Stability of adiabatic reactors

We have already considered the stability of the adiabatic stirred tank (Sec. 7.5) and have observed that since M = 1, the slope condition L N suffices to ensure stability. Now recalling the definitions of L and N this is 

This is the equation of a stirred tank with feed concentration a, temperature F, and composition d. The quantity 6 is a holding time for the particle. 

If the heat of reaction is A// and is negative, then heat will be generated at a rate (—In the steady state this balances the rate of heat transfer where U is the heat transfer coefficient (notation 

The pseudo-homogeneous reaction rate for the packed reactor is 

The right-hand side is the familiar sigmoidal function of t shown in Fig. 8.17. The left-hand side is a family of lines pivoting about the point of ordinate I and abscissa Since T is the intersection of one such line with the horizontal axis, the lines corresponding to T(z) will sweep toward the vertical 

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Backmixing by axial diffusion, and stability of adiabatic reactors, 344... 

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