Modelling the rate of adsorption of carbon dioxide by wheat

Published data are used to evaluate three mathematical models of the adsorption of carbon dioxide by wheat. One is termed a lumped parameter model in which the mass transfer driving force is the difference between the average value of the mass fraction of carbon dioxide adsorbed at the surface of the grain kernels, and the average value of that in the interior. An algebraic expression for the rate constant is presented. Although the lumped parameter model is inherently unable to account for the high mass transfer driving force adjacent to the surface of the grain kernels when they are suddenly immersed in carbon dioxide-rich atmosphere, it is shown to be reasonably accurate. In an attempt to capture the mechanisms of adsorption, two mathematical models are proposed in which mass transfer is deemed to be governed by diffusive processes. In the first model, the mass transfer driving force is the intraparticle gradient of the adsorbed carbon dioxide. In the second model, the mass transfer process is notionally driven by the concentration gradient of gaseous carbon dioxide within the pores of the grain kernels. The gas is subsequently adsorbed by the solid substrate that constitutes the kernels. Of the three models investigated, the last model is found to be the most accurate, but it is computationally expensive. It is suggested that the lumped parameter model is to be preferred because it combines reasonable accuracy and it is very easy to implement. Further research is required to improve the accuracy of models of adsorption and desorption of carbon dioxide by grains and seeds under the diverse and dynamic conditions met in practice.