The design of cyclic adsorption processes is computationally demanding, requiring repeated convergence to cyclic steady state within an iterative optimisation loop. Conventional workflows treat the process simulator as a black box and rely on derivative-free optimisation, resulting in design campaigns that can require hundreds to thousands of CPU hours. This work presents an end-to-end differentiable model of a pressure vacuum swing adsorption process, developed using the JAX differentiable programming framework and applied here to a benchmark post-combustion carbon capture problem. Automatic differentiation provides exact gradients throughout the entire computational workflow. The differentiation of a single process cycle provides the Jacobian for a Newton iteration to decrease both the number of iterations and the simulation time required to reach cyclic steady state by a factor of 20 relative to a representative MATLAB implementation. Exact gradients of the performance metrics with respect to the design variables further enable gradient-based multi-objective optimisation using the IPOPT algorithm. Applied to a six-variable design problem, the latter produces a superior Pareto front with improved coverage of the trade-off space and closer convergence to the optimal front than the genetic algorithm NSGA-II. Notably, the full front is obtained over two orders of magnitude faster than the conventional approach. By retaining the full mechanistic model while making it differentiable, this framework transforms cyclic adsorption process design from slow black-box simulation with derivative-free optimisation to efficient gradient-enhanced modelling and optimisation, enabling rapid and systematic exploration of complex design spaces.

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