A third-order approximate solution of the reaction-diffusion process in an immobilized biocatalyst particle

摘要

A third-order polynomial model was suggested to describe the reaction-diffusion process of substrate in the immobilized biocatalyst particles and further to estiamte their effectiveness factors.Both the numerical solution of the differential equation using the shooting method and the third-order approxiamte solution have been obtained.They were in good agreement for describing the substrate concentration distribution inside the particles when beta=C_s/K_m was was larger than or equal to 0.75 phi~2-1 and phi=(R/S)r_m/DK_m.The relative errors of effectiveness factors obtained by the two methods were found less than 10% in a wide range of phi~2 and berta except for the high values of phi~2.Some published practical systemsw ere alkso examined.The results have indicated that the method propsoed here could be of value for a quick estimation of substrate distribution and effectiveness factor of some systems such as dynamic oxygen transfer into natural mycelial pellets in submerged cultures.