Some explanatory notes on game theoretical method to solve a MOP for the flow structure in bubble columns

Abstract

The mechanism of the meso-scale structure in multi-scale reaction systems in the bubble columns is of great significance in chemical engineering. A typical analytical method to investigate the mechanism for the regime transitions of the flow in the sys-tem is through the EMMS(energy-minimization-multi-scale) model. In the EMMS model, by introducing the stability condition to reflect the idea of ‘compromise-in-competition between dominant mechanisms’, the researchers can transform the multiple objectives(energy consumptions) problem(MOP) in the system into a single objective problem(SOP) to be optimized. In our previous works, we formulated the multi-objective problem(MOP) in the gas-liquid system as a noncooperative game between the tendencies of small and large bubbles. Since there are two players and three free variables, the problem arises to distribute appropriate strategies to the players. Based on this idea, we have build two different game models by two different ways of strat-egy distribution. They showed different systems states at GNE while the first game model seemed to agree with the prediction of EMMS model on the transition regime. In this paper, we will give some explanations on these findings. We will show that the optimal point of the SOP in EMMS model differs with the GNE of the fitst game model actually. This reveals the complexity of the multi-phase reaction systems and implies that the mechanism of the meso-scale structure is absolutely not naive and needs more further investigation.