Spontaneous Imbibition in a Square Tube With Corner Films: Theoretical Model and Numerical Simulation

Abstract

Spontaneous imbibition in an angular tube with corner films is a fundamental problem in many scientific and engineering processes. In this study, a modified interacting capillary bundle model is developed to describe the liquid imbibition dynamics in a square tube with corner films. The square tube is decomposed into several interacting subcapillaries and the local capillary pressure in each subcapillary is derived based on the specific shape of its meniscus. The conductance of each subcapillary is calculated using single‐phase lattice Boltzmann simulation. The modified interacting capillary bundle model and color‐gradient lattice Boltzmann method are used to simulate the liquid imbibition dynamics in the square tube with different fluid properties. The predictions by the modified interacting capillary bundle model match well with the lattice Boltzmann simulation results for different conditions, demonstrating the accuracy and robustness of the interacting capillary bundle model to describe the imbibition dynamics with corner films. In addition, the interacting capillary bundle model is helpful to investigate the mechanisms during spontaneous imbibition and the influences of fluid viscosity, surface tension, wetting phase contact angle and gravity on imbibition dynamics. Finally, a universal scaling law of imbibition dynamics for the main meniscus is developed and the scaling law for arc meniscus is also analyzed.

A Dynamic Pore Network Model for Imbibition Simulation Considering Corner Film Flow

“…R c,max corresponds to the entry capillary pressure of the square tube that can be calculated by (J. Zhao et al, 2021):…”

“…The saturated conductance of all intralayer subthroats is calculated based on single‐phase LBM simulation results allowing to determine the coefficient c ij in Equation . Details can be found in our previous work (J. Zhao et al., 2021). The saturation dependent conductance for the 0th layer subthroat is calculated based on Equations and .…”

Frontier Enhanced Oil Recovery (EOR) Research on the Application of Imbibition Techniques in High-Pressure Forced Soaking of Hydraulically Fractured Shale Oil Reservoirs

“…The results show that the changes of pore size distribution and pore geometry will affect the water imbibition, and the fluid density ratio has a significant effect on water displacement behavior. In Figures 10 and 11, Zhao [108] used a single-phase LBM simulation and interactive capillary bundle model to reveal the dynamic characteristics of spontaneous imbibition capillary in the square tube inner corner. The team of academician Jia Chengzao [109] introduced the molecular interaction between water and solid inner wall into the lattice Boltzmann method and simulated the seepage characteristics in nanopores with different cross-sectional shapes and wettability.…”

Capillary Rising in a Tube with Corners

“…The dynamics of capillary rising in a square tube has been studied both experimentally [24,28,29] and numerically [30,31]. Gurumurthy et al [30] used volume-of-fluid method with adaptive mesh refinement.…”