We present a model for simulation of noisy X-ray computed tomography data sets. The model is made of two main components, a photon transport simulation component that generates the noiseless photon field incident on the detector, and a detector response model that takes as input the incident photon field parameters and given the X-ray source intensity and exposure time can generate noisy data sets, accordingly. The photon transport simulation component combines direct ray-tracing of polychromatic X-rays for calculation of transmitted data, with Monte Carlo simulation for calculation of the scattered-photon data. The Monte Carlo scatter simulation is accelerated by implementing particle splitting and importance sampling variance reduction techniques. The detector-incident photon field data are stored as energy expansion coefficients on a refined grid that covers the detector area. From these data the detector response model is able to generate noisy detector data realizations, by reconstituting the main parameters that describe each detector element response in statistical terms, including spatial correlations. The model is able to generate very fast, on the fly, CT data sets corresponding to different radiation doses, as well as detector response characteristics, facilitating data management in extensive optimization studies by reducing the computation time and storage space demands.