Thermal Source Compatibility Limits for Temperature-Vacuum Swing Adsorption Direct Air Capture: Finite Power, Heat Transfer, and Exergy Constraints for Low-Carbon Thermal Integration

Temperature-vacuum swing adsorption (TVSA) direct air capture (DAC) is often modelled with a prescribed regeneration-wall temperature, which does not identify the thermal source capability required to realise it. This study replaces that boundary with a finite heat source defined by temperature, maximum thermal power, and source-to-wall conductance, with desorption pressure treated as an interacting process variable. A dynamic wall balance distinguishes source heat, wall-to-bed transfer, wall sensible heating, and source-to-wall irreversibility. For the selected APDES contactor under the fixed reference cycle, a 120 °C wall temperature limit, nominally zero external regeneration heat loss, and a desorption pressure of 0.073 bar, the conditional source-power boundary is approximately 4.2–4.3 kWmbed−3 over 120–160 °C, while the conductance boundary decreases from approximately 135 to 48 W mbed−3K−1. These limits are not jointly sufficient: at 130 °C, the minimum feasible conductance decreases from approximately 247 to 82 W mbed−3 K−1 as the power density rises from approximately 4.2 to 8.4 kWmbed−3. Near-equivalent performance requires approximately 14.23 MJ kg−1 CO2 of source heat, while thermal exergy increases from 3.62 to 4.60 MJ kg−1 CO2 between 120 and 160 °C. The resulting 187-point process envelope supports the screening of solar thermal, thermal energy storage, waste heat, and other low-carbon heat supplies for DAC integration.