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Exact solutions for transport of distributed colloids in porous media
We study 1D transport of mobilized particles, detached from the solid matrix, in porous media (so-called fines migration). Three types of colloidal-suspension flow models are considered: (i) averaged model for multicomponent colloids with distributed properties; (ii) flow of binary colloids with interacting particles; (iii) discrete system for multicomponent low-concentration colloid. These models account for distributed particle properties and finite particle sizes (reflected by accessibility and fractional flow functions). Those features are widely spread in nature and industry and highly affect suspension-colloidal-nano transport in porous reservoirs. The analytical models for transport of uniform particles and negligible particle sizes have been obtained in the previous studies, but the exact solutions for 1D flow accounting for either of the above features are not available. For the first time, we derived exact solutions for the three 1D colloidal flows, which account for migration of polydisperse suspensions with finite particle sizes. A unified approach for solving different reactive-colloidal transport models is based on single physical process: in all models, particle-free water is pumped into the inlet of a porous medium, initially filled with a suspension or colloid. The front of clean water, displacing mobilized particles, moves at a variable speed. Ahead of the front the solution to the problem depends only on time, behind the front it depends only on the spatial coordinate. The exact solutions are obtained in closed form for fines migration process. Analytical formulae for the water front are derived by the method of characteristics. The asymptotical expressions for the curved water front are constructed, and the limit concentrations of suspended and retained particles are evaluated. The obtained solutions can be used for interpretation of the laboratory coreflood data, their matching and determining the model parameters, and in 3D streamline reservoir simulation of the pilot tests on colloidal-suspension-nano transport in ground water.