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Fracture is the flow channel of gas (fluid) body in the exploitation of coalbed methane and other energy sources. It has a great influence on gas (fluid) production and work efficiency. Creep results in the proppant embedded in the coal seam leading to fracture damage, reducing fracture permeability. However, there are few studies on a creep model considering proppant embedding in fractures. In this paper, a creep test of proppant embedment in a fracture of a coal seam is carried out, and a creep model considering the damage to proppant embedment is established. The results show that with an increase of closure stress, the range of strain rate first increases and then decreases, and the mean value of strain rate increases slowly and then increases rapidly when the closure stress levels increases in the stable creep stage. During the creep of coal with a fracture proppant, there is not only the hardening and damage of coal, but there is also the damage to proppant embedding. A creep hardening damage model considering the viscosity damage factor of coal, the stress hardening model, the elastic-plastic damage factor, proppant compaction and the embedded viscosity loss factor is established. The creep hardening damage model can better describe the whole process of decelerating creep, stable creep and accelerating creep of coal with proppant fracture.

Proppant placement concentration, particle size and creep time are important factors that affect the embedment of proppant into coal. Based on multistage creep, an orthogonal test is conducted, and an optimal proppant scheme for different closure stresses obtained. The results show that with increased proppant placement concentration, the number of coal fractures increases and the elastic modulus of the fracture area decreases. As the proppant particle size decreases, the plasticity of fracture-proppant assemblies increases gradually. The yield limit is highest when the particle size is 20/40 mesh. During the proppant embedding process, localization or uneven distribution of proppant results in tensile stress parallel to the fracture surface, which induces tensile fracture in the coal. In the fracture-proppant assembly areas, proppant fractures are severe and yield lines appear. As proppant concentration increases, more energy is accumulated during the proppant compaction stage, resulting in energy release producing craters and crevasses. The energy released also causes increased stress in the proppant-coal contact area and fracturing to the coal mass. The longer the creep time, the weaker the impact and the smaller is fluctuation. Moreover, we find that the orthogonal test can effectively analyze the importance of each parameter. Proppant placement concentration was found to have the highest influence on the process of proppant embedding into coal, followed by particle size and then time. Under experimental conditions, the lowest proppant-embedded value in coal samples was observed with proppant placement concentration of 2 kg m−2 and particle size of 20/40 mesh.