Comparison of porous media permeability: experimental, analytical and numerical methods

Permeability is an important property of a porous medium and it controls the flow of fluid through the medium. Particle characteristics are known to affect the value of the permeability. However, experimental investigation of the effects of these particle characteristics on the value of permeability is time-consuming while analytical predictions have been reported to overestimate it leading to inefficient design. To overcome these challenges, there is the need for the development of new models that can predict permeability based on input variables and process conditions. In this research, data from experiments, Computational Fluid Dynamics (CFD) and literature were employed to develop new models using Multivariate Regression (MVR) and Artificial Neural Networks (ANNs). Experimental measurements of permeability were performed using high and low shear separation processes. Particles of talc, calcium carbonate and titanium dioxide (P25) were used in order to study porous media with different particle characteristics and feed concentrations. The effects of particle characteristics and initial stages of filtration as well as the reliability of filtration techniques (constant pressure filtration, CPF and constant rate filtration, CRF) were investigated. CFD simulations were also performed of porous media for different particle characteristics to generate additional data. The regression and ANN models also included permeability data taken from reliable literature sources. Particle cluster formation was only found in P25 leading to an increase of permeability especially in sedimentation. The constant rate filtration technique was found more suitable for permeability measurement than constant pressure. Analyses of data from the experiments, CFD and correlation showed that Sauter mean diameter (ranging from 0.2 to 168 µm), the fines ratio (x50/x10), particle shape (following Heywood s approach), and voidage of the porous medium (ranging from 98.5 to 37.2%) were the significant parameters for permeability prediction. Using these four parameters as inputs, performance of models based on linear and nonlinear MVR as well as ANN were investigated together with the existing analytical models (Kozeny-Carman, K-C and Happel-Brenner, H-B). The coefficient of correlation (R2), root mean square error (RMSE) and average absolute error (AAE) were used as performance criteria for the models. The K-C and H-B are two-variable models (Sauter mean diameter and voidage) and two variables ANN and MVR showed better predictive performance. Furthermore, four-variable (Sauter mean diameter, the x50/x10, particle shape, and voidage) models developed from the MVR and ANN exhibit excellent performance. The AAE was found with K-C and H-B models to be 35 and 40%, respectively while the results of using ANN2 model reduced the AAE to 14%. The ANN4 model further decreased the AAE to approximately 9% compared to the measured results. The main reason for this reduced error was the addition of a shape coefficient and particle spread (fine ratio) in the ANN4 model. These two parameters are absent in the analytical relations, such as K-C and H-B models. Furthermore, it was found that using the ANN4 (4-5-1) model led to increase in the R2 value from 0.90 to 0.99 and significant decrease in the RMSE value from 0.121 to 0.054. Finally, the investigations and findings of this work demonstrate that relationships between permeability and the particle characteristics of the porous medium are highly nonlinear and complex. The new models possess the capability to predict the permeability of porous media more accurately owing to the incorporation of additional particle characteristics that are missing in the existing models