Unified Model for Residence Time Distribution in a Recycle Reactor with Arbitrary Velocity Profiles

In many chemical processes conducted in loop reactor systems, feed reactants are mixed with recycle streams (that may contain a catalyst, for example) in tubes that are fitted with inline static mixers. Mixing and heat exchange are made efficient by static mixers. Quantification of heat transfer and pressure drop through the tubes are important design parameters that affect the performance of the loop reactor system. In this paper, we model flow through a tube fitted with inline static mixers, using the Brinkman equation for porous media. We show how the velocity profiles obtained from such an analysis can be used to quantify the deviations from plug flow behavior. We derive explicit expressions for residence time distribution (RTD) for flow through this tube as a function of the prescribed pressure drop. We quantify this effect through a nondimensional parameter, namely, the Darcy number. We use CFD modeling to compare theoretically derived expressions for RTD, and the results show a discrepancy with the proposed modeling approach, particularly at high Darcy numbers. We use this explicit expression for RTD to derive a composite RTD for the recycle reactor with a known recycle ratio. The once-through RTD is embedded in a reactor with recycle, where the recycle ratio was varied in addition to the Darcy number. It was found that there is a competition between the recycle ratio and Darcy number in determining the nature of the RTD. Higher values of the recycle ratio pushed the system toward a CSTR-like behavior while higher values of the Darcy number (due to the increased flow) moved the system more toward a plug flow type. Thus, when fitting the residence time distribution of a recycle reactor with a static mixer, care must be exercised to include the internal dependence between the Darcy number and recycle ratio. Such a relation would enable accurate system identification and extrapolation of the RTD to other operating regimes with different recycle ratios or throughputs.