Permeability decline modelling and its applications in drilling formation damage
Elferrerious Alim A Albert, Mohd Hafiidz Hassan, Muhammad Faris Arriffin
Engineering Honours Group Project 2009
University of Adelaide
Permeability impairment is primarily caused by the capture of solid particles from invaded fluid in the porous media. Formation damage by suspended solids invasion occurs as follows: large particles bridge the pore entrances at the formation face and form the external filter cake; the small particles invade the formation, retain in pores and form the internal filter cake.
This study derives a new permeability reduction function caused by the transport of particles inside the formation, taking into account the effects of pore lining retention and pore throat plugging. We generalise the traditional Kozeny-Carman equation by representing the pore bodies with plugged throats by pairs of tubes, which corresponds to flux deviation from the plugged throat to the neighbouring pore. The equation for evolution of the Kozeny-Carman porous network was derived. The model is reduced to non-linear system of three ordinary differential equations. The formulated mathematical models have been implemented into Excel spreadsheet by using the fourth order Runge-Kutta method for numerical integration. The model predicts permeability reduction due to particle retention by size exclusion and by pore lining. The model must be used in prediction of formation damage after drilling.