The QMOM Method to Solve The PBE Equations of the Urban Haze

Abstract

Mega and medium-sized cities in China are facing the increasingly serious aerosol pollution, among them Xi’an is one of the typical cities. During the early stage of ash haze, aerosol concentration is rising so fast that the simulation of the process is difficult. This article uses the population balance equation (PBE) describing the distribution of fine particles, and solves the changing process of particle size distribution by the moment method. Population balance equation, a non-linear hyperbolic equation about number density function, is employed to describe micro-behaviors (aggregation, breakage, growth) of disperse phase and resulting variation of particle size distribution. 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. Three examples of simulation results show that compared with the analytical solution, relative error of this method is within 10−5 and has the characteristics of high precision and low computation amount. In early 2016, the early stage of PM2.5 pollution in Xi’an is simulated and the simulation results and experimental results are highly consistent.