Reinfiltration through liquid bridges formed between two matrix blocks in fractured rocks

- Reinfiltration model considers inertia, viscous, gravity, matrix and fracture capillary forces.
- Three reinfiltration regimes with corresponding scaling relations were identified.
- Analytical approximations were presented for crossover times between regimes.
- Effects of matrix permeability, liquid viscosity, and fracture capillary pressure on reinfiltration were investigated.

SummaryLiquid reinfiltration is a significant process, which can considerably retard and slowdown the transport of oil, water and contaminants in fractured subsurface formations. However, accurate modeling of the reinfiltration via liquid bridges formed in a horizontal fracture or space between two rock porous blocks remains a controversial topic. In an attempt to improve an understanding of the problem, the reinfiltration from upper to lower matrix blocks through formation of liquid bridges is theoretically modeled by using generalization of the Lucas-Washburn theory for a porous medium, which takes into account pressure differences due to matrix capillary, gravity, inertia, viscous, and fracture capillary forces. The developed model results in a second-order nonlinear ordinary differential equation (ODE), which is solved numerically to obtain depth and rate of the reinfiltrated liquid versus time. The results showed that three reinfiltration regimes: including Early Time Regime (ETR) (z ∼ t, q = constant), Middle Time Regime (MTR) (z ∼ t, q ∼ 1/t) and Late Time Regime (LTR) (z ∼ t, q = constant) can be observed, where the inertia, viscous, and gravity forces are dominant, respectively. The results also indicated that by increasing the permeability of the porous medium, the durations of the ETR (z ∼ t, q = constant) and the LTR (z ∼ t, q = constant) are prolonged while the duration of the MTR (z ∼ t, q ∼ 1/t) is reduced. Moreover, the results revealed that by increasing the liquid viscosity, the durations of the ETR (z ∼ t, q = constant) and LTR (z ∼ t, q = constant) are reduced whereas the duration of the MTR (z ∼ t, q ∼ 1/t) is prolonged. In addition, the results showed that in the case of high permeability of the porous medium when the fracture capillary pressure is strong enough only the LTR (z ∼ t, q = constant) can be observed. The MTR (z ∼ t, q ∼ 1/t) and the LTR (z ∼ t, q = constant) scalings are of practical significance since the liquid reinfiltration in fractured rocks associated with gas-liquid drainage mechanism is a very slow process. These findings advance the understanding of the two-phase flow in fractured porous media.