Spontaneous Imbibition in a Fractal Network Model with Different Wettabilities

Shaobin Cai,Hai Sun,Lei Zhang,Mozhdeh Sajjadi,Lixin Kang,Yongfei Yang,Wenlong Jing,Chao Xu,Li Zhang

doi:10.3390/w13172370

Abstract

In this work, we derived a mathematical model for spontaneous imbibition in a Y-shaped branching network model. The classic Lucas–Washburn equation was used for modeling the imbibition process occurring in the Y-shape model. Then, a mathematical model for the Newtonian fluid’s imbibition was derived to reveal the relationship between dimensionless imbibition time and length ratio, radius ratio, and wetting strength. The dimensionless imbibition time in the model was adopted to compare with that of the capillary bundle model. Different length and radius ratios were considered in the adjacent two-stage channels, and different wettabilities were considered in the different branches. The optimal radius ratio, length ratio, and wetting strength were calculated under the condition of the shortest imbibition time. In addition, the shortest dimensionless imbibition time of the three-stage Y-shaped branching network model was calculated when the wettability changes randomly. The results indicate that the imbibition time changed mostly when the wettability of the second branch changed, and the second branch was the most sensitive to wettability in the model.

Highlights

Research on percolation theory is of great significance in various disciplines, such as soil physics [1], enhancing oil recovery [2,3,4,5], rock physics [6,7], fluid flows in porous media [8,9,10], and growth of branched structures [11]
The Lucas–Washburn model based on the capillary bundle is the most basic model, from which more complicated models for a wide range of applications have been developed, incorporating the effect of tortuosity [29], different pore geometry [30], and fractal characteristics [31,32,33]
Td and the time flow the end of the the variation model with different wettabilitiestime were β to oftime radius ratio of of fluid length are defined, trend of dimensionless α and studied, and the sensitivity of dimensionless time to wettability changes was investigated

Summary

Introduction

Research on percolation theory is of great significance in various disciplines, such as soil physics [1], enhancing oil recovery [2,3,4,5], rock physics [6,7], fluid flows in porous media [8,9,10], and growth of branched structures [11]. Among this research in porous media, much of the literature concerns drainage processes rather than imbibition processes. Imbibition processes take control of most fluid flows in tight porous media rather than drainage processes. The wetting phase fluid enters the porous medium spontaneously and replaces the nonwetting phase fluid originally existing in the porous medium under the action of capillary force. This process is often referred to as spontaneous imbibition [17,18]. The existing literature on spontaneous imbibition theory is extensive and focuses on the capillary bundle model. A great deal of previous research into imbibition processes has ignored the complex structure of porous media

Objectives

Results

Conclusion