Mathematical Model of Two-Phase Spontaneous Imbibition with Dynamic Contact Angle

Zhang, Lei; Ping, Jingjing; Tang, Bo; Kang, Lixin; Imani, Gloire; Yang, Yongfei; Sun, Hai; Zhong, Junjie; Ye, Jun; Ding, Fan

doi:10.1007/s11242-023-01934-4

Cited by 5 publications

(2 citation statements)

References 54 publications

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“…Based on the reference [ 45 ], when forced imbibition occurs after shut-in, the equilibrium of forces on the fluid in the confined capillary can be expressed as:

where F c is the capillary force; F P is the displacement force; f is the viscous force generated by the friction between fluid molecules and between fluid molecules and the solid pore wall; F i is the inertial force; and F g is gravity. Because the matrix pore width of tight shale reservoirs is extremely small and much smaller than the imbibition height, the influence of F g can be ignored [ 46 ]. Secondly, for pores with extremely small radii, f dominates and the F i can be ignored [ 47 ].…”

Section: Resultsmentioning

confidence: 99%

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopore Imbibition during Shut-in Process by Molecular Dynamics Simulations

Jiang,

Lv,

Jia

et al. 2024

Molecules

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Shut-in after fracturing is generally adopted for wells in shale oil reservoirs, and imbibition occurring in matrix nanopores has been proven as an effective way to improve recovery. In this research, a molecular dynamics (MD) simulation was used to investigate the effects of wettability and pressure on nanopore imbibition during shut-in for a typical shale reservoir, Jimsar. The results indicate that the microscopic advancement mechanism of the imbibition front is the competitive adsorption between “interfacial water molecules” at the imbibition front and “adsorbed oil molecules” on the pore wall. The essence of spontaneous imbibition involves the adsorption and aggregation of water molecules onto the hydroxyl groups on the pore wall. The flow characteristics of shale oil suggest that the overall push of the injected water to the oil phase is the main reason for the displacement of adsorbed oil molecules. Thus, shale oil, especially the heavy hydrocarbon component in the adsorbed layer, tends to slip on the walls. However, the weak slip ability of heavy components on the wall surface is an important reason that restricts the displacement efficiency of shale oil during spontaneous imbibition. The effectiveness of spontaneous imbibition is strongly dependent on the hydrophilicity of the matrix pore’s wall. The better hydrophilicity of the matrix pore wall facilitates higher levels of adsorption and accumulation of water molecules on the pore wall and requires less time for “interfacial water molecules” to compete with adsorbed oil molecules. During the forced imbibition process, the pressure difference acts on both the bulk oil and the boundary adsorption oil, but mainly on the bulk oil, which leads to the occurrence of wetting hysteresis. Meanwhile, shale oil still existing in the pore always maintains a good, stratified adsorption structure. Because of the wetting hysteresis phenomenon, as the pressure difference increases, the imbibition effect gradually increases, but the actual capillary pressure gradually decreases and there is a loss in the imbibition velocity relative to the theoretical value. Simultaneously, the decline in hydrophilicity further weakens the synergistic effect on the imbibition of the pressure difference because of the more pronounced wetting hysteresis. Thus, selecting an appropriate well pressure enables cost savings and maximizes the utilization of the formation’s natural power for enhanced oil recovery (EOR).

show abstract

“…Based on the reference [ 45 ], when forced imbibition occurs after shut-in, the equilibrium of forces on the fluid in the confined capillary can be expressed as:

Section: Resultsmentioning

confidence: 99%

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopore Imbibition during Shut-in Process by Molecular Dynamics Simulations

Jiang,

Lv,

Jia

et al. 2024

Molecules

View full text Add to dashboard Cite

show abstract

“…where F c is the capillary force; F P is the displacement force; f is the viscous force generated by the friction between fluid molecules and between fluid molecules and the solid pore wall; F i is the inertial force; and F g is gravity. Because the matrix pore width of tight shale reservoirs is extremely small and much smaller than the imbibition height, the influence of F g can be ignored [46]. Secondly, for pores with extremely small radii, f dominates and the F i can be ignored [47].…”

Section: K Peak K Slipmentioning

confidence: 99%

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopores Imbibition during Shut-in Process by Molecular Dynamics Simulations

Jiang,

Lv,

Jia

et al. 2024

Preprint

View full text Add to dashboard Cite

Shut-in after fracturing is generally adopted for wells in shale oil reservoirs, and imbibition occurring in matrix nanopores has been proven as an effective way to improve recovery. In this research, the molecular dynamics (MD) simulation was used to investigate the effects of wettability and pressure on nanopores imbibition during shut-in for a typical shale reservoir Jimsar. The results indicate that the microscopic advancement mechanism of the imbibition front is the competitive adsorption between “interfacial water molecules” at the imbibition front and “adsorbed oil molecules” on the pore wall. The essence of spontaneous imbibition involves the adsorption and aggregation of water molecules onto the hydroxyl groups on the pore wall. The flow characteristics of shale oil suggest that the overall push of the injected water to the oil phase is the main reason for the displacement of adsorbed oil molecules. Thus, shale oil especially the heavy hydrocarbon component in the adsorbed layer tends to slip on the walls. However, the weak slip ability of heavy components on the wall surface is an important reason that restricts the displacement efficiency of shale oil during spontaneous imbibition. The effectiveness of spontaneous imbibition is strongly dependent on the hydrophilicity of the matrix pore's wall. The better hydrophilicity of the matrix pore's wall facilitates higher levels of adsorption and accumulation of water molecules on the pore wall and requires less time for “interfacial water molecules” to compete with adsorbed oil molecules. During the forced imbibition process, the pressure difference acts on both the bulk oil and the boundary adsorption oil, but mainly on the bulk oil, which leads to the occurrence of wetting hysteresis. Meanwhile, shale oil still existing in the pore always maintains a good stratified adsorption structure. Because of the wetting hysteresis phenomenon, as the pressure difference increases, the imbibition effect gradually increases, but the actual capillary pressure gradually decreases and there is a loss in the imbibition velocity relative to the theoretical value. Simultaneously, the decline in hydrophilicity further weakens the synergistic effect of pressure difference because of the more pronounced wetting hysteresis. Thus, selecting an appropriate well pressure enables cost savings and maximizes the utilization of the formation's natural power for EOR.

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Pore-scale experimental investigation on the co-current spontaneous imbibition of gas–water two-phase with gravity force

Li,

Yan,

et al. 2023

Physics of Fluids

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Gravity and capillary forces play pivotal roles in the natural capillary-driven spontaneous imbibition process. The opacity of the medium and the intricate pore structure make it challenging to elucidate the influence of gravity force on co-current gas–water imbibition. A series of pore-scale visualization experiments were conducted using capillary tubes of five different diameters (100, 300, 400, 500, and 1000 μm). The vector concept, represented by the interaction angle with the horizontal direction, was employed to quantify the varying levels of gravity force in the imbibition process, and its impact on imbibition recovery was assessed quantitatively. The findings revealed that the primary influence of gravity on gas–water spontaneous imbibition recovery was predominantly observed in the early stage. Due to the water blocking effect, the gas–water spontaneous imbibition process temporarily halted and resumed when the capillary diameter was 300 μm (at an angle of 60°). For capillary diameters between 100 and 500 μm, the water blocking effect induced a wave-like variation in gas–water spontaneous imbibition recovery as the interaction angle increased. Conversely, for a capillary diameter of 1000 μm, imbibition recovery exponentially decreased with the interaction angle, and no water blocking effect was observed. Consequently, the critical range of pore sizes for the water blocking effect in the gas–water spontaneous imbibition process was determined to be between 500 and 1000 μm. This research offers valuable theoretical insights into understanding capillary-driven flow phenomena in porous media.

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Mathematical Model of Two-Phase Spontaneous Imbibition with Dynamic Contact Angle

Cited by 5 publications

References 54 publications

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopore Imbibition during Shut-in Process by Molecular Dynamics Simulations

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopore Imbibition during Shut-in Process by Molecular Dynamics Simulations

Study on the Effects of Wettability and Pressure in Shale Matrix Nanopores Imbibition during Shut-in Process by Molecular Dynamics Simulations

Pore-scale experimental investigation on the co-current spontaneous imbibition of gas–water two-phase with gravity force

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