Due to increasing environmental concerns the focus of traffic management and control is shifting towards optimizing the traffic control measures to also reduce traffic emissions and fuel consumption. In this context we propose a model-based predictive traffic control approach for the balanced reduction of travel times, emissions, and fuel consumption for freeway networks, where not only the local emissions are taken into account but also the dispersion of the emissions to various target zones near the freeways. The core of the approach is a new efficient model for describing the area-wide dispersion of the emissions that is much faster than the models we have proposed in earlier papers. We present a detailed description of the new so-called expanding grid-based model and we embed it in a model-based predictive traffic control approach using variable speed limits.