气液（浆态）反应器广泛应用于石油化工、生物化工和环境工程等领域。关于这类反应器的模型与数值模拟研究已经有很多，但是由于气泡-气泡、气泡-液相之间的相互作用复杂，相间作用力、气泡导致的湍动和气泡聚并、破碎等多种模型的组合形式多样，目前尚没有能够普遍适用的模型。本文从计算流体力学（Computational fluid dynamics, CFD）-群体平衡方程（Population balance equation, PBE）耦合模型出发，对气液鼓泡塔和气升式环流反应器进行了模型与数值模拟研究。首先，利用Fortran自编程序建立气液两相的CFD-PBE耦合模型。针对固定节点法存在的对大颗粒数密度预测偏高的问题，首次将固定节点法改进之后的单元平均法，成功地用于非均相体系PBE的求解。利用该模型对气液鼓泡塔进行了模拟研究，分别采用单元平均法和固定节点法求解模型中的PBE。通过和实验结果的对比发现，两种方法计算得到的气含率、轴向液速等都可以和实验结果较好地吻合，但是采用固定节点法得到的气泡平均直径偏大，气泡大小分布（Bubble size distribution, BSD）较宽且大气泡预测偏高，利用单元平均法得到的气泡平均直径和局部BSD与实验结果更加吻合。随后利用该模型对表观气速的影响进行了研究，结果显示随表观气速增大，模拟得到的反应器内气含率逐渐增大，气泡平均直径呈现先略微增大后减小的趋势。其次，基于开源计算流体力学软件平台OpenFOAM (C++风格)开发了气液两相CFD-PBE求解器，并以鼓泡塔为对象完成了验证。在此基础上进一步耦合了气液传质、反应过程和描述结晶过程的PBE，开发了适用于气液结晶体系的CFD-PBE-PBE的耦合模型与求解器，首次实现这类体系的耦合模拟。以环流结晶器为研究对象，对CO2气和Ca(OH)2溶液反应生成CaCO3结晶的过程进行了研究，分别考察了化学反应增强因子、结晶动力学模型和操作参数对结晶过程的影响。模拟结果显示，考虑化学反应增强因子对溶液pH值和Ca2+浓度的变化略有影响，但是对颗粒的平均直径和颗粒大小分布（Crystal size distribution, CSD）基本没有影响。结晶动力学模型对模拟结果影响显著，选择适当的结晶动力学模型可以得到与实验结果较吻合的模拟结果，准确预测反应器内pH值、Ca2+浓度和晶体直径等随时间的变化情况。表观气速增大会显著加快OH-和Ca2+的消耗速度，但是对晶体粒径没有明显影响。反应物初始浓度增大时，晶粒的平均直径减小且CSD变窄并向左移动。最后，由于大部分工业鼓泡塔通常是在加压的条件下进行操作的，因此在气液两相CFD-PBE求解器中，对曳力模型和气泡破碎模型进行了修正，通过引入修正系数考察了压力对气含率和气泡大小的影响。利用该求解器对不同压力下的鼓泡塔进行了模拟，模拟所得气含率和文献中的实验结果吻合较好。在表观气速较高时气泡直径的预测结果随压力增大而减小，BSD的模拟结果显示随压力增大，大气泡减少、小气泡增多，说明气泡的破碎增强。;Gas-liquid/slurry reactors are widely used in petrochemical, biochemical and environmental engineering processes. There are many mathematical modeling and numerical simulation investigations on these reactors. Because of the complex interactions among bubbles and that of bubbles with liquid, in addition to the diversity of the combination of interphase force models, bubble induced turbulence models and bubble aggregation and breakage models, there is no universally applicable set of models. Mathematical models and numerical simulation studies on bubble columns and airlift loop reactors are carried out in this work based on the computational fluid dynamics-population balance equation (CFD-PBE) coupled model.Firstly, a CFD-PBE coupled model for the gas-liquid two phase system is developed using an in-house code programmed with the Fortran language. In order to overcome the shortcoming of over-estimated large particle fractions by the fixed pivot method, we has realized for the first time the application of the cell average method, which is developed based on the fixed pivot method, in the CFD-PBE coupled model. The model is applied to simulate the gas-liquid flow in a bubble column, and the PBE is solved by using either the cell average method or the fixed pivot method. The simulated results of the gas holdup and axial liquid velocity by using both methods are in reasonable agreement with the experimental data, validating positively this CFD-PBE model. However, the cell average method performs better in predicting the mean bubble diameter and the bubble size distribution (BSD). The fixed pivot method gives a larger mean bubble diameter and a wider BSD, and it also overestimates the probability density function of large bubbles. Then, the effect of superficial gas velocity is investigated numerically. It is indicated that with the increase of superficial gas velocity, the total gas holdup in the bubble column increases and the mean bubble diameter increases slightly first and then decreases.Secondly, a CFD-PBE solver is developed in the framework of OpenFOAM (an open source CFD package written in C++) and verified on a bubble column. Then, the CFD-PBE-PBE coupled model and solver for the gas-liquid crystallization system are developed by coupling the gas-liquid mass transfer, reaction processes, and the second PBE for the crystallization. This solver is used to realize for the first time the fully coupled simulation of a gas-liquid crystallization system. The formation of calcium carbonate via the reaction of gaseous CO2 with Ca(OH)2 solution in an airlift crystallizer is simulated using this solver. The effects of enhancement factor and crystallization kinetics and operation conditions are systematically investigated. The results indicate that the enhancement factor slightly influences the variation of solution pH and the concentration of Ca2+, while basically it has no effect on particle diameter and crystal size distribution (CSD). Crystallization kinetics significantly influences the simulation results. The model can accurately predict the variation of pH, Ca2+ concentration and the mean crystal size with time when an appropriate crystallization kinetics model is used. The increase in superficial gas velocity results in the increasing consumption rates of OH- and Ca2+, while the particle diameter seems unchanged in the present simulation. Higher initial concentrations of reactants lead to a smaller particle diameter and a narrower CSD.At last, as most industrial bubble columns are operated under elevated pressure, some modifications are made in the drag force model and the bubble breakage model in the gas-liquid CFD-PBE solver. By introducing modification factors, the effect of pressure on the gas holdup and bubble size is demonstrated. This solver is employed to simulate the bubble columns operated at different pressures, and the predicted gas holdup is in reasonable agreement with the reported experimental results. At higher superficial gas velocities, the predicted bubble diameter decreases with the increase of pressure. Predicted results of BSDs show the probability distribution function of large bubbles decreases and that of small bubbles increases with increasing pressure, indicating that the bubble breakage rate is enhanced.