5. Heat transfer

The equation of energy balance at the surface of CO2H is given by

$$
\dot{Q}\_H + \lambda\_H \nabla T\_H = \lambda\_L \nabla T\_L \tag{8}
$$

where Q\_ <sup>H</sup> (¼ HLF1, where HL is the latent heat of hydrate dissociation) is the dissociation heat transferred to the CO2H, λ<sup>H</sup> is the thermal conductivity of hydrate. Dissociation heat per mole of hydrate, HL, is interpolated from [2] as

$$H\_L = 207,917 - 530.97 \times T\_I \tag{9}$$

where TI is the surface temperature. Then, we have

∂C

30 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

∂T

To rewrite Eq. (1), the flux at the surface of the hydrate can be discretized as

CI 

where CI is the varying surface concentration calculated locally at each surface cell, C<sup>0</sup> is the centroid concentration, and hI is the thickness of centroid surface cell, as shown in Figure 1.

kblRTln CHsol

The equation of energy balance at the surface of CO2H is given by

Figure 1. Schematic image of discretized surface concentration.

Q\_

hydrate pellet.

4. Mass transfer

5. Heat transfer

<sup>∂</sup><sup>t</sup> <sup>þ</sup> <sup>u</sup> � <sup>∇</sup><sup>C</sup> <sup>¼</sup> <sup>1</sup>

<sup>∂</sup><sup>t</sup> <sup>þ</sup> <sup>u</sup> � <sup>∇</sup><sup>T</sup> <sup>¼</sup> <sup>1</sup>

where the viscosity, diffusivity, and thermal conductivity of pure water are included in dimensionless parameters such as the Reynolds number, the Schmit number, and the Prandtl number, which are interpolated as functions of temperature and are updated at every computational time step as summarized in Table 1. U and d (=0.001 m) are the velocity of inflow and diameter of

ReSc <sup>∇</sup><sup>2</sup>

<sup>¼</sup> <sup>D</sup>∇<sup>C</sup> <sup>¼</sup> <sup>D</sup> CI � <sup>C</sup><sup>0</sup>

hI

<sup>H</sup> þ λH∇TH ¼ λL∇TL (8)

C (5)

(7)

RePr <sup>∇</sup><sup>2</sup><sup>T</sup> (6)

$$T\_I = \frac{\lambda\_L h\_H T\_L + \lambda\_H h\_L T\_H - 207,917 \cdot F\_{\text{cal}} h\_L h\_H}{\lambda\_L h\_H + \lambda\_H h\_L - 530.97 \cdot F\_{\text{cal}} h\_L h\_H} \tag{10}$$

where TL and TH are the temperatures defined at the centroids cell in the aqueous phase and solid hydrate, respectively; hL and hH are half widths of centroid in the aqueous phase and solid hydrate, respectively. Besides, the temperature in the pellet is calculated by using the heat conductivity equation.

$$\frac{\partial T}{\partial t} = \alpha\_H \frac{\partial^2 T}{\partial x^2} \tag{11}$$

where <sup>α</sup><sup>H</sup> <sup>¼</sup> <sup>λ</sup><sup>H</sup> rHC<sup>0</sup> p is the thermal diffusivity of CO2H. These relative properties of CO2H are quoted from [9], the thermal diffusivity of aqueous phase (αH) of 1:<sup>38</sup> � <sup>10</sup>�<sup>7</sup> ms�2, the heat capacity of hydrate (C<sup>0</sup> p) of 2080:0 JK�<sup>1</sup> kg�<sup>1</sup> , and the thermal conductivity (λH) of 0:324 WK�<sup>1</sup> m�1. The density of CO2H (rH) is given as 1116:8 kgm�3.
