The polytropic model to describe air expansion, has been used for years to describe the behavior of surge vessels. In this thesis the alternative to describe this behavior, the Rational Heat Transfer (RHT) equation developed by Graze (1968), is extended with an estimation of all heat terms in surge vessels. The RHT model is compared to the poly- tropic model for isolated and non-isolated vessels and is shown to give a good estimation for the air expansion, which has been checked with measurement data from Shuweihat, a location in Abu Dhabi in the United Arab Emirates where a large pumping station is located. Calculations for the size of the surge vessel point out that the minimal volume of a surge vessel calculated with the RHT model is 10 % smaller than if the volume is calculated with the polytropic model. Furthermore, the heating of the air pocket in a surge vessel has been modeled by a numerical solution of the one-dimensional heat equa- tion with a convective and a non linear source term. From this models can be concluded that the air in a surge vessel warms up slower than the expansion time of that vessel.