Electrospun custom made flow battery electrodes are imaged in 3D using X-ray computed tomography. A variety of computational methods and simulations are applied to the images to determine properties including the porosity, fiber size, and pore size distributions as well as the material permeability and flow distributions. The simulations are performed on materials before and after carbonization to determine the effect it has in the internal microstructure and material properties. It is found that the deposited fiber size is constantly changing throughout the electrospinning process. The results also show that the surfaces of the fibrous material are the most severely altered during carbonization and that the rest of the material remained intact. Pressure driven flow is modeled using the lattice Boltzmann method and excellent agreement with experimental results is found. The simulations coupled with the material analysis also demonstrate the highly heterogeneous nature of the flow. Most of the flow is concentrated to regions with high porosity while regions with low porosity shield other pores and starve them of flow. The importance of imaging these materials in 3D is highlighted throughout.