Numerical bifurcation analysis of delay in a coupled reactor separator system

The effect of delay on the stability of a coupled reactor separator system is investigated in this work, using the DDE-BIFTOOL software package: The reactor considered is a continuously stirred tank reactor (CSTR), and the separator is modeled as a flash unit operating isothermally and isobarically. A first-order isothermal irreversible reaction A -> B is considered to investigate the effect of delay arising as a result of transportation lag from the CSTR to the flash. The dynamic behavior of the coupled CSTR-flash system is governed by the delay differential equations. In this work, the dynamic instability induced by delay that is crucially dependent on the flow control strategy of the system is investigated using DDE-BIFTOOL. It is shown that delay can destabilize the steady state of the coupled system when the reactor effluent flow rate F is flow-controlled, and the molar holdup M-R in the reactor is allowed to vary. When the fresh feed flow rate F-0 is flow-controlled, the system exhibits delay-independent stability. The critical delay and frequency of oscillation obtained using DDE-BIFTOOL show good agreement with the same obtained using the analytical expressions proposed in. the literature.