To describe the heterogeneous reaction between the sorbent and CO_{2}, it was assumed that the particles can be described (see Fig. 5.4) by two distinct zones representing the outer product layer and the inner core (fresh sorbent).

The heterogeneous kinetic model for the reaction between CO_{2} and the sorbent based on a two-zone variable diffusivity shrinking core model is described by Abbasi et al. (2013) as

C_{b} is the CO_{2} concentration in the bulk gas, C_{e} is the equilibrium CO_{2} concentration, D_{g} is the product layer diffusivity of CO_{2}, r_{p} is the radius of the particle, k_{s} is the surface reaction constant rate at each zone, and N^{o}MgO is the initial number of moles of MgO per unit volume. In the above model, the dependence of the gas diffusion coefficient D_{g}, through the porous product layer with respect to conversion, was assumed to follow an exponential decay function (Abbasi et al. 2013). The rate of the carbonation reaction can be calculated from the rate of the sorbent conversion obtained from the two-zone variable diffusivity shrinking core model which gives the dX/dt in the following correlation: