6. Computational conditions

Two types of cells, tetrahedrons and triangular prisms, are applied in the present unstructured grid system, as introduced in Figure 2. In detailed, the surface of hydrate uses prism. Both the flow field and inside the pellet are tetrahedral meshes. Upward is the inflow where initially the uniform velocity profile is adopted. Prism mesh and no-slip condition are imposed at the surface of the pellet. To analyze more detailed mass and heat transfer simulatneously, one cell-layer of the prisms that attached to the CO2H surface is divided into at least five very thin layers as referred in [8] for high Prandtl or Schmidt number. The basic parameters of computation are denoted in Table 1. The initial values of dimensionless parameters are listed in Table 2 at the temperatures from 276.15 to 283.15 K. Reynolds number, Schmidt number, and Prandtl number function of the temperature or pressure are listed in Table 2. The minimum grid size of this computational model is listed in Table 3. Lm, Lc, and LT are the applied mesh thicknesses. δm, δc, and δT are the thickness of momentum, concentration, and thermal boundary layers, respectively. The relationship between δm, δc, and δT quoted from the theory of flat plate boundary layer is listed below:

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

$$
\delta\_m = \frac{5.48 \text{ d}}{\sqrt{\text{Re}} \, \text{2}} \tag{12}
$$

To follow [22] of Eq. (14), the boundary layer's thickness for temperature, δ<sup>T</sup> is assumed as the same size as that for mass concentration, δc. For the initial temperature of the CO2H pellet, Tini

Direct Numerical Simulation of Hydrate Dissociation in Homogeneous Porous Media by Applying CFD Method…

http://dx.doi.org/10.5772/intechopen.74874

33

The in-house code originally developed by [7] has been applied to determine the intrinsic dissociation rate of methane hydrate. The numerical results verified by experimental results are successfully used in calculating one pellet of hydrate in a slow flow rate of high pressure without considering the collapse of hydrate and the nucleation of bubbles referring to [6, 20] as well.

In this study, cases with porosity of 74, 66, and 49 are individually discretized as face-centered unstructured packing of hydrate in sediment. CO2H pellets with initial temperature of 253.15 K dissociate due to the variation of driving force, ex. 0.89 and 0.77 MPa, under thermal stimulation of ambient warm water, ex. 282.15 and 276.15 K. Comparative small driving forces selected here is due to the assumption of no surface's collapse. Computational conditions are listed in Table 2. Result of flux at the surface is the converge value as shown in Figure 3. In Figure 4(a)–(c) at time 0.16(s) show velocity vector of case 1 in three specific sections. In Figure 5, the distributions of concentration at 0.16 s are presented. Slight CO2 discharges at the surface. Relative temperature distributions are indicated in Figure 6. As time increases, the dissociation heat of CO2 hydrate results in water temperature drop significantly as shown in

is assumed as a constant value of 253.15 K.

7. Verification

8. Results of case study

Figure 3. Converge value of case 1.

$$\delta\_c = \frac{\delta\_m}{1.026 \cdot \text{Sc}^{1/3}}\tag{13}$$

$$
\delta\_T = \frac{\delta\_c}{\mathbf{Pr}^{1/3}} \tag{14}
$$

Figure 2. Description of mesh in unstructured grid system of 67,104 cells. (a) Overview, (b) surface of CO2H, (c) water, and (d) pellets of CO2H.


Table 2. Calculation conditions of this work.


Table 3. The thicknesses of boundary layers, δ<sup>m</sup> and δc&T, and grid sizes, Lm and Lc&T (unit: meter).

To follow [22] of Eq. (14), the boundary layer's thickness for temperature, δ<sup>T</sup> is assumed as the same size as that for mass concentration, δc. For the initial temperature of the CO2H pellet, Tini is assumed as a constant value of 253.15 K.
