Prediction of Time of Capillary Rise in Porous Media Using Artificial Neural Network (ANN)

Abstract

An Artificial Neural Network (ANN) was used to analyse the capillary rise in porous media. Wetting experiments were performed with fifteen liquids and fifteen different powders. The liquids covered a wide range of surface tension ( 15.45-71.99 mJ/m 2 ) and viscosity (0.25-21 mPa.s). The powders also provided an acceptable range of particle size (0.012-45 µm) and surface free energy (25.54-63.90 mJ/m 2 ). An artificial neural network was employed to predict the time of capillary rise for a known given height. The network's inputs were density, surface tension, and viscosity for the liquids and particle size, bulk density, packing density, and surface free energy for the powders. Two statistical parameters namely the product moment correlation coefficient (r 2 ) and the performance factor (PF/3) were used to correlate the actual experimentally obtained times of capillary rise to: i) their equivalent values as predicted by a designed and trained artificial neural network; ii) their corresponding values as calculated by the Lucas-Washburn's equation as well as the equivalent values as calculated by its various other modified versions. It must be noted that for a perfect correlation r 2 =1 and PF/3=0. The results showed that only the present approach of artificial neural network was able to predict with superior accuracy (i.e. r 2 = 0.91, PF/3=55) the time of capillary rise. The Lucas-Washburn's calculations gave the worst correlations (r 2 = 0.11, PF/3 = 1016). Furthermore, some of the modifications of this equation as proposed by different workers did not seem to conspicuously improve the relationships giving a range of inferior correlations between the calculated and experimentally determined times of capillary rise (i.e. r 2 = 0.24 to 0.44, PF/3 = 129 to 293).