The environment of coal reservoirs is complex and variable,
with
various factors, not independent, but interlocking and coupled. However,
their coupling effects have rarely been considered in previous theoretical
studies. In addition, when a fractal theory was applied to analyze
the permeability of coal, the linkage between fractal dimensions and
the pore radius under external factors has usually been ignored. In
this study, two parameters, pore compressibility and dynamic water
saturation, were introduced to quantitatively represent the internal
interactions between stress and water. Based on the results, dynamic
fractal dimensions under the coupling actions of stress and water
were obtained by considering variation in the pore radius and the
assignment status of gas and water, following which an apparent permeability
model of coal, with dynamic fractal dimensions, was established. The
newly developed model was verified by reference to published experimental
data. The results showed that stress dominated changes in the fractal
dimension for pore-size distribution under the coupling actions of
stress and water; however, changes in the fractal dimension for tortuosity
was dominated, in turn, by stress and water. Subsequently, it was
found that the fractal apparent permeability model could match the
experimental data well. It revealed that the newly developed model
could predict the evolution of coal permeability under dynamic changes
in stress and water. Further, under the coupling actions of stress
and water, the apparent permeability of coal possessed a positive
correlation with the fractal dimension for pore-size distribution
or water-dominated fractal dimension for tortuosity, while it was
negatively correlated with the critical capillary radius or stress-dominated
fractal dimension for tortuosity. In addition, the evolution of the
apparent permeability was consistent with specific fractal dimensions
and dynamic fractal dimensions, but the evolution of the slippage
factor revealed an opposite result. Consequently, this initiates a
new analytical perspective into investigating change mechanisms relating
to coal permeability.