An unreacted shrinking core model with variable effective diffusivity was applied to sulfation test data from a pressurised thermogravimetric apparatus (P-TGA) for various limestone and dolomite samples. The particle size was 250-300 μm for all sorbents. The tests were carried out under conditions typical for a pressurised fluidised bed combustor, i.e. 850 or 950°C, 1.5 MPa. Under these conditions the limestone remains uncalcined, whilst the dolomite is half-calcined. The sorbents were characterised by chemical composition analysis, particle density measurement, mercury porosimetry and BET internal surface measurement. A key parameter in this study is the conversion-dependent Thiele parameter, which reveals a shift in rate-determining mechanism during the sorbents' sulfation. The extended model allows the effect of particle structure on the reaction rate constant and the product layer diffusivity to be evaluated. Estimates for the apparent activation energy of the kinetics and the product layer diffusion can also be given, based on data from two temperatures.