A Two-Dimensional Model Accounting for Radial

5 A Two-Dimensional Model Accounting for Radial Variations in the Bed Structure 

Assuming plug flow in reactors with low djdp ratio, as encountered in multitubular reactors with fixed bed, is not very realistic. The void fraction in a cross section of the bed has been shown to vary from the wall to the central axis [Benenati and Brosilow, 1962] and this induces a radial variation in flow velocity [Schwartz and Smith, 1953 Cairns and Prausnitz, 1959 Schertz and Bischoff, 1969 Mickley et al, 1965 Lerou and Froment, 1977 McGreavy et al., 1986]. Govindarao and Froment [1986] and Delmas and Froment [1988] derived 

The flow velocity components in this and the following equations are superficial, but these are related to the local void fraction and the interstitial velocity through 

To eliminate the unknown local pressure field, the set is rewritten according to the stream function and vorticity formulation [Bird et al., I960 Patankar, 1980]. This development is explained in detail in the original paper. 

The continuity equations for the various species and the energy equation need to be added to the equations given above. These are of course also two-dimensional and account for the non uniform velocity profile. 

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