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HiWay (or channel) fracturing has been a new technology for development of unconventional oil and gas resources in recent years. It has been carried out more than 4000 times worldwide, and obtained good performance in oil and gas recovery. HiWay fracturing improves the flow conductivity of fractures by constructing inhomogeneous distributions of proppant and stable, open flow channel in hydraulic fractures. However, the mechanism and impact factors of high flow conductivity of HiWay fractures are not very clear. To the best of our knowledge, there are no relevant research reports available for such analysis. In this paper, it is first assumed that the fluid flow in proppant clusters follows the Darcy's law and the flow in the channels with proppant clusters is laminar viscous flow, which can be described using Stokes equation. However, the coupling of Darcy-Stokes equations is difficult, and some untrivial interface conditions at the interface between the porous and free-flow regions should be introduced, this will increase greater complexity in numerical computation. As an alternative approach, the Darcy-Brinkman equation is often used for this coupling flow problem, which provides a unified equation with continuous variable coefficients in the two different flow regions. Therefore, there is not necessary to introduce specific interface conditions any more. In this work, we first applied the Darcy-Brinkman equation to model the fluid flow in hydraulic fractures, and then the upscaling of Darcy-Brinkman equation is conducted to evaluate the equivalent permeability of a fracture by using homogenization theory and finite element numerical simulation. Finally, various impact factors of flow conductivity of a hydraulic fracture, such as the cluster shape, cluster distribution, cluster size, etc., are analyzed based on the equivalent permeability. Results show that the permeability of a hydraulic fracture is considerably greater than thst of proppant cluster when the free-flow region is well connected in the fracture, and the geometric properties of proppant clusters are also the key influencing factors for the flow conductivity. Therefore, in HiWay fracturing process, how to construct the well-connected free-flow region in hydraulic fractures is most important, and the flow conductivity of proppant cluster is not the keypoint. However, the surface roughness and stress sensitivity of the hydraulic fractures have not been considered in this work, it will be considered in the future work.
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Keywords:
- HiWay fracturing /
- fracture conductivity /
- homogenization theory /
- darcy-brinkman
[1] Cai B, Ding Y H, Cui Z Q, Yang Z Z, Shen H 2014 Adv. Mater. Res. 941 2521
[2] Tang Y, Tang X, Wang G Y, Zhang Q 2011 Geol. Bull. Chin. 30 393 (in Chinese) [唐颖, 唐玄, 王广源, 张琴 2011 地质通报 30 393]
[3] Gillard M R, Medvedev O, Hosein P R, Medvedev A, Peñacorada F, d'Huteau E 2010 SPE Annual Technical Conference and Exhibition Florence, Italy, September 19-22, 2010 p1 (SPE 135034)
[4] Medvedev A V, Kraemer C C, Pena A A, Panga M K R 2013 SPE Hydraulic Fracturing Technology Conference The Woodlands, Texas, USA February 4-6, 2013 p1 (SPE 163836)
[5] Valdes-Parada F J, Alberto Ochoa-Tapia J, Alvarez-Ramirez J 2007 Physica A: Statistical Mechanics and its Applications 385 69
[6] Lesinigo, Matteo, D'Angelo, Carlo, Quarteroni, Alfio 2011 Numer. Math. 117 717
[7] Joodi A S, Sizaret S, Binet S, Bruand A, Alberic P, Lepiller M 2010 Hydrogeol. J. 18 295
[8] Ng C O, Wang C Y 2010 Transport Porous Med. 85 605
[9] Hornung U 1997 Homogenization and porous media (Vol. 6) Springer pp 1-21
[10] Huang Z Q, Yao J, Li Y J, Wang C C, Lv X R 2010 Sci. China Ser. E 53 839
[11] Oriani F, Renard P 2014 Adv. Water Resour. 64 47
[12] Qu Z L, Ren C Y, Pei Y M, Fang D N 2015 Chin. Phys. B 24 024303
[13] Li M J, Chen L 2011 Chin. Phys. Lett. 28 085203
[14] Zhao G Z, Yu X J, Guo P Y 2013 Chin. Phys. B 22 050206
[15] Wang X C 2003 Finite Element Method (Bei Jing: Tsinghua University Press) pp98-129 (in Chinese) [王勖成 2003 有限单元法(北京: 清华大学出版社)第 98-129 页]
[16] Huang Z Q, Yao J, Wang Y Y 2013 Commun. Comput. Phys. 13 540
[17] Zhang R P, Yu X J, Zhao G Z 2013 Chin. Phys. B 22 030210
[18] Zhou S T, Zhang Q, Li M Z, Wang W Y 2002 Adv. Mech. 32 119 (in Chinese) [周生田, 张琪, 李明忠, 王卫阳 2002 力学进展 32 119]
[19] Zou Y S, Ma X F, Wang L, Lin X 2011 J. Chin. Coal Soc. 36 473 (in Chinese) [邹雨时, 马新仿, 王雷, 林鑫 2011 煤炭学报 36 473]
[20] Wen Q Z, Zhang S C, Li L D 2006 Pet. Geol. &Recovery Efficiency 13 97 (in Chinese) [温庆志, 张士诚, 李林地 2006 油气地质与采收率 13 97]
[21] Laptev V 2003 Ph. D. Dissertation ( Kaiserslautern: University Kaiserslautern)
[22] Khalili S, Dinarvand S, Hosseini R, Tamim H, Pop I 2014 Chin. Phys. B 23 048203
[23] Beavers G S, Joseph D D 1967 J. Fluid Mech. 30 197
[24] Huang Z Q, Gao B, Yao J 2014 Sci. China Ser. G 44 212 (in Chinese) [黄朝琴, 高博, 姚军 2014 中国科学: 物理学, 力学, 天文学 44 212]
[25] Brinkman H C 1949 Appl. Sci. Res. 1 27
[26] Popov P, Efendiev Y C, Qin G 2009 Commun. Comput. Phys. 6 162
[27] Jiang M, Liu H, Huang H 2009 Software Guide 8 175 (in Chinese) [江明, 刘辉, 黄欢 2009 软件导刊 8 175]
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[1] Cai B, Ding Y H, Cui Z Q, Yang Z Z, Shen H 2014 Adv. Mater. Res. 941 2521
[2] Tang Y, Tang X, Wang G Y, Zhang Q 2011 Geol. Bull. Chin. 30 393 (in Chinese) [唐颖, 唐玄, 王广源, 张琴 2011 地质通报 30 393]
[3] Gillard M R, Medvedev O, Hosein P R, Medvedev A, Peñacorada F, d'Huteau E 2010 SPE Annual Technical Conference and Exhibition Florence, Italy, September 19-22, 2010 p1 (SPE 135034)
[4] Medvedev A V, Kraemer C C, Pena A A, Panga M K R 2013 SPE Hydraulic Fracturing Technology Conference The Woodlands, Texas, USA February 4-6, 2013 p1 (SPE 163836)
[5] Valdes-Parada F J, Alberto Ochoa-Tapia J, Alvarez-Ramirez J 2007 Physica A: Statistical Mechanics and its Applications 385 69
[6] Lesinigo, Matteo, D'Angelo, Carlo, Quarteroni, Alfio 2011 Numer. Math. 117 717
[7] Joodi A S, Sizaret S, Binet S, Bruand A, Alberic P, Lepiller M 2010 Hydrogeol. J. 18 295
[8] Ng C O, Wang C Y 2010 Transport Porous Med. 85 605
[9] Hornung U 1997 Homogenization and porous media (Vol. 6) Springer pp 1-21
[10] Huang Z Q, Yao J, Li Y J, Wang C C, Lv X R 2010 Sci. China Ser. E 53 839
[11] Oriani F, Renard P 2014 Adv. Water Resour. 64 47
[12] Qu Z L, Ren C Y, Pei Y M, Fang D N 2015 Chin. Phys. B 24 024303
[13] Li M J, Chen L 2011 Chin. Phys. Lett. 28 085203
[14] Zhao G Z, Yu X J, Guo P Y 2013 Chin. Phys. B 22 050206
[15] Wang X C 2003 Finite Element Method (Bei Jing: Tsinghua University Press) pp98-129 (in Chinese) [王勖成 2003 有限单元法(北京: 清华大学出版社)第 98-129 页]
[16] Huang Z Q, Yao J, Wang Y Y 2013 Commun. Comput. Phys. 13 540
[17] Zhang R P, Yu X J, Zhao G Z 2013 Chin. Phys. B 22 030210
[18] Zhou S T, Zhang Q, Li M Z, Wang W Y 2002 Adv. Mech. 32 119 (in Chinese) [周生田, 张琪, 李明忠, 王卫阳 2002 力学进展 32 119]
[19] Zou Y S, Ma X F, Wang L, Lin X 2011 J. Chin. Coal Soc. 36 473 (in Chinese) [邹雨时, 马新仿, 王雷, 林鑫 2011 煤炭学报 36 473]
[20] Wen Q Z, Zhang S C, Li L D 2006 Pet. Geol. &Recovery Efficiency 13 97 (in Chinese) [温庆志, 张士诚, 李林地 2006 油气地质与采收率 13 97]
[21] Laptev V 2003 Ph. D. Dissertation ( Kaiserslautern: University Kaiserslautern)
[22] Khalili S, Dinarvand S, Hosseini R, Tamim H, Pop I 2014 Chin. Phys. B 23 048203
[23] Beavers G S, Joseph D D 1967 J. Fluid Mech. 30 197
[24] Huang Z Q, Gao B, Yao J 2014 Sci. China Ser. G 44 212 (in Chinese) [黄朝琴, 高博, 姚军 2014 中国科学: 物理学, 力学, 天文学 44 212]
[25] Brinkman H C 1949 Appl. Sci. Res. 1 27
[26] Popov P, Efendiev Y C, Qin G 2009 Commun. Comput. Phys. 6 162
[27] Jiang M, Liu H, Huang H 2009 Software Guide 8 175 (in Chinese) [江明, 刘辉, 黄欢 2009 软件导刊 8 175]
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