Study on Dynamic Liquid-Carrying Process of Foaming Agent and Establishment of Mathematical Model

The efficiency of foam drainage gas recovery is predominantly dictated by the performance of the foaming agent. To better understand their behavior, a novel testing apparatus was developed to simulate the foam drainage gas recovery process within the wellbore. Through the dynamic liquid-carrying performance tests of four foaming agents under uniform conditions, it was discerned that there existed significant disparities in the liquid-carrying performance and action duration. Further interface performance analysis disclosed that the liquid-carrying capacity and the duration were correlated with their adsorption capacity and interface activity at the gas-liquid interface. Notably, foaming agents with lower adsorption capacity and higher interfacial activity demonstrated superior liquid-carrying performance and longer action duration. By analyzing the consumption of foaming agents during the liquid-carrying process, five dynamic liquid-carrying equations were derived based on first-order reaction kinetics, the Malthusian population model, and the logistic function. The outcomes demonstrated that all these five equations could precisely delineate the dynamic liquid-carrying process of the foaming agent. During the research, we found that the consumption of the foaming agent in the foam drainage gas recovery process is related to its adsorption behavior at the gas-liquid interface, and revealed that the dynamic liquid-carrying process of foaming agent is the increasing process of liquid-carrying capacity under the continuous consumption of limited foaming agent resources. This laid a foundation for the further exploration of the functional mechanism of the foaming agent in the foam drainage gas recovery process.