(463b) Sustainted Oscillations in Continuous Crystallizers

A modeling framework is developed to describe the behavior of a simple continuous crystallizer. The proposed model provides an effective tool to study self-generated oscillations in a mixed suspension, mixed product removal isothermal crystallizer. Furthermore, Tellegen's theorem gives us a useful tool to prove the global instability and show how the key system parameters affect the system stability. We believe this is the first work to model the complex process using discrete population balance coupled with mass balance of the solute. The proposed model requires ignorable computational effort and no model reduction or approximation is needed before solving it numerically. We are the first to achieve the proof for global stability of the process. Mathematical analysis published in the previous work applied local linearization technique before proceeding analysis. We demonstrate the key role of Tellegen's theorem in our stability proof.

It is well known that the solid yield obtained from the oscillating system exceeds that from stable systems for continuous crystallizers. Therefore the prediction of the behavior of the oscillating system in the crystallization process is highly desirable. The analytical results tell us the key parameters for the system stability and those parameters can be controlled to affect the stability of the crystallizers and hence increase the solid yield.