A theoretical study is presented of liquid imbibition and solute absorption from a fracture network into a collection of matrix blocks of varying sizes and shapes. An individual irregularly-shaped matrix block can be modeled with reasonable accuracy using the results for a spherical matrix block, by defining an effective radius a˜=3V/A, where V is the volume of the block and A is its surface area. In the early-time regime, a collection of spherical blocks of different sizes can be replaced by an equivalent spherical block with a radius of aeq=⟨a-1⟩-1, where the average is taken on a volumetrically-weighted basis. In the long-time limit, where no equivalent radius can rigorously be defined, asymptotic expressions are derived for the cumulative uptake as a function of the mean and the standard deviation of the radius distribution function, for both normal and lognormal radius distributions. ¿ American Geophysical Union 1995