Abstract
During the sea/produced water injection, the permeability decline occurs,resulting in well impairment. Solid and liquid particles dispersed in theinjected water are trapped by the porous medium and may increase significantlythe hydraulic resistance to the flow.
Impairment of injectors by injected/reinjected water of a poor qualitypresent a serious problem for development of oil fields submitted towaterflooding.
Similar problems occur in environmental engineering. Propagation ofbacteria, viruses and contaminants in ground water reservoirs present seriousenvironmental concerns. Design and planning of environmental protectionmeasures should be based on reliable mathematical modelling.
The particle transport in porous media is determined by an advective flow ofcarrier water and by hydrodynamic dispersion in micro heterogeneous media. So,the particle flux is a total of advective and dispersive fluxes. Transport ofparticle suspensions in porous media is described by the advection-diffusionequation and by the equation of particle capture kinetics. The conventionalmodel for deep bed filtration accounts for hydrodynamic particle dispersion inmass balance equation but does not consider impact of dispersive flux inretention kinetics.
In the present study, the model for deep bed filtration accounting forparticle hydrodynamic dispersion in both mass balance and retention kineticsequations is proposed. The travelling wave solution was found for the blockingfunction type of filtration coefficient (that becomes zero after the depositreaches some critical value). This critical value can be determined from the particle breakthrough time.