Residence time distribution in MSR

The RTD in chemical reactors is a crucial parameter for process performances and product yield and selectivity. The RTD in tubular reactors can be described by the so-called dispersion model [7]. This model suggests that the RTD can be considered as the result of piston flow with the superposition of axial dispersion. The dispersion is considered by means of an effective axial dispersion coefficient 

which has the same dimension unit as the molecular diffusion coefficient D. Usually is much larger than because it incorporates all effects that may cause deviation from plug flow, such as radial velocity differences, eddies, or vortices. The key parameter determining the width of the RTD is the ratio between the axial dispersion time and the space-time r, which corresponds to the mean residence time in the reactor t at constant fluid density. This ratio is often called Bodenstein number Bo). 

For Bo 0, the axial dispersion time is short compared to the residence time, which results in high backmixing in the reactor, resulting in large RTD. For Bo 00, no dispersion occurs and the reactor behavior corresponds to an ideal plug flow reactor. In practice, axial dispersion can be neglected for Bo 100. 

In microstructured channels, laminar flow can be considered when the hydrodynamic entrance length remains short compared to the channel length. Therefore, the axial dispersion coefficient can be estimated with a relation developed by Aris [20] and Taylor [21]  

The first term in Eq. (11.38) corresponds to the ratio between space-time and the characteristic axial molecular diffusion time. The molecular diffusion coefficient hes in the order 10 m s for gases and 10 m s for liquids. Typical lengths of MSR are several centimeters and the space-time is in the range of seconds. Therefore, the axial dispersion in microchannels is mainly determined by the second term in Eq. (11.38), where the Bodenstein number can be estimated with Eq. (11.39) 

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