Pore-scale modeling of flow in packed beds and fibrous materials allows us to connect engineering-scale observations with fundamental behavior. A common method for pore-scale modeling is a network approach, in which the pore-space is modeled as a discretized network of pores and pore throats. However, this approach is very coarse from a computational perspective, and is therefore unsuitable for modeling details such as mass-transfer boundary layers, which may be relevant in separations processes. To partially address this issue, we have developed an integrated set of algorithms for finite-element method modeling of pore scale flow, which provides a number of advantages: the models operate directly from three-dimensional CT images of real materials; the technique allows for a high level of grid refinement; it can be coupled with other types of models such as stochastic models for mass-transfer simulations. In this work we demonstrate detailed flow simulations in CT images of both packed beds and prototype fibrous materials.