# Improved Delivery of Nanoscale Zero-Valent Iron Particles and Simplified Design Tools for Effective Aquifer Nanoremediation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup and Procedures

^{2}/g and a specific gravity of 1.2 g/cm

^{3}; and (ii) a proprietary polymeric formulation that, upon dilution with water, creates a colloidally stable reactive gel with shear-thinning behavior. To prepare the suspension to be injected, the two components were mixed and diluted with deionized water using a high shear mixer (Ultra Turrax, IKA, Staufen, Germany) to achieve a final iron concentration of 10 g/L and a polymer content of 7.0 g/L. Before injection, the nZVI slurry was finally degassed using a vacuum pump to remove air bubbles.

#### 2.2. Particle Radial Transport Model

- Equation (1) is a modified advection–dispersion equation that describes the particle transport through a porous medium and their deposition due to physical and physicochemical interactions with the solid matrix;
- Within Equation (1), the liquid–solid phase mass exchange term $\frac{\partial \left[{\rho}_{b}{S}_{Fe}\right]}{\partial t}$ can assume different forms according to the particle retention mechanism to be taken into account. A single-site linear irreversible deposition kinetics (Equation (2)) was selected for the interpretation of the nZVI test described in Section 2.1;
- Equation (3) expresses the dependency of the particle-attachment coefficient ${k}_{a}$ on the slurry and aquifer properties, i.e., the water-flow velocity, the suspension viscosity, the aquifer average grain size [25]. The attachment coefficient also depends on the single collector contact efficiency ${\eta}_{0}$ that, in this study, was calculated using the formulation proposed by Messina et al. (2015, ref. [46]). ${\eta}_{0}$ is a theoretical parameter that, under specific assumptions and simplifications (e.g., single spherical collector, infinite fluid domain, uniform flow field), describes the effect of different deposition mechanisms (i.e., gravitational sedimentation, interception, Brownian diffusion) on the particle transport [47,48].

- Equation (4) defines the steady-state flow field resulting from the fluid injection through a single screened well in an infinite, homogeneous and isotropic aquifer system. Under these hypotheses, and assuming negligible influence of the groundwater background velocity on the overall flow field, the Darcy velocity depends only on the injection flow rate and well geometry, and hyperbolically decreases with increasing distance from the injection well. Although previous studies have demonstrated that background flow can have a notable influence on nZVI transport [38,39], in the specific conditions investigated in this study, the assumption of negligible groundwater flow effects can be deemed acceptable. This is due to the fact that the flow field generated by the well during particle injection (with velocities reaching up to 500 m/day) predominates over the natural groundwater velocity, which typically ranges from centimeters to a few meters per day in highly conductive aquifers;
- Equation (5) is a modified Darcy’s law for shear-thinning fluids that expresses the pressure build-up induced by the injection as a function of the porous medium hydraulic conductivity $K$ and fluid viscosity ${\mu}_{m}\left(\dot{{\gamma}_{m}}\right)$.

#### 2.3. Radial Transport Test Interpretation

^{−4}and 6.99 · 10

^{−3}m. A unit-length discharge ${Q}_{s}$ of $1{\mathrm{m}}^{3}/\mathrm{h}/\mathrm{m}$ was applied to reproduce the flow field expected during the experiment. The corresponding steady-state velocity field around the injection well was calculated analytically by the application of Equation (4). For mass transport, a third-type boundary condition was applied by imposing a mass flux of 2.8 · 10

^{−3}kg/s at the domain inlet. A concentration zero-gradient boundary condition was imposed at the outlet. The transport equation system was solved using an implicit finite difference approach with a central-in-space discretization scheme, with a constant time step equal to 2 s.

#### 2.4. Multiparametric Analysis

^{3}of iron slurry from a single well with a six-inch diameter and a 1 m screening length.

^{2}/h and 5 m

^{2}/h for the specific flow rate and from 4 g/l and to 14 g/L for the polymeric stabilizer concentration. Additionally, 2 different aquifer formations were considered (gravelly sand and medium sand) leading to a total of 1800 simulations (i.e., the combination of 30 flow rates, 30 biopolymer concentrations and 2 aquifer formations). The hydrodynamic parameters of each formation are reported in Table 3.

^{2}) is the injected volume per unit length of the screen (and, hence, of the aquifer depth).

^{−2}), $z$ is the injection depth from the ground level (L), ${\rho}_{f}$ is the density of the injected fluid (ML

^{−3}) and $s$ is the depth to water table (L).

## 3. Results

#### 3.1. Slurry Rheology

- the viscosity is in the order of 10
^{4}Pa·s in quasi-static conditions (i.e., at shear rates $\dot{{\gamma}_{m}}={10}^{-3}\xf7{10}^{-2}{\mathrm{s}}^{-1}$), which is optimal to guarantee pre-injection stability of the iron suspensions; - the viscosity decreases to less than 10
^{−3}Pa·s at shear stress values typical of subsurface injections (i.e., at $\dot{{\gamma}_{m}}={10}^{2}\xf7{10}^{3}{\mathrm{s}}^{-1}$), thus allowing the expected pressure build-up to be contained.

^{3}M

^{−1}] and $B=6.3\xb7{10}^{-2}$ [L

^{3}M

^{−1}] are empirical parameters. For a null concentration of ${C}_{P}$, we have $\omega ={\mu}_{w}$ and $n=1$, and the power-law model degenerates into $\mu ={\mu}_{w}$, i.e., the shear-rate independent viscosity of water.

#### 3.2. Radial Transport Experiment

#### 3.3. Predictive Simulations and Implications for Field Applications

_{inj}, whereas the red is associated with high numbers. As expected, an increase of the gel concentration and/or of the injection flow rate results in an increase in both the ROI and the injection pressure (in the graphs color changes from blue to red while moving from bottom to top and from left to right). While the former is desirable, the latter represents an issue as it could lead to porous-medium fracturing due to overpressure, especially at low depths. On the other hand, a slight increase in the injection pressure is also observed when stabilizer concentrations are too low (${C}_{P}<5.0\mathrm{g}/\mathrm{L}$) and specific flow rates (${Q}_{s}<1{\mathrm{m}}^{2}/\mathrm{h}$) are applied (bottom left corner in Figure 4B). In such conditions, the suspension stabilization is less efficient, thus leading to a reduction of the nZVI mobility and to partial porous-medium clogging due to particle accumulation in the vicinity of the injection well. This is more evident in Figure 4D, where the injection pressure is reported as a function of ${Q}_{s}$ for three different gel doses: while the pressure follows the expected monotonic trend for ${C}_{P}$ equal to 8.75 and 10.5 g/L, at the lower value ${C}_{P}=5.0\mathrm{g}/\mathrm{L}$ the pressure shows a minimum at around ${Q}_{s}=1{\mathrm{m}}^{3}/\mathrm{h}/\mathrm{m}$ and increases in smaller and larger flow rate values.

^{3}/h/m and 3.0 m

^{3}/h/m and approaches a constant value for greater values; and (ii) for higher C

_{P}values, indicating a highly stable nZVI suspension, the derivative value decreases, which suggests that under such conditions, increasing the injection flowrate does not significantly enhance particle mobility, as the ROI value remains consistently high across all injection flow rates. Therefore, considering that the use of higher injection flow rates results in increased pressure build-up, particularly for elevated polymer concentrations (Figure 4D), we can deduce that, in practical terms, employing a flow rate greater than 3 m

^{3}/h/m does not offer significant benefits in terms of ROI and may result in excessive pressure and potential fracturing, particularly at shallow depths.

#### 3.4. Multiparametric Graphs

^{2}/h up to a maximum of 5.0 m

^{2}/h). Each group of curves refers to a specific hydrogeological formation. As stated above in Section 2.4, all simulations resulting in injection pressures greater than 10 bar were excluded, as they would lead to fracturing at the typical depth ranges of nZVI injections. This choice leads to the exclusion of low-permeability aquifers, high-injection flowrates, high-stabilizer concentrations, and combinations of them. Conditions leading to intense clogging phenomena (i.e., low stabilizer concentrations and injection flowrates) were not considered either.

#### Example of Use of the nZVI Injection Diagrams

^{3}of a 10 g/L nZVI suspension is injected with the aim of achieving a target concentration of 1 g

_{ZVI}/kg

_{sand}. In such conditions, the maximum injection pressure to be applied to avoid porous medium fracturing, estimated through Equation (16), is equal to 3 bar. Considering a minimum concentration of the stabilizing gel of 5 g/L, which is necessary to ensure the colloidal stability of the suspension, a “safe” operating window can be defined in terms of the injection pressure (${P}_{inj}<3\mathrm{b}\mathrm{a}\mathrm{r}$) and stabilizer concentration (${C}_{P}>5\mathrm{g}/\mathrm{L}$). The adoption of any operating conditions within this region, identified by the white part of the graph in Figure 6, is therefore expected to ensure the nZVI injection to be performed in a permeation regime.

^{3}/h/m, the working point 1 can be identified in Figure 6 by the intersection between the corresponding flowrate curve and the ordinate relative to the chosen concentration (line a in Figure 6). This point corresponds to an expected radius of influence between 1.95 and 2.0 m (as indicated by the relative coloured band) and an injection pressure of 1.45 bar (point b in Figure 6).

- to keep constant the injection flowrate and increase the stabilizer concentration: this can be achieved by going from point 1 to point 2 by moving along the specific flow rate curve of 1 m
^{3}/h/m up to the maximum allowed stabilizer concentration of 10.2 g/L; at this new working point it is possible to increase the radius of influence up to 2.10 m with an injection pressure of 2.9 bar; - to increase both the injection flow rate and the stabilizer concentration: this can be accomplished by imposing ${Q}_{S}$ equal to 5 m
^{2}/h and the injection pressure equal to 2.9 bar, and by deriving from the graph the corresponding maximum dose of stabilizing gel that can be applied to not exceed the pressure threshold (${C}_{P}=9\mathrm{g}/\mathrm{L}$); in these operational conditions, identified by the working point 3, an ROI between 2.05 and 2.10 m is expected. For comparison, if the gel concentration had been increased to 10.2 g/L as in the previous example, the expected injection pressure would have been greater than 4 bar (point 4 in Figure 6), thus leading to potential fracturing of the porous medium.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Glossary

Acronyms | |

DIW | Deionized water |

MNMs | Micro- and Nanoparticle transport, filtration, and clogging Model-Suite |

mZVI | Microscale zero-valent iron |

nZVI | Nanoscale zero-valent iron |

PV | Pore volume |

ROI | Radius of influence |

Latin letters | |

$A$ | Empirical viscosity correction coefficient (m^{3}/kg) |

$a$ | Specific surface area of the porous medium (m^{2}/m^{3}) |

${a}_{0}$ | Initial specific surface area of the porous medium (m^{2}/m^{3}) |

${a}_{Fe}$ | Specific surface area of the iron particles (m^{2}/m^{3}) |

$B$ | Empirical power law correction coefficient (m^{3}/kg) |

$b$ | length of the well screening (m) |

${C}_{a}$ | Empirical attachment coefficient (s^{−1}) |

${C}_{Fe}$ | Iron particles concentration in the mobile phase (kg/m^{3}) |

${C}_{p}$ | Polymeric stabilizer concentration (g/L) |

${D}_{r}$ | Dispersion coefficient (m^{2}/s) |

${d}_{50}$ | Mean diameter of sand grains (m) |

$g$ | Gravity acceleration (m/s^{2}) |

$K$ | Porous medium permeability (m^{2}) |

${K}_{0}$ | Intrinsic permeability (m^{2}) |

${k}_{a}$ | Particle attachment coefficient (s^{−1}) |

$n$ | Power law index (−) |

$P$ | Pressure (Pa) |

${P}_{f}$ | Threshold fracturing pressure (bar) |

$q$ | Darcy velocity (m/s) |

$Q$ | Discharge rate (m^{3}/s) |

${Q}_{s}$ | Unit-length discharge rate (m^{3}/h/m) |

$r$ | Radial distance from well (m) |

${S}_{Fe}$ | Iron particles concentration in the solid phase (−) |

$s$ | Depth to water table (m) |

$t$ | Time (s) |

$z$ | Depth from ground level (m) |

Greek letters | |

$\alpha $ | Shift factor (−) |

$\dot{{\gamma}_{m}}$ | Shear rate (s^{−1}) |

$\epsilon $ | Porosity (−) |

${\epsilon}_{0}$ | Initial porosity (−) |

${\eta}_{0}$ | Single collector contact efficiency (−) |

$\theta $ | Surface increment coefficient (−) |

$\lambda $ | Density reduction coefficient (−) |

${\mu}_{m}$ | Fluid viscosity (Pa·s) |

${\rho}_{b}$ | Density of sand grains (kg/m^{3}) |

${\rho}_{Fe}$ | Density of iron particles (kg/m^{3}) |

${\rho}_{w}$ | Density of injected fluid (kg/m^{3}) |

$\omega $ | Reference viscosity (Pa·s^{n}) |

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**Figure 1.**Experimental setup for nZVI transport tests (modified from Ref. [37]).

**Figure 2.**Rheology of the shear thinning IronGEL at different stabilizer concentrations: (

**A**) viscosity value at different shear rates (10

^{−3}–10

^{4}s

^{−1}) and at different stabilizer concentrations (6.0 g/L, 8.75 g/L and 10.5 g/L); and (

**B**) parameters of the power-law viscosity model obtained at different stabilizer concentrations. Symbols represent the experimental data, whereas black lines indicate the fitting models.

**Figure 3.**Radial injection of nZVI particles: (

**A**) photo of the radial setup at the end of the injection (black plume indicates nZVI particles) and graph of the concentration profiles determined from susceptibility measurements of sand samples collected along three different radial directions (colored dashed lines); and (

**B**) variation over time of the injection pressure measured at the setup inlet. Symbols represent the experimental data, whereas black lines indicate the fitting models.

**Figure 4.**Results of the multiparametric analysis for nZVI injection in a medium sand aquifer: (

**A**) two-dimensional contour graph showing the variation of the radius of influence ($ROI$) as a function of the injection specific flow rate (${Q}_{s}$ ) and stabilizer concentration (${C}_{P}$ ); (

**B**) two-dimensional contour graph showing the variation of the injection pressure (${P}_{inj}$ ) as a function of the injection specific flow rate (${Q}_{s}$ ) and stabilizer concentration (${C}_{P}$ ); (

**C**) partial derivative of the $ROI$ with respect to ${Q}_{s}$ for different ${C}_{P}$ concentrations; and (

**D**) injection pressure as a function of ${Q}_{s}$ for different ${C}_{P}$ concentrations.

**Figure 6.**Example of the application of the multiparametric graphs for the design of an nZVI injection in a medium sand aquifer.

**Table 1.**Model equations for simulation of particle injection and transport in radial coordinates: $\epsilon $ is the porous medium porosity (−), ${C}_{Fe}$ is the nZVI concentration in the mobile phase (kg/m

^{3}), ${\rho}_{b}$ is the bulk density of sand grains (kg/m

^{3}), ${S}_{Fe}$ is the nZVI concentration in the solid phase (−), $t$ is time (s), $r$ is the radial distance from well (m), $q$ is the Darcy velocity (m/s), ${D}_{r}$ is the dispersion coefficient (m

^{2}/s), ${k}_{a}$ is the particle attachment coefficient (s

^{−1}), ${C}_{a}$ is the empirical attachment coefficient (s

^{−1}), ${\eta}_{0}$ is the single collector contact efficiency (−), ${\mu}_{m}$ is the fluid viscosity (Pa·s), $Q$ is the discharge rate (m

^{3}/s), $P$ is the pressure (Pa), $K$ is the porous medium permeability (m

^{2}), $\dot{{\gamma}_{m}}$ is the shear rate (s

^{−1}), $\omega $ is the reference viscosity (Pa·s

^{n}), ${C}_{P}$ is the polymeric stabilizer concentration (g/L), $n$ is the power law index (−), $\alpha $ is the shift factor (−), ${\epsilon}_{0}$ is the initial porosity of the porous medium, ${a}_{0}$ is the initial specific surface area of the porous medium (m

^{2}/m

^{3}), $a$ is the porous medium specific surface area during the deposition process (m

^{2}/m

^{3}), ${K}_{0}$ is the intrinsic permeability (m

^{2}), $\lambda $ is the density reduction coefficient (−) and $\theta $ is the surface increment coefficient (−).

(A) Particle transport | |

Modified advection-dispersion equation | |

$\begin{array}{c}\frac{\partial \left[\epsilon {C}_{Fe}\right]}{\partial t}+\frac{\partial \left[{\rho}_{b}{S}_{Fe}\right]}{\partial t}+\frac{1}{r}\frac{\partial}{\partial r}\left[rq{C}_{Fe}\right]-\frac{1}{r}\frac{\partial}{\partial r}\left[r\epsilon {D}_{r}\frac{\partial {C}_{Fe}}{\partial r}\right]=0\end{array}$ | (1) |

nZVI Deposition kinetics | |

$\frac{\partial \left[{\rho}_{b}{S}_{Fe}\right]}{\partial t}=\epsilon {k}_{a}{C}_{Fe}$ | (2) |

Velocity dependency | |

${k}_{a}\left(q,{\mu}_{m}\right)={C}_{a}\frac{q}{\epsilon {d}_{50,sand}}{\eta}_{0}\left(q,{\mu}_{m}\right)$ | (3) |

(B) Non-Newtonian fluid flow | |

$q=\frac{Q}{2\pi rb}$ | (4) |

$-\frac{\partial P}{\partial r}=\frac{{\mu}_{m}\left(\dot{{\gamma}_{m}}\right)}{K\left({S}_{Fe}\right)}q$ | (5) |

(C) Fluid rheology | |

${\mu}_{m}\left(\dot{{\gamma}_{m}}\right)=\omega \left({C}_{P}\right){\dot{{\gamma}_{m}}}^{\left[n\left({C}_{P}\right)-1\right]}$ | (6) |

$\dot{{\gamma}_{m}}=\alpha \frac{q}{\sqrt{K\epsilon}}$ | (7) |

$\omega \left({C}_{P}\right)={f}_{1}\left({C}_{P}\right)$ | (8) |

$n\left({C}_{P}\right)={f}_{2}\left({C}_{P}\right)$ | (9) |

(D) Porous medium clogging | |

$K\left({S}_{Fe}\right)={\left[\frac{\epsilon \left({S}_{Fe}\right)}{{\epsilon}_{0}}\right]}^{3}{\left[\frac{{a}_{0}}{a\left({S}_{Fe}\right)}\right]}^{2}{K}_{0}$ | (10) |

$\epsilon \left({S}_{Fe}\right)={\epsilon}_{0}-\frac{{\rho}_{b}}{\lambda {\rho}_{Fe}}{S}_{Fe}$ | (11) |

$a\left({S}_{Fe}\right)={a}_{0}+\theta {a}_{Fe}\frac{{\rho}_{b}}{{\rho}_{Fe}}{S}_{Fe}$ | (12) |

Parameter | Values | Units |
---|---|---|

Simulation radius | 0.9 | m |

Cell number | 300 | - |

Time step | 2 | s |

Pore Volume ($PV$) | 8.13 | L |

Injection flow rate ($Q$) | 7 | L/h |

1 | m^{3}/h/m | |

Injected volume | 6.5 | L |

nZVI concentration | 10 | g/L |

Polymer concentration | 7 | g/L |

Sand bulk density (${\rho}_{b}$) | 1.46 · 10^{3} | kg/m^{3} |

Sand specific surface area (${a}_{0}$) | 2.14 · 10^{−4} | m^{2}/m^{3} |

Sand hydraulic conductivity ($K$) ^{1} | 2 · 10^{−4} | m/s |

Sand dispersivity ($\alpha $) ^{1} | 4.2 · 10^{−3} | m |

Sand specific storage (${S}_{s}$) ^{1} | 1 · 10^{−5} | m^{−1} |

Sand porosity ($\epsilon $) | 0.48 | - |

Empirical attachment coefficient (${C}_{a}$) ^{1} | 0.15 | s^{−1} |

Density reduction coefficient ($\lambda $) ^{1} | 0.35 | - |

Surface increment coefficient ($\theta $) ^{1} | 0.85 | - |

Empirical viscosity correction coefficient ($A$) ^{2} | 0.75 | m^{3}/kg |

Empirical power law correction coefficient ($B$) ^{2} | 6.3 · 10^{−2} | m^{3}/kg |

^{1}Obtained by fitting of experimental data of the radial transport experiment.

^{2}Obtained by fitting of rheological experimental data.

**Table 3.**Hydrogeological properties of the aquifer formations considered for the multiparametric analysis: porosity $\epsilon $, hydraulic conductivity $K$, porous medium permeability ${k}_{0}$, bulk density ${\rho}_{b}$, average grain ${d}_{50}$.

Lithology | $\mathit{\epsilon}$ (−) | $\mathit{K}$ (m/s) | ${\mathit{k}}_{0}$ (m^{2}) | ${\mathit{\rho}}_{\mathit{b}}$ (kg/m^{3}) | ${\mathit{d}}_{50}$ (m) | $\mathit{R}\mathit{O}{\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ (m) |
---|---|---|---|---|---|---|

Gravelly sand | 0.25 | 2.5 · 10^{−2} | 2.55 · 10^{−9} | 1961 | 1.58 · 10^{−3} | 2.8 |

Medium sand | 0.27 | 3.0 · 10^{−3} | 3.06 · 10^{−10} | 1736 | 5.48 · 10^{−4} | 2.7 |

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**MDPI and ACS Style**

Bianco, C.; Mondino, F.; Casasso, A.
Improved Delivery of Nanoscale Zero-Valent Iron Particles and Simplified Design Tools for Effective Aquifer Nanoremediation. *Water* **2023**, *15*, 2303.
https://doi.org/10.3390/w15122303

**AMA Style**

Bianco C, Mondino F, Casasso A.
Improved Delivery of Nanoscale Zero-Valent Iron Particles and Simplified Design Tools for Effective Aquifer Nanoremediation. *Water*. 2023; 15(12):2303.
https://doi.org/10.3390/w15122303

**Chicago/Turabian Style**

Bianco, Carlo, Federico Mondino, and Alessandro Casasso.
2023. "Improved Delivery of Nanoscale Zero-Valent Iron Particles and Simplified Design Tools for Effective Aquifer Nanoremediation" *Water* 15, no. 12: 2303.
https://doi.org/10.3390/w15122303