致密气自扩散渗流模型

doi:10.7623/syxb202006008

石油学报 ›› 2020, Vol. 41 ›› Issue (6): 737-744.DOI: 10.7623/syxb202006008

致密气自扩散渗流模型

金衍¹, 韦世明¹, 陈康平², 夏阳¹

1. 中国石油大学(北京)油气资源与探测国家重点实验室北京 102249;
2. 亚利桑那州立大学美国亚利桑那州 85287-6101

收稿日期:2019-05-18 修回日期:2020-01-22 出版日期:2020-06-25 发布日期:2020-07-11
通讯作者: 金衍,男,1972年8月生,1994年获石油大学(华东)学士学位,2001年获石油大学(北京)博士学位,现为中国石油大学(北京)教授、研究生院常务副院长、长江学者特聘教授,主要从事石油工程岩石流固耦合力学与应用研究。
作者简介:金衍,男,1972年8月生,1994年获石油大学(华东)学士学位,2001年获石油大学(北京)博士学位,现为中国石油大学(北京)教授、研究生院常务副院长、长江学者特聘教授,主要从事石油工程岩石流固耦合力学与应用研究。Email:jiny@cup.edu.cn
基金资助:
国家自然科学基金项目（No.51874321）和国家自然科学基金青年科学基金项目（No.51904318）资助。

Self-diffusion flow model of tight gas

Jin Yan¹, Wei Shiming¹, Chen Kangping², Xia Yang¹

1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China;
2. Arizona State University, Arizona 85287-6101, USA

Received:2019-05-18 Revised:2020-01-22 Online:2020-06-25 Published:2020-07-11

摘要/Abstract

摘要：

致密气藏已经开始在世界上大规模开发，但其基本渗流机理尚不明确，现有渗流模型难以对生产数据进行完善的解释。笔者介绍并通过实例对Jin和Chen （2019）提出的新渗流模型及其适用性进行了研究。Jin和Chen从可压缩流体的N-S方程出发，基于Klainerman和Majda （1982）的小马赫数流动理论，利用渐近展开，多尺度分析和体积平均升尺度技巧，得到了时间尺度大于声波时间尺度时致密气藏一次开采油藏尺度下新的渗流方程。新的渗流方程反映了致密气藏一次开采完全是由气体的膨胀性驱动的物理本质，其扩散系数与孔隙度和气体黏度成正比，与气体密度成反比。通过实例对比自扩散模型与目前基于Darcy定律及其修正的渗流模型发现，Darcy渗流以及组合流动模型得到的气体产量仅在生产压差较小时才能与实际生产数据吻合，此时的产量较小；生产压差越大，Darcy渗流模型与实际生产数据偏差越大；而自扩散模型计算的产量能够较好地拟合实际生产数据。

关键词: 致密气, 渗流机理, 一次开采, 可压缩流体N-S方程, 自扩散, 生产

Abstract:

Tight gas reservoirs have begun to be exploitated on a large scale in the world, of which the basic flow mechanism is still unclear. It is difficult to perfectly interpret production data using the existing flow models. Through the comparison of actual cases, this paper introduces and explores the new flow model proposed by Jin and Chen (2019)and its applicability by examples. According to the N-S equation of compressible fluids and based on the theory of Klainerman and Majda (1982)for low Mach number flow, Jin and Chen obtained the new flow equation for the primary recovery of tight gas reservoirs on the reservoir scale in the case of time scale greater than the acoustic time scale using asymptotic expansion, multi-scale analysis and the upscaling technique of volume averaging. The new flow equation reflects the physical nature that the primary recovery of tight gas reservoirs is driven entirely by the expansibility of gas, and its diffusion coefficient is proportional to porosity and gas viscosity, and inversely proportional to gas density. The comparison by case studies between the self-diffusion model and the current flow model based on the Darcy's law and its modification shows that the gas yield obtained by the Darcy and combined flow model can only be consistent with the actual production data when the producing pressure drop is small, and the gas yield at this time is small; the larger the producing pressure drop, the greater the deviation between the Darcy flow model and the actual production data; the gas yield calculated by the self-diffusion model can well fit the actual production data.

Key words: tight gas, flow mechanism, primary recovery, N-S equation of compressible fluid, self-diffusion, production

中图分类号:

TE312

金衍, 韦世明, 陈康平, 夏阳. 致密气自扩散渗流模型[J]. 石油学报, 2020, 41(6): 737-744.

Jin Yan, Wei Shiming, Chen Kangping, Xia Yang. Self-diffusion flow model of tight gas[J]. Acta Petrolei Sinica, 2020, 41(6): 737-744.

参考文献

[1] 邹才能,朱如凯,吴松涛,等. 常规与非常规油气聚集类型、特征、机理及展望——以中国致密油和致密气为例[J].石油学报,2012,33(2):173-187.
ZOU Caineng,ZHU Rukai,WU Songtao,et al.Types,characteristics,genesis and prospects of conventional and unconventional hydrocarbon accumulations:taking tight oil and tight gas in China as an instance[J].Acta Petrolei Sinica,2012,33(2):173-187.
[2] 吴浩,张春林,纪友亮,等.致密砂岩孔喉大小表征及对储层物性的控制——以鄂尔多斯盆地陇东地区延长组为例[J].石油学报,2017,38(8):876-887.
WU Hao,ZHANG Chunlin,JI Youliang,et al.Pore-throat size characterization of tight sandstone and its control on reservoir physical properties:a case study of Yanchang Formation,eastern Gansu,Ordos Basin[J].Acta Petrolei Sinica,2017,38(8):876-887.
[3] 刘春,张荣虎,张惠良,等.致密砂岩储层微孔隙成因类型及地质意义——以库车前陆冲断带超深层储层为例[J].石油学报,2017,38(2):150-159.
LIU Chun,ZHANG Ronghu,ZHANG Huiliang,et al.Genetic types and geological significance of micro pores in tight sandstone reservoirs:a case study of the ultra-deep reservoir in the Kuqa foreland thrust belt,NW China[J].Acta Petrolei Sinica, 2017,38(2):150-159.
[4] 付金华,范立勇,刘新社,等.苏里格气田成藏条件及勘探开发关键技术[J].石油学报,2019,40(2):240-256.
FU Jinhua,FAN Liyong,LIU Xinshe,et al.Gas accumulation conditions and key exploration & development technologies in Sulige gas field[J].Acta Petrolei Sinica,2019,40(2):240-256.
[5] 操应长,葸克来,刘可禹,等.陆相湖盆致密砂岩油气储层储集性能表征与成储机制——以松辽盆地南部下白垩统泉头组四段为例[J].石油学报,2018,39(3):247-265.
CAO Yingchang,XI Kelai,LIU Keyu,et al.Reservoir properties characterization and its genetic mechanism for tight sandstone oil and gas reservoir in lacustrine basin:the case of the fourth Member of Lower Cretaceous Quantou Formation in the southern Songliao Basin[J].Acta Petrolei Sinica,2018,39(3):247-265.
[6] XIA Yang,JIN Yan,CHEN Mian,et al.An enriched approach for modeling multiscale discrete-fracture/matrix interaction for unconventional -reservoir simulations[J].SPE Journal,2019,24(1):349-374.
[7] XIA Yang,JIN Yan,CHEN Mian,et al.Hydrodynamic modeling of mud loss controlled by the coupling of discrete fracture and matrix[J].Journal of Petroleum Science and Engineering,2015,129:254-267.
[8] SAUERLAND H,FRIES T P.The extended finite element method for two-phase and free-surface flows:a systematic study[J].Journal of Computational Physics,2011,230(9):3369-3390.
[9] KLINKENBERG L J.The permeability of porous media to liquids and gases[C]//Proceedings of 1941 Drilling and Production Practice. New York:American Petroleum Institute,1941:200-213.
[10] FRIEDEL T,VOIGT H D.Investigation of non-Darcy flow in tight-gas reservoirs with fractured wells[J].Journal of Petroleum Science and Engineering,2006,54(3/4):112-128.
[11] SONG Hongqing,LIU Qipeng,YANG Dawei,et al.Productivity equation of fractured horizontal well in a water-bearing tight gas reservoir with low-velocity non-Darcy flow[J].Journal of Natural Gas Science and Engineering,2014,18:467-473.
[12] SONG Hongqing,YUE Ming,ZHU Weiyao,et al.Formation pressure analysis of water-bearing tight gas reservoirs with unsteady low-velocity non-Darcy flow[J].Advanced Materials Research,2011,201-203:399-403.
[13] FREEMAN C M,MORIDIS G,ILK D,et al.A numerical study of performance for tight gas and shale gas reservoir systems[J].Journal of Petroleum Science and Engineering,2013,108:22-39.
[14] CRONIN M,EMAMI-MEYBODI H,JOHNS R T.Diffusion-dominated proxy model for solvent injection in ultratight oil reservoirs[J].SPE Journal,2019,24(2):660-680.
[15] CHEN Kangping,SHEN Di.Drainage flow of a viscous compressible fluid from a small capillary with a sealed end[J].Journal of Fluid Mechanics,2018,839:621-643.
[16] CHEN Kangping,SHEN Di.Mechanism of fluid production from the nanopores of shale[J].Mechanics Research Communications,2018,88:34-39.
[17] JIN Yan,CHEN Kangping.Fundamental equations for primary fluid recovery from porous media[J].Journal of Fluid Mechanics,2019,860:300-317.
[18] 张烈辉,张苏,熊燕莉,等.低渗透气藏水平井产能分析[J].天然气工业,2010,30(1):49-51.
ZHANG Liehui,ZHANG Su,XIONG Yanli,et al.Productivity analysis of horizontal gas wells for low permeability gas reservoirs[J].Natural Gas Industry,2010,30(1):49-51.
[19] 孔祥言.高等渗流力学[M].2版.合肥:中国科学技术大学出版社,2010:560-561.
KONG Xiangyan.Advanced flow mechanics in porous medium[M].2nd ed.Hefei:China University of Science and Technology Press,2010:560-561.
[20] KLINKENBERG L J.The permeability of porous media to liquids and gases[C]//Proceedings of 1941 Drilling and Production Practice.New York:American Petroleum Institute,1941:200-213.
[21] SAMPATH K,KEIGHIN C W.Factors affecting gas slippage in tight sandstones of cretaceous age in the Uinta basin[J].Journal of Petroleum Technology,1982,34(11):2715-2720.
[22] 朱光亚,刘先贵,李树铁,等.低渗气藏气体渗流滑脱效应影响研究[J].天然气工业,2007,27(5):44-47.
ZHU Guangya,LIU Xiangui,LI Shutie,et al.A study of slippage effect of gas percolation in low permeability gas pools[J].Natural Gas Industry,2007,27(5):44-47.
[23] 罗瑞兰,程林松,朱华银,等.研究低渗气藏气体滑脱效应需注意的问题[J].天然气工业,2007,27(4):92-94.
LUO Ruilan,CHENG Linsong,ZHU Huayin,et al.Problems on the study of slippage effect in low-permeability gas reservoirs[J].Natural Gas Industry,2007,27(4):92-94.
[24] PATZEK T W.Knudsen-like scaling may be inappropriate for gas shales[R].SPE 187068,2017.
[25] ANDERSON J D.Computational fluid dynamics[M].New York:McGraw-Hill,1995.
[26] KLAINERMAN S,MAJDA A.Compressible and incompressible fluids[J].Communications on Pure and Applied Mathematics,1982,35(5):629-651.
[27] XIA Yang,JIN Yan,CHEN Kangping,et al.Simulation on gas transport in shale:the coupling of free and adsorbed gas[J].Journal of Natural Gas Science and Engineering,2017,41:112-124.
[28] DRANCHUK P M,ABOU-KASSEM H.Calculation of Z Factors for natural gases using equations of state[J].Journal of Canadian Petroleum Technology,1975,14(3):33-36.
[29] HEIDARYAN E,MOGHADASI J,SALARABADI A.A new and reliable model for predicting methane viscosity at high pressures and high temperatures[J].Journal of Natural Gas Chemistry,2010,19(5):552-556.
[30] CRAMER M S.Numerical estimates for the bulk viscosity of ideal gases[J].Physics of Fluids,2012,24(6):066102.
[31] 毛伟,梁政.气井井筒压力、温度耦合分析[J].天然气工业,1999(6):66-69.
MAO Wei,LIANG Zheng.Coupling analysis of the pressure and temperature in gas well borehole[J].Natural Gas Industry,1999(6):66-69.

致密气自扩散渗流模型

Self-diffusion flow model of tight gas

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	谢军, 李骞, 涂汉敏, 赵梓寒. 高含水致密凝析气藏特殊相态变化[J]. 石油学报, 2020, 41(9): 1109-1116.
[2]	赵坤, 李婷婷, 朱光有, 张志遥, 李婧菲, 王鹏举, 闫慧慧, 陈永进. 下寒武统优质烃源岩的地球化学特征与形成机制——以鄂西地区天柱山剖面为例[J]. 石油学报, 2020, 41(1): 13-26.
[3]	王建民, 张三. 特低渗透砂岩油层钻井液侵入程度及影响[J]. 石油学报, 2019, 40(9): 1095-1103.
[4]	赵垒, 闫怡飞, 王鹏, 张庆生, 宋胜利, 赵龙, 韩伟民, 冯耀荣, 闫相祯. 气井生产过程中碳钢管柱CO₂腐蚀规律[J]. 石油学报, 2019, 40(2): 232-239.
[5]	付金华, 范立勇, 刘新社, 黄道军. 苏里格气田成藏条件及勘探开发关键技术[J]. 石油学报, 2019, 40(2): 240-256.
[6]	李友川, 兰蕾, 王柯, 杨永才. 北部湾盆地流沙港组湖相烃源岩的差异[J]. 石油学报, 2019, 40(12): 1451-1459.
[7]	王香增, 冯东, 李相方, 严云奎, 郭向东, 乔向阳, 薛波, 马骋, 王泉波, 雷开宇, 张涛, 姚天福, 赵文. 考虑时变效应的致密气井产能评价——以延安气田为例[J]. 石油学报, 2019, 40(11): 1358-1367.
[8]	贾爱林, 王国亭, 孟德伟, 郭智, 冀光, 程立华. 大型低渗-致密气田井网加密提高采收率对策——以鄂尔多斯盆地苏里格气田为例[J]. 石油学报, 2018, 39(7): 802-813.
[9]	张斌, 何媛媛, 陈琰, 孟庆洋, 黄家旋, 袁莉. 柴达木盆地西部咸化湖相优质烃源岩形成机理[J]. 石油学报, 2018, 39(6): 674-685.
[10]	刘文超, 刘曰武, 朱维耀, 孙贺东. 基于二阶B样条的ILK流量反褶积算法改进及应用[J]. 石油学报, 2018, 39(3): 327-334.
[11]	王玉满, 陈波, 李新景, 王皓, 常立诚, 蒋珊. 川东北地区下志留统龙马溪组上升洋流相页岩沉积特征[J]. 石油学报, 2018, 39(10): 1092-1102.
[12]	胡绍彬, 徐庆龙, 郭玲玲, 王鹏, 刘少克. 采出液含水对生产气油比的影响规律[J]. 石油学报, 2018, 39(1): 116-121,128.
[13]	赵辉, 谢鹏飞, 曹琳, 李颖, 赵艳艳. 基于井间连通性的油藏开发生产优化方法[J]. 石油学报, 2017, 38(5): 555-561.
[14]	穆龙新, 张铭, 夏朝辉, 曲良超, 蒋平. 加拿大白桦地致密气储层定量表征技术[J]. 石油学报, 2017, 38(4): 363-374.
[15]	钟德康. 多次幂指数型广义水驱特征曲线的建模和应用[J]. 石油学报, 2017, 38(3): 333-341.