Solving population balance equations in terms of the gamma distribution

A new approach for solving Population Balance Equations (PBEs) is examined. Evidence from previous research efforts suggests that the General Gamma Distribution is able to describe accurately a general Particle Size Distribution (PSD). We have conjectured that it can be used for the solution of a PBE. The overall project goal aims to develop the tools to solve PBEs by assuming the solution form to be a linear combination of one or more General Gamma Distributions and to assess the respective accuracy.;For uni-modal populations the number density function is assumed to be equal with a single General Gamma Distribution whose parameters are allowed to change over time. The advantage of this method is based on the fact that a very small number of depending variables and their change with time is required, compared to traditional methods. After this approximation is introduced to the PBE, the residual function is calculated. The equations describing the time change in the parameters are obtained by calculating the projections of this residual onto an orthogonal function basis set. General Laguerre Polynomials are selected as the basis set. Approximation of bi-modal distributions is also examined.;Example simulations indicate that the approach is quite accurate.