AN ARTIFICIAL NEURAL NETWORK APPROACH TO CAPILLARY RISE IN POROUS MEDIA

Abstract

An artificial neural network (ANN) was used to analyze the capillary rise in porous media. Wetting experiments were performed with 15 liquids and 15 different powders. The liquids covered a wide range of surface tension (15.45–71.99 mJ/m²) 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 (25.5–62.2 mJ/m²). 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, 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; and (ii) their corresponding values as calculated by the Lucas-Washburn 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 ANN approach was able to predict with superior accuracy (i.e., r ² = 0.92, PF/3 = 51) the time of capillary rise. The Lucas-Washburn calculations gave the worst correlations (r ² = 0.15, PF/3 = 1002). 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 = 0.27 to 0.48, PF/3 = 112 to 285).

Keywords:

• Artificial neural network (ANN)
• Imbibition
• Lucas-Washburn equation
• Porous media
• Time prediction of capillary rise

Notes

^a Glycerine was used only to determine the surface free energy of Printex V (i.e., carbon black powder) since the times of capillary rise for the other liquids were too small.

^a Times of capillary rise, experimentally determined.

^b Times of capillary rise as predicted by the ANN.

^c Times of capillary rise as calculated by Equation (2).

^d Times of capillary rise as calculated by Equation (4).

^e Times of capillary rise as calculated by Equation (5).

^f Times of capillary rise as calculated by Equation (5) taking into consideration the gravity.

^g Times of capillary rise as calculated by Equation (5) taking into consideration Equation (10).

^h Times of capillary rise as calculated by Equation (6).

ⁱ Times of capillary rise as calculated by Equation (7).