Abstract
Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For monodispersed suspension and transport in porous media with distributed pore sizes, the microstochastic model allows for upscaling and the exact solution is derived for the obtained macroscale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores.
Highlights
Transport, filtration, and subsequent retention of suspended particles and colloids in porous media are common phenomena in nature and in many industrial applications
The geometric model of porous media for size exclusion suspension-colloidal transport is a bundle of parallel tubes intercalated by the mixing chambers (Figure 1(a))
The system of three governing equations (9)–(11) determines the suspended and retained particle concentration distributions along with the pore concentration distribution, C, Σ, and H. This completes the stochastic model for suspension transport in porous media with distributed pore and particle sizes
Summary
Filtration, and subsequent retention of suspended particles and colloids in porous media are common phenomena in nature and in many industrial applications. Introduction of accessibility and flux reduction factors into the population balance equations describes simultaneous flow of suspension in accessible pores and flow of particlefree water in inaccessible fraction of porous space; it results in the particle speed that differs from the carrier water velocity [32, 38, 39]. An exact solution for long-term deep bed filtration accounting for accessibility and flux reduction factors is derived. The macroscale equations result in nonlinear retained-particle-concentration dependencies for filtration coefficient as well as the accessibility and flux reduction factors, which generalise the classical DBF model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
