Effect of gravity on spontaneous imbibition from cores with two ends open in the frontal flow period

Spontaneous imbibition is a significant mechanism for oil recovery in naturally fractured reservoirs. Capillary and gravity forces are perhaps the most two important driving mechanisms for spontaneous imbibition. Understanding the relative effect of capillary and gravity forces on oil recovery by spontaneous imbibition is important for the prediction of the production performance in naturally fractured reservoirs. In this paper, a mathematical model considering the effect of capillary and gravity forces for Two Ends Open (TEO) imbibition is developed by assuming a piston-like displacement in the frontal flow period. In addition, a new method is introduced to distinguish the relative effect of capillary and gravity forces on oil production by spontaneous imbibition. Based on the numerical calculation, the effect of gravity on the advancing distance of the two imbibition fronts and the oil production is discussed at variant inverse Bond numbers. The simulated results show that the effect of gravity can be neglected when the inverse Bond number is high, however, when the inverse Bond number is very small, the effect of gravity on oil production is significant. In addition, it is also shown that the correlation between the advancing distance of the two imbibition fronts and the logarithm of inverse Bond number can be modeled by Boltzmann Function and the correlation between the fractional oil production by capillary or gravity forces and the logarithm of inverse Bond number can be modeled by Boltzmann Function as well. Finally, a novel scaling group including the effect of gravity is developed and the scaling results shows that the scaling accuracy is significantly improved using the novel scaling group.