  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.
