The two-stage Lagrangian (TSL) reacting-jet model of Broadwell and Lutz is applied to n-heptane fuel jets to understand soot formation at diesel engine operating conditions. The model employs a diffusion-flame reactor and homogeneous core reactor with jet entrainment rates determined by empirical correlations. Detailed chemical kinetics, consisting of 696 species and 3224 reactions, are used for predictions of n-heptane oxidation and soot precursor formation up to seven-ring polycyclic aromatic hydrocarbons. Boundary conditions are based on realistic diesel operating conditions, mixing rates, and flame lift-off lengths. TSL soot precursor simulations are compared with closed-reactor (Senkin) predictions over a range of temperatures and equivalence ratios. Results show that the equivalence ratio-temperature region of soot precursor formation varies from the closed-reactor predictions and depends upon parameters such as ambient oxygen concentration, injection pressure, nozzle orifice size, and flame lift-off. The lack of a unique equivalence ratio-temperature region for soot precursor formation implies that the soot formation process depends upon the equivalence ratio-temperature path followed during jet mixing, and the residence time along the path.