Spontaneous Imbibition Process in Micro–nano Fractal Capillaries Considering Slip Flow

Abstract

An imbibition process of water into a matrix is required to investigate the influences of large-volume fracturing fluids on gas production of unconventional formations. Slip flow has been recognized by recent studies as a major mechanism of fluid transport in nanotubes. For nanopores in shale, a slip boundary is nonnegligible in the imbibition process. In this study, we established an analytic equation of spontaneous imbibition considering slip effects in capillaries. A spontaneous imbibition model that couples the analytic equation considering the slip effect was constructed based on fractal theory. We then used a model for various conditions, such as slip boundary, pore structure, and fractal dimension of pore tortuosity, to capture the imbibition characteristics considering the slip effect. A dynamic contact angle was integrated into the modeling. Results of our study verify that the slip boundary influences water imbibition significantly. The imbibition speed is significantly improved when slip length reaches the equivalent diameter of a tube. Therefore, disregarding the slip effect will underestimate the imbibition speed in shale samples.

Quantitative Study of the Effects of Pore Structure and Wettability on the Water Spontaneous Imbibition Behaviors in Coal

“…It is worth noting that D T is negatively correlated with n, and related research also shows that the time index decreases with increasing fractal dimension. 56 Therefore, a lower n value is caused by the higher complexity and roughness of pores, corresponding to a larger friction resistance, which is not conducive to the SI of water in coal. However, D T has a weak correlation with abl.…”

An Introduction to Fractal-Based Approaches in Unconventional Reservoirs — Part I

“…The predictions from the proposed analytical model exhibited similar variation trends to the experimental data. Shen et al 17 established an analytic equation of spontaneous imbibition by considering slip effects in capillaries with nanoscale and built a spontaneous imbibition model by coupling the analytic equation based on fractal theory. In addition, Xiao et al 18 derived an analytical model for the capillary pressure and water relative permeability in unsaturated porous rocks by taking into account the fractal distribution of pore size and tortuosity of capillaries.…”

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

“…The results reveal the transport mechanism of dual wettability nano-porous shale [22]. Li et al used the 3D intermingled-fractal model to derive a new permeability model for the organic-rich shale nanopore matrix and Shen et al also developed an apparent permeability model of shale nanopores, which describes the adsorptive gas flow behavior in shale by considering the effects of gas adsorption, stress dependence, and non-Darcy flow [23,24]. In addition, there has been recent work showing that the constitutive equations of classical density functional theory, molecular dynamic simulations, Lattice Boltzmann and multi-continuum are able to reproduce more complex molecular dynamics simulations fluids in nanopores [25][26][27][28].…”