The design of new low-emission systems requires the development of models providing an accurate prediction of soot production for a small computational cost. In this work, a three-equation model is developed based on mono-disperse closure of the source terms from a sectional method. In addition, a post-processing technique to estimate the particles size distribution (PSD) from global quantities is proposed by combining Pareto and log-normal distributions. After validation, the developed strategy is used to perform a large eddy simulation of soot production in a model combustor representative of gas turbine combustion chambers. It is shown that the three-equation model is able to provide a good estimation of soot volume fraction and information on PSD in complex geometries for a low computational time.