**Nomenclature**

*ρ*g Fluid density; *<sup>D</sup>*p Diameter of the particles; *α* Permeability in porous media; *C*2 Inertial drag coefficient; *<sup>M</sup>*CaCO3 Relative molecular mass of calcium carbonate; *d*CaCO3 Diameter of the internal core calcium carbonate; *ρ*CaCO3 density of the calcium carbonate; *R*D Limestone decomposition rate; *k*D Reaction constants; *p*eq Equilibrium partial pressure of carbon dioxide at the front of the reaction zone; *p*co2 CO2 partial pressure in the environment; *T*p Average particle temperature; *T*i Temperature of internal core calcium carbonate; *Y*T.C Reaction rate correction factor; *λ*1 Thermal conductivity of internal core calcium carbonate, *λ*2 Thermal conductivity of external core calcium oxide, *r*c1 Calcium carbonate radius *r*c1.m 1/2 calcium carbonate radius *r*c2.m calcium carbonate radius plus 1/2 calcium oxide layer radius; *ϕ*CaCO3 Volume fraction of calcium carbonate, *ρ*i density of calcium carbonate, *c*i specific heat capacity of calcium carbonate; *Q*D Particle reaction rate; Δ*HR* Heat of decomposition of calcium carbonate(183,000 J/mol); *Vp* Volume of individual particle; *ϕ*CaO Volume fraction of calcium oxide, *ρ*o density of calcium oxide, *c*o specific heat capacity of calcium oxide; *a*v Specific surface area of limestone; *h*v heat transfer coefficient of gas solid two phase flow; σ Stephen Boltzmanns constant; 5.6697 × 10−<sup>8</sup> W/(K4·m<sup>2</sup>); *β* Radiation attenuation coefficient of porous media; *Nu* Nussel number, *lz* Stacked bed feature length, *Pr* Prandtl number, *Re* Reynolds number, *a* Thermal diffusion coefficient; *ν* Kinematic viscosity of gas, *μ* dynamic viscosity of gas, *u* Velocity of gas movement.
