Table 1
Summary of the analytical solution obtained for suspended, attached, and strained nanoparticle concentration (Wang et al., 2016a).
| Zone | Domain | Suspended particulates concentration (C NP) | Attached particulates concentration (σ NP) | Strained particulates concentration (S NP) |
|---|---|---|---|---|
| I |
|
0 | 0 | 0 |
| II |
|
|
|
|
| III |
|
|
|
|
| IV |
|
|
|
|
| V |
|
0 |
|
|
Here, x
D
is the dimensionless distance, t
D
is the dimensionless time, t
Dc is the dimensionless time or injected pore volume at maximum nanoparticles concentration, 
is the dimensionless time or injected pore volume start post-flush without nanoparticles, 
is the volumetric concentration of injected nanoparticles, 
is the straining filtration coefficient, 
is the adsorption filtration coefficient, ϕ is the porosity of sand pack, L is the length of the sand pack, 
is the maximum retention concentration of nanoparticles with maximum nanoparticle adsorption, 
is the maximum retention concentration of nanoparticles at the phase of post-flush. Figure 3 shows the division of the different zones on the distance-time diagram.