Alternative relationships to enhance the applicability of nonlinear filtration models in porous media

Nonlinear filtration in porous packing has remained a research challenge till this day. There have been numerous attempts to model the flow characteristics under such conditions. However, as demonstrated in the present study, these models are applicable for only some specific conditions. The present study attempts to develop an empirical model which can be widely applicable. The Forchheimer-type models have been the most widely used in the literature for prediction of flow in porous media. The study identifies that the Ergun equation (the most popular form of the Forchheimer equation) with its original coefficients is unable to predict the flow properties over a wide range of data. Similar observation can be made for all other identical models. However, by optimising the coefficient values (A = 3705.79 and B = 6.17), the equation's performance can be significantly improved. The current study aims to create a working model that can be used to predict flow in porous media under a variety of packing, fluid, and flow conditions using multivariate polynomial regression and machine learning tools. It was observed that media size has far greater influence on the coefficients than any other parameter. Empirical models were created to predict Forchheimer coefficients, which represent R² values greater than 0.9 for training, validation, and test data. These models were further tested on a separate dataset with velocity and hydraulic gradient data compiled from the literature. The models were found to have very reliable performance with R² values above 0.90.