Penaloza-Giraldo Jorge A, Hsu Tian-Jian, Manning Andrew J, Ye Leiping, Vowinckel Bernhard, Meiburg Eckart
Department of Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, United States.
Department of Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, United States.
Water Res. 2023 Apr 15;233:119780. doi: 10.1016/j.watres.2023.119780. Epub 2023 Feb 24.
Many aquatic environments contain cohesive sediments that flocculate and create flocs with a wide range of sizes. The Population Balance Equation (PBE) flocculation model is designed to predict the time-dependent floc size distribution and should be more complete than models based on median floc size. However, a PBE flocculation model includes many empirical parameters to represent important physical, chemical, and biological processes. We report a systematic investigation of key model parameters of the open-source PBE-based size class flocculation model FLOCMOD (Verney, Lafite, Claude Brun-Cottan and Le Hir, 2011) using the measured temporal floc size statistics reported by Keyvani and Strom (2014) at a constant turbulent shear rate S. Results show that the median floc size d, in terms of both the equilibrium floc size and the initial floc growth, is insufficient to constrain the model parameters. A comprehensive error analysis shows that the model is capable of predicting three floc size statistics d, d and d, which also reveals a clear trend that the best calibrated fragmentation rate (inverse of floc yield strength) is proportional to the floc size statistics considered. Motivated by this finding, the importance of floc yield strength is demonstrated in the predicted temporal evolution of floc size by modeling the floc yield strength as microflocs and macroflocs giving two corresponding fragmentation rates. The model shows a significantly improved agreement in matching the measured floc size statistics.
许多水生环境中含有粘性沉积物，这些沉积物会絮凝形成大小范围广泛的絮体。种群平衡方程（PBE）絮凝模型旨在预测絮体大小随时间的分布，并且应该比基于中位絮体大小的模型更完整。然而，PBE絮凝模型包含许多经验参数来表示重要的物理、化学和生物过程。我们使用Keyvani和Strom（2014年）在恒定湍流剪切速率S下报告的测量絮体大小时间统计数据，对基于开源PBE的粒度类絮凝模型FLOCMOD（Verney、Lafite、Claude Brun-Cottan和Le Hir，2011年）的关键模型参数进行了系统研究。结果表明，就平衡絮体大小和初始絮体生长而言，中位絮体大小d不足以约束模型参数。全面的误差分析表明，该模型能够预测三种絮体大小统计量d、d和d，这也揭示了一个明显的趋势，即最佳校准的破碎率（絮体屈服强度的倒数）与所考虑的絮体大小统计量成正比。受这一发现的启发，通过将絮体屈服强度建模为微絮体和宏絮体并给出两个相应的破碎率，在预测絮体大小的时间演变中证明了絮体屈服强度的重要性。该模型在匹配测量的絮体大小统计量方面显示出显著改善的一致性。
