9. Discussion

Figure 4. Velocity vector in the vicinity of pellets (case 1: T = 282.15 K, Tini = 253.15 K, Re = 50, Sc = 755, Pr = 10, VTL = 5,

Figure 5. Concentration profile in three specific sections of cubic unit (case 1: time = 0.16 s, unit: mole/m<sup>2</sup> s). (a) Front

Figure 6. Temperature profile in three specific sections of cubic unit (case 1, time = 0.16 s, unit: K). (a) Front section, (b)

and time = 0.16 s). (a) Front section, (b) Center section and (c) Back section.

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

section, (b) Center section and (c) Back section.

Center section and (c) Back section.

To follow the modeling illustrated in [14]:

$$F\_3 = k\_D \left( f\_{eq} - f\_{\mathcal{g}} \right) = k\_{D0} \exp \left( -\frac{\Delta E}{RT} \right) \left( f\_{eq} - f\_{\mathcal{g}} \right) \tag{15}$$

where kD<sup>0</sup> mol Pa�<sup>1</sup> <sup>s</sup>�1m�<sup>2</sup> is the rate constant, <sup>f</sup> <sup>g</sup>ð Þ Pa is the fugacity of gaseous CO2, and <sup>f</sup> eq is the fugacity of the quadruple equilibrium. They obtained kD<sup>0</sup> and ΔE for CO2H as <sup>1</sup>:<sup>83</sup> � 108 mol Pa�<sup>1</sup> s�1m�<sup>2</sup> and 102:88 kJ mol�<sup>1</sup> , respectively, at temperature and pressure ranging from 274.15 to 281.15 K and from 1.4 to 3.3 MPa. However, new modified value of ΔE, if considered the real case in the ocean quoted from [16], is 96:49 kJ mol<sup>1</sup> . The order of Reynolds number based on the size of a particle, about 16 μm, is calculated as 50. Clarke et al. [28] determined the dissociation rate of CO2H by measuring the nucleated methane gas in V-L state [14]. The comparison of three models is listed in Table 4. The results of dissociation flux are summarized in Figure 9. Higher water temperature induces higher dissociation flux at the surface of hydrate. Data correlated by [14] show much lower level than both Nihous' model and new model. The numerical results in this work marked as new model in Figure 9 show consistent result compared with Nihous' model. The dissociation flux in various flow rates in cases 5, 7, and 8 are listed in Figure 10. Here, it is noted that porosity is not considered in both Clarke's and Nihous' models, and these two models are only function of temperature and fugacity as presented in Eq. (15). The trend of flux becomes saturated in the figure due to the surface dissociation flux that becomes slow due to the fast mass transfer in bulk flow at Reynolds number over 100.


10. Conclusions

Figure 10. Results of flux in cases 5, 7, and 8.

Acknowledgements

the valuable advices and guidance.

The objective of this work is to establish a new pore-scale model for estimating the dissociation rate of CO2H in laboratory-scale sediment samples. It is assumed that CO2H formed homogeneously in spherical pellets. In the bulk flow, concentration and temperature of liquid CO2 in water flow was analyzed by computational fluid dynamics (CFD) method without considering gas nucleation under high-pressure state. In this work, finite volume method (FVM) was applied in a face-centered regular packing in unstructured mesh. At the surface of hydrate, a dissociation model has been employed. Surface mass and heat transfer between hydrate and water are both visualized. The initial temperature 253.15 K of CO2H pellets dissociated due to ambient warm water flow of 276.15 and 282.15 K and fugacity variation, ex. 2.01 and 1.23 MPa. Three tentative cases with porosity 74, 66, and 49% are individually simulated in this study. In the calculation, periodic conditions are imposed at each surface of packing. Additionally, the flux at CO2H's surfaces is compared to Clarke and Bishnoi [13] and Nihous and Masutani [15] 's correlations at Reynolds number of 50. Numerical results of this work show good agreement with Nihous' model. Kinetic modeling by using 3D unstructured mesh of regular cubic unit and CFD scheme seems to be a simple tool to estimate the dissociation rate of CO2H in laboratory-scale experiments, and could be easily extended to determine complex phenomena

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

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

37

coupled with momentum, mass, and heat transfer in the sediment samples.

This work was supported by DOIT, Ministry of Science and Technology under contract No. MOST 106-3113-M-002-006. The authors also wish to acknowledge Professor Toru SATO for

Figure 9. Results of simulation compared to existing two models.

Direct Numerical Simulation of Hydrate Dissociation in Homogeneous Porous Media by Applying CFD Method… http://dx.doi.org/10.5772/intechopen.74874 37

Figure 10. Results of flux in cases 5, 7, and 8.
