Experimental study of non-Darcy flow characteristics in permeable stones

Abstract

This study provides experimental evidence of Forchheimer flow and the transition between different flow regimes from the perspective of the pore size of permeable stone. We first carry out seepage experiments on four kinds of permeable stones with mesh sizes of 24, 46, 60 and 80, corresponding to mean particle sizes (50 % by weight) of 0.71, 0.36, 0.25 and 0.18 mm, respectively. The seepage experiments show that an obvious deviation from Darcy flow regime is visible. In addition, the critical specific discharge corresponding to the transition between flow regimes (from pre-Darcy to post-Darcy) increases with increasing particle size. When the “pseudo” hydraulic conductivity (K, which is computed as the ratio of the specific discharge q and the hydraulic gradient) increases with increasing q, the flow regime is denoted pre-Darcy flow. After q increases to a certain value, the pseudo hydraulic conductivity begins to decrease; this regime is called post-Darcy flow. In addition, we use the mercury injection technique to measure the pore size distributions of four permeable stones with different particle sizes. 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. The mean pore faithfully reflects the influences of the particle diameter, sorting degree and arrangement mode of the porous medium on seepage parameters. This study shows that the size of pores is an essential factor for determining the flow regime. In addition, the Forchheimer coefficients are discussed. The coefficient A (which is related to the linear term of the Forchheimer equation) is linearly related to 1/d2: A=0.00251/d2+0.003. The coefficient B (which is related to the quadratic term of the Forchheimer equation) is a quadratic function of 1/d: B=1.14×10-61/d2-1.26×10-61/d. The porosity (n) can be used to reveal the effects of the sorting degree and arrangement on the seepage coefficients. A larger porosity leads to smaller coefficients A and B for the same particle size.