# Nomenclature

* A_{s}* Overall external particle surface area to unit volume ratio, m~

* C_{p}* Heat capacity, J/kg K

* C_{b}* CO

_{2}concentration in gas, mol/m

^{3}

* C_{e}* Equilibrium CO

_{2}concentration, mol/m

^{3}

C; Concentration at reaction interface, mol/m^{3}

* D_{g}* Product layer diffusivity, m

^{2}/s

* d_{p}* Particle diameter, m

D_{vg} Moisture diffusivity of gas phase, m^{2}/s

* D_{vs}* Moisture diffusivity of solid phase, m

^{2}/s

* e_{ss}* Particle restitution coefficient

* e_{sw}* Restitution coefficient between solid and wall

* f* Number density function

* f* Dimensionless number density function

g_{0} Radial distribution function at contact during binary collision

* h_{g}* Enthalpy of gas phase per unit mass, J/kg

* h_{s}* Enthalpy of solid phase per unit mass, J/kg

* H_{vap}* Heat of vaporization per unit mass, J/kg

* k_{s}* Reaction rate constant, m/s

* K_{sg}* Mass transfer coefficient, m/s

* m_{sg}* Mass transfer rate, kg/m

^{3}-s

* MW* Molecular weight, kg/kmol

*^{N}°MgO* Initial number of moles of MgO, mol/m

^{3}

* Nu* Nusselt number

* P_{v}* Vapor pressure, N/m

^{2}

* q* Rate of heat flux, W/K

* Q_{sg}* Rate of heat transfer per volume between gas and solid, W/m

^{3}

rr Rate of carbonation reaction, kmol/kg s

* Re_{p}* Particle Reynolds number

* r_{p}* Radius of sorbent particle, m

* r_{c}* Radius of unreacted core of sorbent particle, m

* Sc* Schmidt number

* Sh* Sherwood number

* T* Temperature, K

* v_{g}* Gas-phase velocity, m/s

* v_{p}* Particle-phase velocity, m/s

v_{s} Solid-phase velocity, m/s

* v_{s},_{para}* Particle slip velocity parallel to the wall, m/s

X Sorbent conversion

* X_{cr}* Critical moisture content, kg

_{water}/kg

_{solid}

* Xf* Final volume-averaged moisture content, kg

_{water}/kg

_{so}i

_{id}

* X_{s}* Volume-averaged moisture content of the solid phase, kg

_{water}/kg

_{solid}

Y_{v} Moisture fraction in gas phase

Y* Moisture fraction of saturated drying gas at surface of wet particles

Greek Symbols

ф Specularity coefficient between the particle and the wall * p_{i}* ith moments of density distribution function

*Gas-particle heat transfer coefficient, W/m*

**a**_{gs}^{2}K

*kth phase volume fraction*

**e**_{k}в Granular temperature, m^{2}/s^{2}

? Sorbent density, kg/m^{3}

* p_{k}* kth phase density, kg/m

^{3}

т_{к} kth phase stress tensor, N/m^{2}