低渗透多孔介质渗流动边界模型的解析与数值解
RESEARCH ON ANALYTICAL AND NUMERICAL SOLUTIONS OF A MOVING BOUNDARY MODEL OF SEEPAGE FLOWIN LOW- PERMEABLE POROUS MEDIA
查看参考文献23篇
|
文摘
|
考虑启动压力梯度的低渗透多孔介质非达西渗流模型属于强非线性动边界问题,分别利用相似变量变换方法和基于空间坐标变换的有限差分方法,对内边界变压力情况下、考虑启动压力梯度的一维低渗透多孔介质非达西渗流动边界模型进行了精确解析与数值求解研究.研究结果表明:该动边界模型存在唯一的精确解析解,且所求得的精确解析解可严格验证数值解的正确性;且当启动压力梯度值趋于零时,非达西渗流动边界模型的精确解析解将退化为达西渗流情况下的精确解析解.由求解结果作出的非零无因次启动压力梯度下的地层压力分布曲线表现出紧支性特点,其与达西渗流模型的有显著不同.因此,研究低渗透多孔介质中非稳态渗流问题时,应该考虑动边界的影响.研究内容完善了低渗透多孔介质的非达西渗流力学理论,为低渗透油气藏开发的试井解释与油藏数值模拟技术提供了理论基础. |
|
其他语种文摘
|
The modes of non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient belong to the moving boundary problems with strong nonlinearity. In this paper, a moving boundary model of one- dimensional non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient is studied for the case of a variable pressure at the inner boundary. A similarity transformation method and a spatial coordinate transformation based finite difference method are applied to obtain the exact analytical solution and numerical solution of the moving boundary model, respectively. Research results show that the moving boundary model has a unique exact analytical solution, which also strictly verifies the accuracy of the numerical solution; and when the value of threshold pressure gradient tends to zero, the exact analytical solution of the moving boundary model of non-Darcy seepage flow can reduce to the one corresponding to Darcy's seepage flow. The formation pressure distribution curves with non- zero dimensionless threshold pressure gradient from these solutions exhibit the characteristics of compact support, which is obviously different from those corresponding to Darcy's flow model. Therefore, the study on the unsteady seepage flow problem in low- permeable porous media should take into account the effect of moving boundary condition. The presented research improves the theory of non-Darcy seepage flow in low- permeable porous media, and also builds theoretical foundation for the technologies of well testing interpretation and reservoir numerical simulation involved in the development of low- permeable oil and gas reservoirs. |
|
来源
|
力学学报
,2015,47(4):605-612 【核心库】
|
|
DOI
|
10.6052/0459-1879-14-385
|
|
关键词
|
低渗透油藏
;
启动压力梯度
;
动边界
;
精确解析解
;
数值解
|
|
地址
|
1.
中国科学院力学研究所, 中国科学院流固耦合系统力学重点实验室, 北京, 100190
2.
中国石油大学(华东), 青岛, 266580
3.
卡尔加里大学, 加拿大, 卡尔加里, T2N 1N4
|
|
语种
|
中文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
0459-1879 |
|
学科
|
石油、天然气工业 |
|
基金
|
国家自然科学基金项目
;
国家留学基金委员会（CSC）项目
;
中国博士后科学基金
;
国家重大科技专项
|
|
文献收藏号
|
CSCD:5471358
|
参考文献 共
23
共2页
|
|
1.
黄延章. 低渗透油层非线性渗流特征.
特种油气藏,1997,4(1):9-14
|
CSCD被引
66
次
|
|
|
|
|
2.
Prada A. Modification of Darcy's law for the threshold pressure gradient.
Journal of Petroleum Science and Engineering,1999,22(4):237-240
|
CSCD被引
56
次
|
|
|
|
|
3.
孔祥言.
高等渗流力学,2010
|
CSCD被引
49
次
|
|
|
|
|
4.
Zhu W Y. Pressure characteristics and effective deployment in a water-bearing tight gas reservoir with lowvelocity non-Darcy flow.
Energy & Fuels,2011,25(3):1111-1117
|
CSCD被引
9
次
|
|
|
|
|
5.
姚同玉. 孔隙介质中稠油流体非线性渗流方程.
力学学报,2012,44(1):106-110
|
CSCD被引
9
次
|
|
|
|
|
6.
Cai J C. A fractal approach to low velocity non-Darcy flow in a low permeability porous medium.
Chinese Physics B,2014,23(4):Article ID 044701
|
CSCD被引
1
次
|
|
|
|
|
7.
Pascal H. Nonsteady flow through porous media in the presence of a threshold gradient.
Acta Mechanica,1981,39(3/4):207-224
|
CSCD被引
15
次
|
|
|
|
|
8.
Wu Y S. Flow and displacement of Bingham non-Newtonian fluids in porous media.
SPE Reservoir Engineering,1993,7(3):369-376
|
CSCD被引
2
次
|
|
|
|
|
9.
祝春生. 低渗透油藏不稳定渗流的近似解法.
西南石油大学学报(自然科学版),2008,30(4):69-72
|
CSCD被引
3
次
|
|
|
|
|
10.
程时清. 低速非达西渗流动边界问题的积分解.
力学与实践,2002,24(3):15-17
|
CSCD被引
7
次
|
|
|
|
|
11.
Ghedan S. Pressure behavior of vertical wells in low permeability reservoirs with threshold pressure gradient.
Special Topics and Reviews in Porous Media-An International Journal,2011,2(3):157-169
|
CSCD被引
1
次
|
|
|
|
|
12.
Lu J. Pressure behavior of uniform flux hydraulically fractured wells in low permeability reservoirs with threshold pressure gradient.
Special Topics and Reviews in Porous Media-An International Journal,2012,3(4):307-320
|
CSCD被引
1
次
|
|
|
|
|
13.
郭永存. 动边界低渗透油藏的无网格方法数值模拟.
工程力学,2006,23(11):188-192
|
CSCD被引
6
次
|
|
|
|
|
14.
Li F H. Pressure transient analysis for unsteady porous flow with start-up pressure derivative.
Well Testing,1997,6:1-11
|
CSCD被引
2
次
|
|
|
|
|
15.
Song F Q. Transient pressure of percolation through one dimension porous media with threshold pressure gradient.
Applied Mathematics and Mechanics,1999,20(1):27-35
|
CSCD被引
5
次
|
|
|
|
|
16.
郭永存. 低渗透油藏渗流的差分法数值模拟.
水动力学研究与进展,2004,19(3):288-293
|
CSCD被引
17
次
|
|
|
|
|
17.
姚军. 低渗透油藏非达西渗流动边界模型求解新方法.
力学季刊,2012,33(4):597-601
|
CSCD被引
4
次
|
|
|
|
|
18.
刘文超. 基于渗透率连续变化的低渗透多孔介质非线性渗流模型.
计算力学学报,2012,29(6):885-892
|
CSCD被引
3
次
|
|
|
|
|
19.
Yao J. Numerical solution of a moving boundary problem of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient.
Mathematical Problems in Engineering,2013:Article ID 384246
|
CSCD被引
2
次
|
|
|
|
|
20.
Liu W. Exact analytical solutions of moving boundary problems of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient.
International Journal of Heat and Mass Transfer,2012,55(21/22):6017-6022
|
CSCD被引
4
次
|
|
|
|
|
了解气象卫星更多信息，请访问