Reconstruction of a distribution from a finite number of its moments: A comparative study in the case of depolymerization process

• Three different reconstruction methods are investigated in the case of depolymerization process.
• The maximum entropy-based method reconstructs accurately the analytical solution and converges rapidly.
• The maximum entropy-based method is coupled with the quadrature method of moments (QMOM).
• The reconstruction efficiency with the maximum entropy method depends on the quality of the moments.

The resolution of the population balance equation (PBE) using moment-based methods offers a high computational efficiency however, information on the time evolution of the probability density function (PDF) is out of reach. For this, several PDF reconstruction methods using a finite number of moments are proposed in the literature. In this contribution, three different methods (i.e. beta kernel density function based method, spline based technique and the maximum entropy based approach) are tested and compared to the analytical solution of a depolymerization process. The maximum entropy method gives the most accurate approximations using only a set of six moments. This method is combined with the quadrature method of moments (QMOM) for a simultaneous reconstruction during the PBE resolution. A three nodes and a four nodes quadrature are tested. The results show that the quality of the reconstruction is highly dependent on the accuracy of the computed moments.

Figure optionsDownload as PowerPoint slide