Modeling the extraction of espresso components as dispersed flow through a packed bed

Espresso extraction involves a flow of heated water through a densely packed bed of porous particles driven by high pressure. This flow is impacted by a series of structural changes that the packed bed undergoes during water percolation. In this work, we aim to improve and extend an existing extraction model from Moroney et al. (2015) by integrating the axial dispersive flow through the coffee bed via a characteristic axial diffusion coefficient. This parameter was obtained by means of tracer pulse experiments applied to different packed bed configurations at different stages of the extraction. Increasing axial dispersion of the flow was observed experimentally with progressing extraction time. This characteristic was included in the model by considering a transition of the axial diffusion coefficients from the initial filling phase to the steady-state flow phase. The model was also extended to describe the concentration of individual species in the brew. Lumped mass transfer coefficients and saturation concentrations were fitted to experimental results. The model was then validated against experimental data from extraction trials using different particle size distributions. Good agreement was found for the extracted total dissolved solids as well as for the concentrations of caffeine, trigonelline and 5-caffeoylquinic acid (5-CQA). The proposed approach enables an estimation of the overall and individual component concentrations for various particle size ranges while accounting for the dynamic internal changes inside the packed bed during the extraction time.