Mathematical Modelling of the Coffee Brewing Process

Abstract

The drip filter coffee market is a multi-billion euro industry. Despite this, although the chemistry of coffee brewing has been investigated in great detail, the physics of the process has received relatively little attention. In order to explain in scientific terms correlations between the coffee quality and the process variables, a physical model is required. In this study, flow through a static, saturated coffee bed, under the influence of a pressure gradient, is described using a double porosity model. The model is parametrised using experimentally obtained data from a cylindrical flow-through cell containing a coffee bed. Mass transfer from the coffee grains to the interstitial water is modelled using two mechanisms; mass transfer from the surface of the grains and mass transfer from the interior (bulk) of the grains. Mass transfer resistances are estimated by fitting experimental data. Initially coffee extraction is dominated by mass transfer from the grain surface, while transfer from the kernel of the grain is the rate limiting mechanism once the surface coffee has been exhausted.