# Limit cycles that do not comprise steady states of reactors

## TL;DR

This paper demonstrates through numerical testing that reactors can exhibit limit cycles that do not include steady states, revealing complex oscillatory behaviors that can enhance process efficiency.

## Contribution

It introduces the concept that reactors can have limit cycles separate from steady states, supported by numerical analysis of coupled tank reactors with recycle loops.

## Key findings

- Limit cycles can exist without steady states in reactors.
- Oscillations may increase conversion degrees independently.
- The phenomenon is characterized by phase portrait analysis.

## Abstract

It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested numerically. The above-mentioned phenomenon is characterized by the location of the steady point out of the limit cycle in the phase portrait. This incident may be beneficial to the process, as low steady state does not have to exclude an independent increase of the conversion degree, despite being the only state and not generating oscillations.

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Source: https://tomesphere.com/paper/1706.06860