Two-dimensional transport codes for the simulation of tokamak plasma are reduced version of full 3D fluid models where plasma turbulence has been smoothed out by averaging. One of the main issues nowadays in such reduced models is the accurate modelling of transverse transport fluxes resulting from the averaging of stresses due to fluctuations. Transverse fluxes are assumed driven by local gradients, and characterised by ad hoc diffusion coefficients (turbulent eddy viscosity), adjusted by hand in order to match numerical solutions with experimental measurements. However, these coefficients vary substantially depending on the machine used, type of experiment and even the location inside the device, reducing drastically the predictive capabilities of these codes for a new configuration. To mitigate this issue, we recently proposed an innovative path for fusion plasma simulations by adding two supplementary transport equations to the mean-flow system for turbulence characteristic variables (here the turbulent kinetic energy k and its dissipation rate ) to estimate the turbulent eddy viscosity. The remaining free parameters are more driven by the underlying transport physics and hence vary much less between machines and between locations in the plasma. In this paper, as a proof of concept, we explore, on the basis of digital twin experiments, the efficiency of the assimilation of data to fix these free parameters involved in the transverse turbulent transport models in the set of averaged equations in 2D.