Development of a Supervised Learning Model to Predict Length Scale Dependent Permeability of Porous Carbon Composites

Predicting permeability over a wide range of thermodynamic and geometric conditions is necessary to understand the transport of fluid through porous materials. Permeability is typically calculated over a representative elementary volume (REV), which is the minimum volume that captures all of the inherent features of the porous material. However, there are many instances where the representative volume is so large that permeability must be computed on a volume smaller than an REV. Furthermore, when the flow in the pores occurs in the non-continuum regime, in addition to the dependence on geometric configuration, permeability is also influenced by the temperature and pressure of the gases flowing through the pores. In these cases, permeability must be computed over a multidimensional nonlinear space of length scales, temperature, and pressure. The current state-of-the-art approach is to compute permeability for a limited set of conditions and interpolate across the multidimensional space, which leads to errors because of the nonlinear dependency of permeability on geometric and flow features of the porous material. Alternatively, permeability could be numerically computed in real time for a given set of thermodynamic and geometric parameters, but it would be computationally prohibitive. To overcome these issues, a supervised learning model capable of capturing the nonlinear relationship of permeability with geometric and fluid flow parameters has been developed. The supervised learning model maps the complex features of the multidimensional geometric and flow parameters to an analytical function that can be used to predict the permeability of the porous material under investigation. Additionally, since the function is both continuous and differentiable, it can be easily incorporated into tools that are used for design and analysis of porous systems. The performance of the newly developed model is evaluated by computing the root-mean-square train and test errors indicating no over-fit or under-fit of the model to the dataset. The permeability model is further validated against experimental data to justify the use of the model as an accurate, cost-effective alternative for determining permeability of porous materials.