The Use of the Effective-Medium Theory and a 3D Network Model To Predict Matrix Damage in Sandstone Formations

Abstract

The size-matching technique and the effective-medium theory (EMT) were used to develop a model to predict the in-depth plugging of a formation core as a function of the solids particle size in the injection water. The pore-size distributions were determined with capillary pressure data (measured by the apparatus for pore examination (APEX)) rather than with the conventional capillary pressure curve. The morphology of the pore space was represented by a random 3D disordered network of pore bodies interconnected by pore throats. The absolute air permeability of the network was calculated with the EMT. The calculated permeabilities for Berea and Bentheim sandstones were compared with those calculated by the traditional bundle-of-capillary-tubes model and laboratory-measured values. In this paper a simple method is presented that relates the ratio of plugged to unplugged pore throats to the loss in permeability for a given matching pore-particle-size criterion. With the three particle-pore-pluging criteria, the reduction in permeability caused by matrix plugging was closely predicted as a function of the median diameter of the injected solids for a given concentration.