Carbon capture technologies are studied widely to curb the rising trend in the atmospheric concentration of $CO_2$ causing global warming. The post-combustion carbon capture technology using amine solvents is one of the mature technologies that can be deployed to existing power plants. However, a large amount of energy is required to regenerate the $CO_2$ rich solvent after the absorption. Flexible operation with a properly chosen control strategy is a way to alleviate this problem. Developing a simple, yet accurate dynamic model is a key to finding stable operation conditions while maximizing the flexibility of the process. In this research, chemical absorption process bases on the most widely used amine solvent, monoethanolamine (MEA), is developed using the commercial software of gPROMS. Based on the developed model, industrial scale of $CO_2$ capture process is simulated and dynamic responses of the process are analyzed In addition, it is evaluated whether the overall process can be operated stably for various disturbances that may occur during actual process operation. (e.g. changes in flue gas flow rate, $CO_2$ concentration and large disturbances such as load change in power plant). The objective of this study is to present a proper control strategy for these disturbances by applying basic PI control technique.