A Mathematical Model for Biphasic Hydroformylation Reactor

It is rather difficult to establish a reasonably accurate mathematical model of a gas-liquid-liquid three-phase reactor for biphasic hydroformylation, because of the complexity in formulating all the necessary mechanisms such as phase dispersion and distribution, multiphase flow, interphase mass transfer, micromixing, and the hydroformylation reaction. Besides, the task is further complicated by turbulence in multiphase flow and the complex domain of stirred-tank reactors. 

Although a chemical engineering study is in rapid progress toward this goal, only a few simpler but still rather difficult models, aimed at part of the chemical engineering process taking place in the reactor, have been proposed for application in the biphasic hydroformylation of olefins. 

Lekhal et al. [6] proposed a pseudo-homogeneous gas-liquid-liquid model based on the Higbie penetration theory to account for simultaneous absorption of two gases into the liquid phases. Because of the assumption of rapid liquid-liquid mass transfer of reactants leading to the equilibrium between two liquid phases, the model was simplified greatly and the detail of phase dispersion and distribution and multiphase flow was avoided. Reasonable success was achieved and the results of analysis suggested that the only limitation to the conversion of hydroformylation of 1-octene was the gas-liquid mass transfer of CO and H2. 

Van Elk et al. [27] used a similar mathematical model, based on the penetration model for three reactants in an ideally stirred reactor, to study the dynamic behavior of the gas-liquid homogeneous hydroformylation process. The influence of mass and heat transfer on the reactor stability in the Idnetically controlled regime was analyzed and it brought to mind the existence of a dynamically unstable (limit circle) state under certain operating conditions. This model needs to be extended to account for the presence of a second liquid phase in biphasic hydroformylation. 

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