Injection of CO2 and coal seam gas production induce coal swelling/shrinkage. Laboratory tests indicate that coal swelling may go through several stages from localized swelling at fracture surfaces to bulk rock swelling. The coal Langmuir swelling strain constant normally ranges from 0 to 0.04. This study provides a process-based coal swelling model that covers the whole swelling procedure. We account for three swelling strains, videlicet, the matrix swelling strain, fracture swelling strain, and bulk rock swelling strain. Dynamic partial separation coefficients are employed to quantify the contributions of the matrix swelling strain to bulk swelling and the fracture (cleat) aperture reduction, bridge the gaps between localized swelling and bulk swelling, and link the three types of strains. This model is inserted into a permeability model and verified against permeability measurement and rock swelling data. The three samples used for verification are bituminous coals from the Illinois Basin (depth of ~ 200 m) in the US and Henan Province in China (depth of ~ 310 m). In essence, the swelling model is also applicable to other coal types with a linear relationship between the matrix swelling strain and adsorbed gas content. By matching with long-term permeability measurement data, multiple permeability evolution stages are observed due to the swelling transition. Sensitivity analyses show that the matrix block size, matrix swelling properties, and diffusivity control the duration, occurrence, and magnitude of matrix swelling's contribution to local and bulk swelling during swelling transition, while rock bridge swelling properties have a marginal influence on coal swelling.