The efficient control of compressor stations in gas transportation networks sill posses a mathematical and engineering challenge in the presence of complex gas flow patterns. On the fine scale such patterns are resolved by systems of partial differential equations as for example the isothermal Euler equations. However, the fine scale models are typically computational inefficient. A hierarchy of simplified models are derived starting from isothermal Euler equations by using for example asymptotic analysis. The reduced complexity of those models also allows to efficiently compute flows and pressure changes on large scale networks. Some of the models as well as their studies on their validity are presented with computational results. Further, we apply a space mapping optimization concept to optimize for the fine model using information on the coarse model only.