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A modeling framework for flocculated cohesive sediment transport in the current bottom boundary layer

ADVANCES IN WATER RESOURCES 2025年 195卷

作者： Penaloza-Giraldo, Jorge A. Yue, Liangyi Hsu, Tian-Jian Vowinckel, Bernhard Manning, Andrew Meiburgc, Eckart Oak Ridge Natl Lab Environm Sci Div Oak Ridge TN 37830 USA Oak Ridge Natl Lab Climate Change Sci Inst Oak Ridge TN 37830 USA Univ Delaware Ctr Appl Coastal Res Dept Civil & Environm Engn Newark DE 19716 USA Tech Univ Dresden Inst Urban & Ind Water Management D-01062 Dresden Germany HR Wallingford Ltd Coasts & Oceans Grp Wallingford OX10 8BA England Univ Plymouth Sch Biol & Marine Sci Plymouth PL4 8AA Devon England UC Santa Barbara Dept Mech Engn Santa Barbara CA 93106 USA

Cohesive sediment transport, where its settling velocity is controlled by the flocculation process, is a crucial component in determining biochemical cycles, fate of pollutants, and morphodynamics in many aquatic ecosystems. In this study, a modeling framework is presented to investigate how flocculation influences cohesive sediment transport in the current bottom boundary layer in dilute conditions, consistent with the calibration range of the flocculation model. From a local analysis of floc dynamics in homogenous turbulence, we identify that the floc size distribution is mainly controlled by floc cohesion and yield strength. The uncertainty in fractal dimension plays a minor role for the floc size but it influences the resulting floc density and settling velocity. The transport analysis in the current boundary layer shows that the flocculation process alters the vertical distribution of the settling velocity and hence the sediment concentration with a strong dependence on cohesion, floc yield strength, and floc structure. When the flocs are more susceptible to breaking, a well-mixed concentration profile is obtained. In contrast, for flocs with higher cohesion or yield strength, higher concentration with a sharp gradient is observed close to the bed. Overall, the settling velocity exhibits a low vertical variability within 20 % of the depth-averaged value except near the bed. This suggests that using a depth-averaged settling velocity yields acceptable predictions of the sediment concentration profiles, especially for flocs with lower cohesion.

关键词： Flocculation Cohesive sediment transport population balance equation model Current bottom boundary layer

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On Identifiability and model Validation of a population balance model for Liquid-Liquid-Mixing 11

On Identifiability and Model Validation of a Population Bala...

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11th Vienna International Conference on Mathematical modelling (MATHMOD)

作者： Wilms, Terrance Topalovic, Daniel Bliatsiou, Chrysoula Villwock, Jorn Kraume, Matthias Bueck, Andreas Knorn, Steffi Tech Univ Berlin Chair Control Fak 3 Berlin Germany Tech Univ Berlin Chair Chem & Proc Engn Fak 3 Berlin Germany Friedrich Alexander Univ Erlangen Nurnberg Inst Particle Technol Erlangen Germany

In this paper, liquid-liquid-mixer systems modelled by population balance equations are considered. As the control input / manipulated variable, the stirrer speed (and hence the energy dissipation rate) is used to control the distribution of the particle size. Three different measurement signals are considered. We investigate the observability and identifiability of the system for each measurement option and show that only in one scenario the model is observable and structurally identifiable. Further, it is shown that in this scenario, practical identifiability is generally challenging and particular care must be taken to ensure the model with identified parameter values is able to describe the dynamic behaviour of the system. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Process Control Identifiability Observability population balance equation model Liquid/Liquid-Mixer Systems

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Spatiotemporal Dynamics of Suspended Particulate Matter in Water Environments: A Review

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WATER 2024年第24期16卷 3613-3613页

作者： Huynh, Trung Tin Kim, Jaein Lee, Sang Deuk Fettweis, Michael Bi, Qilong Kim, Sangsik Lee, Sungyun Choi, Yun Young Nguyen, Huu Son Bui, Trong Vinh Lee, Byung Joon Ho Chi Minh City Univ Technol HCMUT VNU HCM Bach Khoa Ho Chi Minh City Sci Technol Joint Stock Ho Chi Minh City 70000 Vietnam Kyungpook Natl Univ KNU Sch Adv Sci & Technol Convergence 2559 Gyeongsang Daero Sangju 37224 South Korea Kyungpook Natl Univ Energy Environm Inst 2559 Gyeongsang Daero Sangju 37224 Gyeongbuk South Korea Nakdonggang Natl Inst Biol Resources NNIBR Sangju 37242 South Korea Royal Belgian Inst Nat Sci Operat Directorate Nat Environm Rue Vautier 29 B-1000 Brussels Belgium Deltares Dept Ecosyst & Sediment Dynam NL-2629 HV Delft Netherlands Kyungpook Natl Univ KNU Dept Energy Chem Engn 2559 Gyeongsang daero Sangju 37224 South Korea Kyungpook Natl Univ Dept Environm & Safety Engn 2559 Gyeongsang Daero Sangju 37224 South Korea Ho Chi Minh City Univ Technol HCMUT Fac Geol & Petr Engn VNU HCM Ho Chi Minh City 70000 Vietnam

Suspended particulate matter (SPM) is an indispensable component of water environments. Its fate and transport involve various physical and biogeochemical cycles. This paper provides a comprehensive review of SPM dynamics by integrating insights from biogeochemical processes, spatiotemporal observation techniques, and numerical modeling approaches. It also explores methods for diagnosing SPM-mediated biogeochemical processes, such as the flocculation kinetics test and organic matter composition analysis. Advances in remote sensing, in situ monitoring, and high-resolution retrieval algorithms are discussed, highlighting their significance in detecting and quantifying SPM concentrations across varying spatial and temporal scales. Furthermore, this review examines integrated models that incorporate population balance equations on the basis of flocculation kinetics into multi-dimensional sediment transport models. The results from this study provide valuable insights into SPM dynamics, ultimately enhancing our knowledge of SPM behavior and transport in water environments. However, uncertainties remain due to limited field data on flocculation kinetics and the need for parameter optimization in numerical models. Addressing these gaps through enhanced fieldwork and model refinement will significantly improve our ability to predict and manage SPM dynamics, which is critical for sustainable aquatic ecosystem management in an era of rapid environmental change.

关键词： suspended particulate matter remote sensing echosounder population balance equation model suspended particulate matter retrieval

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On Identifiability and model Validation of a population balance model for Liquid-Liquid-Mixing ⁎

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IFAC-PapersOnLine 2025年第1期59卷 187-192页

作者： Terrance Wilms Daniel Topalovic Chrysoula Bliatsiou Jörn Villwock Matthias Kraume Andreas Bück Steffi Knorn Chair of Control Fak. III Technische Universität Berlin Germany Chair of Chemical and Process Engineering Fak. III Technische Universität Berlin Germany Institute of Particle Technology Friedrich-Alexander-Universität Erlangen-Nürnberg Germany

关键词： Process Control Identifiability Observability population balance equation model Liquid/Liquid-Mixer Systems

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Reducing model complexity by means of the optimal scaling: population balance model for latex particles morphology formation

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APPLIED MATHEMATICS AND COMPUTATION 2023年 443卷

作者： Rusconi, Simone Schenk, Christina Zarnescu, Arghir Akhmatskaya, Elena BCAM Basque Ctr Appl Math Alameda Mazarredo 14 Bilbao 48009 Spain CUNEF Univ C Pirineos 55 Madrid 28040 Spain IMDEA Mat Inst C Eric Kandel 2Tecnogetafe Getafe 28906 Madrid Spain Basque Fdn Sci IKERBASQUE Plaza Euskadi 5 Bilbao 48009 Spain Romanian Acad Simion Stoilow Inst 21 Calea Grivitei Bucharest 010702 Romania

Rational computer-aided design of multiphase polymer materials is vital for rapid progress in many important applications, such as: diagnostic tests, drug delivery, coatings, additives for constructing materials, cosmetics, etc. Several property predictive models, including the prospective population balance model for Latex Particles Morphology Formation (LPMF PBM), have already been developed for such materials. However, they lack computational efficiency, and the accurate prediction of materials' properties still remains a great challenge. To enhance performance of the LPMF PBM, we explore the feasibility of reducing its complexity through disregard of the aggregation terms of the model. The introduced nondimensionalization approach, which we call Optimal Scaling with Constraints, suggests a quantitative criterion for locating regions of slow and fast aggregation and helps to derive a family of dimensionless LPMF PBM of reduced complexity. The mathematical analysis of this new family is also provided. When compared with the original LPMF PBM, the resulting models demonstrate several orders of magnitude better computational efficiency. (c) 2022 The Authors. Published by Elsevier *** is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/)

关键词： Polymerization Latex particles morphology formation population balance equation model Nondimensionalization Reduction of model complexity Optimal scaling with constraints

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Inverse problem analysis of pluripotent stem cell aggregation dynamics in stirred-suspension cultures

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JOURNAL OF BIOTECHNOLOGY 2015年 208卷 70-79页

作者： Rostami, Mahboubeh Rahmati Wu, Jincheng Tzanakakis, Emmanuel S. Tufts Univ Dept Chem & Biol Engn Medford MA 02155 USA Tufts Med Ctr Tufts Clin & Translat Sci Inst Boston MA 02111 USA

The cultivation of stem cells as aggregates in scalable bioreactor cultures is an appealing modality for the large-scale manufacturing of stem cell products. Aggregation phenomena are central to such bioprocesses affecting the viability, proliferation and differentiation trajectory of stem cells but a quantitative framework is currently lacking. A population balance equation (PBE) model was used to describe the temporal evolution of the embryonic stem cell (ESC) cluster size distribution by considering collision-induced aggregation and cell proliferation in a stirred-suspension vessel. For ESC cultures at different agitation rates, the aggregation kernel representing the aggregation dynamics was successfully recovered as a solution of the inverse problem. The rate of change of the average aggregate size was greater at the intermediate rate tested suggesting a trade-off between increased collisions and agitation-induced shear. Results from forward simulation with obtained aggregation kernels were in agreement with transient aggregate size data from experiments. We conclude that the framework presented here can complement mechanistic studies offering insights into relevant stem cell clustering processes. More importantly from a process development standpoint, this strategy can be employed in the design and control of bioreactors for the generation of stem cell derivatives for drug screening, tissue engineering and regenerative medicine. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Stem cells Bioreactors population balance equation model Inverse problem Aggregation kernel Tissue engineering

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Prediction of emulsion drop size distributions in colloid mills

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CHEMICAL ENGINEERING SCIENCE 2014年 118卷 114-125页

作者： Maindarkar, Shashank Dubbelboer, Arend Meuldijk, Jan Hoogland, Hans Henson, Michael Univ Massachusetts Dept Chem Engn Amherst MA 01003 USA Tech Univ Eindhoven Dept Chem Engn & Chem Eindhoven Netherlands Unilever R&D NL-3133 AT Vlaardingen Netherlands

Colloid mills are the most common emulsification devices used in industry for products with high oil content. Drop breakage occurs when the emulsion is flowed through a small gap between rotor and stator under laminar shear conditions. In this paper, we have developed the first full population balance equation (PBE) model for colloid mills and used the model to better understand the relevant drop breakage mechanisms. The PBE model accounted for both drop breakage and coalescence and generated predictions of the drop size distribution after each pass of the emulsion through the colloid mill. Drops were assumed to break due to capillary instability with the distribution of drop sizes resulting from each breakage event studied in detail. A viscosity model was developed to predict the emulsion viscosity as function of the oil fraction and the high shear rates commonly used. Nonlinear optimization was used to estimate adjustable parameters in the breakage and coalescence functions to minimize the least-squares difference between predicted and measured drop size distributions for high oil-to-surfactant emulsions. We concluded that experimentally observed drop volume distributions could not be predicted with daughter drop distribution functions reported in the literature. Improved predictions were obtained using a new bimodal distribution function which captured drop breakage into multiple, nearly uniform daughter drops with a large number of small satellite drops. We also investigated model extensibility for changes in the oil fraction, emulsion flow rate and rotor speed. Published by Elsevier Ltd.

关键词： Colloid mill Oil-in-water emulsions population balance equation model Capillary breakage Emulsion viscosity

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Achieving Target Emulsion Drop Size Distributions using population balance equation models of High Pressure Homogenization *

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IFAC Proceedings Volumes 2013年第32期46卷 738-743页

作者： Shashank N Maindarkar Michael A Henson Department of Chemical Engineering University of Massachusetts Amherst MA 01003-9303 USA

A population balance equation (PBE) model that accounts for drop breakage and coalescence in high pressure homogenization was used for emulsion product design. Six adjustable parameters were estimated by nonlinear optimization from measured drop volume distributions at a specified operating condition. The values of two parameters were estimated at four different homogenization pressures and interpolated to allow improved prediction over a range of pressures. Using two alternative objective functions, the parameterized model was used to determine the pressure of each homogenization pass needed to achieve the target drop size distribution at the final pass. Homogenization experiments performed to validate the model predictions produced measured distributions in very good agreement with two target distributions.

关键词： Process modeling population balance equation model nonlinear parameter estimation nonlinear optimization particle size control

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Analysis of the effect of temperature, pH, CO₂ pressure and salinity on the olivine dissolution kinetics

Analysis of the effect of temperature, pH, CO<sub>2</sub> pr...

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9th International Conference on Greenhouse Gas Control Technologies

作者： Prigiobbe, V. Haenchen, M. Costa, G. Baciocchi, R. Mazzotti, M. Swiss Fed Inst Technol Inst Proc Engn Zurich Switzerland Univ Rome Dept Civil Engn Rome Italy

The dissolution kinetics of olivine has been extensively studied under several temperatures, CO2 pressures, and solution compositions. Dissolution is an important mechanism in the aqueous mineral carbonation process. The overall carbonation reaction consists of dissolution of mineral silicate, e.g. olivine, serpentine and wollastonite, followed by carbonate precipitation, thus fixing CO2 into naturally occurring stable solids, such as magnesite and calcite. The slowness of the dissolution kinetics hinders the overall carbonation reaction and in order to make the process technically and economically feasible, such a reaction should be sped up by finding the optimum operating conditions. Experiments were performed in a flow-through reactor at 90-120-150 degrees C. The pH was adjusted by adding either acids (e.g., HCl, citric acid) or LiOH, and by changing P-CO2. The salinity was changed by adding NaCl and NaNO3. From the experimental data, the dissolution rate was estimated by using the population balance equation (PBE) model coupled with a mass balance, and the obtained values were regressed with a linear model log (r) = -n pH - B, where r is the specific dissolution rate (mol s(-1) cm(-2)). (C) 2008 Elsevier Ltd. All rights reserved.

关键词： mineral carbonation olivine dissolution population balance equation model

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Analysis of the effect of temperature, pH, CO 2 pressure and salinity on the olivine dissolution kinetics

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Energy Procedia 2009年第1期1卷 4881-4884页

作者： V. Prigiobbe M. Hänchen G. Costa R. Baciocchi M. Mazzotti Institute of Process Engineering ETH Zurich Zurich Switzerland University of Rome “Tor Vergata” Department of Civil Engineering Rome Italy

The dissolution kinetics of olivine has been extensively studied under several temperatures, CO 2 pressures, and solution compositions. Dissolution is an important mechanism in the aqueous mineral carbonation process. The overall carbonation reaction consists of dissolution of mineral silicate, e.g. olivine, serpentine and wollastonite, followed by carbonate precipitation, thus fixing CO 2 into naturally occurring stable solids, such as magnesite and calcite. The slowness of the dissolution kinetics hinders the overall carbonation reaction and in order to make the process technically and economically feasible, such a reaction should be sped up by finding the optimum operating conditions. Experiments were performed in a flow-through reactor at 90–120–150 ∘ C. The pH was adjusted by adding either acids (e.g., HCl, citric acid) or LiOH, and by changing P CO 2 . The salinity was changed by adding NaCl and NaNO3. From the experimental data, the dissolution rate was estimated by using the population balance equation (PBE) model coupled with a mass balance, and the obtained values were regressed with a linear model log ( r ) = − n p H − B , where r is the specific dissolution rate (mol s −1 cm −2 ).

关键词： Mineral carbonation Olivine dissolution population balance equation model

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