# Sorption Dynamics of Uranium onto Anion Exchangers

^{*}

## Abstract

**:**

## 1. Introduction

_{2}

^{2+}) which predominates at acid conditions. At neutral pH conditions, the speciation depends on the counter ions and their concentrations. Under typical groundwater conditions, the predominant uranium species are UO

_{2}(CO

_{3})

_{2}

^{2−}und UO

_{2}(CO

_{3})

_{3}

^{4−}[8,9,10]. Other literature sources mention the existence of non-negligible uranium complexes with different alkaline earth metals such as calcium and magnesium [11,12,13,14,15].

_{2}(CO

_{3})

_{2}

^{2−}and the tetravalent UO

_{2}(CO

_{3})

_{3}

^{4−}complexes mainly exist. With increasing pH, the tetravalent complex becomes predominant.

_{2}(CO

_{3})

_{2}

^{2−}and especially the tetravalent complex UO

_{2}(CO

_{3})

_{3}

^{4−}show a very high affinity to anion exchangers because of their high negative charges of −2 and −4, respectively. In the case of the existence of the neutral calcium uranyl carbonate complex Ca

_{2}UO

_{2}(CO

_{3})

_{3}, no ion exchange can take place. However, according to the literature, at neutral pH conditions a divalent anionic complex of uranium and calcium (CaUO

_{2}(CO

_{3})

_{3}

^{2−}) might exist as well [11,12,14,15,19].

## 2. Materials and Methods

#### 2.1. Exchangers

#### 2.2. Experimental Methods

#### 2.2.1. Column Experiments

_{2}(NO

_{3})

_{2}) from Merck. This is about 10 to 20 times higher than the highest naturally occurring uranium concentrations in German groundwater. This high concentration was chosen to avoid operation periods longer than several months.

#### 2.2.2. Regeneration

#### 2.3. Modelling

_{max}and K

_{L}), and kinetic parameter (D

_{S}and β

_{L}) on the calculated breakthrough curves were checked.

## 3. Theoretical Description of Sorption Dynamics

_{stoich}. Deduced from a simple mass balance, t

_{stoich}can be calculated as shown in Equation (1) [25].

_{0}(in g per g) denotes the equilibrium loading corresponding to the initial concentration c

_{0}, (in g/L), ρ

_{F}is the bulk density (in g/L), V

_{F}is the filter volume (in m

^{3}), and Q is the axial water flow (in m

^{3}/h).

_{L}and q

_{max}) and of sorption kinetics (β

_{L}and D

_{S}). For uranium adsorption to anion exchangers, these parameters have been determined in previous works [19,30].

^{*}= concentration at the particle surface (g/L), D

_{S}= effective particle diffusion coefficient (m²/s), d

_{P}= particle diameter (m), q loading (g/g), q

_{max}= Langmuir isotherm constant (g/g) (corresponds to the maximum loading), K

_{L}= Langmuir isotherm constant (L/g), r = radial intra-particle coordinate (m), t = time (s), z = axial filter coordinate (m), β

_{L}= liquid phase mass transfer coefficient (m/s), ε = bulk porosity.

- No loading on the initial adsorbent:$$q\left(t=0,z,r\right)=0$$
- Symmetry of the loading at the centre of the particle:$${\left[\frac{\partial q\left(t,z,r\right)}{\partial r}\right]}_{r=0}=0$$
- Film mass flow is equal to the mass flow at the exterior of the particle:$${\left[\frac{\partial q\left(t,z,r\right)}{\partial r}\right]}_{r={d}_{P}/2}=\frac{{\beta}_{L}}{{\rho}_{P}{D}_{S}}\left(c\left(t,z\right)-{c}^{*}\left(t,z\right)\right)$$
- Increase of the mean solid phase loading is given by the mass flow through the film:$$\frac{\partial \overline{q}\left(t,z\right)}{\partial t}=\frac{6{\beta}_{L}}{{\rho}_{P}{d}_{P}}\left(c\left(t,z\right)-{c}^{*}\left(t,z\right)\right)=\frac{\partial}{\partial t}\left[\frac{24}{{{d}_{P}}^{3}}\underset{0}{\overset{\raisebox{1ex}{${d}_{P}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{{\displaystyle \int}}}q\left(t,z,r\right){r}_{2}dr\right]$$
- Initial and boundary conditions for the concentration for the filter mass balance:$$c\left(t=0,z\right)=0$$$$c\left(t,z=0\right)={c}_{0}$$

^{*}(Equation (13)), and the Biot number Bi (Equation (14)).

_{0}= initial concentration (g/L), C

_{F}= capacity factor (see Equation (7)), D

_{S}= effective particle diffusion coefficient (m²/s), d

_{P}= particle diameter (m), q

_{0}= loading in equilibrium to c

_{0}= (g/g), β

_{L}liquid phase mass transfer coefficient (m/s), ε = bulk porosity, ρ

_{F}filter density (g/L), ρ

_{P}= sorbent density (g/L), τ = effective residence time (s).

_{F}used in Equation (6) is defined by Equation (15).

^{*}compares the rate of film diffusion to the convective transport through the filter. Thus, high Stanton numbers indicate that the film diffusion is not the transport controlling process.

## 4. Results

#### 4.1. Filter Dynamics

#### 4.1.1. Breakthrough Behaviour of Uranium Species in Bench Scale Experiments

#### 4.1.2. Breakthrough Behaviour of Uranium Species in Pilot Scale Experiments

_{2}(CO

_{3})

^{2−}complex exists. Thus, the lower pH value at waterworks I will lead to a further negative sorption effect. On the other hand, the less functional amine groups of the weak basic anion exchangers are protonated at higher pH values in the neutral pH range. This leads to a smaller sorption capacity above a specific pH. However, experimental investigations show that lower pH values have a positive effect on uranium adsorption [19]. For strong and weak basic anion exchangers, an increasing concentration of bicarbonate also affects the sorption of uranium species positively [19], but these positive conditions seem to be only of minor relevance in waterworks I.

#### 4.1.3. Impact of Various Parameters on the Breakthrough Behaviour

_{S}), liquid phase mass transfer coefficient (β

_{L}), and particle diameter (d

_{P})) were considered based on the data available for the exchanger Amberlite IRA 67 and the results obtained from its application in bench scale column experiments.

_{S}. Both doubling and dividing the initial value of 10

^{−12}m

^{2}/s in half obviously has no effect on the uranium breakthrough. Though the surface diffusion modulus Ed increases with increasing diffusion coefficients, the intra-particle diffusion has no impact on the total uranium transport as long as the film diffusion is rate controlling (Bi << 1). Thus, the particle diffusion coefficient has no effect on the breakthrough of uranium.

_{L}is demonstrated in Figure 7. Doubling this parameter from 1.6 × 10

^{−5}m/s to 3.2 × 10

^{−5}m/s leads to a noticeable delay in uranium breakthrough and the rise in concentration is much steeper. A uranium concentration of 10 µg/L is reached 5000 BV later (37,000 BV instead of 32,000 BV) when β

_{L}is doubled. On the other hand, reducing β

_{L}to 8 × 10

^{−6}m/s leads to a dramatic deterioration of the filter efficiency with a much earlier increase of uranium concentrations at the effluent. A uranium concentration of 10 µg/L is obtained 10,000 BV earlier (at 22,000 BV). This effect becomes clear when considering the dimensionless numbers. As long as the film diffusion is rate controlling (Bi > 1), an increasing modified Stanton number St* sharpens the breakthrough curve and retards the start of the breakthrough.

_{L}is increasing with an increasing filter velocity, thin filters with small filter diameters are more appropriate for an efficient uranium adsorption than filters with larger filter diameters (assuming constant filter volumes). The reduction of the filter diameter is of course limited by the head loss which increases with increasing filter velocity. For example, reducing the filter diameter from 1 m to 0.7 m will lead to a doubling of the filter velocity and, thus, to an approximately 30% increase of the liquid phase mass transfer coefficient β

_{L}(using the relation of Gnielinski to calculate β

_{L}[35], the formula of Worch to compute the liquid phase diffusion coefficient [36], and assuming a constant empty bed contact time).

_{L}. Using the correlation of Wilson [37] to adjust β

_{L}, leads to the both dotted lines in Figure 8. Due to an increasing mass transfer coefficient for smaller particles, uranium breakthrough is further delayed (dotted grey line). When considering larger particles, the breakthrough performance gets even worse because of a decrease of the mass transfer coefficient (dotted black line).

#### 4.1.4. Theoretical Scale-Up and Consequences for Waterworks

_{L}and the Biot number Bi increase accordingly. Therefore, just by increasing the dimension of the filter, the sorption performance improves with a later and steeper breakthrough (as is demonstrated in Figure 7).

_{0}will lead to a reduction of the ratio c

_{0}/q

_{0}(in the case of a favourable equilibrium). This ratio has an effect on the Biot number (Equation (8)) and leads to a decrease of the Bi number. The interfering impact of both effects, the increase of the filter dimension, and the decrease of the initial concentration, is a nearly constant Biot number. Thus, under real full scale conditions, film diffusion will also be the rate controlling mechanism.

^{*}increases in a full scale plant by approximately a factor of three (from 6 to 19) due to a larger liquid phase mass transfer coefficient. Thus, the amount of uranium transported through the liquid film to the resin particles increases in relation to the part which is convectively transported through the column. Hence, the shape of the breakthrough curve becomes steeper and the increase of the uranium concentration at the filter effluent can be expected later.

_{0}/q

_{0}. Therefore, more uranium can be transported via particle diffusion than by the convective transport through the column. However, because the film diffusion is rate controlling, this variation should not result in an observable effect.

#### 4.2. Regeneration

#### 4.2.1. Batch Experiments

_{2}(CO

_{3})

_{3}

^{4−}complex on the other hand. Regarding the acrylic exchanger Amberlite IRA 67, uranium seems to be fixed to the resin so strongly by the change in speciation that no deprotonation of the functional groups can happen.

_{2}

^{2+}which does not attach to the positively charged functional ion exchanger groups. A desorption of uranium is the consequence.

#### 4.2.2. Column Experiments

_{2}(CO

_{3})

_{3}

^{2−}is desorbed in the same manner as UO

_{2}(CO

_{3})

_{2}

^{2−}and does not remain on the ion exchanger to a large extend).

## 5. Discussion

_{F}, e.g., by matching the filter geometry. Thus, for technical filters, smaller column diameters are more appropriate for an efficient uranium adsorption and longer times of operation.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Nolan, J.; Weber, K.A. Natural uranium contamination in major U.S. aquifers linked to nitrate. Environ. Sci. Technol. Lett.
**2015**, 2, 215–220. [Google Scholar] [CrossRef] - Gómez, P.; Garralón, A.; Buil, B.; Turrero, M.J.; Sánchez, L.; de la Cruz, B. Modeling of geochemical processes related to uranium mobilization in the groundwater of a uranium mine. Sci. Total Environ.
**2006**, 366, 295–309. [Google Scholar] [CrossRef] [PubMed] - Birke, M.; Rauch, U.; Lorenz, H. Uranium in stream and mineral water of the Federal Republic of Germany. Environ. Geochem. Health
**2009**, 31, 693–706. [Google Scholar] [CrossRef] [PubMed] - Liesch, T.; Hinrichsen, S.; Goldscheider, N. Uranium in groundwater—Fertilizers versus geogenic sources. Sci. Total Environ.
**2015**, 536, 981–995. [Google Scholar] [CrossRef] [PubMed] - United States Environmental Protection Agency (US-EPA). National Primary Drinking Water Regulations; Radionuclides; Environmental Protection Agency: Washington, DC, USA, 2000.
- World Health Organization (WHO). Guidelines for Drinking-Water Quality, 1st Addendum to 3rd ed.; World Health Organization: Geneva, Switzerland, 2006. [Google Scholar]
- Verordnung über die Qualität von Wasser für den Menschlichen Gebrauch (Trinkwasserverordnung—TrinkwV) (Ordinance on the Quality of Water Intended for Human Consumption) vom 21. Mai 2001. Neufassung vom 10. März 2016. Available online: http://www.gesetze-im-internet.de/bundesrecht/trinkwv_2001/gesamt.pdf (accessed on 24 November 2016).
- Hanson, S.W.; Wilson, D.B.; Gunaji, N.N. Removal of Uranium from Drinking Water by Ion Exchange and Chemical Clarification; U.S. Environmental Protection Agency: Washington, DC, USA, 1987.
- Wazne, M.; Korfiatis, G.P.; Meng, X. Carbonate effects on hexavalent uranium adsorption by iron oxyhydroxide. Environ. Sci. Technol.
**2003**, 37, 3619–3624. [Google Scholar] [CrossRef] [PubMed] - Katsoyiannis, I.A. Carbonate effects and pH-dependence of uranium sorption onto bacteriogenic iron oxides: Kinetic and equilibrium studies. J. Hazard. Mater.
**2007**, 139, 31–37. [Google Scholar] [CrossRef] [PubMed] - Kalmykov, S.N.; Choppin, G.R. Mixed Ca
^{2+}/UO_{2}^{2+}/CO_{3}^{2−}complex formation at different ionic strengths. Radiochim. Acta**2000**, 88, 603–606. [Google Scholar] [CrossRef] - Dong, W.; Brooks, S.C. Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg
^{2+}, Ca^{2+}, Sr^{2+}, and Ba^{2+}) using anion exchange method. Environ. Sci. Technol.**2006**, 40, 4689–4695. [Google Scholar] [CrossRef] [PubMed] - Dong, W.; Brooks, S.C. Formation of aqueous MgUO
_{2}(CO_{3})_{3}^{2−}complex and uranium anion exchange mechanism onto an exchange resin. Environ. Sci. Technol.**2008**, 42, 1979–1983. [Google Scholar] [CrossRef] [PubMed] - Kelly, S.D.; Kemner, K.M.; Brooks, S.C.; Fredrickson, J.K.; Carroll, S.L.; Kennedy, D.W.; Zachara, J.M.; Plymale, A.E.; Fendorf, S. Ca-UO
_{2}-CO_{3}complexation—Implications for bioremediation of U(VI). Phys. Scr.**2005**, T115, 915–917. [Google Scholar] [CrossRef] - Kelly, S.D.; Kemner, K.M.; Brooks, S.C. X-ray absorption spectroscopy identifies calcium-uranyl-carbonate complexes at environmental concentrations. Geochim. Cosmochim. Acta
**2007**, 71, 821–834. [Google Scholar] [CrossRef] - Riegel, M.; Höll, W.H. Removal of natural uranium from groundwater by means of weakly basic anion exchanges. In Proceedings of the IEX 2008, Cambridge, UK, 9–11 July 2008; Cox, M., Ed.; Society of Chemical Industry: London, UK, 2008; pp. 331–338. [Google Scholar]
- Riegel, M. Untersuchungen zur Elimination von Natürlichen Uranspezies aus Wässern mit Hilfe Schwach Basischer Anionenaustauscher (Investigation of Elimination of Natural Occurring Uranium Species from Water by Means of Weak Basic Anion Exchangers). Ph.D. Thesis, Technical University of Karlsruhe, Karlsruhe, Germany, 2009. [Google Scholar]
- Langmuir, D. Uranium solution-mineral equilibria at low temperatures with applications to sedimentary ore deposits, Geochim. Cosmochim. Acta
**1978**, 42, 547–569. [Google Scholar] [CrossRef] - Fox, P.M.; Davis, J.A.; Zachara, J.M. The effect of calcium on aqueous uranium(VI) speciation and adsorption to ferrihydrite and quartz. Geochim. Cosmochim. Acta
**2006**, 70, 1379–1387. [Google Scholar] [CrossRef] - Jekel, M.; Bahr, C.; Riegel, M.; Schlitt, V.; Baldauf, G.; Höll, W.H. Uranentfernung in der Trinkwasseraufbereitung (Elimination of uranium during drinking water treatment). Energ. Wasser Prax.
**2010**, 6, 54–59. [Google Scholar] - Umweltbundesamt (Federal Environmental Agency). Liste der Aufbereitungsstoffe und Desinfektionsverfahren gemäß § 11 Trinkwasserverordnung 2001 (List of Preparation Substances and Disinfection Processes in Compliance with § 11 German Drinking Water Ordinance). 12. Änderung, Stand Dezember 2009. Available online: https://www.umweltbundesamt.de/sites/default/files/medien/481/dokumente/17_aenderung_aufbereitungsstoffe_desinfektionsverfahren_11_trinkwv_11_2012.pdf (accessed on 24 November 2016).
- Water Quality–Application of Inductively Coupled Plasma Mass Spectrometry (ICP-MS)—Part 2: Determination of 62 Elements (ISO 17294-2:2003); Beuth: Berlin, Germany, 2003.
- Agarwal, R.P. Difference Equation and Inequalities; Marcel Dekker: New York, NY, USA, 2000. [Google Scholar]
- Bjoerck, A.; Dahlquist, G. Numerical Mathematics and Scientific Computation; Siam: Philadelphia, PA, USA, 1999. [Google Scholar]
- Sontheimer, H.; Crittenden, J.C.; Summers, R.S. Activated Carbon for Water Treatment; DVGW-Forschungsstelle: Karlsruhe, Germany, 1988. [Google Scholar]
- Crittenden, J.C.; Weber, W.J. Predictive model for design of fixed-bed adsorbers: Single-component model verification. J. Environ. Eng. Div.
**1978**, 104, 433–443. [Google Scholar] - Crittenden, J.C.; Wong, B.W.C.; Thacker, W.E.; Snoeyink, V.L.; Hinrichs, R.L. Mathematical model of sequential loading in fixed-bed adsorbers. J. Water Pollut. Control Fed.
**1980**, 52, 2780–2795. [Google Scholar] - Sperlich, A.; Schimmelpfennig, S.; Baumgarten, B.; Genz, A.; Amy, G.; Worch, E.; Jekel, M. Predicting anion breakthrough in granular ferric hydroxide (GFH) adsorption filters. Water Res.
**2008**, 42, 2073–2082. [Google Scholar] [CrossRef] [PubMed] - Zhang, Q.; Crittenden, J.; Hristovski, K.; Hand, D.; Westerhoff, P. User-oriented batch reactor solutions to the homogeneous surface diffusion model for different activated carbon dosages. Water Res.
**2009**, 43, 1859–1866. [Google Scholar] [CrossRef] [PubMed] - Riegel, M.; Tokmachev, M.; Höll, W.H. Kinetics of uranium sorption onto weakly basic anion exchangers. React. Funct. Polym.
**2008**, 68, 1072–1080. [Google Scholar] [CrossRef] - Grossmann, J.J.; Adamson, A.W. The diffusion process for organolite exchangers. J. Phys. Chem.
**1952**, 56, 97–100. [Google Scholar] [CrossRef] - Helfferich, F. Kinetik des Ionenaustauschs. Angew. Chem.
**1956**, 68, 693–698. [Google Scholar] [CrossRef] - Schlögl, R.; Helfferich, F. Comment on the significance of diffusion potentials in ion exchange kinetics. J. Chem. Phys.
**1957**, 26, 5–7. [Google Scholar] [CrossRef] - Helfferich, F.; Plesset, M.S. Ion exchange kinetics. A nonlinear diffusion problem. J. Chem. Phys.
**1958**, 28, 418–424. [Google Scholar] [CrossRef] - Gnielinski, V. Gleichungen zur Berechnung des Wärme- und Stoffaustausches in durchströmten Kugelschüttungen bei mittleren und großen Peclet-Zahlen. Verfahrenstechnik
**1978**, 12, 363–366. [Google Scholar] - Worch, E. Eine neue Gleichung zur Berechnung von Diffusionskoeffizienten gelöster Stoffe. Vom Wasser
**1993**, 81, 289–297. [Google Scholar] - Wilson, E.J.; Geankoplis, C.J. Liquid mass transfer at very low Reynolds numbers in packed beds. Ind. Eng. Chem. Fundam.
**1966**, 5, 9–14. [Google Scholar] [CrossRef]

**Figure 1.**Calculated uranium speciation, c(U) = 1000 µg/L, total inorganic carbon = 48 mg/L, using the MINEQL© software [17].

**Figure 2.**Experimental and calculated breakthrough curves for Amberlite IRA 67, modelling parameters: q

_{max}= 296 µmol/g, K

_{L}= 9.2 L/mg (equilibrium parameter at pH 7.3), D

_{S}= 10

^{−12}m

^{2}/s, β

_{L}= 1.6×10

^{−5}m/s, d

_{P}= 0.625 mm, ρ

_{F}= 0.68 kg/L, ε = 0.36.

**Figure 3.**Experimental and calculated breakthrough curves for Lewatit MP 62, modelling parameters: q

_{max}= 120 µmol/g, K

_{L}= 4.3 L/mg (≙ equilibrium parameter at pH 7.3 [19]), D

_{S}= 2 × 10

^{−13}m

^{2}/s, β

_{L}= 1.6 × 10

^{−5}m/s, d

_{P}= 0.47 mm, ρ

_{F}= 0.65 kg/L, ε = 0.37.

**Figure 6.**Theoretical impact of the solid phase diffusion coefficient D

_{S}on uranium breakthrough.

**Figure 7.**Theoretical impact of the liquid phase mass transfer coefficient β

_{L}on uranium breakthrough.

**Figure 9.**Level of uranium regeneration during a two-step process, V/m = 200 mL/g (each step); arrows indicate the order of regenerant application.

Amberlite IRA 67 | Lewatit MP 62 | Lewatit S 6368 | ||
---|---|---|---|---|

WBA | WBA | SBA | ||

Matrix ^{1} | Acrylic acid divinylbenzene copolymer | Styrene divinylbenzene copolymer | Styrene divinylbenzene copolymer | |

Functional groups ^{1} | Tertiary and secondary amine | Tertiary amine | Quaternary amine | |

Effective size d_{P} ^{1} | mm | 0.47 | 0.5–0.75 | 0.62 |

Particle density ρ_{P} ^{2} | g/mL | 1.06 | 1.03 | - |

Bulk density ρ_{F} ^{2} | g/mL | 0.68 | 0.65 | - |

Bulk porosity ε ^{2} | - | 0.36 | 0.37 | - |

^{1}Manufacturers’ data,

^{2}Experimentally determined.

Waterworks I | Waterworks II | ||
---|---|---|---|

pH | - | 6.9 | 7.4 |

Ca^{2+} | mg/L | 79 | 48 |

SO_{4}^{2−} | mg/L | 92 | 38 |

HCO_{3}^{−} | mg/L | 350 | 221 |

Cl^{−} | mg/L | 65 | 19 |

DOC | mg/L | 1.8 | 0.6 |

Bench Scale | Full Scale | ||
---|---|---|---|

Filter geometry | |||

Filter diameter | d_{F} | 2 cm | 1 m |

Filter height | h_{F} | 8.5 cm | 1.5 m |

Filter volume | V_{F} | 27 mL | 1.2 m^{3} |

Ion exchanger | |||

Resin amount | m | 18 g | 800 kg |

Kinetics | |||

Solid diffusion coefficient | D_{S} | 10^{–12} m^{2}/s | 10^{–12} m^{2}/s |

Liquid mass transfer coefficient | β_{L} | 1.5 10^{–5} m/s | 5 10^{–5} m/s |

Raw water | |||

Initial concentration | c_{0} | 1000 µg/L | 60 µg/L |

Loading in equilibrium with c_{0} | q_{0} | 267 µmol/L | 42 µmol/L |

Filter conditions | |||

Flux | Q | 20 BV/h | 20 BV/h |

Q | 0.5 L/h | 24 m^{3}/h | |

Filter velocity | V_{F} | 1.7 m/h | 30 m/h |

Stoichiometric throughput | V_{stoich} | 43,000 BV | 113,000 BV |

Time of stoichiometric breakthrough | t_{stoich} | 90 d | 235 d |

Surface diffusion modulus | Ed | 86 | 226 |

Modified Stanton number | St* | 6 | 19 |

Biot number | Bi | 0.07 | 0.08 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Riegel, M.; Schlitt, V.
Sorption Dynamics of Uranium onto Anion Exchangers. *Water* **2017**, *9*, 268.
https://doi.org/10.3390/w9040268

**AMA Style**

Riegel M, Schlitt V.
Sorption Dynamics of Uranium onto Anion Exchangers. *Water*. 2017; 9(4):268.
https://doi.org/10.3390/w9040268

**Chicago/Turabian Style**

Riegel, Marcel, and Volker Schlitt.
2017. "Sorption Dynamics of Uranium onto Anion Exchangers" *Water* 9, no. 4: 268.
https://doi.org/10.3390/w9040268