparticles[J]. Journal of China University of Petroleum (Edition of Natural Science)，2020，44(3)：114−123.

[15] 熊利军，王犁，吴洋，等. 耐高温清洁压裂液的制备及性能评价[J]. 精细化工，2022，39(1)：204−211.

XIONG Lijun，WANG Li，WU Yang，et al. Preparation and performance evaluation of high–temperature resistant clean fracturing fluid[J]. Fine Chemicals，2022，39(1)：204−211.

[16] 乔金林，张星，李雪健，等. 煤体渗透率测试仪的设计与试验研究[J]. 煤炭技术，2023，42(5)：177−181.

QIAO Jinlin，ZHANG Xing，LI Xuejian，et al. Design and experimental study of coal permeability tester[J]. Coal Technology，2023，42(5)：177−181.

[17] 许诗婧，王长权，曾思佳. 致密砂岩气藏气水相对渗透率计算方法改进[J]. 西安石油大学学报(自然科学版)，2023，38(3)：75−80.

XU Shijing，WANG Changquan，ZENG Sijia. Improvement of calculation method for relative permeability of gas and water in tight sandstone reservoirs[J]. Journal of Xi’an Shiyou University (Natural Science Edition)，2023，38(3)：75−80.

[18] TADRIST L，MISCEVIC M，RAHLI O，et al. About the use of fibrous materials in compact heat exchangers[J]. Experimental Thermal and Fluid Science，2004，28(2/3)：193−199.

[19] 马衍坤，胡明烨，张曦，等. 受载褐煤孔隙结构可压缩性与渗透率的相关性试验研究[J/OL]. 煤炭科学技术，2023：1–8 [2023-10-26]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=MTKJ20231019001&dbname=CJFD&dbcode=CJFQ.

MA Yankun，HU Mingye，ZHANG Xi，et al. Experimental study on the correlation between compressibility and permeability of on–load lignite pore structure[J/OL]. Coal Science and Technology，2023：1–8 [2023-10-26]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=MTKJ20231019001&dbname=CJFD&dbcode=CJFQ.

[20] PAEK J W，KANG B H，KIM S Y，et al. Effective thermal conductivity and permeability of aluminum foam materials[J]. International Journal of Thermophysics，2000，21(2)：453−464.

[21] LAGE J L，ANTOHE B V，NIELD D A. Two types of nonlinear pressure–drop versus flow–rate relation observed for saturated porous media[J]. Journal of Fluids Engineering，1997，119(3)：700−706.

[22] 孙文斌，田殿金，马诚，等. 侧限条件下断层破碎岩体变形及渗流侵蚀特性[J]. 煤田地质与勘探，2025，53(1)：193−203.

SUN Wenbin，TIAN Dianjin，MA Cheng，et al. Deformations and seepage–induced erosion of fractured rocks in fault under confined settings[J]. Coal Geology & Exploration，2025，53(1)：193−203.

[23] 陈方兴，郝小礼，陈世强，等. 采空区球–柱组装体压损预测模型及多孔介质流动特性[J/OL]. 煤炭学报，2024：1–13 [2025-04-11]. https://doi.org/10.13225/j.cnki.jccs.2024.0841.

CHEN Fangxing，HAO Xiaoli，CHEN Shiqiang，et al. Prediction model for pressure loss of sphere column assembly in goaf and flow characteristics of porous media[J/OL]. Journal of China Coal Society，2024：1–13 [2025-04-11]. https://doi.org/10.13225/j.cnki.jccs.2024.0841.

[24] RUTH D，MA Huiping. On the derivation of the Forchheimer equation by means of the averaging theorem[J]. Transport in Porous Media，1992，7(3)：255−264.

[25] ERGUN S. Fluid flow through packed columns[J]. Chemical Engineering Progress，1952，48：89−94.

[26] PANG Mingkun，PAN Hongyu，JI Bingnan，et al. Experimental investigation of flow regime transition characteristics of fractured coal bodies around gas extraction boreholes[J]. Energy，2023，270：126758.

[27] 王青祥，王通，唐佳旭，等. 矸石磨料射流冲击煤体的破碎行为及其力学特性研究[J]. 采矿与安全工程学报，2024，41(3)：623−633.

WANG Qingxiang，WANG Tong，TANG Jiaxu，et al. Study on the crushing behavior and mechanical properties of gangue abrasive jet impacting coal[J]. Journal of Mining & Safety Engineering，2024，41(3)：623−633.

[28] 袁帅，李仲夏，熊涛，等. 孔隙介质非达西渗流Forchheimer方程量化评价[J]. 水文地质工程地质，2024，51(3)：12−22.

YUAN Shuai，LI Zhongxia，XIONG Tao，et al. Quantitative evaluation of Forchheimer equation for non–Darcy flow in porous media[J]. Hydrogeology & Engineering Geology，2024，51(3)：12−22.

[29] 张佳亮，陈冬，葛洪魁，等. 基于改进Nelder–Mead算法的井位优选方法[J]. 西华大学学报(自然科学版)，2023，42(5)：44−53.

ZHANG Jialiang，CHEN Dong，GE Hongkui，et al. An improved well location optimization method based on Nelder–Mead algorithm[J]. Journal of Xihua University (Natural Science Edition)，2023，42(5)：44−53.

[30] 张民波，王子超，闫瑾，等. 基于Klinkenberg效应下双渗透模型瓦斯运移规律研究[J]. 煤炭工程，2023，55(5)：116−122.

ZHANG Minbo，WANG Zichao，YAN Jin，et al. Gas migration law based on double penetration model under Klinkenberg effect[J]. Coal Engineering，2023，55(5)：116−122.

[31] 熊峰，姜清辉，陈胜云，等. 裂隙–孔隙双重介质Darcy–Forchheimer耦合流动模拟方法及工程应用[J]. 岩土工程学报，2021，43(11)：2037−2045.

XIONG Feng，JIANG Qinghui，CHEN Shengyun，et al. Modeling of coupled Darcy–Forchheimer flow in fractured porous media and its engineering application[J]. Chinese Journal of Geotechnical Engineering，2021，43(11)：2037−2045.

[32] 陈国芳，吴丹，吕俊良. 求解渗流方程的一种修正的中心型有限体积法[J]. 吉林大学学报(理学版)，2020，58(5)：1135−1141.

CHEN Guofang，WU Dan，LYU Junliang. A modified cell–centered finite volume method for solving filtration equations[J]. Journal of Jilin University (Science Edition)，2020，58(5)：1135−1141.

[33] 王子超. 深部煤层预抽钻孔瓦斯运移规律与抽采技术研究[D]. 武汉：武汉工程大学，2023.

WANG Zichao. Research on gas transport law and extraction technology of deep coal seam pre–pumping borehole[D]. Wuhan：Wuhan Institute of Technology，2023.