A New Cleat Volume Compressibility Determination Method and Corresponding Modification to Coal Permeability Model

Coal is known as a dual-porosity media composed of cleat and matrix pore. Methane can be stored in the cleats or adsorbed on the inner surface of matrix pore. While fluid mobility is mainly controlled by the developed cleat network, methane desorption has a significant effect on cleat deformation. In the process of coalbed methane recovery, both reservoir compaction and matrix shrinkage will occur and have opposite effects on permeability evolutions. A variety of analytical permeability models have been developed to describe the transient characteristics of permeability in coals. In this study, three common permeability models are first revisited and evaluated against the experimental data under uniaxial strain condition. Shi–Durucan (S&D) model demonstrates the best performance among these models. However, constant cleat volume compressibility was used to assume for S&D model, and the generalization of S&D model is significantly limited. For ease of generalization, the relation between cleat volume compressibility and effective horizontal stress is re-derived and introduced to the derivation of permeability model. Since coal reservoirs usually demonstrate strong anisotropy and heterogeneity, the influences of elastic and adsorption properties are further tested to reveal the overall trend of permeability. The results show that S&D model and its modification with the main variable of effective horizontal stress have the best performances in matching the experimental data under uniaxial strain. The relationship between cleat volume compressibility and effective horizontal stress can be better reflected by the inverse proportional function. In addition, the strengths of reservoir compaction effect relative to matrix shrinkage effect in different models only vary with Poisson’s ratio, while their magnitudes are also affected by Young’s modulus. For a typical coal reservoir, the C&B and P&M models will observe a stronger permeability decline at the initial, while the improved P&M model will receive an earlier and more rapid rebound than the S&D and W&Z models.