往复振动萃取塔（Karr萃取塔）在制药、石油化工、污水处理等多个领域应用广泛。由于塔内存在复杂的液液两相流动和传质行为，其准确高效的设计放大仍存在困难，依赖于中试实验和设计经验。塔内液滴不断发生运动、破碎和聚并，这些液滴尺度的行为决定着萃取塔的液滴尺寸分布、轴向扩散和传质性能等参数。本研究旨在基于单液滴的研究建立数学模型，将其应用于描述Karr萃取塔的模型中，预测塔内的流动和传质性能。在单液滴上升实验中，通过高速拍摄记录了液滴的实时运动，关注于液滴上升速度和形变。研究了水相中盐离子浓度和种类对液滴终端速度的影响，基于实验数据得到了低雷诺数下的曳力系数的关联式。在单液滴破碎实验中，观察到两种破碎机制，由剪切力造成的破碎和由板润湿性造成的破碎，前者占比90%以上。对筛板附近的剪切力分布进行了计算流体力学模拟，并将模拟结果与实验观测的破碎位置进行关联分析。在实验统计的基础上，研究了不同条件下破碎概率、破碎时间和子滴数的规律，提出了液滴破碎概率模型，得到了实验条件下的临界韦伯数为0.33。建立了包括液滴上升、破碎和聚并行为的群体平衡模型，采用两步法优化模型参数。模型预测了直径为50 mm的Karr萃取塔中以水-煤油为体系在不同操作条件下的流体力学行为。液滴尺寸分布随往复振动强度的增大而减小，但受两相流速的影响较小。另外，将模型与文献中现有关联式的预测结果进行了比较，研究发现包含低振动条件的模型对Karr萃取塔的预测效果更好。采用返流模型对连续相进行描述，结合分散相群体平衡模型，构成组合模型研究两相流动的非理想性。采用水-苯酚-煤油+10v%磷酸三丁酯的体系，测定了Karr萃取塔内萃取和反萃过程沿塔高方向液滴尺寸分布和浓度分布，在不同操作条件下本文所建立的数学模型对实验结果预测良好。 最后，基于本研究所建立的Karr萃取塔数学模型对萃取塔的设计过程进行优化，通过生物碱萃取和己内酰胺反萃取两个案例计算了满足分离要求所需的塔径和塔高。论文工作针对Karr塔进行了系统的模型化研究，基于对单液滴行为的探究，完善了对塔内两相流动和传质行为的描述，为Karr萃取塔的设计放大提供理论基础。
Reciprocating plate columns （Karr columns） have wide applications in pharmaceutical, petrochemical, and wastewater treatment. It is difficult to design and scale-up because of complex interactions between the two phases in a Karr column, while pilot testing and previous design experience are still required. Drop-scale behaviours in a column such as drop rising, breakage and coalescence determine parameters at column-scale, for example, drop size distribution, axial dispersion and mass transfer performance. The study aims to develop models based on investigations of single drop behaviours to predict the hydrodynamics and mass transfer performance at column scale. Model predictions are compared to the experimental results in a Karr column with different operating conditions.In single drop rising study, drop movement was captured by high-speed recording focusing on the rising velocity and shape of a drop. Effects of salt ions concentration and type in aqueous phase on drop terminal velocity were investigated. A correlation of drag coefficient was derived based on measured data and can be used at low Reynolds number. In drop breakage study, two breakage mechanisms were observed, namely, due to shear stress and plate wettability. The former accounts for more than 90% of drop breakup. Shear stress distribution near the plate region was simulated based on computational fluid dynamics, and was correlated to the measured breakage locations. Breakage probability, breakage time and number of daughter drops were analysed with various operating conditions based on statistical analysis. A correlation of breakage probability was proposed. The critical Weber number was estimated as 0.33.The drop size distribution of the dispersed phase in a Karr column was described by a stagewise population balance model with consideration of drop behaviours such as rising, breakage and coalescence. A two-step optimization method was designed to determine the model parameters. Model predictions were in a good agreement with experimental results at different operating conditions, conducted in a pilot-scale Karr column with a diameter of 50 mm using kerosene-water as test system. Drop size distribution decreased as the increase of plate reciprocating intensity, but changed slightly with two phase velocities. Comparison with some existing correlations in literature showed that correlations with low reciprocating term can provide more accurate predictions for a Karr column in a wide range of operating conditions.To further describe mass transfer performance of a Karr column, the continuous phase was described by a backflow model, along with the previous population balance model to describe the dispersed phase. In this way, the flow non-ideality in both phases were considered in the combined model. Experiments were conducted in a Karr column with water-phenol-kerosene＋10v% tributyl phosphate as test system. Drop size distribution and concentration profiles were measured along the column height for both extraction and stripping. The combined model predicted well with the experimental data at various operating conditions.Finally, a demonstration of column design based on the models established in this study was presented to calculate the required column diameter and column height for alkaloid extraction and caprolactam back-extraction, respectively. A detailed study of modelling in a Karr column was presented in the thesis. Description of hydrodynamics and mass transfer in a Karr column were improved based on single drop investigations, which provides a theoretical basis for the design and scale-up of a Karr column.
