天然气地球科学 ›› 2020, Vol. 31 ›› Issue (3): 340–347.doi: 10.11764/j.issn.1672-1926.2019.12.008

• 天然气开发 • 上一篇    下一篇

多孔介质速度场和流量场分布

戚涛1(),胡勇2,李骞1(),彭先1,赵潇雨3,荆晨4   

  1. 1.中国石油西南油气田公司勘探开发研究院,四川 成都 610041
    2.中国石油西南油气田公司,四川 成都 610051
    3.中国石油西南油气田公司工程技术研究院,四川 成都 610051
    4.中国石油西南油气田公司页岩气研究院,四川 成都 610051
  • 收稿日期:2019-09-05 修回日期:2019-12-14 出版日期:2020-03-10 发布日期:2020-03-26
  • 通讯作者: 李骞 E-mail:qtaoh2018@petrochina.com.cn;liqian05@petrochina.com.cn
  • 作者简介:戚涛(1988-),男,四川南充人,工程师,博士,主要从事油气藏渗流理论和数值模拟研究.E-mail:qtaoh2018@petrochina.com.cn.
  • 基金资助:
    “十三五”国家科技重大专项 “四川盆地大型碳酸盐岩气田开发示范工程”(2016ZX05052-002);中国石油天然气股份公司重大科技专项 “西南油气田天然气上产300亿立方米关键技术研究与应用”(2016E-0605)

Velocity and flow field in porous media

Tao QI1(),Yong HU2,Qian LI1(),Xian PENG1,Xiao-yu ZHAO3,Chen JING4   

  1. 1.Research Institute of Exploration and Development, PetroChina Southwest Oil & Gasfield Company, Chengdu 610041, China
    2.PetroChina Southwest Oil & Gasfield Company, Chengdu 610051, China
    3.Research Institute of Engineering Technology, PetroChina Southwest Oil & Gasfield Company, Chengdu 610051, China
    4.Research Institute of Shale Gas, PetroChina Southwest Oil & Gasfield Company, Chengdu 610051, China
  • Received:2019-09-05 Revised:2019-12-14 Online:2020-03-10 Published:2020-03-26
  • Contact: Qian LI E-mail:qtaoh2018@petrochina.com.cn;liqian05@petrochina.com.cn
  • Supported by:
    The China National Science and Technology Major Project During the 13th Five-year Plan Period(2016ZX05052-002);The Major Science and Technology Projects of CNPC(2016E-0605)

摘要:

流体在多孔介质中的宏观特性由介质本身的孔隙结构直接决定,速度场和流量场作为连接微观和宏观的桥梁显得尤为重要,但相关的研究相对较少。基于孔隙网络模型中的流动模拟,采用欧拉描述方法,系统统计了多孔介质中速度和流量的分布,分析了速度和流量的概率密度函数随孔隙结构的变化关系。研究表明:①随多孔介质无序性的增加,速度的分布范围急剧增加,流量的分布范围变化不大;②速度的概率密度函数随无序因子的减小依次表现为:高斯分布、指数分布、指数截断的幂律分布及幂律分布,流量的概率密度函数主要受孔隙非均质性的影响,表现为高斯分布和指数截断的幂律分布;③归一化流体速度的平均值受变异系数和配位数共同影响,且与配位数成乘幂关系,归一化流体流量的平均值不随配位数的变化而变化,但其随变异系数的增加而降低。

关键词: 速度场, 流量场, 无序因子, 幂律分布, 指数截断的幂律分布

Abstract:

The macroscopic properties characterizing fluid transport in porous media are directly determined by the pore structure of the media itself. Velocity field and flow field, connecting microscopic and macroscopic theories, are particularly important, but few studies have been carried out. Based on the simulation of single-phase flow in pore network model, this paper systematically calculated the distribution of Eulerian velocity and flow in porous media, and analyzed the relationship between pore structure and the probability density function of velocity and flow. And the following research results were obtained. Firstly, with the increase of the disorder of porous media, the distribution range of velocity increases sharply, while that of flow rate does not change much. Secondly, as the disorder factor decreases, the probability density function of velocity satisfies the following distributions in turn: Gauss distribution, exponential distribution, power law with exponential cut-off distribution and power law distribution. The probability density function of the flow is mainly affected by the heterogeneity of porous media, which basically obeys Gauss distribution and power law with exponential cut-off distribution. Thirdly, the average value of the normalized fluid velocity(v*) is affected by both the coefficient of variation and the coordination number, and the relationship between v* and the coordination number obeys power law. The average value of normalized fluid flow(q*) does not change with coordination number, but decreases with the increase of the coefficient of variation.

Key words: Velocity field, Flow field, Disorder factor, Power law distributions, Power law with exponential cutoff

中图分类号: 

  • TE31

图1

大小为5×5×5的体中心网络模型示意"

图2

水力半径为40 μm时不同变异系数下孔隙半径分布"

图3

不同Fdis下的v*与r*关系"

图4

不同Fdis下的v*概率分布"

表1

v*概率分布函数拟合参数"

CVzFdis

拟合

函数类型

函数

表达式

A

a1,a2,a3,a4

B

b1,b2,b3,b4

C

c1, c3

D

d1

0.058160高斯分布y=a1+b1e-x-c122d12-0.000 078 40.026 040.995 520.105 04
0.056.41280.000 137 50.012 540.999 410.208 11
0.054.8960.000 147 60.008 781.002 140.293 43
0.054800.000 092 90.006 541.006 990.396 85
0.053.2640.000 043 30.003 891.022 110.668 77
0.052.448指数分布y=a2eb2x0.002 57-0.409 99
0.55814.550.030 89-1.106 71
0.556.411.640.024 98-0.923 85
0.554.88.720.018 65-0.740 07
0.5547.27指数截断的幂律分布y=a3eb3xxc30.014 65-0.612 32-0.029 09
0.553.25.820.009 62-0.406 97-0.157 08
0.552.44.360.006 38-0.256 04-0.318 91
1.0587.610.098 49-0.359 83-0.799 22
1.056.46.090.081 53-0.201 02-0.978 95
1.054.84.570.071 46-0.082 54-1.108 40
1.0543.800.069 14-0.073 14-1.078 36
1.053.23.040.051 62-0.063 26-0.810 05
1.052.42.28幂律分布y=a4xb40.036 57-0.994 33

图5

归一化流体速度的平均值<v*>"

图6

不同Fdis下的q*与v*关系图版"

图7

不同Fdis下的q*概率分布"

表2

q*概率分布函数拟合参数"

CVzFdis

拟合

函数类型

函数

表达式

A

a1,a3

B

b1,b3

C

c1,c3

D

d1

0.058160高斯分布y=a1+b1e-x-c122d12-0.001 050.015 840.982 290.213 35
0.056.41280.000 102 30.010 980.973 580.253 37
0.054.8960.000 145 60.008 490.974 160.321 78
0.054800.000 152 50.006 690.978 920.407 66
0.053.2640.000 081 60.004 410.996 010.672 11
0.052.448指数截断的幂律分布y=a3eb3xxc30.006 04-0.784 40-0.398 86
0.55814.550.002 69-0.103 72-0.960 91
0.556.411.640.002 92-0.134 28-0.915 36
0.554.88.730.003 41-0.211 55-0.848 22
0.5547.270.004 28-0.349 79-0.716 06
0.553.25.820.005 85-0.574 17-0.517 17
0.552.44.360.008 00-0.760 78-0.237 33
1.0587.620.003 67-0.145 82-0.923 54
1.056.46.090.003 65-0.140 49-0.926 81
1.054.84.570.003 73-0.137 93-0.947 17
1.0543.810.003 39-0.102 91-1.028 72
1.053.23.050.003 48-0.081 51-1.049 74
1.052.42.280.004 22-0.119 34-1.071 45

图8

归一化流体流量的平均值<q*>"

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