Coupled Model of Deep-bed-filtration and Cake Filtration in Porous Media for Gravel Pack Modelling

Gravel packs are widely used as a sand control method. However, clogging and cake growth during the exploration may cause significant decrease in well productivity. The article deals with the problem of mathematical modelling of suspension filtration in porous media of gravel packs. The coupling of deep-bed filtration and cake filtration is proposed. Mathematical model is based on mass balance equations and Darcy’s law. Particle size distribution is also taken into consideration by including multiple solid components into the equations. Much attention is given to the description of cake behavior using averaging procedure. Numerical solution is found using finite-difference method. The good agreement between presented mathematical model and experimental data is reached. The dependence between the permeability reducing rate and sand concentration passed through porous media is investigated. In case of using small gravel particles filter’s permeability strongly reduces due to cake growth. The permeability’s dynamics for different gravel size/formation particles’ size ratio was investigated. Overall, proposed coupled mathematical model of gravel pack allows to determine gravel sizing criteria more accurately than empirical methods.