초록
<P><B>Abstract</B></P><P>A bivariate population balance model is developed for describing the dynamic evolution of a PHB-producing microbial batch culture. The population balance model is solved with three different numerical methods namely, a continuous finite element method, a discrete-continuous finite element method and a discretized method with different high-resolution finite difference schemes for the calculation of the cell flux term. The various numerical methods are evaluated in terms of accuracy and computational requirements by a direct comparison of the leading moments of the bivariate distribution (i.e., <I>M</I><SUB>10</SUB> and <I>M</I><SUB>01</SUB>) to the respective quantities calculated by a simple homogeneous model for the case of zero product inhibition. Furthermore, the results obtained from the solution of the 2-D population balance model are compared with the respective results of a 1-D PBM for the case of product inhibition of the residual biomass growth rate. It is shown that the 1-D PBM cannot accurately describe the dynamics of the microbial production system when the intracellularly accumulated PHB inhibits the residual biomass growth rate and, hence, a bivariate population balance modeling approach is required to describe the dynamic behavior of the microbial culture.</P> <P><B>Highlights</B></P><P>► Numerical solution of the 2-D PBM for microbial PHB production systems. ► Comparison of 3 different numerical methods. ► A 2-D PBM approach is essential when PHB inhibition is substantial.</P>