A new liquid transport model considering complex influencing factors for nano- To micro-sized circular tubes and porous media

Abstract

A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz-van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.