Two-equation soot models, which solve conservation equations for soot number density and mass concentration, have been extensively used to study soot formation in laboratorial turbulent flame and practical gas-turbine combustors. This study investigates the effects of different inception, growth coagulation, and oxidation source terms in a two-equation semi-empirical soot model that has been implemented to model two turbulent ethylene/air jet flames. The gas-phase chemistry is modeled using the laminar flamelet approach. A new soot inception submodel is proposed that is based on the naphthalene formation rate calculated by the detailed chemical kinetics. The expected value of the formation rate is stored in the flamelet library. Model predictions were compared with the measurements of Young and Moss. The predictions of the soot volume fraction are very sensitive to the soot surface growth rate. The soot predictions agree well with measurements when the surface growth rate is assumed to be proportional to the square root of the surface area. The result also indicate that the naphthalene inception route exhibits better performance. Finally a new soot model with an optimal combination of rates was developed. The model predictions provided good agreement with the experimental temperature, mixture fraction, and soot volume fraction distributions along both the axial and radial directions. The optimal soot model was also successfully validated on another turbulent ethylene/air jet flame.