Mathematical Model for the Fluid-Gas Spontaneous Displacement in Nanoscale Porous Media considering the Slippage and Temperature

Abstract

The fracturing fluid-gas spontaneous displacement during the fracturing process is important to investigate the shale gas production and formation damage. Temperature and slippage are the major mechanisms underlying fluid transport in the micro-/nanomatrix in shale, as reported in the previous studies. We built a fracturing fluid-gas spontaneous displacement model for the porous media with micro-/nanopores, considering two major mechanisms. Then, our spontaneous displacement model was verified by the experimental result of the typical shale samples and fracturing fluids. Finally, the influences of temperature, slip length, and pore size distribution on the spontaneous imbibition process were discussed. Slippage and temperature significantly influenced the imbibition process. Lower viscosity, higher temperature, and longer slip length increased the imbibition speed. Ignoring the temperature change and slippage will lead to significant underestimation of the imbibition process.

Advances and challenges in shale oil development: A critical review

“…Regarding the nonlinear flow mechanism, it is commonly recognized the slip effect of single-phase liquid or gas in confined nano-scaled pores, which afterwards results in a nonlinear flow behavior in shale and tight reservoirs. Based on the slip boundary condition observed in molecular simulation and experiments, several improved mathematical models were derived to describe the single-phase flow in shale and numerous investigations have carried out to discuss the influencing factors of the slip lengths and its effect on fluid transport (Xu et al, 2007(Xu et al, , 2015Zhang et al, 2017aZhang et al, , 2017bLiu et al, 2018). Since the interaction between liquid and solid dominated the flow behavior, the mathematical model with introducing the concept of effective slip, which is the function of contact angle and apparent slip, is adopted in nanoconfined flow (Wu et al, 2017(Wu et al, , 2019.…”

Spontaneous Imbibition in Nanomatrix–Fracture of Low Permeability Using Multiscale Nanofluidic Chips

“…The results in the figure demonstrate a consistent power-law relationship between the imbibition length and t 0.5 . Moreover, the slope of the curve increases as the temperature rises, indicating a corresponding increase in the imbibition mass …”

“…Moreover, the slope of the curve increases as the temperature rises, indicating a corresponding increase in the imbibition mass. 54 The viscosity and surface tension were measured using a rheometer and tensiometer as a function of temperature. Further details are available at the Supporting Information.…”

A Generalized Capillary Imbibition Model for Porous Media in Tight Reservoirs

“…With the application of large-scale volume fracturing technology in the development of tight oil and gas, the imbibition is playing an increasingly important role in enhancing the recovery of tight reservoirs [1][2][3][4][5]. As the capillary imbibition of liquids in porous media has been utilized extensively in reservoir development, paper treatment, and antiseepage of the dam and other fields [6][7][8][9][10][11], the subject on imbibition had received wide attention and research from the last century. Bell and Cameron [12], Lucas [13], and Washburn [14] have put forward capillary imbibition equations, based on Hagen-Poseuille (H-P) flow in a cylindrical tube model, which laid the foundation for the development of imbibition model.…”