Numerical study is conducted to predict effects of radiative heat loss and fuel composition in synthetic gas diffusion flame diluted with $CO_2$. The existing reaction models in synthetic gas flames diluted with $CO_2$ are evaluated. Numerical simulations with and without gas radiation, based on an optical thin model, are also performed to concrete impacts on effects of radiative heat loss in flame characteristics. Importantly contributing reaction steps to heat release rate are compared for synthetic gas flames with and without $CO_2$ dilution. It is also addressed that the composition of synthetic gas mixtures and their radiative heat losses through the addition of $CO_2$ modify the reaction pathways of oxidation diluted with $CO_2$.