1D Modeling Approach for Heat Transfer in Packed Beds with Embedded Heat Sources

To improve heat transfer in packed bed temperature swing adsorption processes for direct air capture, reactors with embedded cylindrical heating pipes have been developed. Optimization of these inherently dynamic systems currently requires a transient two-dimensional (2D) model, which is computationally very expensive. In the present work, a method is therefore developed to translate a 2D fixed bed geometry into an equivalent one-dimensional (1D) model by placing line heat sources along the direction modeled in 1D. To determine these sources' strength, a Nusselt correlation is required. It is found that for staggered cylinder configurations, the single cylinder correlation works well. For in-line configurations, an analytical correction factor is successfully developed to account for the effect of the thermal wake of the upstream cylinders on the heat transfer around a cylinder. The 2D to 1D translation approach is then tested with three different cylinder-packing geometries at varying Peclet numbers and for steady-state and dynamic simulations. For the steadystate simulations, the 1D model has a maximum deviation of 10% in the bed mean temperature and for the outlet temperature from the 2D results (scaled to the maximum temperature difference), thus showing good agreement. For the dynamic simulations, the deviation is below 20% for most conditions, showing reasonably good agreement. The merit of the translation approach becomes apparent when looking at the computational time: the 1D model calculations are a factor of 500 faster than the 2D calculations.