Abstract This paper aims to interpret the low-velocity nonlinear flow occurring in low-permeability reservoirs based on the theories of electrokinetic transport and non-Newtonian rheology of fluids. To achieve this end, we simulate the steady-state electroviscous flow of Bingham-Papanastasiou (BP) fluids in circular microtubes by simultaneously solving the Poisson-Boltzmann and the modified Navier-Stokes equations. The induced electrical field strength E s , velocity profiles, and the transport capacity of the non-Newtonian fluid under the effects of various factors (such as capillary radius R, zeta potential ζ, yield stress τ0, and stress growth index m) were examined. The results show that the generated E s of the BP fluid is highly affected by the fluid rheology, which is quite different from that of the Newtonian liquid. The velocity profiles become lower and flatter as m or τ0 increases, and this is more remarkable in smaller microtubes. The apparent viscosity of non-Newtonian fluid declines monotonically with increasing c∞, yet non-monotonically with R, m, τ0, and ζ. In addition, the low-velocity nonlinear flow in microtubes can be successfully captured when considering the electrokinetic flow of the non-Newtonian fluid rheology. While for the Newtonian fluid, only involving the electroviscous effect fails to generate the nonlinear flow behavior. The contributions of electrokinetic parameters versus rheological properties to the degree of flow nonlinearity are also discussed. The impact of electrokinetic parameters (ζ, c∞) on the flow characteristics is significant at high-pressure gradients and becomes trivial when the pressure gradient is relatively low. In contrast, the fluid rheological parameters (m, τ0) greatly determine the magnitude of the flow nonlinearity occurring at the low-pressure gradients. In sum, the electroviscous flow of BP fluids in microchannels provides a possible explanation of the low-velocity non-Darcy flow in porous media.

中文翻译：

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微管中非牛顿流体的电粘性流动及其对多孔介质中非线性流动的影响

摘要 本文旨在基于流体的电动输运和非牛顿流变学理论解释低渗透油藏中发生的低速非线性流动。为此，我们通过同时求解 Poisson-Boltzmann 方程和修正的 Navier-Stokes 方程来模拟圆形微管中 Bingham-Papanastasiou (BP) 流体的稳态电粘性流动。检查了感应电场强度 E s 、速度分布和非牛顿流体在各种因素（如毛细管半径 R、zeta 电位 ζ、屈服应力 τ0 和应力增长指数 m）影响下的传输能力. 结果表明，BP流体产生的E s 受流体流变学的影响很大，这与牛顿流体的流变学有很大的不同。随着 m 或 τ0 的增加，速度分布变得越来越低和平坦，这在较小的微管中更为显着。非牛顿流体的表观粘度随着 c∞ 的增加单调下降，但与 R、m、τ0 和 ζ 非单调下降。此外，在考虑非牛顿流体流变学的电动流动时，可以成功捕获微管中的低速非线性流动。而对于牛顿流体，仅涉及电粘性效应不能产生非线性流动行为。还讨论了电动参数与流变特性对流动非线性程度的贡献。电动参数 (ζ, c∞) 对流动特性的影响在高压梯度下很显着，而在压力梯度相对较低时变得微不足道。相比之下，流体流变参数 (m, τ0) 极大地决定了在低压梯度下发生的流动非线性的大小。总之，微通道中 BP 流体的电粘性流动为多孔介质中的低速非达西流动提供了可能的解释。