Upscaling of Deep Bed Filtration from Core to Near-Welibore Region

摘要

Deep bed filtration of suspensions in porous reservoirs with particle retention by the rock and consequent permeability decrease, takes place during seawater injection and re-injection of produced water in waterflood projects. The invasion of drilling fluid occurs during drilling and affects the return permeability and well index. Deep bed filtration of migrated fines during oil production from heavy-oil, high-clay-contents or low consolidated reservoirs affects well index impairment and fines production. The mathematical-modeling-based reliable prediction of suspension transport in rocks is the essential part of planning and design of the above mentioned technologies. The mathematical models for suspension flow in homogeneous porous media are well developed and validated by numerous laboratory studies. Nevertheless, the above mentioned processes of oil production occur in near-well regions, where the drilling-induced heterogeneity adds to the natural heterogeneity. Yet, the models and laboratory studies for deep bed filtration in micro heterogeneous rocks are poorly available in the literature. In the current paper, the analytical models for colloidal-suspension filtration in composite cores with different types of heterogeneity are derived. The breakthrough concentrations during suspension flow in cores with in-parallel, in-series and combined types of heterogeneity, as obtained from laboratory corefloods and from modeling, are found to be in a good agreement. The analytical formulae for effective filtration coefficient for in-parallel, in-series and combined types of heterogeneity allow proposing the upper and lower estimates of upscaled filtration coefficient for flows in heterogeneous numerical grids with homogeneous cells.