Modification of the Kozeny-Carman equation to quantify formation damage by fines in clean unconsolidated porous media.

Estimating formation permeability as a function of porosity, grain size, and the quantity and structure of fines is important for increasing hydrocarbon extraction from rock formations. The Kozeny-Carman equation can be used to estimate the permeability of clean unconsolidated media as a function of porosity and grain size, but does not account for the quantity and structure of deposited fines. This study shows how incorporating the volume of fines and a dimensionless bulk factor into the Kozeny-Carman equation can be used to model how the quantity and structure of deposited fines controls permeability. Several experimental studies from the literature are analyzed, representing a variety of fines (type and diameter), porous media, fluids, and flow velocities. These studies indicate that, when other variables are held constant, experiments conducted at higher flow velocity result in less plugging. For each experiment, a dimensionless bulk factor in the Kozeny-Carman equation was fitted, using the root mean square method, to best match the experimental data. Fitted values of the bulk factor were then correlated with the Peclet number to investigate how the structure of fines, quantified by the bulk factor, depends on the characteristics of the porous media, the depositing colloids, and the flow velocity. Larger bulk factors are observed at lower Peclet number, when diffusive transport dominates, which could result from more dendritic deposits. Smaller bulk factors are observed at higher Peclet numbers, when advective transport dominates, which could result from deposits that are more compact. By understanding how the bulk factor, and therefore the extent of permeability reduction, depends on the Peclet number, pumping schemes can be optimized in order to enable more complete hydrocarbon recovery. The primary application of this work is to optimize well flow rates to prevent or manage formation damage (i.e., plugging) resulting from deposition of fines in initially clean unconsolidated porous media.