Abstract
Understanding natural flows in porous media with low Reynolds number (Re) has significant implications for both science and engineering. However, knowledge and experimental gaps remain regarding such natural flows. In this context, we designed a sand column-based laboratory filtration experiment to investigate flow characteristics in porous media with low Re. Four media were considered including two silts (silt-I and silt-II), one silty sand, and one medium sand. Results show that constant hydraulic head is presumed to be an important factor that affects flow regime in porous media. In general, the flow approaches Darcian at a constant hydraulic head of ~170 cm, whereas it becomes non-Darcian at a constant hydraulic head of ~230 cm. The type of media determines the Re range that delimitates between Darcy and non-Darcy flows. Specifically, the transition appears at 0.015 < Re < 0.020 for medium sand and 0.000027 < Re < 0.000029 for silt-II, respectively. In the condition of constant hydraulic heads, the breakdown of Darcy’s law may occur at very low Re values (Re→0). Media dependent Re ranges are probably needed to describe the beginning of non-Darcy flows, rather than 1 to 10 or other value for all media. Findings in this study can offer insights into calculation and simulation of flows in low-permeability reservoirs, pumping process of foundation pit excavation, and other non-Darcy flows in low-permeability media.
Highlights
Improving the understanding of natural flow in porous media is important for a range of science and engineering applications [1,2,3]
As the hydraulic gradient increases to a certain value, the average velocity fluctuates or even decreases for medium sand and silt-II
The critical Reynolds number (Re) values mainly depended on particle size and average flow velocity
Summary
Improving the understanding of natural flow in porous media is important for a range of science and engineering applications [1,2,3]. In the field of hydrological research, Darcy’s law is the most fundamental law of groundwater dynamics [4]. The law has been widely used in solving hydrogeological problems such as groundwater seepage and pollutant migration. The analytical solution and numerical solution assume that “groundwater seepage obeys Darcy’s law”. Such solutions include the basic differential equation of groundwater movement, the Dupuit stable well flow model, the Theis unsteady well flow model and the Boulton, Neumen unsteady submersible well flow model. The assumption is used in research and development of groundwater numerical simulation software (e.g., MODFLOW, GMS, and FEFLOW) [5]. In its original form, Darcy’s law was
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