Fluidized bed combustion or gasification allows for in-bed sulfur capture with a calcium-based sorbent such as limestone or dolomite. Sorbent particle size, porosity, internal surface, and their variation during conversion have great influence on the conversion of the sorbent. The uptake of SO2 and H2S by five physically different limestones is discussed, for typical pressurized fluidized bed combustor or gasifier conditions: 850/950°C, 15/20 bar. Tests were done in a pressurized thermogravimetric apparatus (P-TGA), the size of the limestone particles was 250-300 μm. It is stressed that the limestones remain uncalcined. A changing internal structure (CIS) model is presented in which reaction kinetics and product layer diffusion are related to the intraparticle surface of reaction, instead of the outer particle surface as in unreacted shrinking core (USC)-type models. The random pore model was used for describing the changing internal pore and reaction surfaces. Rate parameters were extracted for all five limestones using the CIS model and a USC model with variable effective diffusivity. Differences in the sulfur capture performance of the limestones were evaluated. Plots of the CaSC4 or CaS product layer thickness as a function of conversion are given, and the relative importance of limestone porosity and internal surface is discussed.