  Several natural and industrial processes involve the extraction or retention
of a solute by a fluid invading a network of channels. Examples include aquifer
contamination, chemical filtration, and coffee extraction. We propose a
continuum equation to model these processes, parametrized by the P\'eclet
number and the rate of mass transfer between the solid and the fluid. We study
the time dependence of the extracted mass for different values of the parameter
space. The continuum description is validated by combining extraction
experiments with coffee and computational fluid dynamics. An analytical
solution is derived for the limit of slow mass transfer, which is corroborated
by numerical simulations.
