Driving Force for Spontaneous Imbibition Under Different Boundary Conditions

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

Abstract

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

CLC Number:

TE349

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.

Figures/Tables 10

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

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

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

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

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

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

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

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

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

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

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