An in depth comparison of four permeability models, Palmer and Mansoori (P&M) model, Shi and Durucan (S&D) model, Cui and Bustin (C&B) model and the improved P&M model, developed under uniaxial strain conditions prevailing in coalbed reservoirs, was carried out focusing on the relative influence of the matrix shrinkage term over the compaction term in each model. The ratio of the coefficients of the two terms is shown to have a direct impact on the magnitude of permeability rebound pressure, which is a key parameter controlling the modelled response of coalbed permeability to reservoir drawdown. P&M model and C&B model are found to yield essentially the same permeability rebound pressure, which is significantly lower than that given by S&D model. Cleat porosity change in P&M model has been shown to be controlled by the effective mean stress, indicating that it is essentially a mean stress model (as C&B model). With the introduction of an empirical parameter g (<0.3) in the model equations to suppress the pressure-dependent effect on permeability, the improved P&M model gives rise to a permeability rebound pressure much larger than the original model does. The performances of the three models are evaluated with reference to a set of recently published horizontal stress and permeability data measured under uniaxial strain conditions to simulate field conditions. The same set of data has been successfully matched using S&D model in an earlier study by the authors. The modelling results in this study show that both C&B and P&M models fail to capture the overall rising trend in the measured permeability, subject to the constraint of the horizontal stress variation recorded under uniaxial strain conditions. This may be attributed to the fact that the total horizontal stress varied with the pore pressure under the uniaxial strain conditions, whereas the total vertical stress remained unchanged during the test. The inability of C&B and P&M models to describe the laboratory permeability data obtained under simulated field conditions, in contrast to the performance of S&D model, suggests that the permeability response of coalbed reservoirs to pore pressure depletion is controlled predominantly by the effective horizontal stress, rather than the effective mean stress. (C) 2014 Elsevier B.V. All rights reserved.