The presence of strong imaging artefacts in microtomographic X-ray data makes the CAD modelling process difficult to carry out. As an alternative to traditional image segmentation techniques, we propose to register the CAD models by deploying a realistic X-ray simulation on GPU in an optimisation framework. A user study was also conducted to compare the measurements made manually by a cohort of volunteers and those produced with our framework. Our implementation relies on open source software only. We numerically modelled the real experiment, taking into account geometrical properties as well as beam hardening, impulse response of the detector, phase contrast, and photon noise. Parameters of the overall model are then optimised so that X-ray projections of the registered the CAD models match the projections from an actual experiment. It appeared that manual measurements can be variable and subject to bias whereas our framework produced more reliable results. The features seen in the real CT image, including artefacts, were accurately replicated in the CT image reconstructed from the simulated data after registration: (i) linear attenuation coefficients are comparable for all the materials, (ii) geometrical properties are accurately recovered, and (iii) simulated images reproduce observed experimental artefacts. We showed that the choice of objective function is crucial to produce high fidelity results. We also demonstrated how to automatically produce CAD models as an optimisation problem, producing a high cross-correlation between the experimental CT slice and the simulated CT slice. These results pave the way towards the use of fast realistic simulation for accurate CAD modelling in tomographic X-ray data.