Low-carbon dispatchable power underpins a sustainable energy system, providing load balancing complementing wide-scale deployment of intermittent renewable power. In this new context, fossil fuel-fired power plants must be coupled with a post-combustion carbon capture (PCC) process capable of highly transient operation. To tackle design and operational challenges simultaneously, we have developed a computational framework that integrates process design with techno-economic assessment. The backbone of this is a high-fidelity PCC mathematical model of a pressure-vacuum swing adsorption process. We demonstrate that the cost-optimal design has limited process flexibility, challenging reactiveness to disturbances, such as those in the flue gas feed conditions. The results illustrate that flexibility can be introduced by relaxing the CO$_2$ recovery constraint on the operation, albeit at the expense of the capture efficiency of the process. We discover that adsorption-based processes can accommodate for significant flexibility and improved performance with respect to the operational constraints on CO$_2$ recovery and purity. The results herein demonstrate a trade-off between process economics and process operability, which must be effectively rationalised to integrate CO$_2$ capture units in the design of low-carbon energy systems.
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