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to understand liquid carry-over in the loop reactor. An accurate understanding of the factors controlling the circulation rate and mixing within the reactor is essential for scaling up the reactor.

From this brief description it is clear that the fluid dynamics of the loop reactor is intimately connected to the reaction. The reaction generates volatiles, which ultimately drive the circulation. However, it was found that it is possible, and may be more efficient, to decouple the reaction part from the flow. The overall problem was tackled by dividing it into several sub-problems. The methodology is shown in Fig. 9.19. In the first sub-problem, using the available empirical information about the operating plant, the fluid mechanics and mixing was approximated to develop a reactor model (plug flow for the loop and complete mixing for the vapor-liquid separator). The reactor model was calibrated and validated by comprehensive comparisons of predicted results with plant data. Such a model was used to predict profiles of concentration, temperature and vapor generation. This information, combined with additional information about the flow regimes in the heater section, was supplied to the flow model.

Computational fluid dynamics based flow models were then developed to simulate flow and mixing in the loop reactor. Even here, instead of developing a single CFD model to simulate complex flows in the loop reactor (gas dispersed in liquid phase in the heater section and liquid dispersed in gas phase in the vapor space of the vapor-liquid separator), four separate flow models were developed. In the first, the bottom portion of the reactor, in which liquid is a continuous phase, was modeled using a Eulerian-Eulerian approach. Instead of actually simulating reactions in the CFD model, results obtained from the simplified reactor model were used to specify vapor generation rate along the heater. Initially some preliminary simulations were carried out for the whole reactor. However, it was noticed that the presence of the gas-liquid interface within the solution domain and inversion of the continuous phase,

Vapor outlet

Vapor separator

Product * outlet

Product * outlet

presented severe challenges to numerical methods, leading to difficulties in obtaining converged results. The exact shape of the gas-liquid interface does not significantly affect the flow and mixing in the vapor-liquid separator. The shape of the gas-liquid interface was, therefore, assumed. A typical grid used for flow simulation is shown in Fig. 9.20. A sample of the simulated flow field in the bottom portion of the loop reactor is shown in Fig. 9.21.

In the second part, flow in the vapor space of the separator, where the gas phase is a continuous phase, was modeled. An Eulerian-Lagrangian approach was used to simulate trajectories of the liquid droplets since the volume fraction of the dispersed liquid phase is quite small. The grid used for the vapor space is shown in Fig. 9.20. The simulated gas volume fraction distribution near the gas-liquid interface and corresponding gas flow in the vapor space are shown in Fig. 9.22. The gas volume fraction distribution and the gas velocity obtained from the model of the bottom portion of the loop reactor were used to specify boundary conditions for the vapor space model. In addition to the gas escaping from the gas-liquid interface, it is necessary to estimate the amount of liquid thrown into the vapor space by the vapor bubbles erupting at the

FIGURE 9.19 Methodology used for model loop reactor.

gas-liquid interface. A separate volume of fluid (VOF) based model was developed to understand bubble eruption processes and to estimate the amount of liquid thrown into the vapor space. It was, however, found that the predicted results of amount of liquid thrown per bubble were significantly different than the available data. An expression for estimating the amount of liquid thrown per bubble based on a phenomenological model of Azbel (1981) was, therefore, used to couple the loop part with the vapor space part. In addition, a separate flow model to simulate details of mixing near the feed nozzle (interaction of feed flow with re-circulating flow) was developed. An attempt was made to validate various sub-components of the computational models using the available data. The models were then used to carry out various numerical experiments on computer. These results were used to construct detailed information about the loop reactor and to evolve appropriate scale-up guidelines.

FIGURE 9.20 Computational grid.
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