Axial mass limit

These results indicate that, as n increases, (yij) , the bottom product composition, tends to zero (relation (7.1.86a)). Although as n increases (yij-) increases, relation (7.1.85a) suggests that (yij-) = yiT)n-i- It system, the ratio (yi7-) /(yi does not tend to infinity, as suggested by (7.1.87) for large n-, instead, mass-transfer rate limitations between the phases and axial diffusion limit the possible enrichment (Pigford et ah, 1969a). Figure 7.1.19 compares the predictions from this equilibrium theory with the experimental data on an n-heptane-toluene separation... 

Here, Ca is the capacity of the ion-exchange resin measured in moles of A per unit volume. The integral in Equation (11.49) measures the amount of material supplied to the reactor since startup. Breakthrough occurs no later than zr = L, when all the active sites in the ion-exchange resin are occupied. Breakthrough will occur earlier in a real bed due to axial dispersion in the bed or due to mass transfer or reaction rate limitations. 

Within this approach it was proposed so called improved effective action which is more properly takes into account current quark masses and satisfies axial-anomaly low energy theorems also beyond the chiral limit (M.M. Musakhanov, 1999) at least at 0(m). 

Another potential solution technique appropriate for the packed bed reactor model is the method of characteristics. This procedure is suitable for hyperbolic partial differential equations of the form obtained from the energy balance for the gas and catalyst and the mass balances if axial dispersion is neglected and if the radial dimension is first discretized by a technique such as orthogonal collocation. The thermal well energy balance would still require a numerical technique that is not limited to hyperbolic systems since axial conduction in the well is expected to be significant. 

In this section we have presented the first example of two-point boundary value problems that occur in chemical/biological engineering. The axial dispersion model for tubular reactors is a generalization of the plug flow model for tubular reactors which removes some of the limiting assumptions of plug flow. Our model includes additional axial diffusion terms that are based on the simple physics laws of Fick for mass and of Fourier for heat dispersion. 

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

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