Accounting for dispersion in injectivity decline: travelling wave flow regimes

Abstract

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