# Removal of Cylindrospermopsin by Adsorption on Granular Activated Carbon, Selection of Carbons and Estimated Fixed-Bed Breakthrough

^{*}

## Abstract

**:**

_{f}) of 9 × ${10}^{-6}$ m/s and surface diffusion coefficient (D

_{s}) of 3 × 10

^{−16}m

^{2}/s. It was observed that the increase in EBCT promotes a reduction in the carbon use rate. The best carbon use rate found was 0.43 kg/m

^{3}for a EBCT of 10 min and breakthrough time of 183.6 h.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Water

#### 2.2. Characteristics of Activated Carbons and Adsorption Equilibrium Tests

_{0.95}). Thus, the volume of mesopores was obtained by subtracting the volume of micropores from V

_{0.95}.

_{pcz}), according to the methodology proposed by Moreno-Castilla et al., [44].

_{2}. The suspensions remained for another 12 h in a vacuum desiccator (Nalgon, Itupeva, Brazil) under a negative pressure of 600 mmHg to eliminate the air present in the carbon interstices [20].

#### 2.3. Short-Bed Adsorber Test (SBA)

#### 2.4. Modeling the Adsorption Process

- 1-
- The dispersion of the pollutant through the bed occurs according to a plug-flow system
- 2-
- The applied hydraulic load is constant.
- 3-
- Internal diffusion is the predominant mechanism in mass transport and is independent of the pollutant concentration.
- 4-
- The diffusion in the film is carried out by a linear driving force.
- 5-
- The adsorbent particles are spherical and homogeneous.

**Table 2.**Equation for the Homogeneous Surface Diffusion Model. Adapted from Roy et al., [51].

Equation | Role |
---|---|

$\mathsf{\nu}{\left[\frac{\mathrm{dC}}{\mathrm{dZ}}\right]}_{\mathrm{t}}+{\left[\frac{\mathrm{dC}}{\mathrm{dZ}}\right]}_{\mathrm{z}}+{\mathsf{\rho}}_{\mathrm{p}}\left(\frac{1-\mathsf{\epsilon}}{\mathsf{\epsilon}}\right){\left[\frac{\mathrm{dq}}{\mathrm{dt}}\right]}_{\mathrm{z}}=0$ Where: $\mathrm{C}$: Adsorbate concentration in the liquid phase at time t (${\mathrm{ML}}^{-3})$ ${\mathrm{C}}_{\mathrm{o}}$: Initial concentration (in the influent) of adsorbate in the liquid phase (${\mathrm{ML}}^{-3})$ t: Time (T) Z: Bed height (L) $\mathrm{q}:$ Adsortvate concentration in the solid phase (${\mathrm{MM}}^{-1})$ ${\mathsf{\rho}}_{\mathrm{p}}$: Apparent density (${\mathrm{ML}}^{-3})$ $\mathsf{\epsilon}$: Bed porosity (dimensionless) Initial conditions and limits: $\mathrm{t}=0,0\le \mathrm{Z}\mathrm{L},\mathrm{C}=0$ $\mathrm{t}>0,\mathrm{Z}=0,\mathrm{C}={\mathrm{C}}_{\mathrm{o}}$ | Fixed bed mass balance considering the plug-flow reactor hydraulic model |

${\mathsf{\rho}}_{\mathrm{p}}{\left[\frac{\mathrm{dq}}{\mathrm{dt}}\right]}_{\mathrm{z}}=\frac{3{\mathrm{K}}_{\mathrm{f}}}{{\mathrm{R}}_{\mathrm{p}}}\left(\mathrm{C}-{\mathrm{C}}_{\mathrm{s}}\right)$ Where: ${\mathrm{R}}_{\mathrm{p}}:$ Adsorbent particle radius (L) ${\mathrm{K}}_{\mathrm{f}}$: Film diffusion coefficient (${\mathrm{LT}}^{-1})$ ${\mathrm{C}}_{\mathrm{s}}:$ Adsorbate concentration in the liquid phase at the solid-liquid interface (${\mathrm{ML}}^{-3})$ | Linear driving force |

$\frac{\mathrm{dq}}{\mathrm{dt}}=\frac{\mathrm{Ds}}{{\mathrm{r}}^{2}}\frac{\mathrm{d}}{\mathrm{dr}}\left(\mathrm{r}\xb2\frac{\mathrm{dq}}{\mathrm{dr}}\right)$ Where: $\mathrm{Ds}$: Surface diffusion coefficient ($\mathrm{L}\xb2{\mathrm{T}}^{-1})$ $\mathrm{r}:$ Radial coordinate (L) | Diffusion equation for a spherical particles |

$\mathrm{q}\left(\mathrm{r},0\right)=0$ | Initial condition |

$\frac{\mathrm{dq}}{\mathrm{dr}}=0\mathrm{for}\mathrm{r}=0$ | Boundary condition for the center of the spherical particle |

${\mathsf{\rho}}_{\mathrm{p}}\mathrm{Ds}\frac{\mathrm{dq}}{\mathrm{dr}}={\mathrm{K}}_{\mathrm{f}}\left(\mathrm{C}-{\mathrm{C}}_{\mathrm{s}}\right)$ | Boundary condition for continuity of flux at r = ${\mathrm{R}}_{\mathrm{p}}$ |

_{f}(film mass transfer) and D

_{s}(surface diffusion).

_{f}and D

_{s}coefficients showing the best representation of the breakthrough curve in the SBA tests were used in the HSDM model to simulate the behavior of a full-scale fixed bed adsorbent column applying different empty bed contact times.

## 3. Results and Discussion

#### 3.1. Characteristics of Activated Carbons

_{2}adsorption/desorption isotherms obtained from the textural analysis of activated carbons.

#### 3.2. Adsorption Tests to Define the Equilibrium Time

_{0}) as a function of time for bituminous and wood carbon, respectively.

#### 3.3. Adsorption Equilibrium Assays

^{2}values greater than 0.94, for the adjustment by both linear and non-linear regression. The excellent experimental data fit the isothermal models were also evidenced by the low estimated normalized standard deviation (∆q).

^{2}= 0.978, indicating that CYN adsorption occurs in multilayers in adsorption sites with different adsorption energies [56].

^{2}values of 0.9754 and 0.9252, obtained by linear and non-linear regression, respectively. The best fit of the experimental data to the Langmuir model allows inferring that in wood carbon, the adsorption of CYN tends to occur in a monolayer in adsorption sites with equivalent energy and absence of interaction between the adsorbed molecules [57].

_{L}, and 3.667 µg/mg and 3.8610 µg/mg for q

_{max}.

_{max}value of 3.6670 µg of CYN adsorbed per mg of carbon.

^{2}= 0.977. The satisfactory fit of the isotherm to this model corroborates the adsorption of CYN in this carbon occurs in multilayers.

^{2}values were similar for the adjustment by non-linear regression.

Material | Area BET (m^{2}/g) | Conditions | K_{F} (µg/mg)(L/µg)^{1/n} | 1/n | M_{o} (mg) | References |
---|---|---|---|---|---|---|

Carbon | 1208 | Raw Water; pH = 7.9; Co = 37.4 μg/L | 0.17 | 0.02 | 100 | [55] |

Wood | 519 | Raw Water; pH = 7.9; Co = 37.4 μg/L | 0.13 | 0.05 | 130.77 | [55] |

Carbon Pre-Load | 1057 | Ultrapure Water; pH = 6.6; Co = 100 μg/L | 0.12 | 0.69 | 141.67 | [60] |

Carbon | 1057 | Ultrapure Water; pH = 6,6; Co = 100 μg/L | 1.76 | 0.33 | 9.66 | [60] |

Wood | 1813 | Ultrapure Water; pH = 6.6; Co = 100 μg/L | 0.21 | 0.68 | 80.95 | [60] |

Coconut | 1568 | Ultrapure Water; pH = 6.6; Co = 100 μg/L | 1.34 | 0.38 | 12.69 | [60] |

Bitumen | 819 | Ultrafiltered Water; pH = 6.5; Co = 102.23 μg/L | 0.99 | 0.2 | 17.11 | Present study |

Wood | 726 | Ultrafiltered Water; pH = 6.5; Co = 89.24 μg/L | 1.24 | 0.29 | 13.76 | Present study |

Material | Area BET (m^{2}/g) | Conditions | q_{max} (μg/mg) | KL (L/μg) | RL Factor | M_{o} (mg) | References |
---|---|---|---|---|---|---|---|

Wast tyre | Uninformed | Ultrapure Water—pH = 3; Co = 65 μg/L | 0.11 | 10.10 | 0.0015 | 169.85 | [61] |

Bitumen | 819 | Ultrafiltered Water; pH = 6.5; Co = 102.23 μg/L | 2.30 | 0.25 | 0.0371 | 36.40 | Present study |

Wood | 726 | Ultrafiltered Water; pH = 6.5; Co = 89.24 μg/L | 3.67 | 0.28 | 0.0386 | 21.25 | Present study |

_{o}: Mass of carbon required to achieve Ce = 1 μg/L considering: Co = 35 μg/L and the volume of water = 0.5 L.

_{f}parameter, was a carbon-based adsorbent [60]. However, the same adsorbent presented the lowest CYN adsorption capacity when exposed to water treated by sedimentation before the adsorption process (Pre-Loading). The reduced adsorption capacity is likely associated with the organic matter present in the preloading carbon that may have directly occupied the adsorption sites during the preloading process [60].

_{f}coefficients and lower carbon mass, allows a residual concentration of CYN in the treated water of 1 μg/L.

#### 3.4. SBA Tests

_{0}) obtained in the SBA tests, a simulation of the adsorbing column of GAC in operation was performed using the HSDM model with the aid of the FAST 2.1 software [52].

- adsorption coefficients of Langmuir isotherm (qmax and KL), obtained from the fitting of experimental data to the isotherm model;
- the average influent concentration of CYN and the mass of GAC, obtained using the SBA tests.

_{f}(film diffusion coefficient) and D

_{s}(surface diffusion coefficient) were obtained by fitting the experimental data to the HSDM model using the least-squares method. The average value of the CYN remaining fraction in the effluent of the SBA column—C/C

_{0}) fitted satisfactorily to the HSDM model with a coefficient of determination (R

^{2}) of 0.89. Figure 10 displays the CYN breakthrough curve obtained from the simulation accomplished with the HSDM model.

^{2}/s e ${\mathrm{K}}_{\mathrm{f}}$ = 9 × ${10}^{-6}$ m/s). Then simulations were performed keeping the value of ${\mathrm{D}}_{\mathrm{s}}$ = 3 × ${10}^{-16}$ m

^{2}/s and changing ${\mathrm{K}}_{\mathrm{f}}$ to values 50% higher and lower than the best fit value of this parameter. Later, HSDM model simulated changing the ${\mathrm{D}}_{\mathrm{s}}$ to values 50% higher and lower in relation to the best fit value of ${\mathrm{D}}_{\mathrm{s}}$ keeping the value of ${\mathrm{K}}_{\mathrm{f}}$ = 9 × ${10}^{-6}$ m/s. Figure 11 and Figure 12 show the results of HSDM model simulations.

_{f}value reduces the breakthrough time by 33%. On the other hand, increasing K

_{f}by 50% results in an increase in breakthrough time of 11%.

_{s}, a 50% reduction of this coefficient to the value fitted to the model (Figure 12) reduced the breakthrough time by 49%. In contrast, a 50% increase in the coefficient promoted a 45% increase in the breakthrough time, evidencing that the coefficient D

_{s}had a more significant influence on the breakthrough curve’s behavior.

_{f}values changes seem to influence only the initial stages of adsorbing column operation. On the other hand, changes in the D

_{s}coefficient tend to influence the behavior of the breakthrough curve throughout the entire operating time, corroborating the study by Cook and Newcombe [62], which consider D

_{s}the main fitting parameter of the HSDM model. However, for the analysis of the initial stages of the breakthrough curve, it is important to accurately determine the two mass transfer coefficients since both influenced on the initial stages of the breakthrough curve.

_{0}) in the effluent was higher than 0.1. The authors explained this behavior considering that at the beginning of the column operation (C/C

_{0}< 0.1) the mass transfer zones of organic matter and Bisphenol-A overlap, and the carbon adsorption sites are available for both contaminants. Nevertheless, throughout the column operation time, the mass transfer zone of organic matter advances faster than that of Bisphenol-A, with the adsorption sites being occupied by the organic matter, thus preventing the subsequent adsorption of Bisphenol-A.

## 4. Conclusions

^{2}/g) than bituminous carbon, with more microporous structure associated with a larger BET surface area (819 m

^{2}/g).

_{max}= 3.67 µg/mg) than bituminous carbon (q

_{max}= 2.30 µg/mg). The Langmuir, Freundlich and Rendlich-Peterson models accurately described the adsorption of cylindrospermopsin by bituminous carbon. On the other hand, the Langmuir model better represented the adsorption of cyanotoxin by wood carbon with R

^{2}of 0.9754, for the adjustment by linear regression.

^{2}= 0.89) the dynamics of operation of the GAC column in the SBA tests, accurately reproducing the cylindrospermopsin breakthrough curve to the film diffusion coefficient (K

_{f}) of 9 × ${10}^{-6}$ m/s and surface diffusion coefficient (D

_{s)}of 3 × ${10}^{-16}$ m

^{2}/s.

_{f}) tend to influence the initial stages of column operation and that changes in the surface diffusion coefficient (D

_{s}) influence the behavior of the breakthroughcurve throughout the operating time.

^{3}for a EBCT of 10 min and breakthrough time of 183.6 h.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Molecular structure of common cylindrospermopsins. [10].

**Figure 6.**Results of equilibrium time tests performed for Bituminous and Wood GAC. C0 = Initial CYN concentration; C = CYN concentration in water after the contact time; initial pH of the study water = 6.5; Carbon dose = 80 mg/L; Base water (test with Bituminous GAC): pH = 7.5; Turbidity = 0.05 uT; Base water (test with Wood GAC): pH = 7.6; Turbidity = 0.07 uT.

**Figure 7.**CYN removal as a function of the applied carbon concentration in Paranoá lake water matrix (C0—Bituminous Carbon = 102.23 µg/L; C0—Wood Carbon = 89.24 µg/L); initial pH of the study water = 6.5. Base water: pH = 7.7; Turbidity = 0.07 uT.

**Figure 8.**(

**A**) Bituminous GAC, experimental and calculated data, parameters obtained by linear regression; (

**B**) Wood GAC, experimental and calculated data, parameters obtained by linear regression; (

**C**) Bituminous GAC, experimental and calculated data, parameters obtained by non-linear regression; (

**D**) Wood GAC, experimental and calculated data, parameters obtained by non-linear regression.

**Figure 9.**CYN breakthrough curve obtained in SBA tests—Average values of CYN remaining fraction in the effluent. The bars represent the standard deviations of average values.

**Figure 10.**Average CYN remaining fraction (C/C

_{0}) in the effluent from the SBA column and values predicted by the HSDM model. Input parameters used in the model: Mass of GAC = 1.1296 g; Apparent bed density = 0.476 g/cm

^{3}; Grain density = 0.850 g/cm

^{3}; Average particle diameter = 0.855 mm; Initial CYN concentration = 95.5 μg/L; axial velocity = 200 m

^{3}/(m

^{2}.day); Equilibrium coefficients (Langmuir isotherm) q

_{max}= 3670 μg/g, K

_{L}= 0.2791 L/μg; Mass transfer coefficients D

_{s}= 3 × ${10}^{-16}$ m

^{2}/s and K

_{f}= 9 × ${10}^{-6}$m/s.

**Figure 11.**Sensitivity analysis of the model from changes in the value of the mass transfer coefficient, Kf. Input values used in the model: EBCT = 10 min; Apparent bed density = 0.476 g/cm

^{3}; Grain density = 0.850 g/cm

^{3}; Average grain diameter = 0.855 mm; Initial CYN concentration = 100 μg/L; Flow = 700 L/s; Equilibrium coefficients (Langmuir isotherm) q

_{max}= 3670 μg/g, KL = 0.2791 L/μg; Surface diffusion coefficient, ${\mathrm{D}}_{\mathrm{s}}$ = 3 × ${10}^{-16}$ m

^{2}/s.

**Figure 12.**Sensitivity analysis of the model against changes in the values of the mass transfer coefficient, Ds. Input values used in the model: EBCT = 10 min; Apparent bed density = 0.476 g/cm

^{3}; Grain density = 0.850 g/cm

^{3}; Average grain diameter = 0.855 mm; Initial CYN concentration = 100 μg/L; Flow = 700 L/s; Equilibrium coefficients (Langmuir isotherm) q

_{max}= 3670 μg/g, KL = 0.2791 L/μg; Film diffusion coefficient, ${\mathrm{K}}_{\mathrm{f}}$ = 9 × ${10}^{-6}$ m/s.

**Figure 13.**Simulation of the full-scale GAC adsorbent column operating with different EBCTs. Input values used in the model: Apparent bed density = 0.476 g/cm

^{3}; Grain density = 0.850 g/cm

^{3}; Average grain diameter = 0.855 mm; Initial CYN concentration = 100 μg/L; Flow = 700 L/s; Equilibrium coefficients (Langmuir isotherm) q

_{max}= 3670 μg/g, KL = 0.2791 L/μg; Mass transfer coefficients ${\mathrm{D}}_{\mathrm{s}}$ = 3 × ${10}^{-16}$ m

^{2}/s e ${\mathrm{K}}_{\mathrm{f}}$ = 9 × ${10}^{-6}$ m/s.

Conditions | Unit | GAC 18 × 25 Mesh |
---|---|---|

GAC bed height | cm | 3.0 |

Average particle diameter | mm | 0.855 |

Column diameter | mm | 10 |

Axial velocity | m^{3}/(m^{2}.day) | 200 |

Flow Rate | L/h | 0.6542 |

EBCT | s | 13.06 |

Initial CYN concentration | μg/L | 109.25 |

Apparent (bed) density | g/cm^{3} | 0.476 |

Bed porosity | - | 0.44 |

Adsorbent mass | g | 1.1296 |

Feature | Wood Carbon | Bituminous Carbon |
---|---|---|

Material | Wood | Bitumen |

Area BET (m^{2}/g) | 726 | 819 |

Micropore Volume (cm^{3}/g) | 0.375 | 0.423 |

Mesopore Volume (cm^{3}/g) | 0.081 | 0.053 |

V_{0.95} (cm^{3}/g) | 0.456 | 0.476 |

$p{H}_{pzc}$ | 8.61 | 8.49 |

**Table 4.**Isotherm constants for the adsorption of CYN onto Bituminous and Wood carbons using Paranoá lake water as matrix.

Isotherm Models | Equation | Parameters | Bituminous GAC | Wood GAC | ||
---|---|---|---|---|---|---|

Linear | Non-Linear | Linear | Non-Linear | |||

Freundlich | 1/n | 0.1993 | 0.2137 | 0.2905 | 0.3051 | |

${\mathrm{q}}_{\mathrm{e}}={\mathrm{K}}_{\mathrm{F}}{\mathrm{C}}_{\mathrm{e}}{}^{1/\mathrm{n}}$ | K_{F} (µg/mg)(L/µg)^{1/n} | 0.9935 | 0.9364 | 1.2354 | 1.2164 | |

Δq(%) | 3.196 | 4.782 | 19.4598 | 20.3861 | ||

R^{2} | 0.9783 | 0.9506 | 0.7813 | 0.7342 | ||

Langmuir | q_{max} (µg/mg) | 2.3047 | 2.4029 | 3.667 | 3.8610 | |

${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}}}{1+{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}}}$ | K_{L} (L/µg) | 0.2542 | 0.2068 | 0.2791 | 0.2438 | |

RL Factor | 0.0370 | 0.0452 | 0.0386 | 0.0439 | ||

Δq(%) | 5.2325 | 5.9092 | 9.229 | 9.8743 | ||

R^{2} | 0.957 | 0.941 | 0.9754 | 0.8992 | ||

Redlich-Peterson | ${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{K}}_{\mathrm{R}}{\mathrm{C}}_{\mathrm{e}}}{1+{\mathrm{a}}_{\mathrm{R}}{\mathrm{C}}_{\mathrm{e}}{}^{\mathsf{\beta}}}$ | K_{R} (L/mg) | 2.1193 | 0.9411 | ||

a_{R} (L/µg) | 1.7734 | 0.2438 | ||||

β | 0.8425 | 1.0000 | ||||

Δq (%) | 3.0323 | 9.8743 | ||||

R^{2} | 0.9778 | 0.8992 |

_{max}maximum concentration of the adsorbate in the adsorbent per mass of adsorbent when the adsorption sites are saturated with the adsorbate, K

_{L}: Langmuir adsorption constant, RL Factor: dimensionless constant, K

_{F}: Freundlich constant, 1/n: Freundlich adsorption intensity, K

_{R}e a R; Redlich-Peterson isotherm constant, β: exponent of the Redlich-Peterson isotherm.

Empty Bed Contact Times (min) | Carbon Use Rate (Kg/m^{3}) |
---|---|

5.0 | 1.27 |

7.5 | 0.64 |

10.0 | 0.43 |

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**MDPI and ACS Style**

Antonieti, C.C.; Ginoris, Y.P.
Removal of Cylindrospermopsin by Adsorption on Granular Activated Carbon, Selection of Carbons and Estimated Fixed-Bed Breakthrough. *Water* **2022**, *14*, 1630.
https://doi.org/10.3390/w14101630

**AMA Style**

Antonieti CC, Ginoris YP.
Removal of Cylindrospermopsin by Adsorption on Granular Activated Carbon, Selection of Carbons and Estimated Fixed-Bed Breakthrough. *Water*. 2022; 14(10):1630.
https://doi.org/10.3390/w14101630

**Chicago/Turabian Style**

Antonieti, Caio César, and Yovanka Pérez Ginoris.
2022. "Removal of Cylindrospermopsin by Adsorption on Granular Activated Carbon, Selection of Carbons and Estimated Fixed-Bed Breakthrough" *Water* 14, no. 10: 1630.
https://doi.org/10.3390/w14101630