## ABSTRACT

This chapter presents mathematical methods of analysis of the dispersed systems. In such systems, particles are embedded in the continuous phase and interact with this environment as well as with other entities which form the particle’s population. The chapter focuses on sectional methods commonly used for homogeneous systems and quadrature-based moment methods which were successfully coupled with CFD models. To predict the evolution of population and discrete entities forming this population, one should define a phase space. To determine how the population in some control volume is distributed over particle properties, the number density function, number density function, should be defined. The population balance equation in its general form is a nonlinear integro-partial-differential equation. In the case of multimodal distributions, the population can be divided into groups characterized by delta functions centered on the mean values of internal coordinates or by log-normal distributions.