A pseudo-steady state model of reaction and diffusion has been constructed to model the non-isothermal calcination of limestone particles which have been subjected to a history of cycling between the calcined and carbonated states. This typically occurs when using Ca-based materials for removing CO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ from the flue gas of plants such as a power station, cement plant and steel factory in certain schemes for carbon capture and storage. The model uses a Cylindrical Pore Interpolation Model to describe the intraparticle mass transfer of CO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ through the pores of the material coupled with an experimentally-determined function, $f(X)$, describing the pore evolution as a function of the conversion of the CaCO$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ present to CaO. The intrinsic rate of calcination was taken to be first order in concentration driving force. External to the limestone particle, the Stefan-Maxwell equations were used to describe the diffusion of CO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ away from the particle and into the particulate phase of the fluidised bed. The equation of energy was used to allow for the enthalpy of the reaction. In order to validate the use of the $f(X)$ function, the theoretical predictions were compared with experiments conducted to measure the rates and extent of conversion, at various temperature and different particle sizes, of Purbeck and Compostilla limestones that had been previously cycled between the carbonated and fully-calcined state. Excellent agreement between experiment and theory was obtained, and the model using the $f(X)$ approach predicted the conversion of particles of various sizes well at temperatures different to that at which the function was derived, thus indicating that the $f(X)$ solely dependent on the evolution of the morphology of the particle.