Models describing how fillers affect the barrier properties of polymers remain an important research topic to improve applications such as hydrogen storage or food preservation. The Nielsen model, one of the earliest models for such predictions, is still one of the most widely used in the literature. However, it does not provide quantitative information on arrangements of fillers inside a polymer matrix, which is crucial for the definition of suitable filler distributions in barrier materials. Therefore, the channel model was developed in this work, which extends the Nielsen model by determining the relative distances between the fillers in regular filler arrangements in polymer matrices. This allows us to relate the permeation properties of filled polymer membranes to the geometric properties of the filler arrangement in simulations and experimental measurements. Simulations with geometries defined according to the channel model showed good agreement with the predictions of the Nielsen model. This demonstrated that the channel model can be a valuable tool for predicting at least mean geometric distances in studied polymer membranes. The validity range of the channel model was limited to a value range of the filler volume fraction 0.01≤ϕf≤0.5 based on theoretical considerations.