Fixing flow rates in recycle systems: Luyben's rule revisited

This paper analyzes the nonlinear behavior of several recycle systems involving first- and second-order reactions. The results, presented in term of dimensionless numbers, explain some control difficulties reported by previous studies. It is shown that conventional control structures, fixing the flow rate of fresh reactants and relying on self-regulation, can lead to parametric sensitivity, unfeasibility, state multiplicity, or instability, particularly at low conversions. These problems can be solved by fixing the flow rate in the recycle loop, as stated by Luyben's rule. This paper demonstrates that a particular location for fixing the recycle flow rate is advantageous, namely, the reactor inlet. This decouples the reactor from the rest of the plant and avoids undesired phenomena due to mass recycles. For example, the unstable closed-loop behavior observed with nonisothermal PFRs disappears. The HDA plant case study illustrates the proposed strategy.