# Measurement and Modelling of Moisture Distribution and Water Binding Energy of Dredged Sludge

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{1}H nuclear magnetic resonance spectroscopy (LF-NMR) has been widely used to measure water distribution in solid–liquid mixtures, including food [11], sewage sludge [12,13], and petroleum sludge [14,15]. Compared with other water measurement methods, LF-NMR is nondestructive, rapid, and accurate. The bound level of water is the key factor influencing the relaxation time of hydrogen protons. LF-NMR retrieves the state of water through detecting the variations of

^{1}H relaxation time. According to the Carr–Purcell–Meiboom–Gill sequences, the spin–spin relaxation time (T

_{2}) is largely determined by the specific surface area of the tested sample [16,17]. A smaller pore structure results in a larger specific surface area and stronger restraints of water mobility, which would subsequently shorten T

_{2}measured by LF-NMR. Thereby, LF-NMR can be applied to characterize the degree to which water is bound within a solid and the moisture distribution in mixtures. The application of LF-NMR has rarely been reported for the measurements of water content and moisture distribution in dredged sludge.

## 2. Water Binding Energy Calculation Model

_{1}; (2) the energy required for water molecules to overcome the intermolecular physical interactions Q

_{2}; (3) the energy required for droplets to overcome the capillary force Q

_{3}; (4) latent heat of water phase change Q

_{4}. The sediments of an urban watercourse are rich with microorganisms and inorganic salts [22]. Q

_{1}comes from the powerful chemical bounds mainly found in intracellular bound water and crystal water of inorganic salts. These bounds are difficult to break during low-temperature thermal drying [23]. Therefore, to simplify the model, Q

_{1}is excluded from the calculation. Q

_{2}is generated from intermolecular interactions, including Keesom force, Debye force, London dispersion force and repulsive force, and it is one or two orders of magnitude smaller than chemical bonding energy, reaching thousands of kJ/mol [24,25]. According to quantum-mechanical theories, molecular attraction is inversely proportional to the sixth power of the intermolecular distance, while molecular repulsive force is inversely proportional to the 12th power of the distance between molecules [26]. Then, the energy for overcoming these forces between separate molecules can be described by Lennard-Jones’ (L-J) potential energy function, which is an approximate approach commonly used in thermodynamics and dynamics simulation to compute the potential energy of intermolecular interactions [27,28,29]. For the present study, the Lennard-Jones 10-4-3 function [30], as represented in Equation (1), is implemented to calculate Q

_{2}, which simultaneously considers molecular attraction and repulsive force:

_{2}represents the energy required by water molecules to overcome the physical binding force from particle surface; ρ

_{s}represents the solid number density (the number of the solid particles per unit of volume); ∇ is the distance between the lattice planes, and z is the vertical distance between the interacting molecules. The model assumes that water molecules are attached on the surface of particles layer-by-layer. For each additional layer, the increment of z-value equals the radius of the water molecule. ε represents the minimum potential energy, and σ is the distance when the potential energy equals zero.

_{3}is a function of relative saturated vapor pressure, as given by Equation (3):

_{1}are the surface tension of liquid, curvature radius of the capillary, and specific volume of liquid, respectively.

_{3}is obtained as below:

_{2}and Q

_{3}, while the total energy consumption of water evaporation during thermal drying can be obtained by summing all mentioned energy:

_{2}+ Q

_{3}+ Q

_{4}

## 3. Materials and Methods

#### 3.1. Sample Preparation and Characterization

#### 3.2. LF-NMR Analysis

#### 3.3. TG-DTA Analysis

## 4. Results and Discussion

#### 4.1. Water Distribution in Dredged Sludge Detected by LF-NMR

_{2}) distribution curves of the samples, with T

_{2}marked in the corresponding peaks. There are three relatively independent peaks for each sample. We defined three kinds of water according to these detected peaks: free water, capillary water, and bound water. Based on our previous work [31], there is a linear relationship between water content and the peak area of T

_{2}curve, and thus each peak could be transferred into the mass of water.

_{2}of free water is probably distributed between 40 ms and 81 ms [31]. As shown in Figure 1, the content of free water in the LS sludge is relatively high, and this part of the water can be easily removed by traditional mechanical dehydration. With the T

_{2}shortening, the mobility of water gradually decreases. The second peak presents a relatively wide distribution of T

_{2}, which demonstrates the existence of multi-scale micropores in the LS sludge. The amplitude of the third peak is small, illustrating the low mass content of bound water in the sample. Though the content of bound water is low, rare drying technologies can exceed the threshold energy of dewatering.

_{2}at peak value than LS. This can be explained by chemically conditioning, as the sludge particles flocculated and formed a smaller size capillary-channel, and consequently enhanced the constraints of the droplets. The third peak is about as large as that of the LS sample; however, it presents a stronger interaction between the bound water and the sludge.

#### 4.2. Model Analysis

^{−3}[36]. The model assumes that water molecules are attached on the skeleton particles layer-by-layer, and the film thickness of each layer equals the radius of the water molecule. Thus, Q

_{2}under different water content can be accumulated on the basis of the number of attached water layers.

^{−2}N/m; υ

_{1}= 10

^{−3}m

^{3}/kg. With this model, it is assumed that a dried particle and a particle with water are both cube structures. Selecting a certain diameter from the range of size distribution of the sample as, d

_{i}the average center distance between two particles is obtained by introducing Equation (11). Assuming that the water surface in capillary is hemispherical and the curvature radius of the capillary δ is equal to the radius of capillary. The clear distance of capillary radius is correspondingly achieved by deducting ${d}_{i}$, as shown in Equation (12),

_{i}is the volume of a single dried particle; m and ρ represent the mass and true density of dried sludge, respectively. Therefore, Q

_{3}with different water content can be obtained from Equation (5).

#### 4.3. Comparison of Model Calculation and Experimental Result

#### 4.4. Gradient of Energy Consumption Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Amar, M.; Benzerzour, M.; Kleib, J.; Abriak, N.-E. From dredged sediment to supplementary cementitious material: Characterization, treatment, and reuse. Int. J. Sediment Res.
**2021**, 36, 92–109. [Google Scholar] [CrossRef] - Oh, H.; Lee, J.; Banthia, N.; Talukdar, S. An Experimental Study of the Physicochemical Properties of a Cement Matrix Containing Dredged Materials. Mater. Sci. Appl.
**2011**, 2, 847–857. [Google Scholar] [CrossRef] [Green Version] - Bhairappanavar, S.; Liu, R.; Coffman, R. Beneficial Uses of Dredged Material in Green Infrastructure and Living Architecture to Improve Resilience of Lake Erie. Infrastructures
**2018**, 3, 42. [Google Scholar] [CrossRef] [Green Version] - Tri, D.Q.; Kandasamy, J.; Don, N.C. Quantitative Assessment of the Environmental Impacts of Dredging and Dumping Activities at Sea. Appl. Sci.
**2019**, 9, 1703. [Google Scholar] [CrossRef] [Green Version] - Zonta, R.; Cassin, D.; Pini, R.; Dominik, J. Substantial Decrease in Contaminant Concentrations in the Sediments of the Venice (Italy) Canal Network in the Last Two Decades—Implications for Sediment Management. Water
**2020**, 12, 1965. [Google Scholar] [CrossRef] - Cappuyns, V.; Deweirt, V.; Rousseau, S. Dredged sediments as a resource for brick production: Possibilities and barriers from a consumers’ perspective. Waste Manag.
**2015**, 38, 372–380. [Google Scholar] [CrossRef] - Bagarani, M.; De Vincenzo, A.; Ievoli, C.; Molino, B. The Reuse of Sediments Dredged from Artificial Reservoirs for Beach Nourishment: Technical and Economic Feasibility. Sustainability
**2020**, 12, 6820. [Google Scholar] [CrossRef] - Molino, B.; Bufalo, G.; De Vincenzo, A.; Ambrosone, L. Semiempirical Model for Assessing Dewatering Process by Flocculation of Dredged Sludge in an Artificial Reservoir. Appl. Sci.
**2020**, 10, 3051. [Google Scholar] [CrossRef] - Song, Z.; Zhang, W.; Gao, H.; Wang, D. Comprehensive assessment of flocculation conditioning of dredged sediment using organic polymers: Dredged sediment dewaterability and release of pollutants. Sci. Total Environ.
**2020**, 739, 139884. [Google Scholar] [CrossRef] - Wang, J.; Huang, G.; Fu, H.; Cai, Y.; Hu, X.; Lou, X.; Jin, Y.; Hai, J.; Ni, J.; Zou, J. Vacuum preloading combined with multiple-flocculant treatment for dredged fill improvement. Eng. Geol.
**2019**, 259, 105194. [Google Scholar] [CrossRef] - Pan, L.; Xing, J.; Luo, X.; Li, Y.; Sun, D.; Zhai, Y.; Yang, K.; Chen, Z. Influence of Electron Beam Irradiation on the Moisture and Properties of Freshly Harvested and Sun-Dried Rice. Foods
**2020**, 9, 1139. [Google Scholar] [CrossRef] - Zhao, C.; Zheng, H.; Feng, L.; Wang, Y.; Liu, Y.; Liu, B.; Djibrine, B.Z. Improvement of Sludge Dewaterability by Ultrasound-Initiated Cationic Polyacrylamide with Microblock Structure: The Role of Surface-Active Monomers. Materials
**2017**, 10, 282. [Google Scholar] [CrossRef] - Mao, H.; Chi, Y.; Wang, F.; Mao, F.; Liang, F.; Lu, S.; Cen, K. Effect of Ultrasonic Pre-treatment on Dewaterability and Moisture Distribution in Sewage Sludge. Waste Biomass Valoriz.
**2018**, 9, 247–253. [Google Scholar] [CrossRef] - Jin, Y.; Zheng, X.; Chi, Y.; Ni, M. Rapid, Accurate Measurement of the Oil and Water Contents of Oil Sludge Using Low-Field NMR. Ind. Eng. Chem. Res.
**2013**, 52, 2228–2233. [Google Scholar] [CrossRef] - Zheng, X.; Jin, Y.; Chi, Y.; Ni, M. Simultaneous Determination of Water and Oil in Oil Sludge by Low-Field 1H NMR Relaxometry and Chemometrics. Energy Fuels
**2013**, 27, 5787–5792. [Google Scholar] [CrossRef] - Meiboom, S.; Gill, D.R. Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Rev. Sci. Instrum.
**1958**, 29, 688–691. [Google Scholar] [CrossRef] [Green Version] - Yao, W.; She, A.; Yang, P. 1H-NMR relaxation and state evolvement of evaporable water in cement pastes. J. Chin. Ceram. Soc.
**2009**, 37, 1. [Google Scholar] - Karr, C. Analytical Methods for Coal and Coal Products: Volume II; Academic press: Cambridge, MA, USA, 2013; Volume 2. [Google Scholar]
- Chen, G.W.; Hung, W.T.; Chang, I.L.; Lee, S.F.; Lee, D.J. Continuous Classification of Moisture Content in Waste Activated Sludges. J. Environ. Eng.
**1997**, 123, 253–258. [Google Scholar] [CrossRef] - Slimanou, H.; Bouguermouh, K.; Bouzidi, N. Synthesis of geopolymers based on dredged sediment in calcined and uncalcined states. Mater. Lett.
**2019**, 251, 188–191. [Google Scholar] [CrossRef] - Li, Y.; Yang, F.; Miao, S.; Wang, D.; Li, Z.; Yuan, X.; Yuan, L.; Liu, Q. Achieved deep-dewatering of dredged sediments by Fe(II) activating persulfate pretreatment: Filtrating performance and mechanistic insights. Chem. Eng. J.
**2021**, 405, 126847. [Google Scholar] [CrossRef] - Zhang, X.; Gu, Q.; Long, X.-E.; Li, Z.-L.; Liu, D.-X.; Ye, D.-H.; He, C.-Q.; Liu, X.-Y.; Väänänen, K.; Chen, X. Anthropogenic activities drive the microbial community and its function in urban river sediment. J. Soils Sediments
**2015**, 16, 716–725. [Google Scholar] [CrossRef] - Huang, P.L. A Review of: “Modern Drying Technology, Second Enhanced Edition Editors: Yongkang Pan, Xizhong Wang and Xiangdong Liu”. Dry. Technol.
**2007**, 25, 2057–2058. [Google Scholar] [CrossRef] - Yariv, S.; Cross, H. Physical Chemistry of Surfaces. Geochem. Colloid Syst.
**1979**, 150, 93–155. [Google Scholar] [CrossRef] - Prausnitz, J.M.; Lichtenthaler, R.N.; De Azevedo, E.G. Molecular Thermodynamics of Fluid-Phase Equilibria; Pearson Education: Hoboken, NJ, USA, 1998. [Google Scholar]
- Hirschfelder, J.O.; Curtiss, C.F.; Bird, R.B.; Mayer, M.G. Molecular Theory of Gases and Liquids; Wiley: New York, NY, USA, 1964; Volume 165. [Google Scholar]
- Ansari, R.; Kazemi, E. Detailed investigation on single water molecule entering carbon nanotubes. Appl. Math. Mech.
**2012**, 33, 1287–1300. [Google Scholar] [CrossRef] - Lin, D.T.W.; Chen, C.-K. A molecular dynamics simulation of TIP4P and Lennard-Jones water in nanochannel. Acta Mech.
**2004**, 173, 181–194. [Google Scholar] [CrossRef] - Da Silva, L.B. Structural and dynamical properties of water confined in carbon nanotubes. J. Nanostruct. Chem.
**2014**, 4, 1–5. [Google Scholar] [CrossRef] [Green Version] - Fort, T.; Putnam, F. The interaction of gases with solid surfaces. J. Colloid Interface Sci.
**1976**, 57, 190–191. [Google Scholar] [CrossRef] - Mao, H.; Wang, F.; Mao, F.; Chi, Y.; Lu, S.; Cen, K. Measurement of water content and moisture distribution in sludge by1H nuclear magnetic resonance spectroscopy. Dry. Technol.
**2016**, 34, 267–274. [Google Scholar] [CrossRef] - Ahunbay, M.G. Monte Carlo simulation of water adsorption in hydrophobic MFI zeolites with hydrophilic sites. Langmuir
**2011**, 27, 4986–4993. [Google Scholar] [CrossRef] - Prost, R.; Koutit, T.; Benchara, A.; Huard, E. State and location of water adsorbed on clay minerals: Consequences of the hydration and swelling-shrinkage phenomena. Clays Clay Min.
**1998**, 46, 117–131. [Google Scholar] [CrossRef] - Steele, W.A. The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci.
**1973**, 36, 317–352. [Google Scholar] [CrossRef] - Smith, L.S.; Lee, L.L. The Lennard-Jones 9:3 adsorptive system I: The Percus–Yevick and hypernetted chain theories and their modifications. J. Chem. Phys.
**1979**, 71, 4085. [Google Scholar] [CrossRef] - Huang, Q.; Zhou, G.; Yu, B.; Wang, S.; Chi, Y.; Yan, J. Quantitative model for predicting the desorption energy of water contained in lignite. Fuel
**2015**, 157, 202–207. [Google Scholar] [CrossRef] - Bushuev, Y.G.; Sastre, G. Atomistic Simulation of Water Intrusion—Extrusion in ITQ-4 (IFR) and ZSM-22 (TON): The Role of Silanol Defects. J. Phys. Chem. C
**2011**, 115, 21942–21953. [Google Scholar] [CrossRef] - Fitts, T.G.; Brown, K. Stress-induced smectite dehydration: Ramifications for patterns of freshening and fluid expulsion in the N. Barbados accretionary wedge. Earth Planet. Sci. Lett.
**1999**, 172, 179–197. [Google Scholar] [CrossRef] - Allardice, D.; Evans, D. The-brown coal/water system: Part 2. Water sorption isotherms on bed-moist Yallourn brown coal. Fuel
**1971**, 50, 236–253. [Google Scholar] [CrossRef]

**Figure 1.**Relaxation time (T

_{2}) distribution curves of Lishui sludge (LS) and Hangzhou sludge (HZ) samples.

Density g/cm ^{3} | Specific Surface Area m ^{2}/g | Particle Size Distribution nm | |
---|---|---|---|

HZ sample | 1.42 | 32.5 | 25~130 |

LS sample | 1.58 | 25.4 | 18~85 |

Free Water % | Capillary Water % | Bound Water % | |
---|---|---|---|

HZ sample | 82.0~82.4% | 33.6~82.0 | 0~33.6% |

LS sample | 84.9~93.5% | 43.3~84.9 | 0~43.3% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 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**

Mao, F.; Zhao, Y.; Zhang, Y.; Chen, Z.; Yin, L.
Measurement and Modelling of Moisture Distribution and Water Binding Energy of Dredged Sludge. *Water* **2020**, *12*, 3395.
https://doi.org/10.3390/w12123395

**AMA Style**

Mao F, Zhao Y, Zhang Y, Chen Z, Yin L.
Measurement and Modelling of Moisture Distribution and Water Binding Energy of Dredged Sludge. *Water*. 2020; 12(12):3395.
https://doi.org/10.3390/w12123395

**Chicago/Turabian Style**

Mao, Feiyan, Yingjie Zhao, Yiping Zhang, Zhou Chen, and Lu Yin.
2020. "Measurement and Modelling of Moisture Distribution and Water Binding Energy of Dredged Sludge" *Water* 12, no. 12: 3395.
https://doi.org/10.3390/w12123395