Continuously increasing amounts of solid plastic waste (SPW) are being generated worldwide. Chemical recycling techniques, e.g. pyrolysis, show a great potential to reduce the environmental harm induced by SPW pollution. These techniques can be combined with innovative chemical processes driven by renewable energy, resulting in carbon circularity. Detailed kinetic modeling is required to understand and optimize these processes. The main aim of this work is to develop a detailed kinetic model for the thermal pyrolysis of vinyl polymers. The model combines a detailed explicit simulation of the chemistry of the light species with the Method of Moments to simulate heavy species. The model contains 9 reaction families, 45 species, and 66 moments. The explicit simulation and MoM are linked via a dedicated routine, based on the gamma distribution. The model simulations are performed with a new computational framework that implements an evaporation model, the exact simulation of the light species, the MoM-based simulation of the heavy species, and the links between these modeling regimes. The constructed preliminary model is validated against detailed pyrolysis product distributions. The preliminary model results yield a proof of concept for this new modeling approach.