Experimental study of non-Darcian flow characteristics in permeable stones
Abstract. This study provides experimental evidence of Forchheimer flow and transition between different flow regimes from the perspective of pore size of permeable stone. We have firstly carried out the seepage experiments of permeable stones with four different mesh sizes, including 24 mesh size, 46 mesh size, 60 mesh size, and 80 mesh size, which corresponding to mean particle sizes (50 % by weight) of 0.71 mm, 0.36 mm, 0.25 mm, and 0.18 mm. The seepage experiments show that obvious deviation from Darcian flow regime is visible. In addition, the critical specific discharge corresponding to the transition of flow regimes (from pre-Darcian to post-Darcian) increases with the increase of particle sizes. When the “pseudo” hydraulic conductivity (K) (which is computed by the ratio of specific discharge and the hydraulic gradient) increases with the increase of specific discharge (q), the flow regime is denoted as the pre-Darcian flow. After the specific discharge increases to a certain value, the “pseudo” hydraulic conductivity begins to decrease, and this regime is called the post-Darcian flow. In addition, we use the mercury injection experiment to measure the pore size distribution of four permeable stones with different particle sizes, and the mercury injection curve is divided into three stages. The beginning and end segments of the mercury injection curve are very gentle with relatively small slopes, while the intermediate mercury injection curve is steep, indicating that the pore size in permeable stones is relatively uniform. The porosity decreases as the mean particle sizes increases, and the mean pore size can faithfully reflect the influence of particle diameter, sorting degree and arrangement mode of porous medium on seepage parameters. This study shows that the size of pores is an essential factor for determining the flow regimes. In addition, the Forchheimer coefficients are also discussed in which the coefficient A (which is related to the linear term of the Forchheimer equation) is linearly related to 1/d 2 as A = 0.0025 (1/d 2) + 0.003; while the coefficient B (which is related to the quadratic term of the Forchheimer equation) is a quadratic function of 1/d as B =1.14E-06 (1/d)2 − 1.26E-06 (1/d). The porosity (n) can be used to reveal the effect of sorting degree and arrangement on seepage coefficient. The larger porosity leads to smaller coefficients A and B under the condition of the same particle size.
