Dynamics of Processes with Recycle: Multifeed Ternary Systems

We explore the dynamics and control of plants with recycle and multiple feed streams under different process designs, taking as an example a ternary system with a second-order irreversible reaction:  A + B → 2C. Process transfer function matrices are derived analytically in terms of design variables. It is shown analytically that plants with recycle and multiple feeds are internally unstable systems with a pole at the origin, thus proving Luyben's conjecture that reactant feed flow rates must be balanced down to the last molecule. Therefore, a feed-ratio control scheme will not work in practice; one of the feed flows must be adjusted via feedback. Remaining candidate control structures are evaluated using linear and nonlinear analysis. Finally, dynamic compensation of the feed flow is applied such that almost perfect production rate control is achieved. Simulation results clearly indicate that the correct control structure can be selected and that almost perfect production rate changes can be achieved.