Pressure behavior of shale-gas flow in dual porous medium based on fractal theory

The shale gas reservoir is a complex subject with a multiscale nanopore and fracture system, and the gas flow mechanism indicates an evident difference from the conventional gas reservoir. We have introduced fractal theory to characterize the multiscale distribution of pores and fractures, and we have developed a single-phase radial flow model considering nonequilibrium adsorption to describe the flow characteristics in the shale gas reservoir. The numerical solution of the flow model in Euclidean space is obtained by inversing the analytical solution derived in Laplace space through the Stehfest numerical inversion method, and the log-log curve of the dimensionless bottom-hole pressure (BHP) and its derivative versus dimensionless time are analyzed. The log-log curve of the dimensionless BHP has two distinct straight-line segments: The unit slope line reflects early well-storage effect, and the straight line with slope [Formula: see text] reflects reservoir fractal characteristics. The slope of the straight line will become smaller with the increasing fractal dimension. The adsorption coefficient mainly affects the middle and late period of the log-log curves, and more shale gas will desorb from the matrix with the increasing adsorption coefficient. The wellbore storage coefficient has a significant negative correlation with dimensionless BHP especially at the early and transitional stages. The skin factor mainly affects the transition section; a smaller skin factor generally leads to the earlier appearance of the transition section. In addition, a smaller interporosity flow coefficient also results in an earlier transition stage appearance. The lower storativity ratio means a higher dimensionless BHP and an earlier appearance of the transition stage.