不同边界条件下的渗吸驱动因素

doi:10.19596/j.cnki.1001-246x.8391

摘要/Abstract

摘要：

建立不同边界条件下的渗吸数学模型, 分别研究在单一边界(OEO边界条件)和混合边界条件(TEO-OW边界条件)下重力和毛管压力对渗吸作用的驱动。结果表明: OEO边界条件下, 只存在逆向渗吸, 并且当开启端面在下端时, 重力抑制渗吸进行; 当开启端面在上端时, 重力促进渗吸进行; TEO-OW边界条件下, 同时存在逆向渗吸和同向渗吸, 对于逆向渗吸, 重力是阻力, 对于同向渗吸, 重力是动力, 当Bond数倒数较小时, 重力在渗吸作用中占主导地位, 当Bond数倒数较大时, 毛管力占主导地位。对比OEO开启端面在上端时和TEO-OW边界条件下重力和毛管力对渗吸作用的大小。结果显示, 在相同Bond数倒数下, OEO边界条件下重力作用的渗吸排油比例要高于TEO-OW边界条件下重力作用的渗吸排油比例。对比不同Bond数倒数下OEO和TEO-OW渗吸速度发现, 当Bond数倒数较小时, 重力起主导作用, OEO边界渗吸速度更快; 当Bond数倒数较大时, 毛管力起主导作用, TEO-OW边界条件渗吸速度更快。

关键词: 自发渗吸, 边界条件, 毛管压力, 重力作用

Abstract:

Mathematical models of imbibition under different boundary conditions were built with piston-like displacement assumption. Effect of gravity and capillary pressure on imbibition under OEO (single boundary) and TEO-OW (mixed boundary) boundary conditions are studied. It shows that oil is produced only by counter-current imbibition under OEO boundary conditions. Gravity inhibits imbibition as the open face is at the lower end face of core and gravity promotes imbibition as the open face is at the upper end face of core. Oil is produced by combination of co-and counter-current imbibition under TEO-OW boundary condition. Gravity inhibits counter-current imbibition and promotes co-current imbibition under TEO-OW boundary condition. Gravity is dominant driving force as the inverse Bond number is smaller and capillary pressure is dominant driving force as inverse Bond number is greater. In addition, effect of gravity and capillary pressure on imbibition under OEO and TEO-OW boundary conditions are studied. It shows that oil production by gravity under OEO boundary condition is greater than that under TEO-OW boundary condition with same inverse Bond number. The rate of oil production under OEO boundary condition is faster than that under TEO-OW boundary condition as inverse Bond number is smaller and opposite phenomena is observed as inverse Bond number is greater.

Key words: spontaneous imbibition, boundary conditions, capillary pressure, gravity

中图分类号:

TE349

张震杰, 冯建园, 蔡建超, 陈康力, 孟庆帮. 不同边界条件下的渗吸驱动因素[J]. 计算物理, 2021, 38(5): 513-520.

Zhenjie ZHANG, Jianyuan FENG, Jianchao CAI, Kangli CHEN, Qingbang MENG. Driving Force for Spontaneous Imbibition Under Different Boundary Conditions[J]. Chinese Journal of Computational Physics, 2021, 38(5): 513-520.

图/表 10

图1 OEO边界条件开启面在上端渗吸作用岩心内部流体及压力分布

Fig.1 Schematic of fluid and pressure distribution under OEO boundary condition with open face in the upper end

图2 OEO边界条件开启面在下端渗吸岩心内部流体及压力分布

Fig.2 Schematic of fluid and pressure distribution under OEO boundary condition with open face in the bottom end

图3 TEO-OW边界条件渗吸作用岩心内部流体及压力分布

Fig.3 Schematic of fluid and pressure distribution under TEO-OW boundary condition

图4 OEO边界条件开启面在上端时渗吸数学模型求解流程图

Fig.4 Flow chart for solving mathematical model of imbibition under OEO boundary condition with open face in the upper end

表1 模型计算相关参数

Table 1 Digital-analog related parameters

参数	参数值
岩心长度，L/m	0.063 5
岩心距水面距离，h/m	0.1
岩心截面积，A/m²	1.135 4×10^-3
岩心孔隙度，φ	0.185
界面张力，δ/(mN·m^-1)	32
束缚水饱和度，S_wi	0
渗吸前缘上游平均含水饱和度，S_wf	0.55
湿相黏度，μ_w/(mPa·s)	1
非湿相黏度，μ_nw/(mPa·s)	2.5
湿相等效相渗，K_rw	0.035
非湿相同向渗吸等效相渗，K_{rnw, co}	1
非湿相逆向渗吸等效相渗，K_{rnw, cou}	0.102

图5 OEO边界条件下开启面在下端时有无重力渗吸推进距离与时间的关系

Fig.5 Relation between advancing distance and time under OEO boundary condition with open face in the bottom end

图6 OEO边界条件下开启面在上端时有无重力渗吸推进距离与时间的关系

Fig.6 Relation between advancing distance and time under OEO boundary condition with open face in the upper end

图7 TEO-OW边界条件下有无重力时渗吸推进距离与时间的关系

Fig.7 Relation between advancing distance and time under TEO-OW boundary condition

图8 不同NB-1下重力与毛管力渗吸排油比例对比

Fig.8 Fraction of oil production by capillary and gravity forces at various NB-1

图9 OEO和TEO-OW边界条件下渗吸时间比值

Fig.9 The ratio of imbibition time under OEO and TEO-OW boundary conditions

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