A new method for the solution of population balance equations(PBE) describing the micro-processes such as nucleation,growth,aggregation of particle swarms in a multiphase system is proposed.The method is based on the fixed pivot moment and allows arbitrary number of moments to be tracked si-multaneously.By expressing PBEs for both batch and continuous operations in a general form,and using weighted residual method to derive the moment equations,different moments can be tracked directly.The numerical density function is assumed to be a summation of several weighted Dirac Delta functions,and the integral and derivative terms in PBEs are transformed to a summation in order to reduce computational cost.Simulations of a batch nucleation-growth process and a continuous ag-gregation-growth process have demonstrated good agreement with the corresponding analytical solu-tions,with relative errors less than 108%.Simulation of a combined nucleation-growth-aggregation process,which does not have an analytical solution,is also included,so as to reproduce the mi-cro-behaviors of such a complex system,demonstrating the feasibility and reliability of this method. A new method for the solution of population balance equations (PBE) describing the micro-processes such as nucleation, growth, aggregation of particle swarms in a multiphase system is proposed. The method is based on the fixed pivot moment and allows arbitrary number of moments to be tracked si-multaneously.By expressing PBEs for both batch and continuous operations in a general form, and using weighted residual method to derive the moment equations, different moments can be tracked directly. The numerical density function is assumed to be a summation of several weighted Dirac Delta functions, and the integral and derivative terms in PBEs are transformed to a summation in order to reduce computational costs. Simulations of a batch nucleation-growth process and a continuous ag-gregation-growth process have demonstrated good agreement with the corresponding analytical solu-tions, with relative errors less than 108%. Simulation of a combined nucleation-growth-aggregation process, which does not have a n analytical solution, is also included, so as to reproduce the mi-cro-behaviors of such a complex system, demonstrating the feasibility and reliability of this method.