Differentiable Programming for Cyclic Adsorption Processes

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Abstract
The design of cyclic adsorption processes is computationally expensive as it involves screening many process designs, each of which involve a time-consuming simulation to reach cyclic steady state. In this work, we demonstrate how differentiable programming can be used to accelerate both the simulation and attainment of cyclic steady state for a four-step pressure vacuum swing adsorption (PVSA) process to concentrate carbon dioxide from flue gas. A mechanistic one-dimensional dynamic adsorption model was implemented in JAX, enabling automatic differentiation and just-in-time compilation for efficient solution and accurate sensitivity evaluation. The latter was exploited to implement a Newton-based direct determination method for accelerated convergence to cyclic steady state, avoiding repeated cycle simulations. Across 4096 designs sampled in a six-dimensional design space, the direct determination method converged in an average of 4.6 iterations, compared to 145 cycles required by successive substitution. When combined with the computational gains from the JAX framework, this resulted in an overall speed-up of over 20 times relative to the conventional MATLAB-based implementation.

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