EFFECTIVE BLOCK SIZE FOR IMBIBITION OR ABSORPTION IN DUAL-POROSITY MEDIA

A theoretical study is presented of liquid imbibition and solute absor ption from a fracture network into a collection of matrix blocks of va rying sizes and shapes. An individual irregularly-shaped matrix block can be modeled with reasonable accuracy using the results for a spheri cal matrix block, by defining an effective radius ($) over tilde a = 3 V/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 s izes can be replaced by an equivalent spherical block with a radius of a(eq) = < a(-1) >(-1), where the average is taken on a volumetrically -weighted basis. In the long-time limit, where no equivalent radius ca n rigorously be defined, asymptotic expressions are derived for the cu mulative uptake as a function of the mean and the standard deviation o f the radius distribution function, for both normal and lognormal radi us distributions.