An engineering model that can be used to obtain predictions of axial distributions of temperature and species concentrations in dump combustors has been formulated and used to study controlled waste (benzene) incineration. The model incorporates mean convection and molecular diffusion in a quasi-one dimensional formulation and uses a stochastic model to approximate the effects of turbulent mixing on the scalar fields. The inputs to the model are extracted from experimental data and results of Large Eddy Simulations (LES). It is shown here that this approach allows the model to be developed without requiring any ad-hoc constants that have to be calibrated or tuned. Comparisons of waste consumption rates and pollutant formation in the dump combustor with experimental data show that the model can capture the experimentally observed trends correctly. Furthermore, the predicted destruction efficiency of benzene and the predicted levels of CO and NO emission show that this model also achieves fairly good quantitative agreement. The ability of this model to do scaleup design studies of large scale incinerator is also demonstrated.