Heterogeneous materials are omnipresent in several critical engineering applications such as polymer electrolyte fuel cells (PEFCs), coal bio-conversion process, geological storage of CO₂ and membrane water filtration. These applications rely on physical processes such as transport (e.g., mass, momentum, or energy) and chemical reactions for their functioning. The physical processes in the porous media are strongly dependent on morphology of the porous media structure. A detailed understanding of the porous media is therefore necessary for understanding and improving the physical processes in the porous media. A detailed understanding of microstructure can be utilized to find the physical properties, and then to estimate and improve the performance.

This work is focused on using statistical correlation functions for characterization and reconstruction of porous media structure. The statistical method is chosen due to its ability to capture stochastic nature of porous media in practical amount of cost and time. A simulated annealing based reconstruction method is used to reconstruct porous media structures with different statistical properties. A new unified pixel swapping method is presented, which can implement all available pixel swapping techniques in literature. The new pixel swapping method results in time reduction by a factor of 3-4 compared to conventional random swapping. Furthermore, compared to available biased pixel swapping methods, current method does not cause unrealistic structures to be reconstructed. A new different phase neighbor based multigrid hierarchical method has been developed, which reduces reconstruction time by one to two orders of magnitude, while improving reconstruction accuracy.

Multiple statistical correlation functions are used to reconstruct porous media structures which can closely match the original structure in terms of statistical and physical properties. Effect of different correlation functions on transport properties is studied in order to find a set of statistical correlation functions which can accurately characterize transport properties of a porous media. The effective molecular diffusivity was found to strongly depend on the two-point correlation function of porous media.

Overall, this work provides a novel method for fast and accurate characterization of porous media structures and transport properties by statistical correlation functions. This provides an ideal framework for reconstructing random porous media structures, and understanding the relationship between correlation functions and their transport properties. With the relationship between correlation functions and properties known, this work paves way for designing porous media structures with desired transport properties.