Problem 1: 40 Points Fluid exchange between a three-dimensional matrix and surrounding fractures for pressure diffusion is often modelled using spherical block approximation. Use a non coupled approach when fracture acts as a boundary condition to the matrix block and a) write the governing equation along with appropriate initial and boundary conditions for a spherical matrix block at initial pressure, pi, exposed to a constant ux, gm 1)) convert the governing equation along with appropriate initial and boundary conditions to dimensionless form, and c) derive an expression for dimensionless shape factor, 0L2, in Laplace domain