Resistance Analysis of Low Reynolds number flow in porous media

At present, some researchers believe that Darcy's law may not be valid, which may be the root cause of complex porous media problems. Porous media flow model is generally regarded as pipe flow, but in theory, it is necessary to consider it as bypass flow. However, there are few studies in this area. According to the seepage characteristics, we established the model of flowing around a single sphere in porous media and derived the resistance correlation of Darcy velocity (Re < 1). However, the Darcy experimental data analysis shows that the predicted value of the flow around the sphere is far lower than the experimental value, which proves that the assumption of the model of flowing around a single sphere is unreasonable. Even for the seepage of the extremely low Reynolds number, the flow interference around the sphere should be taken into account. Therefore, when the interference coefficient is 45, our formulas are superior to the classical Kozeny-Carman equation and Ergun equation in the prediction of all Darcy's experimental data and Charles Ritter's experimental data. Ergun equation has the largest error.