Steady-State Multiplicity of a Tubular Reactor

The analysis of multiplicity for a tubular reactor is involved because its mass and energy balances are governed by nonlinear boundary-value problems. The uniqueness conditions for a tubular reactor are more conservative than those for a CSTR. The exact bounds for the uniqueness require numerical solutions. 

The dimensionless mass and energy balance in a tubular reactor are (Morbidelli et al. 1986) 

When the condition in Equation (2.282) is violated, the following condition ensures uniqueness  

The exact bounds for multiplicity can be determined by computationally solving the boundary-value problems with the use of the singularity theory. 

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