1. Introduction

Computational fluid method (CFD) is popular in either large-scale or meso-scale simulations. One example is to establish a new pore-scale (m~μm) model of laboratory-scale sediment

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

samples for estimating the dissociation rate of synthesized CO2 hydrate (CO2H) reported by [1]. To decrease the CO2 concentration in the air, carbon dioxide capture and storage (CCS) is regarded to be an effective way. One concept of CCS is to store CO2 in gas hydrate in subseabed geological formation, as was illustrated by [6]. Besides, many studies about the formation and dissociation of CO2 hydrate (CO2H) while stored in the deep ocean or geologic sediment have been introduced. In particular, flow and transport in sediment is multidisciplinary science including the recovery of oil, groundwater hydrology and CO2 sequestration. It reported the measurements of the dissociation rate of well-characterized, laboratory-synthesized carbon dioxide hydrates in an open-ocean seafloor [5]. The pore effect in the phase equilibrium mainly due to the water activity change was discussed in [7]. The reactive transport at the pore-scale to estimate realistic reaction rates in natural sediments was discussed in [3]. This result can be used to inform continuum scale models and analyze the processes that lead to rate discrepancies in field applications. Pore-scale model is applied to examine engineered fluids [4]. Unstructured mesh is well suited to pore-scale modeling because of adaptive sizing of target unit with high mesh resolution and the ability to handle complicated geometries [17, 18]. Particularly, it can easily be coupled with computational fluid dynamics (CFD) methods, such as finite volume method (FVM) or finite element method (FEM). Unstructured tetrahedral mesh used to define the pore structure is discussed in [19]. Another case includes a numerical simulation of laminar flow based on FVM with unstructured meshes was used to solve the incompressible, steady Navier-Stokes equations through a cluster of metal idealized pores by [20].

where kbl is the rate constant mol2 J

3. Basic transport equations

C and temperature T are also considered.

∂u

T <sup>η</sup>LV0:<sup>6</sup> A

<sup>∂</sup><sup>t</sup> <sup>þ</sup> <sup>∇</sup> � ð Þ¼� uu <sup>∇</sup><sup>P</sup> <sup>þ</sup>

<sup>2</sup> <sup>ν</sup><sup>L</sup> <sup>¼</sup> <sup>8</sup>:<sup>8286</sup> � <sup>10</sup>�<sup>10</sup> � �T<sup>2</sup> � <sup>5</sup>:<sup>3886</sup> � <sup>10</sup>�<sup>7</sup> � �<sup>T</sup> <sup>þ</sup> <sup>8</sup>:<sup>314</sup> � <sup>10</sup>�<sup>5</sup> <sup>ν</sup><sup>L</sup> ms�<sup>2</sup> � �: kinematic viscosity

<sup>3</sup> <sup>λ</sup><sup>L</sup> <sup>¼</sup> <sup>487</sup>:85lnð Þ� <sup>T</sup> <sup>2173</sup>:<sup>8</sup> <sup>λ</sup><sup>L</sup> WKm�<sup>1</sup> � �: heat conductivity of water

� � � <sup>103</sup> <sup>α</sup>=44.580 and <sup>β</sup> <sup>=</sup> � 10246.28

No. Function Definition

below:

the hydrate CI.

<sup>1</sup> <sup>D</sup> <sup>¼</sup> <sup>7</sup>:<sup>4</sup> � <sup>10</sup>�<sup>12</sup> ð Þ <sup>φ</sup>MB <sup>1</sup>=<sup>2</sup>

<sup>4</sup> <sup>α</sup><sup>L</sup> <sup>¼</sup> <sup>λ</sup><sup>L</sup> r<sup>W</sup> Cp

<sup>5</sup> Peq <sup>¼</sup> exp <sup>α</sup> <sup>þ</sup> <sup>β</sup>

T

Table 1. Parameters used in this study.

<sup>6</sup> CHsol <sup>¼</sup> <sup>a</sup>∙exp <sup>b</sup>∙<sup>P</sup> � <sup>10</sup>�<sup>6</sup> <sup>þ</sup> <sup>1</sup>:<sup>321</sup> � <sup>10</sup>�<sup>4</sup><sup>T</sup> � �2:<sup>292</sup> � <sup>10</sup>�<sup>2</sup>Þ∙1:<sup>8</sup> � <sup>10</sup>�<sup>5</sup>

�<sup>1</sup> s�1m�<sup>2</sup> � � of dissociation. According to [21], kbl is listed as

<sup>T</sup> <sup>þ</sup> <sup>26</sup>:<sup>398</sup> � � (2)

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

29

∇ � u ¼ 0 (3)

D: diffusion coefficient of CO2 in water

ηL[mPa∙s]: viscosity of water

m3 � �: density of water

(275.15 K < T < 281.15 K) <sup>a</sup> <sup>¼</sup> <sup>0</sup>:0016ð Þ <sup>T</sup> � <sup>273</sup>:<sup>15</sup> <sup>0</sup>:<sup>9211</sup> b ¼ �0:0199logð Þþ T � 273:15 0:0942

kg ∙K

CHsol mole∙m�<sup>3</sup> � �: solubility of hydrate

<sup>r</sup><sup>W</sup> <sup>¼</sup> <sup>997</sup>:<sup>1</sup> kg

Cp <sup>¼</sup> <sup>4</sup>; <sup>180</sup> <sup>J</sup>

Englezos [12]

φ(=2.6): association parameter for the solvent water MB <sup>¼</sup> 18 gmol�<sup>1</sup> � �: molecular weight of water VA <sup>¼</sup> <sup>3</sup>:<sup>4</sup> � <sup>10</sup>�<sup>5</sup> <sup>m</sup>3mol�<sup>1</sup> � �: molar volume of CO2

α<sup>L</sup> ms�<sup>2</sup> � �: the thermal diffusivity of aqueous phase

by Aya et al. [10], Yang et al. [11], and Servio and

� �: isobaric specific heat, quoted from "Chemical Engineering Handbook", Japan (1985)

Fn<sup>2</sup> <sup>g</sup> (4)

kbl <sup>¼</sup> exp � <sup>11</sup>; <sup>729</sup>

where CHsol is the mole fraction of CO2 in the aqueous solution at equilibrium state with hydrate, and CI means surface concentration in the ambient aqueous solution at the surface of

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

Flow in the porous media around CO2H is governed by the continuity and the Navier-Stoke's equations. The advection-diffusion equations of non-conservative type for mass concentration

1

Re <sup>∇</sup> � <sup>∇</sup><sup>u</sup> <sup>þ</sup> ð Þ <sup>∇</sup><sup>u</sup>

<sup>T</sup> h i <sup>þ</sup> <sup>r</sup><sup>w</sup>

The objective of this work is to develop a new pore-scale model for estimating the dissociation rate of CO2H in homogeneous porous media. To cooperate with molecular simulation and field-scale simulators, we aim at establishing pore-scale modeling to analyze the simultaneous kinetic process of CO2H dissociation due to non-equilibrium states. Major assumptions in this study are listed as below:

