Moura Maria J, Vertis Carolina S, Redondo Vítor, Oliveira Nuno M C, Duarte Belmiro P M
Instituto Politécnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal.
Centro de Investigação em Engenharia dos Processos Químicos e dos Produtos da Floresta, Universidade de Coimbra, Rua Sílvio Lima, Pólo II, 3030-790 Coimbra, Portugal.
Materials (Basel). 2023 Jul 4;16(13):4822. doi: 10.3390/ma16134822.
The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions.
连续增稠器和澄清器的设计通常基于固体通量理论。在不同固体浓度下进行的间歇沉降实验仍可为其应用提供有用信息。沉降速度模型的构建有助于估算整个时间段内的固体通量，进而可用于确定在澄清液流中达到给定固体浓度所需的设备面积。本文探讨了从碳酸钙颗粒间歇沉降实验中获取的数据的数值处理方法。我们提出了一个系统框架，用于拟合一个能够表征过程特征的模型，这些特征包括：（i）对数据进行数值微分以生成沉降瞬时速度的初始估计值；（ii）对微分方程进行积分以拟合沉降速度模型；（iii）使用常见统计指标评估拟合质量。用于演示的模型具有理论基础并结合了经验成分，以考虑颗粒浓度及其聚集状态的影响。获得的数值参数值与聚集体的特征尺寸及其质量-长度分形维数相关。
