We study mass transfer to a flowing fluid in porous media from stationary sources of various geometries. Effects of the porous medium and the source geometry are explored using a modification of the local mass transfer coefficients. We develop exact solutions for mass transfer in flow over a flat plate and asymptotic and numerical solutions in flow over sources of various geometries, including self-similar surfaces, such as a Koch surface and a percolation cluster. For the latter, as well as for sources distributed at the pore-network scale, a pore-network representation of the porous medium is used. The dependence of the overall mass transfer rates on various parameters, and particularly on the flow rate, is analyzed. The analysis allows for macroscopic coefficients in equations, which lump the process in terms of an effective, first-order reaction, to be interpreted in terms of the microstructure of the porous medium and the source geometry. ¿ 1999 American Geophysical Union