The underlying detailed TVSA model used to train the machine learning surrogate models was described in detail in previous work and now in the Electronic Supplementary Information (ESI) Section 1. However, we applied two slight process variations within this model. These variations are a) a TVSA process using indirect heating via heat exchange pipes within the adsorbent bed (TVSA), shown Email: jpy1@hw.ac.uk RCCS, Heriot-Watt University in Figure , and b) a TVSA process with a steam purge as the desorption step (S-TVSA), shown in Figure . Process cycle diagram of an S-TVSA process that uses a steam purge during the desorption step. Both figures have been adapted from . Rather than using times to define the heating, desorption and cooling steps, we terminated these steps when a predefined temperature level was reached. The S-TVSA process required alterations to the boundary conditions and variables that defined the desorption step. For example, the boundary conditions for the S-TVSA desorption step are now the same as the adsorption step, with the inlet conditions defined as the steam properties and the outlet pressure defined as the vacuum pressure. The ESI Section 1 provides more details of the model equations, boundary conditions, performance indicator calculations, and variables. Additionally, the work equivalent is calculated from the specific thermal energy and the specific electricity consumption using the Carnot efficiency. Here, we assumed a turbine efficiency of 0.75. The Toth and Guggenheim-Anderson-de Boer (GAB) models were used to model the CO2 and H2O adsorption equilibrium, respectively, whilst the mechanistic co-adsorption model from Young et al. was used to model the co-adsorption effect. Meanwhile, it is assumed that no nitrogen is adsorbed, as is true experimentally for Lewatit® VP OC 1065. Additionally, the linear driving force (LDF) model was used to model the adsorption mass transfer and kinetics. The model for both processes was implemented in gPROMS, discretised using a central finite differences scheme, and solved using an implicit Runge-Kutta method with a variable time step. The processes were run until cyclic steady state was achieved, defined as when the composition, Email: jpy1@hw.ac.uk RCCS, Heriot-Watt University pressure, and temperature at five equidistant points along the column at the end of a cycle, but also the step times, are within 0.5% of their value at the end of the previous cycle.