As a long term objective we would like to define the required conditions to detect oil spills, using high frequency surface wave radar (HFSWR). Assuming that the presence of oil spills on the sea surface modifies the surface tension which in turn affects the dynamics of the sea, we would like to determine the minimal surface tension which makes this phenomenon observable on a Doppler spectrum. For this purpose we have developed a simulator based on a realistic modeling of the sea and of its temporal variation as well as on an exact modeling of the interactions between the electromagnetic waves and the environment. We have chosen to implement a full wave model called ELSEM3D, developed by ONERA. This tool is based on the method of moments (MoM) which can be accelerated by the fast multipole method (FMM). The issues of such a modeling are numerous: computational time due to the number of temporal realizations required to generate a Doppler spectrum and the dimension of the scene. In this paper, we will discuss the issues raised by this study and outline how we can overcome them. We will also present some simulated Doppler spectra for different sea states and radar configurations.