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Based on the theories of mass conservation and coalbed methane (CBM) adsorption/desorption, this paper first establishes a novel reservoir pressure model for CBM production, following which, the CBM concentration and production models are also proposed. Then, these models are programmed and solved by means of the finite element method. Taking the Hunchun CBM field in Jilin province, China, as an example, the reservoir pressure, gas concentration, and production characteristics under different hydraulic fracture forms are simulated and investigated. In conclusion, the reservoir pressure decreases very rapidly in a small region near the fracture tip, which we called the "reservoir pressure singularity". The existence of a hydraulic fracture greatly reduces the reservoir pressure in the process of CBM exploitation. The permeability sensitivity coefficient of reservoir pressure, Rpk, is defined to quantitatively describe the influence of coal seam permeability on the evolution of reservoir pressure. Rpk decreases logarithmically as the distance from the CBM extraction well increases. The reservoir pressure and CBM recovery rate characteristics in the presence of multiple hydraulic fractures are also investigated. We believe these results could contribute to the design of hydraulic fracturing wells and the evaluation of gas production in a CBM reservoir. [ABSTRACT FROM AUTHOR]