Transient linear stability of a Simons-process gas–liquid electrochemical flow reactor using numerical simulations

Abstract

A transient mathematical model and a modified linear perturbation analysis are developed to examine the stability of a gas–liquid, parallel-plate electrochemical flow reactor. Dynamic terms are added to our one-dimensional steady-state conservation equations of momentum, continuity, and thermal energy (Drake et al., Ind. Eng. Chem. Res. 40 (2001a), 3117–3116). The stability analysis is applied to a previously unconsidered, relatively general form for dynamic equations. The perturbation analysis method of linearizing a transient mathematical system and solving the resultant eigenvalue differential equations for stability is automated using a numerical algorithm. At the inlet temperature, exit pressure, and liquid feed flow rate considered, our linear perturbation analysis and nonlinear transient simulations demonstrate the stability of some states and instability of others. Steady-state operation below 60 mA/ cm 2 average current density proves stable to infinitesimal disturbances. Beyond this production rate, however, a gas–liquid vertical flow regime, called heading flow, occurs in part of the reactor, causing unstable steady states. This flow regime permits a particular coupled flow disturbance to magnify. Namely, a liquid-flow-rate increase with position leads to local depletion of the liquid phase, as required by mass conservation. Then, the depletion of liquid creates a lighter two-phase mixture, further accelerating the fluid. Beyond the short times accessible by nonlinear transient simulation, we speculate that the unstable disturbance results in an oscillatory state or a new high-potential state. Operating conditions for avoiding instability are outlined.