  Prediction of flow to boreholes or excavations in fractured low-permeability
rocks is important for resource extraction and disposal or sequestration
activities. Analytical solutions for fluid pressure and flowrate, when
available, are powerful, insightful, and efficient tools enabling parameter
estimation and uncertainty quantification. A flexible porous media flow
solution for arbitrary physical dimension is derived and extended to double
porosity for converging radial flow when permeability and porosity decrease
radially as a power law away from a borehole or opening. This distribution can
arise from damage accumulation due to stress relief associated with drilling or
mining. The single-porosity graded conductivity solution was initially found
for heat conduction, the arbitrary dimension flow solution comes from
hydrology, and the solution with both arbitrary dimension and graded
permeability distribution appeared in reservoir engineering. These existing
solutions are here combined and extended to two implementations of the
double-porosity conceptual model, for both a simpler thin-film mass transfer
and more physically realistic diffusion between fracture and matrix. This work
presents a new specified-flowrate solution with wellbore storage for the
simpler double-porosity model, and a new more physically realistic solution for
any wellbore boundary condition. A new closed-form expression is derived for
the matrix diffusion solution (applicable to both homogeneous and graded
problems), improving on previous infinite series expressions.
