Research on the permeability coefficient theory of porous media in triangular pipe ball model

Permeability coefficient is an extremely important parameter in many engineering fields such as environmental, chemical, geotechnical, hydraulic, oil and gas extraction, and nuclear reactors. However, theoretical prediction of this parameter is highly challenging. There are few theoretical formulas for permeability coefficient, and many empirical formulas have a narrow applicability range due to the inclusion of empirical constants with unclear physical significance, resulting in prediction errors typically ranging from 1 to 3 orders of magnitude. In this study, we aim to establish a theoretical calculation formula for permeability coefficient with a wide applicability range and small prediction errors through theoretical derivation. A triangular pipe ball seepage flow model is established based on the properties of permeable materials and seepage characteristics, assuming that the flow resistance is caused by the viscous resistance of pipe flow and the flow around the balls. The theoretical calculation formula for permeability coefficient is derived using flow resistance theory. To verify the accuracy of the formula, the average permeability coefficient of 46 soil samples from the central urban area of Nanping City, Fujian Province, China, was tested, and 11 sets of experimental data from the literature were collected. The results show that the average deviation between the theoretical calculation results and the literature data is 48.74%, and the average deviation from the experimental data is 70.21%, which is lower than that of the widely used Kozeny-Carman equation.