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.

Experimental Investigation on the Effect of Pore Size on Spontaneous Imbibition Recovery in Oil-Wet Reservoirs

“…The idealized capillary model was upgraded to a core scale in order to make use of the above cognition derived from visual imbibition tests. Based on the classical Kozeny-Carman equation described relationship between permeability and pore radius, the permeability of rock samples corresponding to capillaries ranging from 10 μm to 60 μm could be estimated to be 80 mD, 300 mD, 700 mD, 1000 mD, 2000 mD, and 3000 mD [25,26]. The oilsaturated artificial cores were aged for three days prior to the imbibition experiment.…”

Current advances in capillarity: Theories and applications

“…Xueling Zhang, from the Zhengzhou University of Light Industry, has been committed to the study of the theory and simulation of nanoscale seepage mechanics, gave a presentation "Experimental study and mechanism analysis of spontaneous imbibition of surfactants in tight oil sandstone". Spontaneous imbibition experiments were conducted on tight oil sandstone, the mechanism of different surfactants was revealed, the nonionic surfactants altered the wettability of the core from weakly hydrophilic to strongly hydrophilic and achieved relatively high recovery rate due to the Van der Waals force and hydrogen bonds (Zhang et al, 2019). The enhanced recovery rate of spontaneous imbibition requires a sufficiently low wettability factor and a suitably high interfacial tension factor.…”

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

“…Abundant physical experiments (Bear, 1972;Prada and Civan, 1999;Dou et al, 2014;Wang et al, 2016;Hu et al, 2018;Tian et al, 2018;Wang and Cheng, 2020;Chi and Wang, 2021;Zhao et al, 2021;Yin et al, 2022) and theoretical analysis (Cai, 2014;Wang et al, 2018;Zhang et al, 2018;Zhang et al, 2019a;Ye et al, 2019) have demonstrated when the formation permeability is low, the seepage flow in the formation will belong to the low-velocity non-Darcian flow with a threshold pressure gradient (TPG). The TPG can introduce additional formation energy consumption, which hinders the fluid flow ability through the formation.…”

“…The low-velocity non-Darcian flow phenomena can be explained by the boundary layer theory and strong fluid-solid interaction (Xiong et al, 2009;Yang et al, 2016) in tiny micro-throats in low-permeability porous media. In addition, there also exists a TPG during the non-Newtonian Bingham fluid seepage flow process (Wang et al, 2006;Wang and Yu, 2011;Fusi and Farina, 2017;Bauer et al, 2019;Zhang et al, 2019b;Zhang et al, 2022). It can be explained by the existence of yield stress in the Bingham fluid.…”