Inert matrix fuels are a possible option to reduce plutonium stockpiles by burning it in LWRs. These fuels, which host plutonium in a U-free inert matrix phase, may reach high burning efficiency while preventing new plutonium build-up under irradiation. In last ten years ENEA has been studying innovative U-free fuels focusing its investigation on Calcia-Stabilised Zirconia (CSZ) and thoria matrices. The high resistance to radiation damage and leaching, which characterizes the designed compounds, support a once-through fuel cycle strategy, while a decrease of fuel thermal conductivity with respect to std. UOX fuel (markedly for CSZ matrix), is a main drawback for the fuels under consideration. A first inreactor testing of these innovative fuels, has been performed through the IFA-652 experiment in the OECD Halden HBWR. Irradiation conditions were similar to the Westinghouse AP-600 fuel with 45 MWd/kgU eq burnup as target. The test-rig consists of a six-rod bundle loaded with IM, IMT and T fuel. IM and T fuel are based, respectively, on CSZ and thoria matrices, the fissile phase being HEU oxide (93% 235U enriched). IMT is a ternary fuel composed by CSZ+thoria matrix and HEU oxide as fissile phase. The thoria content in IMT fuel is adjusted so as to improve the reactivity feedbacks. Pins are equipped with fuel temperature thermocouple, internal pressure gauge and fuel stack elongation sensor. In this paper, a TRANSURANUS modelling of inert matrix fuels is discussed. In particular, a comparison of the code predictions with IM IFA-652 experimental data is performed up to 40 MWd/kgUeq average discharge burnup. Main issues of under-irradiation response (thermal conductivity and its degradation with burnup, densification-swelling behaviour and FGR) are addressed. It is expected that these results together with future PIE and parallel experiments findings, may highlight prominent features of these innovative nuclear fuels.