# Species Balance Equation for Water

In order to simulate moisture transfer from the solid phase to the gas phase, the following water species transport equations for each phase are considered:

where Y_{v} is the moisture content of the gas phase, * X_{s}* is the moisture content of the solid phase, D

_{vg}

*are the moisture diffusion coefficient in the gas and the solid phases, respectively, and*

**and D**_{v},_{s}*is the moisture mass transferrate between the gas and the solid phase.*

**m**# Drying Rate Model (Calculation of m)

The drying rate is controlled by two mechanisms: the constant drying rate period and the falling rate period. The surface moisture on the particle and the water in the large pores of the particle predominantly influence the constant drying rate period. The moisture trapped or bound within the porous structure of the particles controls the falling rate period.

The expression for the mass transfer rate per unit volume for the constant rate period can be expressed as

where Y* is the moisture content of the saturated drying gas at the surface of the wet particles and Y_{v} is the moisture content of the gas phase. The mass transfer coefficient * K_{sg}* can be expressed by the Gunn (1978) equation

where Sch is the Sherwood number, Sc is the Schmidt number, and A_{s} is the overall external particle surface area to unit volume ratio.

When the moisture content of the solid particles (X,) reaches a critical value of (X_{cr}), the falling rate period begins. This means that the moisture transfer of the gas and the solid phase at the external surface is significantly decreased so that the diffusion process controls the rate of drying.

The mass transfer rate per unit volume for the falling rate period can be expressed by

Dv_{s} is assumed to have a typical value of 2 x 10~^{12} m^{2}/s. * Xs* is the volume-averaged moisture content of the particles, and

*is the final volume-averaged moisture content or volume-averaged equilibrium moisture content of the particles.*

**Xf**For more details regarding governing and constitutive equations, see Jang and Arastoopour (2014).