Integral Method Solution for Diffusion into a Spherical Block

Abstract An approximate analytical solution is derived for the problem of a Newtonian fluid infiltrating into a porous spherical block. The fluid in the block is initially at a constant pressure p i , and the pressure at the outer boundary is held at a constant value p o . Using the simple assumption of linear pressure profiles, the instantaneous and cumulative fluxes into the sphere are predicted with surprisingly high accuracy. The solution applies to all other physical processes governed by the same equation, such as heat conduction and chemical diffusion. The solution should be very useful for incorporation into double-porosity models for fractured reservoirs and aquifers.