A simple inverse solver for the permeability function for flow of water with particles in porous media
D. Marchesin | Hime, G.
Inverse problem | Formation damage | Deep bed filtration | Convection-reaction equations
In secondary oil recovery, water is injected into the petroleum reservatory to push out the oil. This procedure accounts for most of the oil a reservoir produces. The efficiency of an injection well is measured in terms of its injectivity : the ratio between the injection flow rate and the injection pressure required to maintain this rate. Injection of unclean water causes the well injectivity to decline, because the porous medium acts as a filter to the particles suspended in the water. The capture of suspended particles and consequent loss of permeability characterize a phenomenon called deep bed filtration with formation damage. Retention of particles on the surface of the porous medium, where injection takes place, also causes injectivity decline, and is known as cake formation. Models for deep bed filtration correlate the pressure drop to particle deposition through an empirical permeability reduction function, which represents the macroscopic e#ect of particle retention on the permeability. Di#erent laboratory experiments using rock samples from oil reservoirs can be performed to determine this function. We describe a practical method for recovering the permeability reduction function from experimental data consisting of deposition profiles and pressure measurements during the injection of a suspension of solid particles in a linear rock core.